Earth Resources Laboratory

Permeability Estimation from Field Data

2019-04-11T02:51:18Z

Permeability Estimation from Field Data Burns, D. R.; Cheng, C. H.; Schmitt, D. P.; Toksoz, M. N. Strong correlations exist between core measured permeability values and the phase velocity and attenuation of the tube wave obtained from full waveform acoustic logs. A number of authors have applied the Biot theory to the borehole wave propagation problem in order to explain the observed correlations with reasonably good success. In this paper we present two methods of estimating the absolute in-situ permeability from acoustic log data. Comparisons between measured tube wave velocity and attenuation and model predictions indicate that the Rosenbaum formulation of the Biot model can explain most of the tube wave attenuation data. Based on these findings, an inverse problem is formulated to estimate in-situ permeability from tube wave attenuation measurements using the Biot-Rosenbaum model. Resulting permeability estimates from two field data sets are in agreement with smoothed core permeability measurements. A second estimation method is based on tube wave velocity measurements. By taking the difference between the measured tube wave travel time and the calculated elastic travel time, a new measure is obtained which is referred to as the AAT value. A cross plot of logarithmic core permeability values versus AAT values for data from two different lithologies gives an excellent linear trend for the permeability range of 0.1 to 2000 millidarcies.

Laboratory Borehole Model

2019-04-11T07:12:35Z

Laboratory Borehole Model Shortt, E. R. An experimental method for acquisition offull waveform acoustic logging (FWAL) data from scaled laboratory borehole/formation models is under development. A spark-gap source, fabricated in the lab, is used in conjunction with a piezoelectric receiver. It is found that the source/receiver signature covers a suitable frequency range for the 32:1 scaling required by the 6.4 mm model borehole diameter. Waveforms collected from water-filled boreholes in aluminum and Lucite, simulating fast and slow formations, clearly exhibit the characteristic arrivals of those formations.

Determination Of In-Situ Permeability From Tube Wave Velocity And Attenuation

2019-04-11T07:12:35Z

Determination Of In-Situ Permeability From Tube Wave Velocity And Attenuation Burns, D. R.; Cheng, C. H. Recent investigations by a number of different authors have shown that the phase velocity and attenuation of the tube (Stoneley) wave in the borehole is correlated with in situ permeability. Specifically, velocity decreases and attenuation increases as a function of in situ permeability. Hsui et al. (1985) presented two theoretical models relating in situ permeability to tube wave attenuation. The results obtained from one of the models, the modified Biot-Rosenbaum model, agreed well with the data of Williams et al. (1984). We have extended the results from the modified Biot-Rosenbaum model to examine the relationship between tube wave velocity and in situ permeability. It is found that with an open borehole Biot-Rosenbaum model, i.e., allowing for the communication between the pore and borehole fluid pressures, we can match the variation of tube wave phase velocity with in situ permeability in the data presented by Williams et al. and by Zemanek et al. (1985). Furthermore, by the introduction of intrinsic attenuation, i.e., attenuation not caused by Biot fluid flow mechanism, we can fit both the velocity and attenuation data simultaneously. Williams et al. had also observed that the existence of a mudcake did not appear to significantly affect the observed correlation of tube wave velocity and attenuation with permeability. In the Biot-Rosenbaum model, this is explained by the fact that a mudcake is not rigid, and there can be communication between the pore and borehole fluid pressure systems without actual fluid exchange between them. Thus if one can determine the formation P- and S-wave velocity and attenuation, the in situ permeability may be obtainable using the Biot-Rosenbaum model.

Shear Wave Logging In (Multilayered) Elastic Formations: An Overview

2019-04-12T20:30:45Z

Shear Wave Logging In (Multilayered) Elastic Formations: An Overview Schmitt, D. P.; Cheng, C. H. We perform the analysis of the dispersion and attenuation of the modes generated both by a dipole and quadrupole source in a fluid filled borehole surrounded by a (multilayered) elastic formation. The displacement-stress vectors are propagated through the layers using the Thomson-Haskell method. Only the well bonded configuration is investigated. In the time domain, we investigate the effects of the source center frequency on synthetic full waveform microseismograms computed using the discrete wavenumber method. Whatever the formation (fast or slow) and the configuration, the low frequency part of both the flexural and screw modes follows the virgin formation shear wave characteristics. Their high frequency parts behave like that of the Stoneley wave excited by a monopole source. As a result, the fundamental modes are very sensitive to the properties of the inner layers at intermediate and high frequencies. In the presence of an invaded zone, the internal dynamics of the waveforms can be significantly modified, while the useful starting energy of the fundamental modes is shifted toward lower frequencies. The reverse phenomenon occurs when the borehole is cased. For this last configuration, it is only with low source center frequencies that multipole sources can log a slow formation shear wave due to the leaky character of the fundamental modes.

Modelling Of Full Waveform Acoustic Logs In Soft Marine Sediments

2019-04-11T01:22:10Z

Modelling Of Full Waveform Acoustic Logs In Soft Marine Sediments Cheng, C. H.; Wilkens, R. H.; Meredith, J. A. Full waveform acoustic logs obtained from the Deep Sea Drilling Project (DSDP) were modelled using synthetic full waveform acoustic logs. These synthetic logs were calculated using the discrete wavenumber method. The model is that of a fluid-filled borehole with a rigid logging tool in the center. Results from the modelling indicate that V[subscript p],V[subscript 3] and V[subscript f] along with P wave attenuation (l/Q[subscript 3]) are the primary controls on the full waveform acoustic logs of these soft sediments. S-wave attenuation (l/Q[subscript 3]) does not play a major role because the S-wave velocities (V[subscript 3]) of these fluid-saturated marine oozes are lower than the borehole fluid velocity (V[subscript f]), thus there is no refracted S-wave or pseudo-Rayleigh wave. However, the formation S-wave velocity does affect the amplitude of the observed P-wave train. Density variations by themselves have almost no discernible effect on the synthetics although in practice a change in density often is concurrent with a change in lithology and formation velocities. Matching the synthetic full waveform acoustic logs to those obtained during Leg 95 of the DSDP was formally done by a least squares linearized iteration inversion procedure. Only the P wavetrain and its associated leaky modes were taken into account. The forward model used in the inversion was a P-wave train generated by the branch cut integral method. Stable results in V[subscript 3] and Q[subscript p] were obtained. Variations in the velocity and attenuation from the inversion correlates with sedimentary units delineated from conventional logs and lithologic units identified by shipboard stratigraphers for the Baltimore Canyon Trough area. Full waveform logs, in combination with conventional logs, help to identify changes in the physical properties of these sediments as a result of the diagenesis of biogenic silica and calcium carbonate.

Velocity Analysis Of Multi-Receiver Full Waveform Acoustic Logging Data In Open And Cased Holes

2019-04-12T20:46:38Z

Velocity Analysis Of Multi-Receiver Full Waveform Acoustic Logging Data In Open And Cased Holes Block, Lisa V.; Cheng, C. H.; Duckworth, Gregory L. Average semblance and maximum-likelihood spectral analysis are applied to synthetic full waveform acoustic logging data to determine formation velocities. Of particular interest is the ability of these methods to resolve the P wave and pseudo-Rayleigh wave arrivals in data from poorly-bonded cased boreholes. In open-hole data the velocity analyses generally yield results within 0.15 km/s of the true velocities. For cased-hole models with no steel/cement bonding (free pipe), the measured P-wave velocities are 0.2 to 0.6 km/s less than the actual formation velocities, and the S-wave velocities are within 0.15 km/s of the true velocities. If the P-wave velocity is fairly close to the plate velocity of the steel pipe (within 0.7 km/s or so), then the P-wave arrival is not separated from the steel arrival by the semblance method, but the P wave is resolved by the spectral analysis. For cased-hole models with no cement/formation bonding (unbonded casing), accurate formation velocities are obtained if the velocities are not too great. When the formation P-wave velocity approaches the velocity of the casing arrival, the P-wave resolution is lost by both methods. Further work needs to be done to better define this limit.

Shear Wave Logging In Semi-Infinite Saturated Porous Formations

2019-04-09T17:33:18Z

Shear Wave Logging In Semi-Infinite Saturated Porous Formations Schmitt, D. P.; Zhu, Y.; Cheng, C. H. Recent theoretical and experimental studies have demonstrated the interest of using non-axisymmetric sources, such as dipole and quadrupole, to record shear wave events in any kind of formation (fast or slow). Non-axisymmetric sources excite surface waves whose Airy phase is predominant in the records at intermediate frequencies ( ≃ 3 to 6 kHz). They are referred to as the flexural and screw mode, respectively, for the dipole and the quadrupole source. We study their dispersion and attenuation in a fluidfilled borehole embedded in a homogeneous saturated porous formation. The two phase medium is modeled using Biot's theory modified in accordance with homogenization theory. Calculation of synthetic full waveform logs is also performed using the discrete wavenumber method. Whatever the formation, the most reliable information which can be extracted from low frequency parts of the wavetrains is the formation shear wave velocity and attenuation. It is of great interest in the inversion of Stoneley wave velocity and attenuation for the determination of in situ permeability. In the presence of fast formations the flexural and screw mode are sensitive to the in situ permeability. The same conclusion holds for the slow formations only when they are saturated by a fluid of low viscosity and high compressibility.

Fracture Characterization From Attenuation And Generation Of Tube Waves

2019-04-11T01:22:11Z

Fracture Characterization From Attenuation And Generation Of Tube Waves Hardin, E. L.; Cheng, C. H.; Paillet, F. L.; Mendelson, J. D. Results are presented from experiments carried out in conjunction with the USGS at the Hubbard Brook Experimental Forest near Mirror Lake, New Hampshire. The study focuses on our ability to obtain orientation and transmissivity estimates of naturally occuring fractures. The collected dataset includes a four-offset hydrophone vertical seismic profile, full waveform acoustic logs at 5, 15 and 35 kHz, borehole televiewer, temperature, resistivity, and SP logs, and well-to-well pu,mp test data. While the basic assumptions of the VSP generation model are found to be tenable, fracture aperture estimates from VSP were generally one order of magnitude lower than corresponding pump test or Stoneley wave attenuation results. A new model for tube wave generation which makes use of fracture stiffnes (stress/length) is presented.

Free Pipe Effects On Guided Wave Propagation

2019-04-11T07:12:34Z

Free Pipe Effects On Guided Wave Propagation Burns, D. R.; Cheng, C. H. The effects of free pipe on the pseudo-Rayleigh and Stoneley waves are studied by introducing a fluid annulus between the casing and cement layers of a cased borehole model. The existence of a fluid annulus region results in a second Stoneley mode being generated which propagates primarily in the annulus. The propagation and attenuation of this second mode are controlled by the fluid annulus, cement, and formation properties. The primary or central Stoneley mode becomes decoupled from the effects of formation when the free pipe situation exists, and its propagation and attenuation are controlled by the central fluid and casing properties only. The amplitude of the second Stoneley mode increases as the annulus thickness increases, but in most cases is an order of magnitude less than the primary mode amplitude. The pseudo-Rayleigh wave becomes more dispersive as the annulus region increases in thickness.

Report Summary

2019-04-12T20:46:38Z

Report Summary Toksoz, M. N.; Cheng, C. H. This report contains the results of work completed during the fourth year of the Full Waveform Acoustic Logging Consortium in the Earth Resources Laboratory at M.LT. This is the first year of the second phase of the Consortium, and the emphasis in our research has evolved from a primarily theoretical study of wave propagation in a borehole to a more balanced treatment of all aspects of the problem. As a result, theoretical models developed over the past years are now being applied to field data for the determination of the physical properties of formations in a variety of situations. The knowledge gained from these applications is in turn helping us to refine the theoretical models used. One of the most important parameters in formation evaluation is the in situ permeability. In this report we have a number of papers dealing with the subject, from theoretical papers investigating the Biot-Rosenbaum model in detail, to the application of the model to field data, and a field comparison of in situ fracture permeability obtained from pump test, full waveform acoustic log, and hydrophone VSP studies. We also have synthetic microseismograms generated for formations with fractures of different thicknesses using the finite difference method. We have continued our study of the use of full waveform acoustic logs in a poorly bonded cased hole. In this report we have one paper each on theory and on data analysis in this subject. We have also made initial attempts in the inversion of real data. In this particular case, we made use of the P wave and PL mode to obtain formation S-wave velocity in soft sediments. The preliminary results are very encouraging. Last, but not least, we have included a preliminary report on the model experiment setup in the laboratory. Modelling allows us to study complicated boreholes under controlled conditions. The following is a summary of the different papers in this report.

Report Summary

2019-04-11T01:22:09Z

Report Summary Toksoz, M. N.; Cheng, C. H. This report contains the results ot work completed during the fifth year of the Full Waveform Acoustic Logging Consortium in the Earth Resources Laboratory at M.l.T. During this past year, the emphasis in our research has continued in the direction of a more balanced treatment of all aspects of the acoustic logging problem, namely, theory, data processing, and interpretation. The aim is faster and more accurate determination of formation properties from the full waveform acoustic logs under. a variety of conditions one might encounter in the field. In situ permeability, in both porous and fractured formations, remains the focus of our research efforts. In this report we have a number of papers dealing with the subject, from theoretical papers studying wave propagation in a radially layered porous formation and shear wave logging in a porous medium, to a progress report on finite difference modelling of wave propagation in a porous material, and ultrasonic modelling of the effects of fractures on full waveform logs. We have also examined the correlation between permeabilities obtained from full waveform logs and those measured in core samples. A paper on the depth of investigation of different methods of in situ fracture permeability determination is also included in the report. Data processing received more attention in the past year. We have continued to work on some of the projects we had started last year, namely, the inversion of the P wavetrain for V, and Qp in a slow formation, and the determination of formation velocities behind (poorly bonded) casing using velocity analysis. In addition, we have initiated efforts in array processing of full waveform logging data using the extended Prony's method. This method is very promising for the accurate determination of formation guided (both pseudo-Rayleigh and Stoneley) wave dispersion and attenuation. In an effort to further study how the borehole affects the determination of formation properties, we have studied the effect of the viscosity of the borehole fluid on full waveform logs. We have also made laboratory measurements of the quality factor of a drilling mud. Lastly, but not least, we have initiated efforts of incorporating expert system approaches in the interpretation of full waveform logs. Two papers, one on the correlation of waveforms for better velocity determination, and the other on well-to-well log correlation, represent our initial efforts in this area. The following is a summary of the papers in this report.

A Finite Difference Formulation of Biot's Equations for Vertically Heterogeneous Full Waveform Acoustic Logging Problems

2019-04-12T20:46:49Z

A Finite Difference Formulation of Biot's Equations for Vertically Heterogeneous Full Waveform Acoustic Logging Problems Stephen, R. A. In this paper we present a finite difference formulation for Biot's equations for wave propagation in saturated porous media which vary in range and depth. One objective of well logging petroleum exploration holes is to determine the permeability of a section. There are indications that the Stoneley wave in the full waveform acoustic logging tool is sensitive to permeability, but we need modeling techniques to fully understand the mechanism. One question to be addressed is how narrow horizontal fissures of varying permeability affect Stoneley or tube wave propagation in the borehole. Another question is the trade-off between attenuation due to viscous losses in the pore fluid and due to scattering. A technique for modeling acoustic logs in two-dimensionally varying Biot solids will give insight into these problems.

Viscous Fluid Effects on Guided Wave Propagation in a Borehole

2019-04-12T20:46:49Z

Viscous Fluid Effects on Guided Wave Propagation in a Borehole Burns, D. R. In order to investigate the effect of borehole fluid viscosity on the attenuation and dispersion of the guided waves present in full waveform acoustic logs, the problem of wave propagation in a borehole containing a viscoelastic fluid surrounded by an infinite elastic formation is solved using boundary layer theory. The results indicate that the losses due to viscous drag along the borehole wall are a small component of the overall guided wave attenuation for the frequencies of interest in full waveform acoustic logging (2-15kHz) and for reasonable viscosity values (1-1000cP). These losses, however, can be significant at low frequencies. In addition, the variations in viscosity have a negligible effect on the guided wave dispersion for this range of frequency and viscosity. These findings indicate that friction between grains in fluid suspension may be the dominant attenuation mechanism in the drilling fluids present in boreholes.

Viscous Fluid Effects on Guided Wave Propagation in a Borehole

2019-04-11T01:22:12Z

Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part II: Simple Configuration

2019-04-09T16:03:02Z

Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part II: Simple Configuration Schmitt, D. P. The discrete wavenumber method is used to compute synthetic full waveform acoustic logs in an axisymmetric fluid-filled borehole surrounded by a porous medium. The two phase formation is modeled following Biot's theory. It is modified by the introduction of an unified definition of the coupling coefficients related to the pore shape in accordance with homogenization theory. Both permeable and impermeable borehole walls are considered. The study focuses on the permeabilty, source center frequency and radius effects on guided modes and especially the Stoneley wave for various types of formations and saturant fluids. Comparison is made with homogeneous elastic formations. Plots of the spectral energy density in the frequency axial wavenumber domain allow the recognition and identification of the different wave types. When the pores are occluded at the borehole wall, the wavefield behavior is nearly equivalent to that of an elastic formation (with body wave attenuation added). The Stoneley wave is only very slightly affected. When the fluid flow is free, the distortions are more important because of the relative motion between the two phases at the borehole wall. With increasing permeability, Stoneley wave absolute and relative energy decreases and is relegated to a narrower low frequency band. It is then associated with a phase velocity lower than the" tube" wave velocity in an elastic formation. Its dispersion increases, especially in the low frequency range. Its attenuation correspondingly increases, reinforced by an increase of the shear wave attenuation. Due to an apparent increase of the borehole radius, the low cut-off frequencies of the pseudo-Rayleigh modes are shifted toward lower frequencies. The P to guided wave amplitude ratio is enhanced. For a given permeability, porosity and pore geometry, these characteristics are enhanced when the saturant fluid mobility increases and/or when the borehole radius decreases.

Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part I: A Review Of Biot's Theory

2019-04-12T20:46:39Z

Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part I: A Review Of Biot's Theory Schmitt, D. P. Hydrocarbon exploration is especially concerned with two phase media. Following Biot, such finite porosity rocks are modeled as statistically isotropic materials composed of a solid elastic matrix permeated by a network of interconnected pores saturated with a compressible viscous liquid. In a first step, the constitutive equations of a saturated porous medium are reviewed, using mixtures theory and homogenization theory. This study focuses on the assumptions which are necessary but not always explicit. Biot's formulation is then modified by the introduction of a unified definition of the viscous and mass coupling coefficients which are both frequency dependent. The continuity equations at different kinds of interfaces are also analyzed. The body wave velocities and attenuations are then computed, using the cylindrical duct model for pores. The effects of the saturant fluid, the permeability and the porosity are studied.

Inversion of Borehole Guided Wave Amplitudes for Formation Shear Wave Attenuation Values

2019-04-12T20:46:50Z

Inversion of Borehole Guided Wave Amplitudes for Formation Shear Wave Attenuation Values Burns, D. R.; Cheng, C. H. A linear least squares inversion, based on analytic partition coefficient expressions, is developed to estimate the fluid and formation shear wave Q values from spectral ratio measurements-of the guided wave arrivals of full waveform acoustic logs recorded in open boreholes. The method provides excellent results when applied to synthetic data. Real data applications provide useful results, but noise reduces the resolution and increases the variance of the estimates. Permeability related losses and transmission losses (if interfaces are present) can have large effects on the estimated values. A similar procedure is developed for cased hole geometries. In this situation, the guided wave measurements are used to provide estimates of the fluid, formation shear wave, and cement shear wave Q values. Application of the method to synthetic data indicates that the formation shear Q estimate is extremely sensitive to the pseudo-Rayleigh wave data quality very close to the cutoff frequency.

Synthetic Acoustic Logs Over Bed Boundaries And Horizontal Fissures

2019-04-12T20:46:40Z

Synthetic Acoustic Logs Over Bed Boundaries And Horizontal Fissures Stephen, R. A. The finite difference method is used to predict the effects of wave propagation in boreholes with vertically varying elastic properties. Specifically horizontal interfaces between rock types (for example shales and sandstones) and between rock and horizontal liquid fissures of varying width are considered. The amplitudes of the transmitted compressional head waves and Stoneley waves are only slightly affected by thin horizontal fissures and stringers. On the other hand, the pseudo-Rayleigh wave, when it is present (e.g., in sandstones), can be almost totally blocked by a very thin (1 em) horizontal fissure. Both compressional head waves and pseudo-Rayleigh waves show significant reflections at horizontal discontinuities. Stoneley waves and PL modes are not significantly reflected. In general, mode conversion is not a significant effect in the bed boundary and horizontal fissure models considered. Although some very strong effects can be observed on the transmitted and reflected waves none of the models showed significant scattering (for example, from pseudo-Rayleigh waves to compressional head waves). The effects observed at bed boundaries in the field (for example, Paternoster and Larrere, 1985) are adequately simulated by the synthetics. Adjusting for the differences in offsets of the two cases, arrival times and amplitudes correspond well. The only exception to this is the absence of identifiable mode conversions. Larger offset models will be necessary to clearly distinguish any mode conversions that may be occurring.

Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part Ill: Pore Shape And Pore Geometry Effects

2019-04-10T19:32:16Z

Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part Ill: Pore Shape And Pore Geometry Effects Schmitt, D. P. Homogenization theory states that the viscous and mass coupling coefficients of a fully saturated porous medium depend upon the pore shape and the pore geometry. Using an approximate formula, the three body wave velocities and attenuations are analyzed for different configurations. The results show a strong influence of the mass coupling coefficient on these properties. The greater it is, the less biphase the porous medium is. Hence, in the high frequency range, the body wave velocities and attenuations decrease. Using the discrete wavenumber method, synthetic microseismograms are computed in an axisymmetric water-filled borehole. In the presence of a given porous formation with a permeable interface, whatever the mass coupling coefficient, Stoneley wave attenuation and dispersion characteristics are only slightly affected. The reliability of the indirect permeability determination is then ensured. On the other hand, the pseudo-Rayleigh modes are less attenuated with increasing mass coupling coefficient. In the absence of any borehole fluid attenuation, they may become dominant with a high source center frequency. This emphasizes the requirement for low band pass frequency records to be able to easily determine the rheological parameters of a formation. Complex geometries are shown which would allow one to take into account an anisotropic permeability distribution.

New Applications In The Inversion Of Acoustic Full Waveform Logs - Relating Mode Excitation To Lithology

2019-04-11T07:12:33Z

New Applications In The Inversion Of Acoustic Full Waveform Logs - Relating Mode Excitation To Lithology Paillet, Frederick L.; Cheng, C. H.; Meredith, J. A. Existing techniques for the quantitative interpretation of waveform data have been based on one of two fundamental approaches: 1) simultaneous identification of compressional and shear wave velocities; and 2) least-squares minimization of the difference between experimental waveforms and synthetic seismograms. Techniques based on the first approach do not always work, and those based on the second seem too numerically cumbersome for routine application during data processing. An alternative approach is tested here, in which synthetic waveforms are used to predict relative mode excitation in the composite waveform. Synthetic waveforms are generated for a series of lithologies ranging from hard, crystalline rocks (V[subscript p] = 6.0 km/s and Poisson's ratio = 0.20) to soft, argillaceous sediments (V[subscript p] = 1.8 km/s and Poisson's ratio = 0.40). The series of waveforms illustrates a continuous change within this range of rock properties. Mode energy within a characteristic velocity window is computed for each of the modes in the set of synthetic waveforms. The results indicate that there is a consistent variation in mode excitation in lithology space that can be used to construct a unique relationship between relative mode excitation and lithology.

Logging in Multilayered Saturated Porous Formations

2019-04-12T11:17:05Z

Logging in Multilayered Saturated Porous Formations Schmitt, D. P.; Cheng, C. H.; Toksoz, M. N. We present a general formulation based on the Thomson-Haskell method which allows the study of complex models. The surrounding formation may be composed of several coaxial porous shells or of a combination of both porous and elastic layers. At any kind of interface, welded contact is assumed. The two phase media are modeled following Biot's theory which is modified through a unified definition of frequency dependent coupling coefficients in accordance with homogenization theory. Calculations of dispersion and attenuation of both the Stoneley wave and first pseudo-Rayleigh mode are performed. Also displayed are synthetic microseismograms computed using the discrete wavenumber method. The configuration of a damaged (invaded or flushed) zone resulting from radial variation of permeability and/or porosity, with or without modification of the saturant fluid is investigated. When the borehole wall is impermeable, the effects of a porous radial layering are analogous to those observed in the presence of only elastic media, with body wave attenuations added, whatever the formation (fast or slow). When the borehole is permeable, as soon as the inner layer thickness reaches a few centimeters, Stoneley wave dispersion and attenuation are representative of the rheological properties of that inner layer. As a result, the determination of the in situ permeability of the virgin formation, based on Stoneley wave characteristics, is ill posed. Also studied is the presence of a mudcake at the borehole wall. Whatever its rheological properties, this additional layer leads to a decrease of Stoneley wave phase velocity compared to the sealed pores situation. Compared to the simple open hole model with a permeable borehole wall, the same effect can be noted but only for frequencies greater than≃ 2 kHz, and a significantly thick mudcake. With any elastic or low permeability mudcake, with the absence or inefficient pressure continuity between the bore and saturant fluids, one cannot generate the variations of attenuations displayed by real data. Further investigations will need experimental measurements of the mudcake properties. Whatever the configuration, the phase velocity and attenuation of the first pseudo-Rayleigh mode starts at those of the virgin formation. The low frequency part of the pseudo-Rayleigh wavetrain can then be used for the indirect estimation of the formation shear wave characteristics.

Real-time ensemble control with reduced-order modeling

2019-04-10T21:00:08Z

Real-time ensemble control with reduced-order modeling Lin, Binghuai; McLaughlin, Dennis The control of spatially distributed systems is often complicated by significant uncertainty about system inputs, both time-varying exogenous inputs and time-invariant parameters. Spatial variations of uncertain parameters can be particularly problematic in geoscience applications, making it difficult to forecast the impact of proposed controls. One of the most effective ways to deal with uncertainties in control problems is to incorporate periodic measurements of the system’s states into the control process. Stochastic control provides a convenient way to do this, by integrating uncertainty, monitoring, forecasting, and control in a consistent analytical framework. This paper describes an ensemble-based approach to closed-loop stochastic control that relies on a computationally efficient reduced-order model. The use of ensembles of uncertain parameters and states makes it possible to consider a range of probabilistic performance objectives and to derive real-time controls that explicitly account for uncertainty. The process divides naturally into measurement updating, control, and forecasting steps carried out recursively and initialized with a prior ensemble that describes parameter uncertainty. The performance of the ensemble controller is investigated here with a numerical experiment based on a solute transport control problem. This experiment evaluates the performance of open and closed-loop controllers with full and reduced-order models as well as the performance obtained with a controller based on perfect knowledge of the system and the nominal performance obtained with no control. The experimental results show that a closed-loop controller that relies on measurements consistently performs better than an open loop controller that does not. They also show that a reduced-order forecasting model based on offline simulations gives nearly the same performance as a significantly more computationally demanding full order model. Finally, the experiment indicates that a moderate penalty on the variance of control cost yields a robust control strategy that reduces uncertainty about system performance with little or no increase in average cost. Taken together, these results confirm that reduced-order ensemble closed-loop control is a flexible and efficient control option for uncertain spatially distributed systems.

Efficient characterization of uncertain model parameters with a reduced-order ensemble Kalman filter

2019-04-10T19:36:12Z

Efficient characterization of uncertain model parameters with a reduced-order ensemble Kalman filter Lin, Binghuai; McLaughlin, Dennis Spatially variable model parameters are often highly uncertain and di fficult to observe. This has prompted the widespread use of Bayesian characterization methods that can infer parameter values from measurements of related variables, while explicitly accounting for uncertainty. Ensemble versions of Bayesian characterization are particularly convenient when uncertain variables have complex spatial structures that do not conform to Gaussian descriptions. However, ensemble methods can be time-consuming for high-dimensional problems. This paper describes a reduced-order approach to ensemble characterization that is particularly well-suited for subsurface flow and transport problems. It uses a truncated discrete cosine transform (DCT) to reduce the dimensionality of spatially variable time-invariant model parameters and a nonlinear extension of principle orthogonal decomposition (POD) to reduce the dimensionality of dynamic model states. The resulting nonlinear reduced-order model can be included in the forecast step of a reduced-order ensemble Kalman fi lter. These concepts are illustrated in a subsurface solute transport problem using ensembles produced by full and reduced-order order models. These ensembles are very similar when there are no measurement updates. When the forecast ensemble is recursively updated with measurements the reduced-order Kalman fi lter does at least as well as the full-order fi lter in characterizing a dynamic solute plume, even though its augmented state dimension is only 2% of the dimension of the full-order state. This substantial increase in effi ciency implies that a reduced-order fi lter with the same ensemble size as its full-order counterpart can give comparable performance for orders of magnitude less computational e ffort or can use a much larger ensemble for the same computational e ffort. The possibility of substantial increases in ensemble size could lead to performance improvements through reductions in sampling error and in the rank of the ensemble null space. Also, a reduced-order model similar to the one described here could be used in ensemble real-time control applications, where it can decrease the eff ort required for both characterization and control.

Efficient Double-Beam Characterization for Fractured Reservoir

2019-04-12T22:12:31Z

Efficient Double-Beam Characterization for Fractured Reservoir Zheng, Yingcai; Fang, Xinding; Fehler, Michael; Burns, Daniel R. We proposed an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacing and orientation and output an interference pattern as a function of the spacing and orientation the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are sparse spatially, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validated our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.

Experimental studies of the acoustic wave field near a borehole

2019-04-09T18:53:56Z

Experimental studies of the acoustic wave field near a borehole Zhu, Zhenya; Liu, Xien; Gu, Chen; Toksoz, M. Nafi A monopole or a dipole source in a fluid borehole generates acoustic waves, part of which propagate along the borehole and the other part enter the formation propagating as P- or S-waves. The refracted waves propagating along the borehole wall are used to determine P- and S-wave velocities. However, a significant fraction of the seismic energy radiates into the formation. In this laboratory study, we measure the acoustic waves in the borehole and the seismic waves in the formation at different distances from the borehole. We use scaled borehole models made of Lucite and of concrete to simulate a soft and a hard formation, respectively. The waveforms are measured in the boreholes as well as in the formations with different radial distances from the axis of the borehole. The results show that the investigation depth of the wave measured in the borehole is less than one half of the wavelength. The seismic energy radiating into the formation and scattered from interfaces and heterogeneities can be used for imaging the formation.

Seismic characterization of reservoirs with variable fracture spacing by double focusing Gaussian beams

2019-04-11T09:46:09Z

Seismic characterization of reservoirs with variable fracture spacing by double focusing Gaussian beams Zheng, Yingcai; Fang, Xinding; Fehler, Michael Fractured reservoirs account for a majority of the oil production worldwide and often have low recovery rate. Fracture characterization is important in building reservoir flow models for enhanced oil recovery. Information about fracture orientation, fracture spacing, and fracture compliances is essential. When a fracture network consisting of multiple sets of fractures with variable fracture spacing/orientation is present, we have to determine the spatial information about them as this may represent important connectivity information for fluid flow. We present a seismic method that can achieve the above goals in the context of seismic scattering, when the fracture spacing is on the order of half of the wavelength. The method is based measuring the beam interference pattern for two Gaussian beams focused on a fractured reservoir location, one beam from the sources and the other from the receivers. Numerical examples show that our method can provide spatially dependent information on fracture parameters.

Time-stepping beyond CFL: a locally one-dimensional scheme for acoustic wave propagation

2019-04-12T22:12:31Z

Time-stepping beyond CFL: a locally one-dimensional scheme for acoustic wave propagation Zepeda Nunez, Leonardo Andres; Hewett, Russell J.; Rao, Minghua Michel; Demanet, Laurent In this abstract, we present a case study in the application of a time-stepping method, unconstrained by the CFL condition, for computational acoustic wave propagation in the context of full waveform inversion. The numerical scheme is a locally one-dimensional (LOD) variant of alternating dimension implicit (ADI) method. The LOD method has a maximum time step that is restricted only by the Nyquist sampling rate. The advantage over traditional explicit time-stepping methods occurs in the presence of high contrast media, low frequencies, and steep, narrow perfectly matched layers (PML). The main technical point of the note, from a numerical analysis perspective, is that the LOD scheme is adapted to the presence of a PML. A complexity study is presented and an application to full waveform inversion is shown.

Simultaneous Estimation of Reflectivity and Geologic Texture: Least-Squares Migration with a Hierarchical Bayesian Model

2019-04-10T18:31:29Z

Simultaneous Estimation of Reflectivity and Geologic Texture: Least-Squares Migration with a Hierarchical Bayesian Model Zamanian, S. Ahmad; Kane, Jonathan; Rodi, William L.; Fehler, Michael In many geophysical inverse problems, smoothness assumptions on the underlying geology are utilized to mitigate the effects of poor resolution and noise in the data and to improve the quality of the inferred model parameters. Within a Bayesian inference framework, a priori assumptions about the probabilistic structure of the model parameters impose such a smoothness constraint or regularization. We consider the particular problem of inverting seismic data for the subsurface reflectivity of a 2-D medium, where we assume a known velocity field. In particular, we consider a hierarchical Bayesian generalization of the Kirchhoff-based least-squares migration (LSM) problem. We present here a novel methodology for estimation of both the optimal image and regularization parameters in a least-squares migration setting. To do so we utilize a Bayesian statistical framework that treats both the regularization parameters and image parameters as random variables to be inferred from the data. Hence rather than fixing the regularization parameters prior to inverting for the image, we allow the data to dictate where to regularize. In order to construct our prior model of the subsurface and regularization parameters, we define an undirected graphical model (or Markov random field) where vertices represent reflectivity values, and edges between vertices model the degree of correlation (or lack thereof) between the vertices. Estimating optimal values for the vertex parameters gives us an image of the subsurface reflectivity, while estimating optimal edge strengths gives us information about the local “texture” of the image, which, in turn, may tell us something about the underlying geology. Subsequently incorporating this information in the final model produces more clearly visible discontinuities in the final image. The inference framework is verified on a 2-D synthetic dataset, where the hierarchical Bayesian imaging results significantly outperform standard LSM images.

Using Image Warping for Time-lapse Image Domain Wavefield Tomography

2019-04-12T22:15:02Z

Using Image Warping for Time-lapse Image Domain Wavefield Tomography Yang, Di; Malcolm, Alison E.; Fehler, Michael Time-lapse seismic data are widely used for monitoring subsurface changes. A quantitative assessment of how reservoir properties have changed allows for better interpretation of fluid substitution and migration during processes like oil and gas production, and carbon sequestration. Full waveform inversion has been proposed as a way to retrieve quantitative estimates of subsurface properties through seismic waveform fitting. However, for most monitoring systems, the offset range versus depth of interest is not large enough to provide information about the low wavenumber velocity model. In this study, we present a wavefield tomography method using the local warping between baseline and time-lapse images as the cost function. The new cost function is sensitive to volumetric velocity anomalies, and capable of handling large velocity changes, where traditional full waveform inversion fails. In this paper, we first describe the theory and workflow of our method, and then we show a numerical example to demonstrate its advantages.

Double-Difference Waveform Inversion of 4D Ocean Bottom Cable Data: Application to Valhall, North Sea

2019-04-12T22:15:02Z

Double-Difference Waveform Inversion of 4D Ocean Bottom Cable Data: Application to Valhall, North Sea Yang, Di; Fehler, Michael; Malcolm, Alison E.; Liu, Faqi; Morton, Scott Changes in reservoir properties resulting from extracting hydrocarbons and injecting fluid are critical to optimize production. These properties can be characterized using waveform inversions of time-lapse seismic data. The conventional approach for analysis using waveform tomography is to take the difference of seismic inversion obtained using baseline and subsequent time-lapse datasets that are imaged independently. By contrast, double-difference waveform inversion (DDWI) jointly inverts time-lapse seismic datasets for reservoir changes. We use a 2D synthetic example to demonstrate the advantage of DDWI in mitigating spurious estimates of property changes. We then apply both conventional full waveform inversion(FWI) and DDWI to time-lapse datasets collected by ocean bottom cables (OBC) in the Valhall field in the North Sea. The data sets are acquired one year apart. DDWI gives a cleaner and more easily interpreted image of the model changes, as compared to that obtained with the conventional FWI scheme.

Efficient stochastic Hessian estimation for full waveform inversion

2019-04-12T22:15:05Z

Efficient stochastic Hessian estimation for full waveform inversion Willemsen, Lucas Abraham; Malcolm, Alison E.; Hewett, Russell J. In this abstract we present a method that allows arbitrary elements of the approximate Hessian to be estimated simultaneously. Preliminary theoretical and numerical investigations suggest that the number of forward models required for this procedure does not increase with the number of shots. As the number of shots increases this means that the cost of estimating these approximate Hessian entries becomes negligible relative to the cost of calculating the gradient. The most obvious application would be to estimate the diagonal of the approximate hessian. This can then be used as a very inexpensive preconditioner for optimization procedures, such as the truncated Newton method.

Full-waveform Based Microseismic Source Mechanism Studies in the Barnett Shale: Linking Microseismicity to Reservoir Geomechanics

2019-04-12T22:15:05Z

Full-waveform Based Microseismic Source Mechanism Studies in the Barnett Shale: Linking Microseismicity to Reservoir Geomechanics Song, Fuxian; Warpinski, Norm R.; Toksoz, M. Nafi Microseismic moment tensor (MT) contains important information on the reservoir and fracturing mechanisms. Difficulties arise when attempting to retrieve complete MT with conventional amplitude inversion methods if only one well is available. With the full-waveform approach, near-field information and non-direct waves (i.e. refracted/reflected waves) help stabilize the inversion and retrieve complete MT from the single-well dataset. However, for events which are at far field from the monitoring well, a multiple-well dataset is required. In this study, we perform the inversion with a dual-array dataset from a hydrofracture stimulation in the Barnett shale. Determining source mechanisms from the inverted MTs requires the use of a source model, which in this paper is the tensile earthquake model. The tensile model could describe the source more adequately and predict non-DC components. The source information derived includes the fault plane solution (FPS), slip direction, Vp/Vs ratio in the focal area and seismic moment. The primary challenge of extracting source parameters from MT is to distinguish the fracture plane from auxiliary plane. We analyze the microseismicity using geomechanics and use the insights gained from geomechanical analysis to determine the fracture plane. Furthermore, we investigate the significance of non-DC components by F-test. We also study the influence of velocity model errors, event mislocations and data noise using synthetic data. The results of source mechanism analysis are presented for the events with good signal-to-noise ratios (SNRs). Some events have fracture planes with similar orientations to natural fractures delineated by core analysis, suggesting reactivation of natural fractures. Other events occur as predominantly tensile events along the unperturbed maximum horizontal principal stress (SHmax) direction, indicating an opening mode failure on hydraulic fractures. Microseismic source mechanisms not only reveal important information about fracturing mechanisms, but also allow fracture characterization away from the wellbore, providing critical constraints for understanding fractured reservoirs.

Full-waveform Based Microseismic Event Detection and Signal Enhancement: The Subspace Approach

2019-04-12T22:15:05Z

Full-waveform Based Microseismic Event Detection and Signal Enhancement: The Subspace Approach Song, Fuxian; Warpinski, Norm R.; Toksoz, M. Nafi; Kuleli, Huseyin Sadi Microseismic monitoring has proven to be an invaluable tool for optimizing hydraulic fracturing stimulations and monitoring reservoir changes. The signal to noise ratio (SNR) of the recorded microseismic data varies enormously from one dataset to another, and it can often be very low especially for surface monitoring scenarios. Moreover, the data are often contaminated by correlated noises such as borehole waves in the downhole monitoring case. These issues pose a significant challenge for microseismic event detection. On the other hand, in the downhole monitoring scenario, the location of microseismic events relies on the accurate polarization analysis of the often weak P-wave to determine the event azimuth. Therefore, enhancing the microseismic signal, especially the low SNR P-wave data, has become an important task. In this study, a statistical approach based on the binary hypothesis test is developed to detect the weak events embedded in high noise. The method constructs a vector space, known as the signal subspace, from previously detected events to represent similar, yet significantly variable microseismic signals from specific source regions. Empirical procedures are presented for building the signal subspace from clusters of events. The distribution of the detection statistics is analyzed to determine the parameters of the subspace detector including the signal subspace dimension and detection threshold. The effect of correlated noise is corrected in the statistical analysis. The subspace design and detection approach is illustrated on a dual-array hydrofracture monitoring dataset. The comparison between the subspace approach, array correlation method, and array short-time average/long-time average (STA/ LTA) detector is performed on the data from the far monitoring well. It is shown that, at the same expected false alarm rate, the subspace detector gives fewer false alarms than the array STA/LTA detector and more event detections than the array correlation detector. The additionally detected events from the subspace detector are further validated using the data from the nearby monitoring well. The comparison demonstrates the potential benefit of using the subspace approach to improve the microseismic viewing distance. Following event detection, a novel method based on subspace projection is proposed to enhance weak microseismic signals. Examples on field data are presented indicating the effectiveness of this subspace-projection-based signal enhancement procedure.

Converted Phase Elastic Migration Velocity Analysis

2019-04-10T18:31:58Z

Converted Phase Elastic Migration Velocity Analysis Shabelansky, Andrey Hanan; Malcolm, Alison E.; Fehler, Michael; Shang, Xuefeng; Rodi, William L. Multi-component elastic seismic data collected at large offsets have the potential to be used in seismic imaging and velocity analysis. In this study, we present an approach for converted-phase elastic-transmission migration velocity analysis with an application for VSP and micro-seismic studies. Our approach is based on the cross-correlation between converted-phase P- and S-waves propagated backward in time, and is formulated as an inverse problem with a differential semblance criterium objective function for the simultaneous update of both P- and S-wave velocity models. The merit of this approach is that it is fully data-driven and requires only one elastic backward propagation to form an image rather than the two (one forward and one backward) acoustic propagations needed for standard RTM. Moreover, as the method does not require forward propagation, it does not suffer from migration operator source aliasing when a small number of shots are used. We present a derivation of the method and test it with the synthetic Marmousi model. We also show the differences between the standard reflection offset domain common image gathers and the converted-phase image gathers that we use for model updates.

Reverse Time Migration in the presence of known sharp interfaces

2019-04-12T22:15:03Z

Reverse Time Migration in the presence of known sharp interfaces Richardson, Alan; Malcolm, Alison E. We propose using the forward propagated source wave to create synthetic receiver data on the surfaces of the computational domain where real receiver data is not available as a means of exploiting known information about reflector locations in Reverse Time Migration. The inclusion of synthetic boundary data can make true amplitude imaging possible, and reduce the artifacts associated with the inclusion of multiples. Here, we describe the new method, present synthetic examples, and propose an appropriate imaging condition.

A unified Bayesian framework for relative microseismic location

2019-04-09T18:22:45Z

A unified Bayesian framework for relative microseismic location Poliannikov, Oleg V.; Prange, Michael; Malcolm, Alison E.; Djikpesse, Hugues We study the problem of determining an unknown microseismic event location relative to previously located events using a single monitoring array in a monitoring well. We show that using the available information about the previously located events for locating new events is advantageous compared to locating each event independently. By analyzing confidence regions, we compare the performance of two previously proposed location methods, double-difference and interferometry, for varying signal-to-noise ratio and uncertainty in the velocity model. We show that one method may have an advantage over another depending on the experiment geometry, assumptions about uncertainty in velocity and recorded signal, etc. We propose a unified approach to relative event location that includes double-difference and interferometry as special cases, and is applicable to velocity models and well geometries of arbitrary complexity, producing location estimators that are superior to those of double-difference and interferometry.

Joint microseismic event location with uncertain velocity

2019-04-14T07:29:27Z

Joint microseismic event location with uncertain velocity Poliannikov, Oleg V.; Prange, Michael; Malcolm, Alison E.; Djikpesse, Hugues We study the problem of the joint location of seismic events using an array of receivers. We show that locating multiple seismic events simultaneously is advantageous compared to the more traditional approaches of locating each event independently. Joint location, by design, includes estimating an uncertainty distribution on the absolute position of the events. From this can be deduced the distribution on the relative position of one event with respect to others. Many quantities of interest, such as fault sizes, fracture spacing or orientation, can be directly estimated from the joint distribution of seismic events. Event relocation methods usually update only the target event, while keeping the reference events fixed. Our joint approach can be used to update the locations of all events simultaneously. The joint approach can also be used in a Bayesian sense as prior information in locating a new event.

Using SVD for improved interferometric Green's function retrieval

2019-04-11T09:46:10Z

Using SVD for improved interferometric Green's function retrieval Melo, Gabriela; Malcolm, Alison E.; Mikesell, Dylan; van Wijk, Kasper Seismic interferometry (SI) is a technique used to estimate the Green’s function (GF) between two receiver locations, as if there were a source at one of the receiver locations. However, in many applications, the requirements to recover the exact GF are not satisfied and SI yields a poor estimate of the GF. For these non-ideal cases, we improve the interferometric GFs, by applying Singular Value Decomposition (SVD) to the crosscorrelations before stacking. The SVD approach preserves energy that is stationary in the crosscorrelations, which is the energy that contributes most to the GF recovery, and attenuates non-stationary energy, which leads to artifacts in the interferometric GF. We apply this method to construct virtual shot gathers (for both synthetic and field data) and demonstrate how using SVD enhances physical arrivals in these gathers. We also find that SVD is robust with respect to weakly correlated random noise, allowing a better recovery of events from noisy data, in some cases recovering energy that would otherwise be completely lost in the noise and that the standard seismic interferometry technique fails to recover.

Analysis of location uncertainty for a microearthquake cluster: A case study

2019-04-11T09:46:11Z

Analysis of location uncertainty for a microearthquake cluster: A case study Melo, Gabriela; Malcolm, Alison E.; Poliannikov, Oleg V.; Fehler, Michael In many reservoirs, an increase in permeability and conductivity is achieved by hydraulic fracturing/stimulations which open cracks and fractures that then act as pathways for fluids to navigate in the subsurface. Mapping, localization, and general characterization of these fracture systems is of key importance in oil, gas, and geothermal energy production. The location of the microseismic events triggered during hydraulic fracturing or stimulation can help to characterize the properties of the fracture system. There are many different methods for localizing microearthquakes and, in general, these methods yield different locations, velocity models, and event origin times, due to differences in algorithms and input models. Here we focus on studying location confidence intervals associated with two localization methods, classical (triangulation) and Double-Difference, where uncertainties due to origin times can be marginalized away, thus decreasing uncertainties in the event locations. We relocate events using these two methods and three different velocity models. Of the two methods used here, Double-Difference produces smallest confidence regions. We also illustrate that, for our dataset in particular, marginalizing away the influence of the unknown origin times also improves the confidence intervals.

Estimating the fracture density of small-scale vertical fractures when large-scale vertical fractures are present

2019-04-09T15:40:24Z

Estimating the fracture density of small-scale vertical fractures when large-scale vertical fractures are present Liu, Yuwei; Fehler, Michael; Fang, Xinding; Liu, Cai When fractures are vertical, aligned and their dimensions are small relative to the seismic wavelength, the medium can be considered to be an equivalent Horizontal Transverse Isotropic (HTI) medium. However, geophysical data acquired over naturally fractured reservoirs often reveal the presence of multiple fracture sets. We investigate a case where there are two vertical sets of fractures having differing length scales. One fracture set has length scale that is much smaller than the seismic wavelength but the other has length scale that is similar to the seismic wavelength. We use synthetic data to investigate the ability to infer the properties of the small-scale fractures in the presence of the large-scale fracture set. We invert for the Thomsen-type anisotropic coefficients of the small-scale fracture set by using the difference of the P-wave amplitudes at two azimuths, which makes the inversion convex. Then we investigate the influence of the presence of the large-scale fractures on our ability to infer the properties of the small-scale fracture set. Surprisingly, we find that we can reliably infer the fracture density of the small scale fractures even in the presence of large scale fractures having significant compliance values.

3D Weak-Dispersion Reverse-Time Migration with a StereoModeling Method

2019-04-12T22:15:05Z

3D Weak-Dispersion Reverse-Time Migration with a StereoModeling Method Li, Jingshuang; Fehler, Michael; Yang, Dinghui; Huang, Xueyuan The finite difference method has been widely used in seismic modeling and reverse time migration. However, it generally has two issues: large computational cost and numerical dispersion. Recently, a nearly-analytic discrete operator was developed to approximate the partial differential operators. Based on this spatial discretization, many weak-dispersion and efficient StereoModeling methods have been developed, which are found to be superior to conventional algorithms in suppressing numerical dispersion. In this paper, we generalize one StereoModeling method, the nearly-analytic central difference method (NACD), from 2D to 3D and apply it to 3D reverse-time migration. Numerical results show that the NACD can be used effectively as a new tool for seismic modeling and migration. The reverse time migration (RTM) results for the 3D SEG/EAGE Phase A classic dataset 1 show that the NACD can get a much better image than the Lax-Wendroff correction (LWC) method particularly when using a coarse grid size.

High-dimensional wave atoms and compression of seismic datasets

2019-04-11T09:46:10Z

High-dimensional wave atoms and compression of seismic datasets Leinonen, Matti; Hewett, Russell J.; Zhang, Xiangxiong; Ying, Lexing; Demanet, Laurent Wave atoms are a low-redundancy alternative to curvelets, suitable for high-dimensional seismic data processing. This abstract extends the wave atom orthobasis construction to 3D, 4D, and 5D Cartesian arrays, and parallelizes it in a shared-memory environment. An implementation of the algorithm for NVIDIA CUDA capable graphics processing units (GPU) is also developed to accelerate computation for 2D and 3D data. The new transforms are benchmarked against the Fourier transform for compression of data generated from synthetic 2D and 3D acoustic models.

Joint flow-seismic inversion for characterizing fractured reservoirs: theoretical approach and numerical modeling

2019-04-12T22:15:06Z

Joint flow-seismic inversion for characterizing fractured reservoirs: theoretical approach and numerical modeling Kang, Peter K.; Zheng, Yingcai; Fang, Xinding; Wojcik, Rafal; McLaughlin, Dennis; Brown, Stephen; Fehler, Michael; Burns, Daniel R.; Juanes, Ruben Traditionally, seismic interpretation is performed without any account of the flow behavior. Here, we present a methodology to characterize fractured geologic media by integrating flow and seismic data. The key element of the proposed approach is the identification of the intimate relation between acoustic and flow responses of a fractured reservoir through the fracture compliance. By means of synthetic models, we show that: (1) owing to the strong (but highly uncertain) dependence of fracture permeability on fracture compliance, the modeled flow response in a fractured reservoir is highly sensitive to the geophysical interpretation; and (2) by incorporating flow data (well pressures and production curves) into the inversion workflow, we can simultaneously reduce the error in the seismic interpretation and improve predictions of the reservoir flow dynamics.

Effect of borehole stress concentration on compressional wave velocity measurements

2019-04-12T22:15:04Z

Effect of borehole stress concentration on compressional wave velocity measurements Fang, Xinding; Fehler, Michael; Cheng, Arthur Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could lead to a biased estimation of formation elastic properties measured from sonic logging data. To study the effect of stress concentration around a borehole on sonic logging, we first use an iterative approach, which combines a rock physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole when it is subjected to an anisotropic stress loading. Then we use the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response in a borehole. Our numerical results are consistent with published laboratory measurements of the azimuthal velocity variations caused by borehole stress concentration. Both numerical and experimental results show that the variation of P-wave velocity versus azimuth has broad maxima and cusped minima, which is different from the presumed cosine behavior. This is caused by the preference of the wavefield to propagate through a higher velocity region.

Sensitivity of time lapse seismic data to the compliance of hydraulic fractures

2019-04-10T18:31:54Z

Sensitivity of time lapse seismic data to the compliance of hydraulic fractures Fang, Xinding; Shang, Xuefeng; Fehler, Michael We study the sensitivity of seismic waves to changes in the fracture normal and tangential compliances by analyzing the fracture sensitivity wave equation, which is derived by differentiating the elastic wave equation with respect to the fracture compliance. The sources for the sensitivity wavefield are the sensitivity moments, which are functions of fracture compliance, background elastic properties and the stress acting on the fracture surface. Based on the analysis of the fracture sensitivity wave equation, we give the condition for the weak scattering approximation to be valid for fracture scattering. Under the weak scattering approximation, we find that the percentage change of fracture compliance in hydraulic fracturing is equal to the percentage change of the recorded time-lapse seismic data. This could provide a means for monitoring the opening/closing of fractures in hydraulic fracturing through time-lapse seismic surveys.

The failure mode of correlation focusing for model velocity estimation

2019-04-10T18:31:50Z

The failure mode of correlation focusing for model velocity estimation Baek, Hyoungsu; Calandra, Henri; Demanet, Laurent We analyze the correlation focusing objective functional introduced by van Leeuwen and Mulder to avoid the cycle-skipping problem in full waveform inversion. While some encouraging numerical experiments were reported in the transmission setting, we explain why the method cannot be expected to work for general reflection data. We characterize the form that the adjoint source needs to take for model velocity updates to generate a time delay or a time advance. We show that the adjoint source of correlation focusing takes this desired form in the case of a single primary reflection, but not otherwise. Ultimately, failure owes to the specific form of the normalization present in the correlation focusing objective.

Registration-guided least-squares waveform inversion

2019-04-11T09:46:10Z

Registration-guided least-squares waveform inversion Baek, Hyoungsu; Calandra, Henri; Demanet, Laurent Full waveform inversion with frequency sweeping cannot start from zero frequency because of the lack of low-frequency data, requiring a good starting model. We study a di fferent iterative scheme where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. In order to create transported data, we introduce a nonconvex optimization problem and solve it in a multiscale fashion from low to high frequencies. This process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Successful registrations of noisy data, and application of the new method to model velocity estimation are demonstrated. In a crosshole seismic inversion example (transmission setting), we show that the new method decreases the model velocity error while conventional least-squares inversion converges to a spurious model.

Numerical modeling of elastic wave scattering by near-surface heterogeneities

2019-04-10T18:31:48Z

Numerical modeling of elastic wave scattering by near-surface heterogeneities Al Muhaidib, Abdulaziz; Toksoz, M. Nafi A perturbation method for elastic waves and numerical forward modeling are used to calculate the effects of seismic wave scattering from arbitrary shape shallow subsurface heterogeneities. Wave propagation is simulated using elastic finite difference for several earth models with different nearsurface characteristics. The near-surface scattered wavefield is modeled by separating the incident wavefield from the total wavefield by means of a perturbation method. We show that the scattered field is equivalent to the radiation field of an equivalent elastic source excited at the scatterer locations. The scattered waves consist mostly of body waves scattered to surface waves and are, generally, as large as, or larger than, the reflections. The results indicate that the scattered energy depends strongly on the properties of the shallow scatterers and increases with increasing impedance contrast, increasing size of the scatterers relative to the incident wavelength, and decreasing depth of the scatterers. Also, sources deployed at depth generate weaker surface waves, whereas deep receivers record weaker surface and scattered body-to-surface waves.

Earth Resources Laboratory Annual Report 2013 Table of Contents

2019-04-10T18:31:58Z

Earth Resources Laboratory Annual Report 2013 Table of Contents

Seismic imaging of hydraullically-stimulated fractures: A numerical study of the effect of the source mechanism

2019-04-10T21:28:39Z

Seismic imaging of hydraullically-stimulated fractures: A numerical study of the effect of the source mechanism Shabelansky, Andrey Hanan; Malcolm, Alison E.; Fehler, Michael; Bakku, Sudhish Kumar We present a numerical study of seismic imaging of hydraulically stimulated fractures using a single source from an adjacent fracturing-process. The source is either a point force generated from the perforation of the casing of the well or a double-couple as is typically observed from the induced microseismicity. We assume that the fracture is sufficiently stimulated to be imaged by reflected seismic energy. We show for a specific monitoring geometry of hydrofracturing that not only different waves (P and S) but also different source mechanisms from the same region form an image of different parts of the target fracture and thus add complementary information. The strategy presented here might be used as an additional monitoring tool of the hydrofracturing process.

A unified framework for relative source localization using correlograms

2019-04-10T22:03:48Z

A unified framework for relative source localization using correlograms Poliannikov, Oleg V.; Prange, Michael; Malcolm, Alison E.; Djikpesse, Hugues We study the problem of determining an unknown event location relative to previously located events using a single monitoring array in a monitoring well. We show that using the available information about the previously located events for locating new events is advantageous to localizing each event independently. By analyzing confidence regions, we compare the performance of two previously proposed localization methods, double-difference and interferometry, in varying signal noise and velocity uncertainty. We show that the double-difference method combats the signal noise much better due to the averaging over a larger number of travel time measurements. The interferometric method is superior where the main source of error is the velocity uncertainty between the event locations and the monitoring array. We propose a hybrid method that automatically balances these two approaches and produces a location estimator that is superior to either.

Comparison of microearthquake locations using seismic interferometry principles

2019-04-09T19:01:56Z

Comparison of microearthquake locations using seismic interferometry principles Melo, Gabriela; Malcolm, Alison E.; Fehler, Michael Mapping, localization, and general characterization of problems in reservoir fracture systems is one of the most important in oil, gas, and geothermal energy production. One way to study and monitor these fracture systems is to analyze the microearthquakes triggered during hydraulic fracturing or stimulation, as these events generally occur along newly created and preexisting fractures. Thus, the location of the microseismic events can be used to characterize the properties of the fracture system. There are many different methods for localizing microearthquakes and, in general, these methods yield different locations, velocity models, and event origin times, due to differences in algorithms and input models. This makes it very difficult to know which one gives the most accurate and consistent results in practice. The goal of this work is to use basic concepts from seismic interferometry for estimating constraints on the P and S traveltimes between two microearthquake locations. Information obtained through seismic interferometry pertains to only the Earth parameters between two receivers or, by reciprocity, two sources. This information is also less dependent on the velocity model, and less susceptible to errors in arrival time picking and noise in the data due to averaging over receivers. This information can then be used to evaluate and compare different sets of results obtained through different localization methods. Here we illustrate this comparison method by comparing localization results from two different methods. For our data set, in particular, seismic interferometry cannot give hard constrains but it gives bounds that can be used to asses results from different localization methods.

Multipole seismoelectric logging while drilling (LWD) for acoustic velocity measurements

2019-04-09T18:49:31Z

Multipole seismoelectric logging while drilling (LWD) for acoustic velocity measurements Zhu, Zhenya; Wang, Jun; Toksoz, M. Nafi In seismoelectric well logging, an acoustic wave propagates along a borehole and induces electrical signals along the borehole wall. The apparent velocities of these seismoelectric signals are equal to the formation velocities. Laboratory scale-model multipole acoustic and seismoelectric LWD tools are built to conduct measurements in a borehole drilled into a sandstone formation. The tools include either an acoustic receiver array of an electrode receiver array along with four acoustic sources to allow the generation of monopole, dipole, and quadrupole modes. Results show that the standard acoustic measurement of formation velocities are impacted by strong tool wave contamination in most situations. However, because the propagating tool waves do not induce any electrical signals, the seismoelectric measurements can provide a more robust velocity measurement. The multipole seismoelectric logging-while-drilling (LWD) could be used as a new logging method to measure the acoustic velocities of the borehole formations.

Seismic characterization of fractured reservoirs using 3D double beams

2019-04-10T21:28:33Z

Seismic characterization of fractured reservoirs using 3D double beams Zheng, Yingcai; Fang, Xinding; Fehler, Michael; Burns, Daniel R. We propose an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. We use both singly scattered and multiply scattered seismic waves by fractures. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacing and orientation and output an interference pattern as a function of the spacing and orientation. If multiple targets are used, the interference pattern is spatially varying and the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are sparse spatially, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validated our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.

Scholte waves generated by seafloor topography

2019-04-12T22:07:56Z

Scholte waves generated by seafloor topography Zheng, Yingcai; Fang, Xinding; Liu, Jing; Fehler, Michael Seafloor topography can excite strong interface waves called Scholte waves that are often dispersive and characterized by slow propagation but large amplitude. This type of wave can be used to invert for near seafloor shear wave velocity structure that is important information for multi-component P-S seismic imaging. Three different approaches are taken to understand excitation of Scholte waves and numerical aspects of modeling Scholte waves, including analytical Cagniard-de Hoop analysis, the boundary integral method and a staggered grid finite difference method. For simple media for which the Green’s function can be easily computed, the boundary element method produces accurate results. The finite difference method shows strong numerical artifacts and stagnant artificial waves can be seen in the vicinity of topography at the fluid-solid interface even when using fine computational grids. However, the amplitude of these artificial waves decays away from the seafloor. It is sensible to place receivers away from the fluid-solid interface for seismic modeling. To investigate Scholte wave generation, one needs to correctly implement the fluid-solid boundary condition. It is also shown through numerical examples including using a seafloor profile from the recent SEG Advanced Modeling (SEAM) Project that even mild topographic features can generate Scholte waves and these waves can be used to constrain near seafloor S wave velocity by dispersion analysis of interface Scholte waves. The implication to the full waveform inversion is that, although low frequency data are crucial for convergence, seafloor topography may have a large effect on low frequency seismic waves.

Advanced 3D Geophysical Imaging Technologies for Geothermal Resource Characterization

2019-04-12T22:06:07Z

Advanced 3D Geophysical Imaging Technologies for Geothermal Resource Characterization Zhang, Haijiang; Gasperikova, Erika; Parker, Beatrice; Tryggvason, Ari; Gudmundsson, Olafur; Seher, Tim; Newman, Gregory; Fehler, Michael; Arnason, Knutur We describe the ongoing development of joint geophysical imaging methodologies for geothermal site characterization and demonstrate their potential in two regions: Krafla volcano and associated geothermal fields in Northeastern Iceland, and Coso Hot Springs in California, USA. The Coso field is a high temperature reservoir similar to Krafla in Iceland. Each area is a locus of significant geothermal energy production. The complex geology of these sites also makes them excellent targets for developing and testing of strategies for joint imaging of magnetotelluric (MT) and micro-earthquake (MEQ) data. Our ultimate aim is to construct coupled 3D resistivity and velocity models of these geothermal systems and use them to better understand and exploit them.

A Bayesian framework for fracture characterization from surface seismic data

2019-04-12T22:06:07Z

A Bayesian framework for fracture characterization from surface seismic data Zamanian, S. Ahmad; Fehler, Michael; Burns, Daniel R. We describe a methodology for quantitatively characterizing the fractured nature of a hydrocarbon or geothermal reservoir from surface seismic data under a Bayesian inference framework. Fractures provide pathways for fluid flow in a reservoir, and hence, knowledge about a reservoir’s fractured nature can be used to enhance production of the reservoir. The fracture properties of interest in this study (to be inferred) are fracture orientation and excess compliance, where each of these properties are assumed to vary spatially over a 2D lateral grid which is assumed to represent the top of a reservoir. The Bayesian framework in which the inference problem is cast has the key benefits of (1) utilization of a prior model that allows geological information to be incorporated, (2) providing a straightforward means of incorporating all measurements (across the 2D spatial grid) into the estimates at each grid point, (3) allowing different types of measurements to be combined under a single inference procedure, and (4) providing a measure of uncertainty in the estimates. The observed data are taken from a 2D array of surface seismic receivers responding to an array of surface sources. Well understood features from the seismic traces are extracted and treated as the observed data, namely the P-wave reflection amplitude variation with acquisition azimuth (amplitude versus azimuth, or AvAz, data) and fracture transfer function (FTF) data. AvAz data are known to be more sensitive to fracture properties when the fracture spacing is significantly smaller than the seismic wavelength, whereas fracture transfer function data are more sensitive to fracture properties when the fracture spacing is on the order of the seismic wavelength. Combining these two measurements has the benefit of allowing inferences to be made about fracture properties over a larger range of fracture spacing than otherwise attainable. Geophysical forward models for the measurements are used to arrive at likelihood models for the data. The prior distribution for the hidden fracture variables is obtained by defining a Markov random field (MRF) over the lateral 2D grid where we wish to obtain fracture properties. The fracture variables are then inferred by application of loopy belief propagation (LBP) to yield approximations for the posterior marginal distributions of the fracture properties, as well as the maximum a posteriori (MAP) and Bayes least squares (BLS) estimates of these properties. Verification of the inference procedure is performed on a synthetic dataset, where the estimates obtained are shown to be at or near ground truth for a large range of fracture spacings.

Target-oriented Time-lapse Waveform Inversion using Virtual Survey

2019-04-10T21:28:35Z

Target-oriented Time-lapse Waveform Inversion using Virtual Survey Yang, Di; Zheng, Yingcai; Fehler, Michael; Malcolm, Alison E. Time-lapse seismic data are widely used for monitoring time-variant subsurface changes. Conventional analysis provides qualitative information by comparing results from consecutive surveys, whereas waveform inversion can retrieve quantitative estimates of reservoir properties through seismic waveform fitting. The quantitative evaluation of the physical parameters obtained by waveform inversion allows for better interpretation of fluid substitution and migration during processes like oil and gas production, and carbon sequestration. Since reservoir changes are localized and only part of the data are of interest, the time-lapse waveform inversion can be optimized in terms of computational cost and convergence rate. In this study, we propose a scheme of localized waveform inversion with computed datasets we refer to as virtual surveys. Both the model domain and trace duration in forward modeling are reduced by the reorganization of the data. We show a numerical example in which the recovery of the reservoir change is computationally faster and more robust to source-receiver locations than inversion with original survey.

Nonlinear Frechet derivative and its De Wolf approximation

2019-04-10T20:14:27Z

Nonlinear Frechet derivative and its De Wolf approximation Wu, Ru-Shan; Zheng, Yingcai We introduce and derive the nonlinear Frechet derivative for the acoustic wave equation. It turns out that the high order Frechet derivatives can be realized by consecutive applications of the scattering operator and a zero-order propagator to the source. We prove that the higher order Frechet derivatives are not negligible and the linear Frechet derivative may not be appropriate in many cases, especially when forward scattering is involved for large scale perturbations. Then we derive the De Wolf approximation (multiple forescattering and single backscattering approximation) for the nonlinear Frechet derivative. We split the linear derivative operator (i.e. the scattering operator) onto forward and backward derivatives, and then reorder and renormalize the nonlinear derivative series before making the approximation by dropping the multiple backscattering terms. Numerical simulations for a Gaussian ball model show significant difference between the linear and nonlinear Frechet derivatives.

Data-Driven Estimation of the Sensitivity of Target-Oriented Time-Lapse Seismic Imaging to Source Geometry

2019-04-10T23:51:17Z

Data-Driven Estimation of the Sensitivity of Target-Oriented Time-Lapse Seismic Imaging to Source Geometry Shabelansky, Andrey Hanan; Malcolm, Alison E.; Fehler, Michael The goal of time-lapse imaging is to identify and characterize regions in which the earth's material properties have changed between surveys. This requires an effective deployment of sources and receivers to monitor the region where changes are anticipated. Because each source adds signi ficant cost to the acquisition, we should ensure that only those sources that best image the target are collected and used to form an image of the target region. This study presents a data-driven approach that estimates the sensitivity of a target-oriented imaging approach to source geometry. The approach is based on the propagation of the recorded baseline seismic data backward in time through the entire medium and coupling it with the estimated perturbation in the subsurface. We test this approach using synthetic surface seismic and time-lapse VSP field-data from the SACROC field. These tests show that the use of the baseline seismic data enhances the robustness of the sensitivity estimate to errors, and can be used to select data that best image a target zone, thus increasing the SNR of the image of the target region and reducing the cost of time-lapse acquisition, processing, and imaging.

Monitoring Seismic Attenuation Changes Using a 4D Relative Spectrum Method in Athabsca Heavy Oil Reservoir, Canada

2019-04-10T21:28:32Z

Monitoring Seismic Attenuation Changes Using a 4D Relative Spectrum Method in Athabsca Heavy Oil Reservoir, Canada Shabelansky, Andrey Hanan; Malcolm, Alison E.; Fehler, Michael Heating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring these changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we measure the changes in the seismic wave attenuation of a heavy oil reservoir by constructing time-lapse Q[superscript -1] factor maps using a 4D-relative spectrum method. This method estimates seismic attenuation from surface reflection seismic surveys by calculating, for each trace in each survey, the attenuation (Q[superscript -1]) using the spectral ratio (Toksoz et al. (1979)) between a reference reflector above the reservoir and a second reflector below the reservoir. The results of our study on a real data set exhibit alignment along the injection wells, indicating that seismic attenuation can be used to monitor changes in a heavy oil reservoir.

A multi-pass one way method to include turning waves and multiples

2019-04-12T22:05:08Z

A multi-pass one way method to include turning waves and multiples Richardson, Alan; Malcolm, Alison E. Conventional one way migration methods exclude turning waves and multiples. We propose an algorithm that uses multiple passes to extend the one way method to efficiently include these wavepaths. A comparison of the images produced by the regular one way algorithm, RTM, and the new method, shows that this new method can significantly improve the image in regions of interest, and in certain situations may even provide more useful information than RTM. The runtime is demonstrated to be in between that of regular one way and RTM, while the physical memory required is considerably lower than that of RTM.

Approximate inversion of the wave-equation Hessian via randomized matrix probing

2019-04-12T22:07:56Z

Approximate inversion of the wave-equation Hessian via randomized matrix probing Letourneau, Pierre-David; Demanet, Laurent; Calandra, Henri We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a procedure called matrix probing. We show numerical indications that randomness is important for generating a robust preconditioner, i.e., one that works regardless of the model to be corrected. To be successful, matrix probing requires an accurate determination of the nullspace of the Hessian, which we propose to implement as a local dip-dependent mask in curvelet space. Numerical experiments show that the novel preconditioner fits 70% of the inverse Hessian (in Frobenius norm) for the 1-parameter acoustic 2D Marmousi model.

A fast butterfly algorithm for the hyperbolic Radon transform

2019-04-10T21:28:35Z

A fast butterfly algorithm for the hyperbolic Radon transform Hu, Jingwei; Fomel, Sergey; Demanet, Laurent; Ying, Lexing We introduce a fast butterfly algorithm for the hyperbolic Radon transform commonly used in seismic data processing. For two-dimensional data, the algorithm runs in complexity O(N[superscript 2] logN), where N is representative of the number of points in either dimension of data space or model space. Using a series of examples, we show that the proposed algorithm is significantly more efficient than conventional integration.

Surface-wave eikonal tomography for dense geophysical arrays

2019-04-12T22:07:57Z

Surface-wave eikonal tomography for dense geophysical arrays Gouedard, Pierre; Yao, Huajian; Ernst, Fabian; van der Hilst, Robert D. Surface-wave tomography often involves the construction of phase (or group) velocity maps through linearized inversion of measured phase (group) arrival times. Such inversions require a priori information about the medium (that is, a reference model) in order to calculate source-receiver paths, which is inaccurate for complex media, and requires regularization. The surface-wave eikonal tomography proposed here bypasses these limitations and has the advantage of being simple to implement and use, with virtually no input parameters. It relies on accurate phase arrival time measurement, which can be challenging for dispersive waves and complex waveforms. We present a measurement method based on the evaluation of phase arrival time diff erences at nearby receivers.We show, using an exploration data set, that the produced Rayleigh-wave velocity maps are in agreement with results from traditional tomography, but the latter have lower resolution due to the need of regularization to accommodate for the heterogeneity of the study area and noise in data. Eikonal tomography requires averaging over results from multiple sources to produce a proper image, and we evaluate this requirement to a 200 m source spacing in the considered scattering environment. In addition, we validate the approach of combining seismic interferometry and eikonal tomography, for the cases where the source coverage is inappropriate.

An approach for predicting stress-induced anisotropy around a borehole

2019-04-12T22:09:18Z

An approach for predicting stress-induced anisotropy around a borehole Fang, Xinding; Fehler, Michael; Zhu, Zhenya; Chen, Tianrun; Brown, Stephen; Cheng, Arthur; Toksoz, M. Nafi Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could result in a biased estimation of formation properties but could provide a means to estimate in situ stress from sonic logging data. In order to properly account for the formation property alteration, we propose an iterative numerical approach to calculate the stress-induced anisotropy around a borehole by combining the rock physics model of Mavko et al. (1995) and a finite-element method. We show the validity and accuracy of our approach by comparing numerical results to laboratory measurements of the stress-strain relation of a sample of Berea sandstone, which contains a borehole and is subjected to uniaxial stress loading. Our iterative approach converges very fast and can be applied to calculate the spatially varying stiffness tensor of the formation around a borehole for any given stress state.

Predicting stress-induced anisotropy around a borehole

2019-04-10T21:28:35Z

Predicting stress-induced anisotropy around a borehole Fang, Xinding; Fehler, Michael; Zhu, Zhenya; Chen, Tianrun; Brown, Stephen; Cheng, Arthur; Toksoz, M. Nafi Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could result in a biased estimation of formation properties but could provide a means to estimate in situ stress from sonic logging data. In order to properly account for the formation property alteration, we propose an iterative numerical approach to calculate the stress-induced anisotropy around a borehole by combining Mavko’s rock physics model and a finite-element method. We show the validity and accuracy of our approach by comparing numerical results to laboratory measurements of the stress-strain relation of a sample of Berea sandstone, which contains a borehole and is subjected to uniaxial stress loading. Our iterative approach converges very fast and can be applied to calculate the spatially varying stiffness tensor of the formation around a borehole for any given stress state.

Reservoir fracture characterizations from seismic scattered waves

2019-04-12T22:09:18Z

Reservoir fracture characterizations from seismic scattered waves Fang, Xinding; Fehler, Michael; Zhu, Zhenya; Zheng, Yingcai; Burns, Daniel R. The measurements of fracture parameters, such as fracture orientation, fracture density and fracture compliance, in a reservoir is very important for field development and exploration. Traditional seismic methods for fracture characterization include shear wave birefringence (Gaiser and Dok, 2001; Dok et al., 2001; Angerer et al., 2002; Vetri et al., 2003) and amplitude variations with offset and azimuth (AVOA) (Ruger, 1998; Shen et al., 2002; Hall et al., 2003; Liu et al., 2010; Lynn et al., 2010). These methods are based on the equivalent medium theory with the assumption that fracture dimension and spacing are small relative to the seismic wave length, so a fracture zone behaves like an equivalent anisotropic medium. But fractures on the order of seismic wave length are also very important for enhanced oil recovery, and they are one of the important subsurface scattering sources that generate scattered seismic waves. Willis et al. (2006) developed the Scattering Index method to extract the fracture scattering characteristics by calculating the transfer funtion of a fracture zone. Fang et al. (2011) proposed a modification of the SI method (the Fracture Transfer Function (FTF) method) that leads to a more robust fracture characterization. In this paper, we use both laboratory data and field data to explore the capability of the FTF method.

Source-Indexed Migration Velocity Analysis with Global Passive Data

2019-04-09T18:01:51Z

Source-Indexed Migration Velocity Analysis with Global Passive Data Burdick, S.; de Hoop, M. V.; van der Hilst, Robert D. The reverse-time migration of global seismic data generated by free-surface multiples is regularly used to constrain the crustal structure, but its accuracy is to a large extent determined by the accuracy of the 3-D background velocity model used for wave propagation. To this improve the velocity model and hence the accuracy of the migrated image, we wish to apply the technique of migration velocity analysis (MVA) to global passive data. Applications of MVA in the active setting typically focus on o ffset- or angle-gather annihilation, a process that takes advantage of data redundancy to form an extended image, and then applies an annihilation operator to determine the success of image formation. Due to the nature of regional-scale passive seismic arrays, it is unlikely that the data in most of these studies will be su cient to form an extended image volume for use in annihilation-based MVA. In order to make use of the sparse and irregular array design of these arrays, we turn towards a shot-pro le moveout scheme for migration velocity analysis introduced by Xie and Yang (2008). In the place of extended image annihilation, we determine the success of the migration velocity model by using a weighted image correlation power norm. We compare pairs of images formed by migrating each teleseismic source by image cross-correlation in the depth direction. We look for a suitable background model by penalizing the amount of correlation power away from zero depth shift. The total weighted correlation power between source-pro le images is then used as the error function and optimized via conjugate gradient. We present the method and a proof-of-concept with 2-D synthetic data.

Fluid Flow Property Estimation from Seismic Scattering Data

2019-04-12T22:09:18Z

Fluid Flow Property Estimation from Seismic Scattering Data Brown, Stephen; Fang, Xinding We present a methodology for relating seismic scattering signals from fractures to the fluid permeability field of the fracture network. The workflow is used to interpret seismic scattering signals for the reservoir permeability of the Emilio Field in the Adriatic Sea.

Multiple aperture INSAR (MAI) with C-band and L-band data: Noise and precision

2019-04-12T22:07:58Z

Multiple aperture INSAR (MAI) with C-band and L-band data: Noise and precision Bechor Ben Dov, Noah; Herring, Thomas A. MAI is a technique to extract along-track (horizontal) phase-based displacements from InSAR data. MAI’s theoretical precision can be at the centimeter level, an order of magnitude improvement over amplitude-based pixel offset approaches. However, MAI has been challenging to implement with most academic InSAR processors, and the theoretical precision difficult to reach for low to medium coherence terrains. We implement MAI with the JPL/CALTECH InSAR processor ROI PAC. We study the MAI noise structure with Envisat, Radarsat-1, ERS, and ALOS data, and develop phase corrections and filtering based on the results. We study the MAI noise with ’zero’ signal, all noise data. We process 11 Envisat pairs presenting low to medium coherence with less than 2 cm along track displacements, taken over the larger Los Angeles basin/San Gabriel Mountains in California, US. The test data contain a variety of decorrelation sources and cover different types of terrain, including urban, mountainous, vegetated and sea surfaces, as well as variety in temporal and spatial baselines. To test the MAI filter we superimpose the MAI noise images with signal simulating coseismic displacements from the 1812 Mw 7 Wrightwood earthquake sequence. The results present a correlation dependent RMSE ranging from 8 cm in correlation coefficient 0.4 to 2 cm in correlation coefficient 0.75. In an actual signal case (Hawaii, L-band), the random component of the noise for correlation coefficient of 0.5 to 0.95 varies from 2 cm to 4 mm.

Fracture characterization from attenuation of Stoneley waves across a fracture

2019-04-10T23:50:28Z

Fracture characterization from attenuation of Stoneley waves across a fracture Bakku, Sudhish Kumar; Fehler, Michael; Burns, Daniel R. Fractures contribute significantly to the permeability of a formation. It is important to understand the fracture distribution and fluid transmissivity. Though traditional well logs can image fractures intersecting the borehole, they provide little information on the lateral extent of the fractures, away from the borehole, or the fluid transmissivity. Experiments in the past demonstrated that fracture compliance can be a good proxy to fracture fluid conductivity. We describe a method to estimate fracture compliance from the attenuation of Stoneley waves across a fracture. Solving the dispersion relation in the fracture, transmission coefficient of Stoneley waves across a fracture is studied over all frequency ranges. Based on the observations from the model, we propose that measuring the transmission coefficient near a transition frequency can help constrain fracture compliance and aperture. Comparing attenuation across a finite fracture to that of an infinitely long fracture, we show that a bound on the lateral extent of the fracture can be obtained. Given the limitation on the bandwidth of acoustic logging data, we propose using the Stoneley waves generated during micro-seismic events for fracture characterization.

Annual Report 2012 Table of Contents

2019-04-10T23:50:28Z

Annual Report 2012 Table of Contents

AVO Monitoring of CO[subscript 2] Sequestration

2019-04-12T22:08:11Z

AVO Monitoring of CO[subscript 2] Sequestration Brown, Stephen; Hagin, Paul; Bussod, Gilles Standard geophysical methods for monitoring CO[subscript 2] injection have been proposed but many have severe limitations. In particular, while they can be used to monitor the presence or absence of CO[subscript 2] during an injection, they are unable to quantify changes in CO[subscript 2] saturation in most reservoirs. Amplitude versus Offset (AVO) attributes may be able to provide more sensitive discriminators for CO[subscript 2] presence. We propose a workflow useful for the prediction of the AVO response under arbitrary geologic conditions. Using this method we perform an experiment where AVO is combined with an upscaling scheme that propagates the effects of small-scale heterogeneities up to the scale of seismic observation. This experiment demonstrates the ability of the AVO technique to not only determine the presence or absence of CO[subscript 2], but also to determine the degree of CO[subscript 2] saturation in the reservoir.

Experimental Studies of Reflections from Single and Multiple-Fractures Using Lucite Models

2019-04-09T18:44:12Z

Experimental Studies of Reflections from Single and Multiple-Fractures Using Lucite Models Zhu, Zhenya; Burns, Daniel R.; Fehler, Michael; Brown, Stephen Laboratory acoustic measurements are performed with Lucite fracture models to understand the reflection characteristics of a seismic wave in a fracture zone. The fracture models include single fracture, dual fracture, and fracture zones having different fracture geometries. First we check the acoustic measurement system without fractures so we can identify the surface waves and the characteristics of the acoustic source and receiver. We then measure P-waves reflected and scattered by the different fracture models using a suite of illumination directions and receiver positions. The acoustic waves are reflected from the top of the fractures and their arrival times, frequencies and amplitudes are related to the depth and width of the fracture. We compare the acoustic waves reflected from dual fracture with those reflected from the single fracture and observe the effects of multiple scattering between the two fractures. In the fracture zone model, the scattered waveforms vary in different acquisition directions, which can help determine the fracture orientation. Variations in the scattering characteristics from the top and base of the fractures may provide information on fracture geometry, spacing, and orientation.

Double-beam stacking to infer seismic properties of fractured reservoirs

2019-04-12T22:08:14Z

Double-beam stacking to infer seismic properties of fractured reservoirs Zheng, Yingcai; Fang, Xinding; Fehler, Michael; Burns, Daniel R. We develop a theory for using 3D beam interference to infer scattering properties of a fractured reservoir using reflected seismic P data. For the sake of simplicity, we use Gaussian beams. The scattering properties are important to infer fracture spacing, orientation and compliance. The method involves the interference of two beams, one from the source region and the other from the receiver region. Each beam is formed by first windowing the data in space and time and then performing f-k filtering. The interference pattern depends on frequency, the incident angle, the reflection angle, and the azimuth. We try to interpret the interference pattern using local Born scattering in the target region. This interpretation is motivated by the observation that full-wave finite difference simulation of waves propagating through a set of vertical fractures using Schoenberg’s linear-slip boundary condition and fracture compliances consistent with those inferred from field and laboratory data shows that single scattering dominates in the reflection data. The methodology is versatile in that by adjusting the window sizes we can obtain plane wave interference as well as interference for a single shot or receiver gather. By suitable choice of pairs of source and receiver beams, the spatially varying fracture properties as well as the fracture orientation can be inferred.

Carbon sequestration monitoring with acoustic double-difference waveform inversion: A case study on SACROC walkaway VSP data

2019-04-12T22:06:08Z

Carbon sequestration monitoring with acoustic double-difference waveform inversion: A case study on SACROC walkaway VSP data Yang, Di; Fehler, Michael; Malcolm, Alison E.; Huang, Lianjie Geological carbon sequestration involves large-scale injection of carbon dioxide into underground geologic formations and is considered as a potential approach for mitigating global warming. Changes in reservoir properties resulting from the CO[subscript 2] injection and migration can be characterized using waveform inversions of time-lapse seismic data. The conventional approach for analysis using waveform tomography is to take the difference of the images obtained using baseline and subsequent time-lapse datasets that are inverted independently. By contrast, double-difference waveform inversion uses timelapse seismic datasets to jointly invert for reservoir changes. We apply conventional and double difference methods to a field time-lapse walkaway VSP data set acquired in 2008 and 2009 for monitoring CO[subscript 2] injection at an enhanced oil recovery field at SACROC, Texas. The double-difference waveform inversion gives a cleaner and more easily interpreted image of reservoir changes, as compared to that obtained with the conventional scheme. Our results from the application of acoustic double-difference waveform tomography shows some zones with decreased P-wave velocity within the reservoir due to CO[subscript 2] injection and migration.

Full-waveform Based Complete Moment Tensor Inversion and Stress Estimation from Downhole Microseismic Data for Hydrofracture Monitoring

2019-04-10T19:56:10Z

Full-waveform Based Complete Moment Tensor Inversion and Stress Estimation from Downhole Microseismic Data for Hydrofracture Monitoring Song, Fuxian; Toksoz, M. Nafi Downhole microseismics has gained increasing popularity in recent years as a way to characterize hydraulic fracturing and to estimate in-situ stress state. Conventional approaches only utilize part of the information contained in the microseismic waveforms such as the P/S far-field amplitudes to determine the focal mechanisms and infer stress state. The situation becomes more serious for downhole monitoring where only limited azimuthal coverage is available. In this study, we developed a full-waveform based approach to invert for complete moment tensor. We use the discrete wavenumber integration method as the fast forward modeling tool to calculate the full wavefield in the layered medium. By matching the waveforms across the array, a stable moment tensor solution can be obtained without imposing additional constraints. We show that by using full waveforms, the resolution of the full seismic moment tensor is improved even with data from a single monitoring well. We also determine the stress drop from the S-wave displacement spectrum. We test our method using a downhole microseismic dataset from hydraulic fracturing treatments in East Texas. The results indicate the existence of non-double-couple components in the moment tensor. The derived fracture plane direction also agrees with that derived from multiple event location.

SVD enhanced seismic interferometry for traveltime estimates between microquakes

2019-04-10T23:50:29Z

SVD enhanced seismic interferometry for traveltime estimates between microquakes Melo, Gabriela; Malcolm, Alison E. In general, Green’s functions obtained with seismic interferometry are only estimates of the true Green’s function, introducing uncertainties to the information recovered from them. However, there are still many cases in which the source-receiver geometries are suitable for seismic interferometry, usually allowing the recovery of kinematic information. Here we show how to use the singular value decomposition to re-enforce the accuracy of traveltimes obtained from interferometric Green’s functions. We apply the combination of seismic interferometry and the singular value decomposition to obtain physically accurate inter-event traveltimes for microquake pairs at a geothermal reservoir. With a synthetic example, we show that the P-wave phase and coda-wave energy information are closer to correct with the singular value decomposition than without. These traveltimes could be used for velocity tomography and event location algorithms to obtain more accurate event locations and locally accurate velocity models.

Microquake seismic interferometry with SVD enhanced Green's function recovery

2019-04-12T22:09:13Z

Microquake seismic interferometry with SVD enhanced Green's function recovery Melo, Gabriela; Malcolm, Alison E. The conditions under which seismic interferometry (SI) leads to the exact Green’s function (GF) are rarely met in practice, resulting in errors in the recovered GF. To alleviate this problem, we employ additional information than what is typically used in SI. This information comes from the collection of crosscorrelated traces, one for each source for a pair of receivers, which we shall refer to as the crosscorrelogram. It is by stacking the crosscorrelogram in the source dimension that we obtain an interferometric GF. In general, this crosscorrelogram has both stationary energy that contributes to the estimated GF and non-stationary energy that does not. Stationary energy in the crosscorrelogram is characterized by linearity, coherency, low wavenumber, and thus nearly in-phase events along the source dimension. Non-stationary energy by contrast is characterized by non-linearity, incoherency, high wavenumber, and out-of-phase events along the source dimension. We exploit these differences to separate the two parts of the energy in the crosscorrelogram to obtain more accurate GF estimates for non-ideal cases. In order to perform this separation and extract more information from the crosscorrelograms we use the singular value decomposition (SVD). We find that SVD is able to enhance physical arrivals that are not properly recovered using standard stacking in SI and inmany cases to recover arrivals that would otherwise be obscured by noise. Here, we filter the crosscorrelograms by using a lower-rank approximation, computed with SVD by keeping only the largest singular values, to enhance events that are coherent across multiple sources, thus isolating this stationary energy that gives the primary contribution to the GF. We illustrate this method with synthetic results for both homogeneous and scattering media simulating a possible application in microseismic monitoring with downhole receivers.

Visibility Analysis using Reverse Time Wave Sensitivity for Time-Lapse Target-Oriented Imaging

2019-04-12T22:09:13Z

Visibility Analysis using Reverse Time Wave Sensitivity for Time-Lapse Target-Oriented Imaging Shabelansky, Andrey Hanan; Malcolm, Alison E.; Fehler, Michael Identifying the relationship between surface seismic data and a particular region in the earth, referred to as visibility analysis, is important because it facilitates the optimization of the quality and speed of the imaging and monitoring processes. This study presents a data-driven approach that estimates a visibility relationship by propagating the recorded seismic data backward in time through the entire medium and coupling it with the region of interest in the subsurface. The region of interest is defined by a specific time-lapse perturbation in geophysical parameters. We show that by back-propagating in time only a limited number of shot records, a reliable visibility relationship can be established for target-oriented imaging of changes in a particular region in the subsurface. The established visibility relationship implies that in a subsequent time-lapse survey, only data corresponding to the visible shot records need to be collected, reducing the costs of the time-lapse acquisitions.

Hydraulic Fracture Monitoring: A Jonah Field Case Study

2019-04-12T22:09:13Z

Hydraulic Fracture Monitoring: A Jonah Field Case Study Seher, T.; Rondenay, Stephane; Djikpesse, H. Hydraulic fracturing involves the injection of a fluid to fracture oil and gas reservoirs, and thus increase their permeability. The process creates numerous microseismic events, which can be used to monitor subsurface operations. In this study we introduce a novel microearthquake relocation workflow based on crosswell seismic observations and in-situ velocity measurements, and then apply it to data from two hydraulic fracture stages conducted at the Jonah field (Wyoming). The relocation is carried out by global optimization of a probability density function including P- and S-wave traveltimes, as well as source-receiver azimuths. By averaging multiple cross-well observations, we reorient the three component receivers and reduce the scatter of measured azimuth values by 50-60%. By simultaneously relocating the observed microearthquake ensemble for one fracture stage, we derive a more reliable image of the average fracture orientation and reduce the scatter of microearthquake locations by 20-40% as compared to conventional approaches. For the two stages of fracturing investigated, the microearthquakes are found to follow a NW-SE trend that places constraints on the local stress field and on the newly created fluid paths.

Geophysical Monitoring of Multiple Phase Saturation of Rocks: Application to CO[subscript 2] Sequestration

2019-04-10T21:28:31Z

Geophysical Monitoring of Multiple Phase Saturation of Rocks: Application to CO[subscript 2] Sequestration Brown, Stephen 4-D seismic techniques rely on measuring changes in velocity over time in order to detect changes during activities such as CO[subscript 2] flooding and storage in a reservoir. Wang et al. [1998] detail a laboratory study of the seismic detectability of CO[subscript 2] flooding in a series of carbonate reservoir rocks taken from the McElroy field, West Texas. The basic findings of the paper suggest that while “ . . . laboratory results show that the largest V[subscript P] and V[subscript S] changes caused by CO[subscript 2] injection are associated with high-porosity, high-permeability rocks, . . . ” velocity changes in low-porosity (< 10%) and low-permeability carbonates are less than 1% and are undetectable using traditional 4-D seismic techniques.

2011 Earth Resources Laboratory Founding Member Consortium Meeting Table of Contents

2019-04-10T17:33:23Z

2011 Earth Resources Laboratory Founding Member Consortium Meeting Table of Contents

Interferometric hydrofracture microseism localization using neighboring fracture

2019-04-10T17:33:16Z

Interferometric hydrofracture microseism localization using neighboring fracture Poliannikov, Oleg V.; Malcolm, Alison E.; Djikpesse, Hugues; Prange, Michael Hydraulic fracturing is the process of injecting high-pressure fluids into a reservoir to induce fractures and thus improve reservoir productivity. Microseismic event localization is used to locate created fractures. Traditionally, events are localized individually. Available information about events already localized is not used to help estimate other source locations. Traditional localization methods yield an uncertainty that is inversely proportional to the square root of the number of receivers. However, in applications where multiple fractures are created, multiple sources in a reference fracture may provide redundant information about unknown events in subsequent fractures that can boost the signal-to-noise ratio, improving estimates of the event positions. We propose to use sources in fractures closer to the monitoring well to help localize events further away. It is known through seismic interferometry that with a 2D array of receivers, the travel time between two sources may be recovered from a cross-correlogram of two common source gathers. This allows an event in the second fracture to be localized relative to an event in the reference fracture. A difficulty arises when receivers are located in a single monitoring well. When the receiver array is 1D, classical interferometry cannot be directly employed because the problem becomes underdetermined. In our approach, interferometry is used to partially redatum microseismic events from the second fracture onto the reference fracture so that they can be used as virtual receivers, providing additional information complementary to that provided by the physical receivers. Our error analysis shows that, in addition to the gain obtained by having multiple physical receivers, the location uncertainty is inversely proportional to the square root of the number of sources in the reference fracture. Since the number of microseism sources is usually high, the proposed method will usually result in more accurate location estimates as compared to the traditional methods.

Focal Mechanism Determination of Induced Microearthquakes in an Oil Field Using Full Waveforms from Shallow and Deep Seismic Networks

2019-04-11T07:52:37Z

Focal Mechanism Determination of Induced Microearthquakes in an Oil Field Using Full Waveforms from Shallow and Deep Seismic Networks Li, Junlun; Kuleli, Huseyin Sadi; Zhang, Haijiang; Toksoz, M. Nafi A new, high frequency, full waveform matching method is used to study the focal mechanisms of small, local earthquakes induced in an oil field, which are monitored by a sparse near-surface network and a deep borehole network. The determined source properties are helpful for understanding the local stress regime in this field. During the waveform inversion, we maximize both the phase and amplitude matching between the observed and modeled waveforms. We also use the polarities of the first P-wave arrivals and the average S/P amplitude ratios to better constrain the matching. An objective function is constructed to include all four criteria. For different hypocenters and source types, comprehensive synthetic tests show that our method is robust to determine the focal mechanisms under the current array geometries, even when there is considerable velocity inaccuracy. The application to several tens of induced microseismic events showed satisfactory waveform matching between modeled and observed seismograms. The majority of the events have a strike direction parallel with the major NE-SW faults in the region, and some events trend parallel with the NW-SE conjugate faults. The results are consistent with the in-situ well breakout measurements and the current knowledge on the stress direction of this region. The source mechanisms of the studied events together with the hypocenter distribution indicate that the microearthquakes are caused by the reactivation of preexisting faults. We observed that the faulting mechanism varies with depth, from strike-slip dominance at shallower depth to normal faulting dominance at greater depth.

A robust method for fracture orientation and density detection from seismic scattered energy

2019-04-09T17:46:45Z

A robust method for fracture orientation and density detection from seismic scattered energy Fang, Xinding; Fehler, Michael; Zhu, Zhenya; Chen, Tianrun; Burns, Daniel R. The measurements of fracture parameters, such as fracture orientation, fracture density and fracture compliance, in a reservoir is very important for field development and exploration. Traditional seismic methods for fracture characterization include shear wave birefringence (Gaiser and Dok, 2001; Dok et al., 2001; Angerer et al., 2002; Vetri et al., 2003) and amplitude variations with offset and azimuth (AVOA) (Ruger, 1998; Shen et al., 2002; Hall et al., 2003; Liu et al., 2010; Lynn et al., 2010). These methods are based on the equivalent medium theory with the assumption that fracture dimension and spacing are small relative to the seismic wave length, so a fracture zone behaves like an equivalent anisotropic medium. But fractures on the order of seismic wave length are also very important for enhanced oil recovery, and they are one of the important subsurface scattering sources that generate scattered seismic waves. Willis et al. (2006) developed the Scattering Index method to extract the fracture scattering characteristics by calculating the transfer funtion of a fracture zone. This method has two sources of uncertainty: (1) calculation of the transfer function is sensitive to the analysis time window; (2) the interpretation of the transfer function is based on the assumption that the background reflectivity of the medium is white. Here we propose a modification of the SI methods that addresses these issues and leads to a more robust fracture characterization.

SH Wave Scattering from Fractures using Boundary Element Method with Linear Slip Boundary Condition

2019-04-12T22:03:24Z

SH Wave Scattering from Fractures using Boundary Element Method with Linear Slip Boundary Condition Chen, Tianrun; Fehler, Michael; Fang, Xinding; Shang, Xuefeng; Burns, Daniel R. A boundary element method (BEM) combined with a linear slip boundary condition is proposed to calculate SH wave scattering from fractures. The linear slip boundary condition was proposed by Schoenberg (1980) to model elastic wave propagation through an imperfectly bonded interface, where the traction cross the interface is continuous and displacement is discontinuous. Here, we demonstrate how to simulate SH wave scattering from fractures by applying the BEM and this linear slip boundary. Comparisons between results obtained using our model with those obtained using a computationally expensive finite difference method (FDM) (Coates and Schoenberg, 1995; Kruger et al., 2005) are performed to show the validity and accuracy of our approach. An example of SH wave scattering from three curved, crossing fractures is also given. Although our discussion here is focused on the linear slip boundary condition, our approach can easily be adopted to various slip boundary conditions that specify the displacement discontinuity and traction relations depending on different physical models of fractures.

Simulating Shear Wave Propagation in Two-Dimensional Fractured Heterogeneous Media by Coupling Boundary Element and Finite Difference Methods

2019-04-12T11:22:17Z

Simulating Shear Wave Propagation in Two-Dimensional Fractured Heterogeneous Media by Coupling Boundary Element and Finite Difference Methods Chen, Tianrun; Li, Junlun; Toksoz, M. Nafi A hybrid method to model the shear wave (SH) scattering from 2D fractures embedded in a heterogeneous medium is developed by coupling Boundary Element Method (BEM) and Finite Different Method (FDM) in the frequency domain. FDM is used to propagate an SH wave from a source through heterogeneities to localized homogeneous domains where fractures are embedded within artificial boundaries. According to Huygens’ Principle, the boundary points can be regarded as “secondary” point sources and their values are determined by FDM. Given the incident fields from these point sources, BEM is applied to model scatterings from fractures and propagate them back to the artificial boundaries. FDM then takes the boundaries as secondary sources and continues propagating the scattered field into the heterogeneous medium. The hybrid method utilizes both the advantage of BEM and FDM. A numerical iterative scheme is also presented to account for the multiple scattering between different sets of fractures. The results calculated from this hybrid method with pure BEM method are first compared to show the accuracy of the hybrid approach and the iterative scheme. This method is then applied to calculate the wave scattered from fractures embedded in complex media.

Estimation of fracture compliance from tubewaves generated at a fracture intersecting a borehole

2019-04-10T17:33:23Z

Estimation of fracture compliance from tubewaves generated at a fracture intersecting a borehole Bakku, Sudhish Kumar; Fehler, Michael; Burns, Daniel R. Understanding fracture compliance is important for characterizing fracture networks and for inferring fluid flow in the subsurface. In an attempt to estimate fracture compliance in the field, we developed a new model to understand tubewave generation at a fracture intersecting a borehole. Solving the dispersion relation in the fracture, amplitude ratios of generated tubewave to incident P-wave were studied over all frequency ranges. Based on the observations from the model, we propose that measuring amplitude ratios near a transition frequency can help constrain fracture compliance and aperture. The transition frequency corresponds to the regime where the viscous skin depth in the fracture is comparable to its aperture. However, measurements in the high frequency limit can place a lower bound on fracture compliance. Comparing the model to a previously published VSP dataset, we argue that compliance values of the order 10[superscript −10] −10[superscript −9] m/Pa may be possible in the field.

Integration of Geology, Rock-Physics, Logs, and Pre-stack Seismic for Reservoir Porosity Estimation

2019-04-11T05:33:05Z

Integration of Geology, Rock-Physics, Logs, and Pre-stack Seismic for Reservoir Porosity Estimation Al Muhaidib, Abdulaziz; Sen, Mrinal K.; Toksoz, M. Nafi The main objective of this paper is to obtain reservoir properties, such as porosity, both at the well locations and in the inter-well regions from seismic data and well logs. The seismic and well-log datasets are from an oil field in eastern Saudi Arabia, and the main target is a Jurassic carbonate reservoir. The geology of carbonate reservoirs in Saudi Arabia is well understood. However, reservoir porosity estimation is essential and needs to be determined for flow simulation and reservoir management. One of the main components of this project is establishing the relation between the Pimpedance and porosity using well log data. An amplitude-versus-angle (AVA) seismic inversion algorithm was employed to invert for the 3-D impedance volumes (i.e., Pimpedance and S-impedance) given partial angle stacks of seismic traces representing reflection amplitude variations with angle of incidence. These impedance volumes were used to estimate porosity between the well locations. The seismic and log data provided a priori information (i.e., the initial starting model and source wavelet estimate) to obtain geologically consistent results.

Finite Difference Elastic Wave Modeling Including Surface Topography

2019-04-12T22:03:23Z

Finite Difference Elastic Wave Modeling Including Surface Topography Al Muhaidib, Abdulaziz; Fehler, Michael; Toksoz, M. Nafi; Zhang, Yang Surface topography and the weathered zone (i.e., heterogeneity near the earth’s surface) have great effects on elastic wave propagation. Both surface waves and body waves are contaminated by scattering and conversion by the irregular surface topographic features. In this paper, we present a 2D numerical solver for the elastic wave equation that combines a 4th-order ADER scheme (Arbitrary high-order accuracy using DERivatives) with the characteristic variable method at the free surface boundary. The method is based on the velocity-stress formulation. We demonstrate the method by calculating synthetic seismograms for simple features.

Nonlinear Conjugate Gradients Algorithm For 2-D Magnetotelluric Inversion

2019-04-12T20:32:38Z

Nonlinear Conjugate Gradients Algorithm For 2-D Magnetotelluric Inversion Rodi, William L.; Mackie, Randall L. We investigate a new algorithm for computing regularized solutions of the two-dimensional magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such 'minimum-structure' models: the Gauss-Newton method, which solves a sequence of linearized inverse problems and has been the standard approach to nonlinear inversion in geophysics, and an algorithm due to Mackie and Madden, which solves a sequence of linearized inverse problems incompletely using a (linear) conjugate gradients technique. Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie-Madden) are more efficient than the GaussNewton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size. This owes largely to the fact that the conjugate gradients-based algorithms avoid two computationally intensive tasks that are performed at each step of a Gauss-Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space. The numerical tests also show that the Mackie-Madden algorithm reduces the objective function more quickly than our new NLCG algorithm in the early stages of minimization, but NLCG is more effective in the later computations. To help understand these results, we describe the Mackie-Madden and new NLCG algorithms in detail and couch each as a special case of a more general conjugate gradients scheme for nonlinear inversion.

Simulation Of An Acoustically Induced Electromagnetic Field In A Borehole Embedded In A Porous Formation

2019-04-10T23:57:26Z

Simulation Of An Acoustically Induced Electromagnetic Field In A Borehole Embedded In A Porous Formation Hu, Hengshan; Wang, Kexie; Wang, Jingnong When an acoustic point source located on the borehole axis emits an acoustic wave, an electric field, as well as an acoustic field, is generated in the porous formation around the borehole due to an electrokinetic effect. The coupled acoustic and electromagnetic wavefields were formulated by applying Pride's (1994) governing equations and boundary conditions at the borehole wall. Numerical examples show that two kinds of electric fields can be received on the borehole axis. The propagating electromagnetic wave arrives at different receivers almost simultaneously, and appears as the first wave packet in the full electric field waveform. Another kind of electric field accompanies the acoustic pressures, and consists of the same component waves as that of the acoustic waveforms. On the borehole axis, the coupled electric field vector is in the axial direction on the borehole axis. A study of the ratio of the magnitude of electric field strength to the magnitude of pressure, or REP, shows that the compressional wave has the largest REP value, the Stoneley wave the next, and the shear wave the smallest. The peak value of the electric field strength at 1 kHz is about 100 times larger than that at 10 kHz, while the REP at 1 kHz is about five times larger than REP at 10 kHz. Off the borehole axis, the electric field has a radial and axial component, and one Can also receive a circumferential magnetic field. When the interdependence between porosity, tortuosity and permeability is ignored, the REP increases rapidly with porosity, decreases with tortuosity, and changes little with permeability. The electric field strength decreases with borehole fluid salinity and formation water salinity.

Aeolian And Fluvial Depositional Systems Discrimination In Wireline Logs: Unayzah Formation, Central Saudi Arabia

2019-04-10T23:57:25Z

Aeolian And Fluvial Depositional Systems Discrimination In Wireline Logs: Unayzah Formation, Central Saudi Arabia Al-Dajani, AbdulFattah; Burns, Daniel; Toksoz, M. Nafi The objective of tills study is to discriminate between aeolian and fluvial deposits of the Permian Unayzah formation in Central Saudi Arabia by using wireline logs. The analysis is conducted on wire-line logs (field data): Density, sonic, gamma, and neutron, from two vertical wells (U1 and U2) in Central Saudi Arabia. Core data are available at well location U1 but not at U2. We apply an automated neural-network method to the wireline data for facies discrimination. Our analysis has been applied to the logs of well U2 after training the method on U1 logs using available core information. Results indicate that the Unayzah formation at well location U2 consists mainly of fluvial deposits (about 90%), which is consistent with previous studies and is supported by surface seismic images. We also investigate an analysis method based On the Fourier transform. We study the decay of the energy spectrum in the frequency domain and estimate the associated power-law exponent (i.e., the slope of the decay) for each depositional system. Analysis on the porosity logs (density, neutron, sonic, and shear), which are highly influenced by deposition composition and texture, has shown that the exponent is about the same for fluvial deposits at both well locations, while it is different for aeolian deposits.

The Effect Of Image Resolution On Fluid Flow Simulations In Porous Media

2019-04-12T20:32:25Z

The Effect Of Image Resolution On Fluid Flow Simulations In Porous Media Edie, Margaret S.; Olson, John F.; Burns, Daniel R.; Toksoz, M. Nafi Realistic simulations of flow in porous media are dependent upon having a three-dimensional, high resolution image of pore structure which is difficult to obtain. So, we ask the question, "How fine a resolution is necessary to adequately model flow in porous media?" To find the answer, we take a 7.5 p,m resolution image and coarsen it to five different resolutions. Lattice gas simulations are performed on each image. From the simulation results, we observe changes in permeability and velocity fields as the resolution is altered. The results show permeability varies by a factor of 5 over the resolution range. Flow paths change as the resolution is changed. We also find that the image processing has a large impact on the outcome of the simulations.

Effects Of Formation Stress On Logging Measurements

2019-04-10T23:57:29Z

Effects Of Formation Stress On Logging Measurements Huang, Xiaojun; Zhu, Zhenya; Toksoz, M. Nafi; Burns, Daniel R. We show both theoretically and experimentally how stress concentrations affect the velocity field around a borehole surrounded by a formation with intrinsic ortohombic anisotropy. When F[subscript x] = F[subscript y], no extra anisotropy is induced, however, isotropic stress concentrations are developed in the neighborhood of the borehole. Extra anisotropy is induced only when F[subscript x] ≠ F[subscript y], and the level of induced anisotropy is affected by the intrinsic anisotropy of the formation. Experiments show that monopole acoustic waves are more sensitive to properties in the neighborbood of the borehole than dipole waves. However, only dipole logging can determine the direction of anisotropy. A combination of monopole and dipole logging may lead to a better investigation of intrinsic as well as induced anisotropy of the formation.

Shear-Wave Reflection Moveout For Azimuthally Anisotropic Media

2019-04-10T23:57:29Z

Shear-Wave Reflection Moveout For Azimuthally Anisotropic Media Toksoz, M. Nafi; Al-Dajani, AbdulFattah The presence of azimuthal anisotropy causes shear wave propagation to split into fast and slow shear waves. The most common azimuthally anisotropic models used to describe fractured reservoirs are transverse isotropy with a horizontal axis of symmetry (HTI), and orthorhombic. In this paper, we study shear-wave reflection moveout in azimuthally anisotropic media with special attention paid to orthorhombic media with horizontal interfaces. In such cases the shear-wave reflection moveout is azimuthally variant and nonhyperbolic. We analyze the azimuthal dependence of normal moveout (NMO) velocity and we validate the accuracy of the conventional hyperbolic moveout equation. The azimuthal variation of NMO velocity is elliptical for both wave modes. In the presence of anisotropy-induced, nonhyperbolic moveout (NHMO), the hyperbolic moveout equation loses its accuracy with increasing offset (e.g., offset-to-depth ratio> 1). To study the azimuthal behavior of the NHMO for shear-wave reflections, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime. In an orthorhombic medium the quartic coefficient for shearwave reflections has a relatively simple form, especially in comparison to P-wave. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. The nonhyperbolic portion of the moveout, on the other hand, reaches its maximum along the polarization direction, and it reduces rapidly away from the direction of pOlarization. As a result, the anisotropy-induced, nonhyperbolic reflection moveout is significant in the vicinity of the polarization directions (e.g., ±30° and for large offset-to-depth ratios). The implementation of the NHM0 equation and the utilization of the moveout coefficients allow for not only enhanced seismic imaging but also provide the link between seismic signatures and medium parameters.

Imaging With Reverse Vertical Seismic Profiles Using A Downhole, Hydraulic, Axial Vibrator

2019-04-10T23:57:08Z

Imaging With Reverse Vertical Seismic Profiles Using A Downhole, Hydraulic, Axial Vibrator Krasovec, Mary; Turpening, Roger; Paulsson, Bjorn; Haldorsen, Jakob; Coates, Richard; Greaves, Robert We present the analysis of a reverse vertical seismic profile (RVSP) acquired over a pinnacle reef in the northern Michigan reef trend. The survey exhibited two features of note: (1) a new, strong, downhole vertical vibrator, and (2) a random distribution of surface receiver locations. A short sequence of processing steps followed by diffraction summation migration provide a high-resolution image of a portion of the target reef at 4600 feet depth. The high-resolution of the image is due largely to the downhole source, which generated a high-powered signal at frequencies up to several hundred Hz. The source signal was repeatable, allowing our processing scheme to recover these high frequencies. Due to adverse conditions, a large portion of the surface spread was abandoned. The reduced spatial coverage limits the extent of the migrated image, and therefore precludes an evaluation of the effectiveness of the random receiver spread. However, the partial image agrees with our previous interpretation of the reef. The high-resolution offers new insight into the structure of the reef, although a detailed geological interpretation is not possible due to the limited extent of the image.

Seismic Facies Characterization By Scale Analysis

2019-04-12T20:32:25Z

Seismic Facies Characterization By Scale Analysis Herrmann, Felix J. Over the years, there has been an ongoing struggle to relate well-log and seismic data due to the inherent bandwidth limitation of seismic data, the problem of seismic amplitudes, and the apparent inability to delineate and characterize the transitions that can be linked to and held responsible for major reflection events and their signatures. By shifting focus to a scale invariant sharpness characterization for the reflectors, we develop a method that can capture, categorize, and reconstruct the main features of the reflectors, without being sensitive to the amplitudes. In this approach, sharpness is defined as the fractional degree of differentiability, which refers to the order of the singularity of the transitions. This sharpness determines mainly the signature/waveform of the reflection and can be estimated with the proposed monoscale analysis technique. Contrary to multiscale wavelet analysis the monoscale method is able to find the location and sharpness of the transitions at the fixed scale of the seismic wavelet. The method also captures the local orders of magnitude of the amplitude variations by scale exponents. These scale exponents express the local scale-invariance and texture. Consequently, the exponents contain local information on the type of depositional environment to which the reflector pertains. By applying the monoscale method to both migrated seismic sections and welllog data, we create an image of the earth's local singularity structure. This singularity map facilitates interpretation, facies characterization, and integration of well and seismic data on the level of local texture.

Scaling And Seismic Reflectivity: Implications Of Scaling On Avo

2019-04-12T20:32:25Z

Scaling And Seismic Reflectivity: Implications Of Scaling On Avo Herrmann, Felix J. AVO analysis of seismic data is based on the assumption that transitions in the earth consist of jump discontinuities only. The generalization of this type of transition to a more realistic class of transitions shows a drastic change in observed AVO behavior, especially for the large angles currently attained by increasing cable lengths. We propose a simple approach that accounts for this anomalous behavior by renormalizing the observed AVO. This renormalization allows for a separation of the observed AVO effects in terms of a conventional Zoeppritz contribution and a scaling contribution in those cases where the transitions can no longer be considered as isolated jump discontinuities. After renormalization, the inverted fluctuations regain their relative magnitudes which, due to the scaling, may have been significantly distorted. An example of these distortions are tuning effects, often erroneously interpreted as bright spots.

3-D Geostatistical Seismic Inversion With Well Log Constraints

2019-04-09T18:22:42Z

3-D Geostatistical Seismic Inversion With Well Log Constraints Kane, Jonathan; Rodi, William; Toksoz, M. Nafi Information about reservoir properties usually comes from two sources: seismic data and well logs. The former provide an indirect, low resolution image of rock velocity and density. The latter provide direct, high resolution (but laterally sparse) sampling of these and other rock parameters. An important problem in reservoir characterization is how best to combine these data sets, allowing the well information to constrain the seismic inversion and, conversely, using the seismic data to spatially interpolate and extrapolate the well logs. We develop a seismic/well log inversion method that combines geostatistical techniques for well log interpolation (i.e., kriging) with a Monte Carlo search method for seismic inversion. We cast our inversion procedure in the form of a Bayesian maximum a posteriori (MAP) estimation in which the prior is iteratively modified so that the algorithm converges to the model that maximizes the likelihood function. We follow the approach used by Haas and Dubrule (1994) in their sequential inversion algorithm. Kriging is applied to the well data to obtain velocity estimates and their covariances for use as a priori constraints in the seismic inversion. Inversion of a complete 3-D seismic section is performed one trace at a time. The velocity profiles derived from previous seismic traces are incorporated as "pseudo well logs" in subsequent applications of kriging. Our version of this algorithm employs a more efficient Monte Carlo search method in the seismic inversion, and moves sequentially away from the wells so as to minimize the kriging variance at each step away from the inverted wells. Numerical experiments with synthetic data demonstrate the viability of our seismic/ well data inversion scheme. Inversion is then performed on a real 3-D data set provided by Texaco.

Seismic Facies Classification And Identification By Competitive Neural Networks

2019-04-12T20:32:25Z

Seismic Facies Classification And Identification By Competitive Neural Networks Saggaf, Muhammad M.; Toksoz, M. Nafi; Marhoon, Maher I. We present an approach based on competitive networks for the classification and identification of reservoir facies from seismic data. This approach can be adapted to perform either classification of the seismic facies based entirely on the characteristics of the seismic response, without requiring the use of any well information, or automatic identification and labeling of the facies where well information is available. The former is of prime use for oil prospecting in new regions, where few or no wells have been drilled, whereas the latter is most useful in development fields, where the information gained at the wells can be conveniently extended to inter-well regions. Cross-validation tests on synthetic and real seismic data demonstrated that the method can be an effective means of mapping the reservoir heterogeneity. For synthetic data, the output of the method showed considerable agreement with the actual geologic model used to generate the seismic data, while for the real data application, the predicted facies accurately matched those observed at the wells. Moreover, the resulting map corroborates our existing understanding of the reservoir and shows substantial similarity to the low frequency geologic model constructed by interpolating the well information, while adding significant detail and enhanced resolution to that model.

Application Of Smooth Neural Networks For Inter-Well Estimation Of Porosity From Seismic Data

2019-04-12T20:32:24Z

Application Of Smooth Neural Networks For Inter-Well Estimation Of Porosity From Seismic Data Saggaf, Muhammad M.; Toksoz, M. Nafi; Mustafa, Husam M. We apply an approach based on smooth neural networks to a 3D seismic survey in the Shedgum area of the Ghawar Field to estimate the reservoir porosity distribution of the Arab-D Member. We conducted numerous systematic cross-validation tests to assess the accuracy of the method and to compare it to that of traditional back-propagation networks. The results obtained from these tests indicate that the regularized back-propagation network can be quite adept at estimating the porosity distribution of the reservoir in the inter-well regions from seismic data. The accuracy remained consistent as the network parameters (size and training length) were varied. On the other hand, the traditional back-propagation network gave acceptable results only when the optimal network parameters were used, and the accuracy deteriorated significantly as soon as deviations from these optimal parameters occurred. Moreover, utilizing smooth networks, the final porosity volume corroborates our existing understanding of the reservoir and shows substantial similarity to the simple geologic model constructed by interpolating the well information, while adding significant detail and enhanced resolution to that model. We also scrutinize multi-attribute analysis, analyze how attributes can be both constructive and damaging to the prediction of the reservoir properties, and evaluate their effectiveness in enhancing the accuracy of the solution.

Estimation Of Reservoir Properties From Seismic Data By Smooth Neural Networks

2019-04-12T20:32:24Z

Estimation Of Reservoir Properties From Seismic Data By Smooth Neural Networks Saggaf, Muhammad M.; Toksoz, M. Nafi; Mustafa, Husam M. Traditional joint inversion methods reqnire an a priori prescribed operator that links the reservoir properties to the observed seismic response. The methods also rely on a linearized approach to the solution that makes them heavily dependent on the selection of the starting model. Neural networks provide a useful alternative that is inherently nonlinear and completely data-driven, but the performance of traditional back-propagation networks in production settings has been inconsistent due to the extensive parameter tweaking needed to achieve satisfactory results and to avoid overfitting the data. In addition, the accuracy of these traditional networks is sensitive to network parameters, such as the network size and training length. We present an approach to estimate the point-values of the reservoir rock properties (such as porosity) from seismic and well log data through the use of regularized back propagation and radial basis networks. Both types of networks have inherent smoothness characteristics that alleviate the nonmonotonous generalization problem associated with traditional networks and help to avert overfitting the data. The approach we present therefore avoids the drawbacks of both the joint inversion methods and traditional back-propagation networks. Specifically, it is inherently nonlinear, requires no a priori operator or initial model, and is not prone to overfitting problems, thus requiring no extensive parameter experimentation.

Executive Summary

2019-04-10T23:57:08Z

Executive Summary Burns, Daniel R. During the past year we have continued to make progress on the difficult problems associated with extracting geological information from geophysical data sets. Our research results focus on three major areas of characterization of reservoir heterogeneity and its effects on fluid flow: (1) facies analysis and reservoir property estimation from seismic and well log data, (2) fluid flow characterization and property estimation, and (3) anisotropy estimation from borehole and surface seismic data. Our theoretical work continues to be supported by laboratory experimentation (in the large sediment dynamics tank, as well as the borehole scale model facilities) and field data analysis. Finally, because of our interest in data inversion for reservoir properties, we include a paper from Rodi and Mackie on a nonlinear conjugate gradient inversion method. They show results applied to magnetotelluric data, although the method can also be applied to other types of data. The following sections provide a brief summary of the papers included in this report.

Variable Grid Finite-Difference Modeling Including Surface Topography

2019-04-10T23:57:03Z

Variable Grid Finite-Difference Modeling Including Surface Topography Hayashi, Koichi; Burns, Daniel R. We have developed a two-dimensional viscoelastic finite-difference modeling method for highly complex topography. Realistic modeling of seismic wave propagation in the near surface is complicated by many factors, such as strong heterogeneity, topographic relief and large attenuation. In order to account for these complications, we use a velocity-stress staggered grid and employ an 0(2,4) accurate viscoelastic finite-difference scheme. The implementation includes an irregular free surface condition for topographic relief and a variable grid technique in the shallow parts of the model. Numerical tests indicate that approximately ten grid-points per shortest wavelength results in accurate calculations. The method is accurate and stable, and allows us to handle complex structure in finite-difference modeling.

An Analysis Of Deconvolution: Modeling Reflectivity By Fractionally Integrated Noise

2019-04-12T20:32:24Z

An Analysis Of Deconvolution: Modeling Reflectivity By Fractionally Integrated Noise Saggaf, Muhammed M.; Toksoz, M. Nafi Reflection coefficients are observed in nature to have stochastic behavior that departs significantly from the white noise model. Conventional deconvolution methods, however, assume reflectivity to be a white noise process. In this paper we analyze the deconvolution process, study the implications of the assumption of white noise, and show that the conventional operator can recover only the white component of reflectivity. A new stochastic model, fractionally integrated noise, is proposed for modeling reflectivity. This model more closely approximates its spectral character and that encompasses white noise as a special case. We discuss different techniques to generalize the conventional deconvolution method based on the new model in order to handle reflectivity that is not white, and compare the results of the conventional and generalized filters using data derived from well logs.

Reflection Moveout Inversion In Azimuthally Anisotropic Media: Accuracy, Limitation, And Acquisition

2019-04-12T20:32:23Z

Reflection Moveout Inversion In Azimuthally Anisotropic Media: Accuracy, Limitation, And Acquisition AI-Dajani, AbdulFattah; Alkhalifah, Tariq; Morgan, Dale Parameter estimation from elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of the NMO ellipse, the parameter cr, in particular, is also sensitive to the strength of anisotropy. To invert for the parameters the NMO ellipse, at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60° apart. Having more than three distinct source-to-receiver azimuths (e.g., full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates. In orthorhombic media, inverting for the semi-axes of the NMO-ellipse allows the computation of the difference in the anisotropic parameters δ[superscript (1)] and δ[superscript (2)]. Additional information such as well data, is necessary in order to determine δ[superscript (1)] and δ[superscript (2)]. Furthermore, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any strength of anisotropy. To maximize quality in the inversion process, it is recommended that at the design stage of seismic data acquisition to have small sector sizes (≤ 10°) with adequate fold and offset distribution. For three azimuth directions, 60° apart, to perform the inversion, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might happen for fractured reservoirs) should have a time thickness, relative to the total time, of at least the ratio of the error in the NMO (stacking) velocity to the interval anisotropy strength of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50% depending on the number of observations (NMO Velocities) that enter the inversion procedure.

Nonhyperbolic Reflection Moveout For Azimuthally Anisotropic Media

2019-04-10T23:57:04Z

Nonhyperbolic Reflection Moveout For Azimuthally Anisotropic Media AI-Dajani, AbdulFattah; Toksoz, M. Nafi Reflection moveout in azimuthally anisotropic media is not only azimuthally dependent but it is also nonhyperbolic. As a result, the conventional hyperbolic normal moveout (NMO) equation parameterized by the exact NMO (stacking) velocity loses accuracy with increasing offset (i.e., spreadlength). This is true even for a single-homogeneous azimuthally anisotropic layer. The most common azimuthally anisotropic models used to describe fractured media are the horizontal transverse isotropy (HTI) and the orthorhombic(ORT) symmetry. Here, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime for pure mode reflection (I.e., no conversion) in arbitrary anisotropic media with arbitrary strength of anisotropy. In addition, we present an analytic description of the long-spread (large-offset) nonhyperbolic reflection moveout (NHMO). In multilayered azimuthally anisotropic media, the NMO (stacking) velocity and the quartic moveout coefficient can be calculated with good accuracy using the known averaging equations for VTI media. The interval NMO velocities and the interval quartic coefficients, however, are azimuthally dependent. This allows us to extend the nonhyperbolic moveout (NHMO) equation, originally designed for VTI media, to more general horizontally stratified azimuthally anisotropic media. As a result, our formalism allows rather simple transition from VTI to azimuthally anisotropic media. Numerical examples from reflection moveout in orthorhombic media, the focus of this paper, show that this NHMO equation accurately describes the azimuthally-dependent P-wave reflection traveltimes, even on spreadlengths twice as large as the reflector depth. This work provides analytic insight into the behavior of nonhyperbolic moveout, and it has important applications in modeling and inversion of reflection moveout in azimuthally anisotropic media.

Frequency Dependence Of Seismic Data From Nigeria: Preliminary Results

2019-04-10T19:49:51Z

Frequency Dependence Of Seismic Data From Nigeria: Preliminary Results Krasovec, Mary L.; Burns, Daniel R.; Toksoz, M. Nafi Seismic data from the Niger Delta is used to test processing sequences involved in prestack and poststack amplitude and frequency analysis of marine seismic data. Water bottom reverberations are found to present a formidable challenge in poststack frequency and amplitude analysis. However, reflectors with anomalously high amplitudes show low frequency content both in deconvolved poststack data and in the near offsets of prestack data with no deconvolution, which agrees with results in the literature. Lack of detailed knowledge of the lithology prevents investigation of the physical nature of the amplitude and frequency variations.

Azimuthal Offset-Dependent Attributes (AVO And FVO) Applied To Fracture Detection

2019-04-10T23:57:03Z

Azimuthal Offset-Dependent Attributes (AVO And FVO) Applied To Fracture Detection Shen, Feng; Sierra, Jesus; Burns, Daniel R.; Toksoz, M. Nafi Using the amplitude versus offset (AVO) and the frequency versus offset (FVO) information, the diagnostic ability of P-wave seismic data in fracture detection is investigated. The offset-dependent attributes (AVO and FVO) are estimated by using an eigenvector based estimation technique, the multiple signal classification frequency estimator. These attributes are applied to the determination of principal orientation of fractures in carbonate fractured reservoirs located in the Maporal field in the Barinas basin of southwestern Venezuela. Our studies show that, in the crack normal direction, P-wave reflectivity is characterized by a large increase of amplitude with offset (large positive AVO gradient) and a large frequency decay with offset (large negative FVO gradient). In the crack strike direction, P-wave reflectivity is characterized by a wide range of AVO gradients but a small variation of FVO gradients. The analyses of inverted offset-dependent velocities and theoretical calculations show that the lateral heterogeneity in the reservoir zone can lead to large variations of AVO signatures. The offset-dependent frequency attribute can help lessen the ambiguity in fracture detection. The combination of the offset-dependent frequency attribute is more beneficial than using the offset-dependent amplitude attribute alone.

Geostatistical Seismic Inversion Using Well Log Constraints

2019-04-12T20:32:24Z

Geostatistical Seismic Inversion Using Well Log Constraints Kane, Jonathan; Rodi, William; Herrmann, Felix; Toksoz, M. Nafi Information about reservoir properties usually comes from two sources: seismic data and well logs. The former provide an indirect, low resolution image of rock velocity and density. The latter provide direct, high resolution (but laterally sparse) sampling of these and other rock parameters. An important problem in reservoir characterization is how best to combine these data sets, allowing the well information to constrain the seismic inversion and, conversely, using the seismic data to spatially interpolate and extrapolate the well logs. We have developed a seismic/well log inversion method that combines geostatistical methods for well log interpolation (i.e., kriging) with a Monte Carlo search technique for seismic inversion. Our method follows the approach used by Haas and Dubrule (1994) in their sequential inversion algorithm. Kriging is applied to the well data to obtain velocity estimates and their variances for use as a priori constraints in the seismic inversion. Further, inversion of a complete 2-D seismic section is performed one trace at a time. The velocity profiles derived from previous seismic traces are incorporated as "pseudo well logs" in subsequent applications of kriging. Our version of this algorithm employs a more efficient Monte Carlo search algorithm in the seismic inversion step, and moves progressively away from the wells so as to minimize the kriging variance at each step. Numerical experiments with synthetic data demonstrate the viability of our seismic/well data inversion scheme.

Seismoelectric And Seismomagnetic Measurements In Fractured Borehole Models

2019-04-12T20:32:18Z

Seismoelectric And Seismomagnetic Measurements In Fractured Borehole Models Zhu, Zhenya; Toksoz, M. Nafi Seismoelectric and seismomagnetic fields generated by acoustic waves in fluid-saturated fractured borehole models are experimentally investigated with an electrode and a Halleffect sensor. In a borehole with a horizontal fracture, the Stoneley and flexural waves induce seismoelectric and seismomagnetic fields on the borehole wall and an electromagnetic wave propagating with light speed at the horizontal fracture. In a borehole with a vertical fracture, the acoustic field generated by a monopole or dipole source is similar to that in a borehole without a vertical fracture. However, the acoustic wave propagating along the vertical fracture induces seismoelectric and seismomagnetic fields, whose apparent velocities are equal to that. of a Stoneley wave. Experimental results show that two different kinds of electric and magnetic fields are generated by acoustic waves in borehole models with horizontal and/or vertical fractures. One is an electromagnetic wave propagating with light speed. The second is a stationary or localized seismoelectric and seismomagnetic field. Seismoelectric and seismomagnetic measurements might be a new logging technique for exploring fractures in a borehole.

Fluid Flow In Porous Media: NMR Imaging And Numerical Simulation

2019-04-10T23:57:07Z

Fluid Flow In Porous Media: NMR Imaging And Numerical Simulation Edie, Margaret S.; Olson, John F.; Burns, Daniel R.; Toksoz, M. Nafi We use nuclear magnetic resonance (NMR) imaging to obtain a three-dimensional image of the pore structure in a limestone core, 4.5 mm in diameter and 10 mm in length, with a resolution of 40 μm. This image is converted into boundary conditions for simulation of fluid flow through the rock using the lattice gas method. The computed permeability is several orders of magnitude lower than the laboratory measured permeability, most likely a result of the image resolution being too coarse to resolve the smaller pore throats, which are believed to be significant for flow in this sample.

Pore-Scale Simulation Of Experimentally Realizable, Oscillatory Flow In Porous Rock

2019-04-12T20:32:23Z

Pore-Scale Simulation Of Experimentally Realizable, Oscillatory Flow In Porous Rock Olson, John F. We report new simulations of oscillating flow in porous rock. Our goal is to better understand the frequency dependence of pore-scale fluid motion, which should ultimately help us to interpret attenuation and electroseismic measurements. We use a lattice gas cellular automaton (Rothman and Zaleski, 1997) to perform the calculations in a pore space geometry measured from Fontainebleau sandstone by X-ray microtomography (Spanne et al., 1994; Auzerais et al., 1996). We chose this method because it is fast and efficient in the complex geometry of the porous rock. We show that the Biot critical frequency (Biot, 1956) is accessible to simulation, and we perform simulations at a range of frequencies around the critical frequency. In addition, we show that the dynamical properties of the lattice gas fluid can be mapped onto reasonable real fluids. As the frequency varies through the critical range, we observe qualitative and quantitative changes in the amplitude and phase of fluid velocity distributions. We also report preliminary calculations of the local viscous dissipation, which should provide a means to compare our simulations with existing theories of attenuation (e.g., Johnston et al., 1979; Dvorkin and Nur, 1993; Akbar et al., 1994).

Multi-And Monoscale Attributes For Well And Seismic Data

2019-04-10T23:57:04Z

Multi-And Monoscale Attributes For Well And Seismic Data Herrmann, Felix J. Edges in a medium are the primary source of coherent reflections because they exhibit a large or even diverging amplitude behavior for their derivatives. Generally the medium properties are not only assumed to jump across interfaces, limiting the edge's singular behavior to that of a jump discontinuity, but the interfaces are also assumed to be well separated. Multiscale analysis on well data shows that the model of a jump discontinuity is too limited to account for the scaling behavior displayed by these types of data sets across the seismic scale range. It also demonstrates that the edges are not well separated. These observations coined two generalizations. First the jump is generalized to a wider class of scale exponent indexed transitions of which the jump is a special case. Secondly the edges are allowed to accumulate. The first part of this paper is devoted to the substantiation of these two generalizations. It introduces the necessary tools for the multiscale analysis, which characterizes the individual edges by means of scaling exponents and the overall texture by singularity spectra. The first part is concluded with a discussion on the application to well and seismic data. In the second part a complementary method to obtain information on the scaling is proposed. It is aimed to deal with the unfortunate fact that the scale content of the seismic signal is relatively small, making it difficult to conduct the multiscale analysis. For instance it is hard to obtain estimates for the local scaling exponents, characterizing the different types of transitions via their induced reflectivity. The novel method presented uses fractional differentiations/integrations to estimate the scale exponents at a fixed scale. The estimated scale exponents not only capture the local scaling characteristics but are also related to the local frequency behavior of the reflections. In this capacity they constitute local stratigraphical texture parameterizations. Local texture is relevant for the identification of the major geological markers as well as for localization and characterization of the major channels and barriers for the fluid flow being all important characteristics for the reservoir. Multifractal singularity spectra, on the other hand, provide more general information on the global texture and they are highly relevant for geological sequences and for the properties of the reservoir rock.

Models In LWD Applications

2019-04-10T23:57:06Z

Models In LWD Applications Rao, V. N. Rama; Burns, Daniel R.; Toksoz, M. Nafi A model for a fluid-filled borehole with an LWD tool is used to identify and analyze the monopole, dipole, and quadrupole modes that are present. The modes can be classified into three groups and have dispersion behavior that is influenced predominantly by the geometry and material properties of the three borehole layers (inner fluid column, tool, and annulus fluid column). However, this simple dependence gets complicated in regions of the frequency-wavenumber plane, where modes related to different layers interact and exchange their dispersion characteristics. The dipole modes exhibit the effects of interaction below 2 kHz and above 20 kHz.

In Situ Permeability Estimation: A Comparison Between Acoustic And NMR Logs

2019-04-12T20:32:24Z

In Situ Permeability Estimation: A Comparison Between Acoustic And NMR Logs Chen, Wei; Burns, Daniel R.; Tang, Xiao-ming Permeability estimates from acoustic logs (Stoneley waves) and NMR logs were compared using data from a geologic section consisting of sandstone and shale beds. The permeability results show very good correlation for these two different methods. Data from a gas-bearing zone shows high permeability values from acoustic data and low values from NMR. The difference between these two permeability results can be used as a gas zone indicator.

Formation Stress Estimation Using Standard Acoustic Logging

2019-04-10T23:57:04Z

Formation Stress Estimation Using Standard Acoustic Logging Huang, Xiaojun; Sinha, Bikash K.; Toksoz, M. Nafi; Burns, Daniel R. In situ formation stress directions and magnitudes are estimated by inverting the borehole flexural and Stoneley dispersions obtained from standard acoustic logging data (dipole and monopole logs). The underlying procedure consists of the following steps: first, we locate stressed zones in the formation by searching for crossovers in flexural dispersions. Second, the fast shear direction is estimated from the cross-dipole waveforms. It corresponds to the direction of the maximum horizontal stress (S[subscript H]). Finally, a multi-frequency inversion of both the Stoneley and flexural dispersions yields the maximum (S[subscript H]) and minimum (S[subscript h]) horizontal stress magnitudes together with the three formation nonlinear elastic constants, C[subscript 111], C[subscript 112] and C[subscript 113], defined about the selected reference (isotropic) state. The inversion method is based on equations that relate S[subscript H] and S[subscript h] with variations in phase velocities of the borehole flexural and Stoneley waves in the stressed state from those in the assumed reference state, the state that is hydrostatically loaded and isotropic. Phase velocities of the borehole flexural and Stoneley modes as a function of frequency can be obtained from processing the cross-dipole and monopole waveforms, respectively. The borehole flexural and Stoneley dispersions in the assumed reference (isotropic) state are obtained from the solution of a standard boundary-value problem. The sensitivity functions for the inversion model are obtained from the eigenfunctions of the boundary-value problem in the reference state. Results for the stress directions and magnitudes obtained from the inversion of the Stoneley and flexural dispersions over a selected bandwidth are consistent with focal mechanism and borehole breakout data present in the world map database (Zoback, 1992).

Estimation Of Lithologies And Depositional Facies From Wireline Logs

2019-04-10T23:57:03Z

Estimation Of Lithologies And Depositional Facies From Wireline Logs Saggaf, Muhammed M.; Nebrija, Ed L. We approach the problem of identifying facies from well logs though the use of neural networks that perform vector quantization of input data by competitive learning. The method can be used in either an unsupervised or supervised manner. Unsupervised analysis is used to segregate a well into distinct facies classes based on the log behavior. Supervised analysis is used to identify the facies types present in a certain well by making use of the facies identified from cores in a nearby well. The method is suitable for analyzing lithologies and depositional facies of horizontal wells, which are almost never cored, especially if core data is available for nearby vertical wells. Both types of modes are implemented and used for the automatic facies analysis of horizontal wells in Saudi Arabia. In addition to the identification of facies, the method is also able to calculate confidence measures for each analysis that is indicative of how well the analysis procedure can identify those facies given uncertainties in the data. Moreover, constraints derived from human experience and geologic principles can be applied to guide the inference process.

Dispersion Analysis Of Cross-Dipole Data

2019-04-10T23:56:58Z

Dispersion Analysis Of Cross-Dipole Data Huang, Xiaojun; Burns, Daniel R.; Toksoz, M. Nafi In this paper, we demonstrate that dispersion analysis of cross-dipole data has promising potential not only for differentiating stress-induced anisotropy from intrinsic anisotropy, but also for providing information on radial heterogeneity of formations. A dispersion analysis using improperly rotated data, however, exhibits spurious results because of the cross-contamination of the fast and slow flexural waves at different frequencies. When using Alford rotation, if the two orthogonal sources and/or receivers do not have matching signatures, the estimation of polarization directions of the split flexural waves will deviate from the actual directions, an important parameter that reflects vertical fracture orientation or regional stress direction. In addition, the two split flexural waves may not be separated completely. We present a new rotation scheme carried out in the frequency domain that takes into account signature mismatch of both the sources and the receivers. The new technique is applied to a set of four-component cross-dipole data from the Cymric Oil Field, and the estimated polarization direction of the fast flexural wave is compared with that from Alford rotation. The results show that the new rotation scheme yields the same trend as Alford rotation as a function of depth. However, at each depth, the results of these two methods can differ by as many as 50°. Moreover, the length of the time window over which the new rotation method is applied has little effect on the crossover of dispersion curves, whereas Alford rotation is very sensitive to the time window length. Since the crossover of dispersion curves is an indicator of stress-induced anisotropy, the new rotation method offers advantages over standard Alford rotation.

Toward The Simulation Of Attenuation: Oscillatory Flow In Porous Rock

2019-04-12T20:32:23Z

Toward The Simulation Of Attenuation: Oscillatory Flow In Porous Rock Olson, John F. Fluid flow in porous rock due to an oscillatory pressure gradient is simulated. We observe distributions of density and velocity in the rock which point to viscous dissipation. We will use this method to seek a deeper understanding of the physics of attenuation.

Interval Attenuation Estimation

2019-04-10T23:56:51Z

Interval Attenuation Estimation Alshammery, Hafiz J.; Toksoz, M. Nafi The goal of this paper is to study the accuracy of estimating the Quality Factor (Q) from ultrasonic pre-stack P-wave reflection data. Q is estimated by applying the spectral ratio method to the top and bottom reflections of the target. The data used to estimate Q are shot gathers acquired over different target materials submerged in a water tank. Using this setup, Q is estimated for Lucite, rubber and Berea sandstone. The behavior of Q estimates with offset is also investigated. Theoretical error analysis shows that non-zero estimates are contaminated by the overburden (water) attenuation. It is predicted that this error is directly proportional to the ratio of target depth to its thickness, target Q value, overburden attenuation and the difference between the top and bottom reflection ray trajectories in the overburden. The estimation error for Lucite is around 20%. For the Sandstone the error is about 10%. The estimated rubber Q is between 17 and 20. The estimates of all the targets show increasing estimated Q with increasing offset. This behavior is correctly predicted in the error analysis and is due to the difference between the top and bottom reflection ray path lengths within the overburden and the target Q value.

Laboratory Study Of Frequency Dependent Streaming Potentials

2019-04-12T20:32:23Z

Laboratory Study Of Frequency Dependent Streaming Potentials Reppert, Philip M.; Morgan, F. Dale Frequency dependent streaming potentials were measured on a glass capillary, porous filter, and a sample of Boise sandstone. The pore diameters for these three samples range from 1 millimeter to 34 micrometers. The frequencies used in these experiments range from 0-600 Hz with the critical frequencies being 6.8 Hz, 90 Hz, and 400 Hz for the three specimens. The fluid was moved relative to the sample with the pressure measured by hydrophones and the streaming potential measured using silver silverchloride electrodes. Both Packard's (1953) and Pride's (1994) models satisfactorily predict the streaming potential behavior for these frequencies, and the measured critical frequencies are directly related to the sample pore diameters.

Seismoelectric Laboratory Measurements In A Borehole

2019-04-12T20:32:22Z

Seismoelectric Laboratory Measurements In A Borehole Zhu, Zhenya; Toksoz, M. Nafi The seismoelectric logging method is based on measuring the electric field generated by seismic waves in a fluid-filled borehole. Two kinds of electromagnetic (EM) fields can be generated within the formation and at the interface of formations. One is a stationary or local EM wave and the other is a radiating EM wave. In this paper, we make various fractured borehole models with artificial materials or natural rocks and measure the electric field generated by a seismic source in a water-filled borehole. The experimental results show that the Stoneley wave generates both a stationary EM wave at the borehole wall and a radiating EM wave on the fracture, which propagates with light speed in the borehole. When the aperture of the fracture increases, the amplitude of the seismoelectric wave decreases due to the low ion concentration in the fracture. In a layered borehole model, a thin, permeable glued-sand zone is sandwiched between two nonpermeable or low-permeable layers, and the Stoneley wave generates two kinds of seismoelectric signals at the permeable zone. Compared with the acoustic waveforms in the same borehole, the seismoelectric waveforms are more effective in determining and characterizing a fracture or a fractured zone filled with a permeable layer.

Electroseismic Logging For The Detection And Characterization Of Permeable Zones: Field Measurements And Theory

2019-04-10T23:57:00Z

Electroseismic Logging For The Detection And Characterization Of Permeable Zones: Field Measurements And Theory Mikhailov, Oleg V.; Burns, Daniel R.; Toksoz, M. Nafi A Stoneley wave propagating in a borehole generates pore fluid flow within the permeable zones intersected by the borehole. In turn, the fluid flow induces a streaming electrical potential. This electrical potential induced by the Stoneley wave can be -measured in the field at frequencies from 100Hz to 4000Hz. Measurements of this Stoneley-wave-induced electrical potential can be used to detect fractures and permeable zones. The amplitude-versus-frequency dependence of this electroseismic phenomenon provides a new way to test theories of the acoustics and the electrokinetics of porous media against field measurements in real :oeks.

Borehole Electroseismic Measurements In Dolomite: Identifying Fractures And Permeable Zones

2019-04-10T23:57:02Z

Borehole Electroseismic Measurements In Dolomite: Identifying Fractures And Permeable Zones Mikhailov, Oleg V.; Toksoz, M. Nafi Measuring the electrical field induced by a borehole Stoneley wave is a new method for characterizing a rock formation around a borehole. Our field measurements demonstrate that the Stoneley-wave-induced electrical field can be detected in sedimentary rocks (dolomite in our experiment), and that the amplitude of this electroseismic phenomenon can be used to detect isolated fractures and permeable zones.

Reflection Moveout Inversion For Horizontal Transverse Isotropy: Accuracy And Limitation

2019-04-12T20:32:22Z

Reflection Moveout Inversion For Horizontal Transverse Isotropy: Accuracy And Limitation Al-Dajani, AbdulFattah; Alkhalifah, Tariq Horizontal transverse isotropy (HTI) is the simplest azimuthally anisotropic model used to describe vertical fracturing in an isotropic matrix. Using the elliptical variation of P-wave normal-moveout (NMO) velocity with azimuth, measured in three different source-to-receiver orientations, we can obtain the vertical velocity V[subscript Pvert], anisotropy parameter δ[superscript (V)], and the azimuth a of the symmetry-axis plane. Parameter estimation from variations in the moveout velocity in azimuthally anisotropic media is quite sensitive to the angular separation between the survey lines in 2D, or equivalently source-to-receiver azimuths in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the parameter α, in particular, is also sensitive to the strength of anisotropy. The accuracy in resolving δ[superscript (V)] and [subscript Pvert] is about the same for any strength of anisotropy. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to- receiver directions 60° apart. In land seismic data acquisition having wide azimuthal coverage is quite feasible. In marine seismic data acquisition, however, where the azimuthal data coverage is limited, multiple survey directions are necessary to achieve such wide azimuthal coverage. Having more than three distinct source-to-receiver azimuths (e.g., full azimuthal coverage) provides useful data redundancy that enhances the quality of the estimates, and sets the stage for a least-square type of inversion in which the errors in the parameters estimates are minimized in a least-square sense. In layered azimuthally anisotropic media, applying Dix differentiation to obtain interval moveout velocity provides sufficient accuracy in the inversion for the medium parameters, especially where the direction of the symmetry planes is uniform. In order to obtain acceptable parameter estimates, an HTI layer overlain by an azimuthally isotropic overburden (as might happen for fractured reservoirs) should have a thickness (in time) relative to the total thickness. The total thickness should be equal to or greater than the ratio of the error in the NMO (stacking) velocity to the interval anisotropy strength of the fractured layer.

Shear Wave Birefringence In Reverse VSP: An Approach To 3-D Surface P To S Converted Waves

2019-04-10T23:57:01Z

Shear Wave Birefringence In Reverse VSP: An Approach To 3-D Surface P To S Converted Waves Sierra, Jesus; Queen, John H. We present an original method to estimate local shear wave birefringence properties for 3-D surface P to S converted waves. To accomplish this we approach the problem in reverse VSP (RVSP), and we show that they are equivalent. The method works in the pre-stack domain and uses the converted P to S waves as hypothetical sources to study the problem under the propagator matrix method in transmission. The importance of this method is that no information is required about layering above the zone of interest to obtain an accurate estimation of the anisotropy parameters. The method involves solving a nonlinear problem in the frequency domain where a global minimization technique called Simulation Annealing is used. The procedure also allows us to estimate the axis of anisotropy independently of the offset angle in the range of angles considered in VSPs and in surface profiles. The proposed method is validated with synthetic RVSP data for two models with different densities of vertical fractures. Results show good accuracy in the estimation of the angle of the fractures for the whole range of offsets. Also, results show a dependence on the frequency and offset ranges considered in the analysis.

Scattering Characteristics In Heterogeneous Fractured Reservoirs From Waveform Estimation

2019-04-12T20:32:22Z

Scattering Characteristics In Heterogeneous Fractured Reservoirs From Waveform Estimation Shen, Feng; Toksoz, M. Nafi Offset-dependent characteristics of seismic scattering are useful in the interpretation of fractured reservoirs. Synthetic seismograms generated by a 3-D finite difference modeling are used to study elastic wave propagation and scattering in heterogeneous fractured reservoirs. We use two models having different background medium properties and different azimuthal AVO responses and build heterogeneous fracture density realizations through stochastic modeling. Gas-saturated fractured reservoirs and waveforms ill fracture normal and strike directions are considered in this paper. The multiple signal classification (MUSIC) frequency estimator is used in waveform estimation to provide frequency domain attributes related to seismic wave scattering by fractures. Our results indicate that the strength of the scattered field increases with increasing fracture scatter density and decreasing correlation length of spatial variations of fracture density. It is also a function of the background medium. The strength of the scattering field is stronger in model 1 which has smaller property contrasts in the background medium than model 2. The scattering characteristics for both models are different at the top and the base of the fractured reservoir. Our results show that the scattered field is weak at the top of a fractured reservoir. The first order results are dominated by velocity anisotropy of a mean crack density field. However, the base of the fractured reservoir corresponds to a strong scattered field on which fracture heterogeneity has a larger effect.

Sensitivity Analysis Of Amplitude Variation With Offset (Avo) In Fractured Media

2019-04-12T20:32:20Z

Sensitivity Analysis Of Amplitude Variation With Offset (Avo) In Fractured Media Krasovec, Mary L.; Rodi, William L.; Toksoz, M. Nafi The variation in seismic P to P reflection amplitude with offset (AVO) caused by a system of fractures embedded in an isotropic background is investigated. Additionally. a sensitivity analysis of AVO parameters with respect to the fracture system parameters is made. The fracture system is assumed to be aligned vertically or horizontally and can be gas filled or fluid filled. Elastic constants are calculated by using formulations of Schoenberg (1988). From the elastic constants, the reflection amplitude as a function of angle is calculated using equations from Ruger (1997). Theoretical results for a single interface between fractured and unfractured media, both with and without lithology change, show opportunities for extraction of crack density information from seismic P-wave data collected in fractured geothermal or hydrocarbon reservoirs. For vertically oriented fractures, wide angle data (> 30°) is crucial for the estimation of fracture parameters.

Scale And Frequency Dependence Of Reflection And Transmission Coefficients

2019-04-10T18:05:24Z

Scale And Frequency Dependence Of Reflection And Transmission Coefficients Imhof, Matthias G. Well-logs show that heterogeneities occur at many different spatial scales. In this paper, we want to characterize how waves are affected by these heterogeneities, and we study how reflection and transmission coefficients depend on temporal frequency and spatial scale. We use wavelet transformations to filter certain spatial scales from the velocity logs. The scale-filtered logs serve as input for a numerical layer-stack model to calculate reflection and transmission coefficients as functions of frequency and scale. We find that transmission coefficients are largely independent of frequency or scale. They depend mostly on average slowness. Contrarily, reflection coefficients are extremely sensitive to the perturbations of the slownesses, even at low frequencies.

Near-Surface Scattering From High Velocity Carbonates In West Texas

2019-04-12T20:32:22Z

Near-Surface Scattering From High Velocity Carbonates In West Texas Imhof, Matthias G.; Toksoz, M. Nafi; Burch, Charles I.; Queen, John H. Seismic data acquired directly over near-surface limestone formations are commonly observed to be of inferior quality. A possible cause for this degradation is scattering in the near-subsurface by, e.g., the weathering layer, rough free-surface topography, or heterogeneities such as cavities or clusters of vugs. We applied different numerical scattering schemes to study the effects of each of these three scattering mechanisms. For a particular dataset acquired in West Texas, we find that a weathering layer is the dominant cause of noise on records acquired in valleys. However on mesas, nearsubsurface heterogeneity is the primary cause of scattered wave-energy. Topography turned out to be of only secondary importance. As additional attributes, we use energy-density and energy-flux vectors to study the frequency dependence of the different scattering models. These attributes allow us to study where energy concentrates and in which direction it flows. For example, we observed that near sub-surface heterogeneities build up waveguides which efficiently trap seismic energy near the surface.

Executive Summary-Characterization Of Reservoir Fluid Flow Properties

2019-04-12T20:32:15Z

Executive Summary-Characterization Of Reservoir Fluid Flow Properties Burns, Daniel R.; Toksoz, M. Nafi The characterization of subsurface fluid flow is the key to exploration, production, and management of oil, gas, geothermal, and groundwater reservoirs. From a research perspective the question then becomes how can we measure or estimate the spatial variations in physical properties which control the flow of these fluids? Ideally we would like to be able to remotely identify fluid type and provide accurate estimates of in-situ porosity and permeability values in three dimensions. In some situations this may be possible, but in others such a goal may not be attainable. If accurate estimates of these physical properties cannot be achieved, there may still be important and useful related information available. For example, being able to provide accurate estimates of the direction of maximum fluid flow may be a very important piece of information for field development and drilling decisions. The Earth Resources Laboratory has focused on developing methods for using seismic waves to estimate fluid flow properties. Seismic waves provide higher resolution data than potential field measurements, can be polarized for anisotropy measurements, can be used in surface and borehole applications. and ERL has significant experience in the physics and modeling of wave propagation ill complex media. Our report this year provides results in three specific areas related to our overall goal of fluid flow characterization. The first. involves research into methods which utilize the actual motion, induced by seismic waves, of fluids ill porous rock. The passing of a seismic wave through a rock containing a viscous fluid results in relative motion between the fluid and the solid matrix. This mot.ion dissipates seismic energy resulting in the attenuation of the passing wave. The motion of the fluid, which contains ions, also creates an electrical field which can be measured. We present results in both of these areas in this report. A second research area is the measurement of flow directionality. The presence of open fractures with a preferred orientation will control the direction of fluid flow in a reservoir. Such fractures will also have a large effect on the elastic properties of the reservoir rock. The resulting elastic anisotropy may be observable in both surface seismic data as well as borehole acoustic logs. We present several papers on the effects of anisotropy on surface seismic data and AVO signatures, as well as on dipole sonic logs. Finally, because fluid flow is only one of the many factors which effect seismic waves, we must continue to improve our understanding of wave propagation in complex media. We present two such papers which look at scattering and scale dependent issues. The way in which property variations at different spatial scales affect seismic waves is an important research area that we will continue to investigate in the coming year. The following sections provide a more detailed summary of the results in each of these three broad areas.

P and SV waves 3-D Numerical Modeling of AVOA from Heterogeneous Fractured Reservoirs

2019-04-12T20:32:13Z

P and SV waves 3-D Numerical Modeling of AVOA from Heterogeneous Fractured Reservoirs Zhu, Xiang; Shen, Feng; Toksoz, M. Nafi We study the effects of fracture-induced anisotropy and lateral fracture density heterogeneity on the reflected P and SV wave amplitude variation with offset and azimuth (AVOA), using 3-D finite-difference simulations. The models show that for an isotropic layer overlying on a fractured reservoir, the anisotropic behavior of AVOA depends on fracture density as well as the contrast in elastic properties between the reservoir layer and the overlying material. It is also verified that the SV wave is more sensitive to fractures than the P wave. The sensitivity of AVOA to spatial variations of fracture density is also investigated.

Dispersion Analysis Of Split Flexural Waves

2019-04-10T23:56:54Z

Dispersion Analysis Of Split Flexural Waves Nolte, Bertram; Rao, Rama; Huang, Xiaojun In this paper we first present a technique for measuring dispersion curves from array data, that is both simple and efficient. We demonstrate its performance on both synthetic and field data. We then use the technique to compute dispersion curves for split flexural waves from cross-dipole data from the Powder River Basin in Wyoming. In this data set we consistently observe crossover of the fast and slow flexural waves, an indication of stress-induced anisotropy. Next, we demonstrate the effect that dispersion-curve crossover has on Alford rotation. Finally, we give a procedure for rapidly determining stress-induced anisotropy from crossed-dipole logs.

Borehole Resistivity Inversion

2019-04-10T18:05:23Z

Borehole Resistivity Inversion Garipova, Yulia V. In this paper we perform the inversion of borehole resistivity data using the software package developed by Western Atlas Logging Services, Houston, TX. Direct current resistivity methods, namely lateral sounding and conventional laterolog methods, are the main interest in this paper. In resistive formations drilled with a conductive mud, where induction methods are not logged, it becomes imperative to combine these two methods in order to provide a reliable solution to the inversion problem. Lateral sounding provides comprehensive information about the resistivity distribution away from the borehole, while the higher resolution of the laterolog allows for detailed delineation of the formation. We perform the inversion computationally using the constrained least-squares Marquardt algorithm combined with singular value decomposition. The nonlinear inversion problem is linearized after each iteration of the Marquardt method. One of the main benefits of the algorithm is its ability to incorporate all resistivity/conductivity methods into a unique solution that is able to explain and satisfy all measurements. Several levels of inversion analysis are considered, from one-dimensional inversion to a rigorous and comprehensive two-dimensional approach. We demonstrate the method with multiple synthetic examples in which the algorithm successfully recovers the formation parameters. Different noise levels, resistivity contrasts, borehole conditions, and initial guesses are considered. We then apply the method to field data consisting of lateral sounding logs and laterologs. The inversion results are then checked against the available sampling data.

Experimental Studies Of Seismoelectric Measurements In A Borehole

2019-04-10T23:56:54Z

Experimental Studies Of Seismoelectric Measurements In A Borehole Zhu, Zhenya; Haartsen, Matthijs W.; Toksoz, M. Nafi Experimental and theoretical studies show that there are two kinds of electromagnetic (EM) fields generated by seismic waves in a fluid-saturated porous medium. First, at an interface where the formation properties are different, the generated seismoelectric wave is a propagating electromagnetic wave that can be received anywhere. The second kind of field occurs inside a homogeneous formation where the seismic wave generates an electromagnetic field which exists only in the area disturbed by the seismic wave and whose apparent velocity is that of the seismic wave. An electrode, used as a receiver located on the ground surface, can only receive the propagating EM wave. However, when an electrode is in a borehole and close to the porous formation, it can receive both of the above EM waves. In this study, electrokinetic measurements are performed with borehole models made of natural rocks or artificial materials. The results of the experiment show that the Stoneley wave and other acoustic modes excited by a monopole source in the borehole models generate seismoelectric waves in fluid-saturated formations. The electrical components of the seismoelectric waves can be received by an electrode in the borehole or on the borehole wall. The amplitude and frequency of the seismoelectric wave are related not only to the seismic wave, but also to the formation properties, such as permeability, conductivity, etc. Therefore, seismoelectric logging may explore different properties of the formation than those investigated by standard acoustic logging. Electroseismic measurements are also performed with these borehole models. The electric pulse introduced through the electrode in the borehole or on the borehole wall induces a Stoneley wave in the fluid-saturated model which can be received by a monopole transducer in the same borehole. These measurement methods, seismoelectric logging or electroseismic logging, can be applied to field borehole logging to investigate formation properties relating to pore fluid flow.

Experimental Studies Of Electroseismic Conversion In A Fluid-Saturated Porous Medium

2019-04-10T18:05:23Z

Experimental Studies Of Electroseismic Conversion In A Fluid-Saturated Porous Medium Zhu, Zhenya; Haartsen, Matthijs W.; Toksoz, M. Nafi The coupling between seismic and electromagnetic waves in a fluid-saturated porous medium is essentially controlled by the electrokinetic effect. The inverse effect of the seismoelectric conversion, the electroseismic conversion, is investigated experimentally in the laboratory. The electric field induces movement of the ions in a pore fluid relative to the solid matrix. The interaction between the pore fluid and the solid matrix generates acoustic waves known as electroseismic waves. Our studies confirm experimentally that the electroseismic conversion at ultrasonic frequencies is the electrokinetic effect in nature. In measurements with a homogeneous rock cylinder, P- and S-wave transducers receive, respectively, the P- and S- components of the extensional and flexural waves generated by an electric pulse with ring or parallel electrodes when the electrodes are on the surface or inside a porous medium. The electroseismic waves are measured in layered models, made of sandstone or artificial materials, to determine the area where the electroseismic waves are generated. Further experiments with the layered model investigate the relationship between electroseismic conversion and the conductivity of the fluid-saturated medium or the pore fluid. When fluid conductivity increases, the amplitude of the electroseismic wave increases. Experimental results show that electroseismic conversion is different from the piezoelectric effect of quartz grains in sandstone and is closely related to the relative motion between the fluid and the solid. The results also eliminate the possibility that the electroseismic wave is generated by a spark of a high-voltage pulse. Electroseismic waves can be generated at low voltage and increased continually with the voltage, without a big voltage jump similar to the spark in an isolated material. Our results confirm the existence and measurability of electroseismic conversion in porous formation at ultrasonic frequency ranges. Therefore, electroseismic measurements may be an effective means to investigate the pore fluid flow and rock properties.

Using Borehole Electroseismic Measurements To Detect And Characterize Fractured (Permeable) Zones

2019-04-09T16:12:41Z

Using Borehole Electroseismic Measurements To Detect And Characterize Fractured (Permeable) Zones Mikhailov, Oleg V.; Queen, John H.; Toksoz, M. Nafi We present a new type of field measurement capable of detecting and characterizing fractured (permeable) zones intersecting a borehole. The method is based on measuring electrical fields generated by a borehole Stoneley wave. In this paper, we describe the measurement technique, present field data, and propose a theoretical model, which correctly predicts amplitudes and phases of the electrical fields measured in the borehole experiment. The theoretical model and the field data demonstrate that the measurements of the Stoneley-wave-induced electrical fields can yield information about the interconnected porosity, and possibly about the permeability of the formation around the borehole. We derive an estimate of the interconnected porosity from the field data, and show that it correlates well with the density of fractures intersecting the borehole. Our results suggest that the borehole electroseismic method can be developed into a logging or a VSP tool, with possible applications in reservoir characterization.

Measurements Of Shear-Wave Azimuthal Anisotropy With Cross-Dipole Logs

2019-04-12T20:32:18Z

Measurements Of Shear-Wave Azimuthal Anisotropy With Cross-Dipole Logs Tao, Guo; Cheng, Arthur C. H.; Toksoz, M. N. Three methods for analyzing azimuthal anisotropy from cross-dipole logs are applied to data from the Powder River Basin in Wyoming. These techniques are based on the phenomena of flexural wave splitting in anisotropic materials and are analogous to the techniques used for VSP data processing. The four-component cross-dipole logging data obtained with a Schumberger tool from a vertically-fractured section of 56 m at a depth of 3550 m are processed with three different techniques. The results demonstrate that the non-orthogonal rotation method works best for the data. The results from the linear transform and polar energy spectrum methods are acceptable. The linear transform processing takes much less computing time, while the polar energy spectrum method is computationally-intensive.

Cement Bond Evaluation Using Early Refracted Arrivals

2019-04-12T20:32:18Z

Cement Bond Evaluation Using Early Refracted Arrivals Rao, Rama V.N.; Mandal, Batakrishna; Cheng, Arthur C. H.; Toksoz, M. Nafi The cement bond evaluation tool is a device used to examine the integrity of cement bonding to the casing. A conceptual tool operating between 80-200 kHz is considered here, with a transmitter and two receivers, oriented parallel to the axis of the borehole and next to the casing. The compressional head wave in the casing, excited by the transmitter, will be the first arrival to be measured by the two receivers in most situations. With both receivers on the same side of the transmitter, the attenuation of this wave in traveling between the two receivers is dependent on the properties of the medium immediately outside the casing. The radially layered borehole was modeled as a layered plane medium for large operating frequency. A spectral integral approach (complete wave synthesis) was used to compute the response at the receiver locations, which then provided attenuations. Different parameters, such as transducer separation (1-12 in), annulus thickness (0-6 in), annulus impedance (free pipe to good cement), casing thickness (0.25-0.45 in), standoff distance (0.5-1 in) and source frequency (80-200 kHz) were varied in the evaluation of the operation of the tool. The parameter studies based on the theoretical computations revealed that free pipe could be distinguished from the presence of cement in a variety of situations. Additionally, lower bounds on receiver separations are given for reliable operation of the tool.

Simulation Of Elastic Wave Propagation In Models Containing Irregular Interfaces Parameterized On Irregular Grids

2019-04-09T16:04:45Z

Simulation Of Elastic Wave Propagation In Models Containing Irregular Interfaces Parameterized On Irregular Grids Nolte, Bertram Thus study demonstrates the advantages of a recently-developed irregular-grid modeling technique (Nolte, 1996). This technique can model irregular interfaces more accurately than a standard regular-grid finite-difference method. I show this by comparison of both methods for a simple model containing a sloping interface. While the discrete approximation to the sloping interface results in numerical inaccuracies for the finite-difference method, the irregular-grid technique produces superior results. I then show that the method can also be applied to a free surface with irregular topography, suggesting that it may be a valuable alternative to existing finite-difference free-surface algorithms.

Effects Of Fractured Reservoir Elastic Properties On Azimuthal Avo

2019-04-12T21:17:41Z

Effects Of Fractured Reservoir Elastic Properties On Azimuthal Avo Shen, Feng; Zhu, Xiang; Toksoz, M. Nafi Aligned vertical fractures introduce velocity anisotropy which is directly related to parameters, such as fracture density, fracture shape and fracture contents. Effective medium models allow us to study qP- and qS-wave velocity anisotropy in rocks with aligned vertical fractures, intersecting fracture sets and aligned fractures with smallscale porosity. Spatially varying fracture density distributions result in velocity spatial variations. Stochastic modeling is used to quantify velocity heterogeneity in a fractured reservoir, where the fracture density field is modeled as a stationary Gaussian random field specified by a covariance function describing the amplitude, orientation, characteristic wavenumbers, and roughness of a fracture density field. The goal of the modeling is to relate the stochastic forward model to the statistics of the velocity and seismic reflectivity fields. Three-dimensional finite difference modeling has been used to investigate the seismic response of fractured reservoirs in P-wave seismic data, and the effects of background Vs/Vp contrasts and anisotropic overburden. The numerical results indicate that background Vs/Vp contrasts across the reflecting boundary, and the presence of anisotropy above the reservoir, have significant effects on azimuthal AVO response at the top of fractured reservoirs. Although a larger Vs/Vp contrast gives rise to a strong AVO response in isotropic media, it is not necessary to give rise to a strong azimuth AVO response. Our numerical modeling shows that the smaller Vs/Vp contrast model gives rise to a strong azimuthal AVO response. Anisotropic overburden always modifies the azimuthal AVO response.

Ultrasonic And Numerical Modeling Of Reflections From Simulated Fractured Reservoirs

2019-04-10T18:05:27Z

Ultrasonic And Numerical Modeling Of Reflections From Simulated Fractured Reservoirs Theophanis, Stephen; Zhu, Xiang Vve examine seismic waves scattered from anisotropic heterogeneity with laboratory data and numerical modeling in order to develop modeling techniques for the characterization of fracture properties in tight gas sands from surface seismic reflection data. Laboratory models representing features of a fractured reservoir were constructed using Phenolite (the "reservoir") embedded in a Lucite background, and seismic surveys were gathered over these models. In parallel with laboratory measurements, finite-difference modeling of reflections from a fractured medium were carried out. Fracture zone properties were calculated using an effective medium theory; the variation of fracture density produced a heterogeneous medium. The heterogeneity was modeled with a stochastic process, characterized by a probability density function and an auto-correlation function. Results from both modeling efforts show that prestacked AVO data can contain important information describing reservoir heterogeneity.

Detection Of Fracture Orientation Using Azimuthal Variation Of P-Wave Avo Responses

2019-04-10T18:05:24Z

Detection Of Fracture Orientation Using Azimuthal Variation Of P-Wave Avo Responses Perez, Maria Auxiliadora; Gibson, Richard L., Jr. Azimuthally-dependent P-wave AVO (amplitude variation with offset) responses can be related to open fracture orientation and have been suggested as a geophysical tool to identify fracture orientation in fractured oil and gas reservoirs. A field experiment recently conducted over a fractured reservoir in the Barinas Basin (Venezuela) provides data for an excellent test of this approach. Three lines of data were collected in three different azimuths, and three component receivers were used. The distribution of fractures in this reservoir was previously obtained using measurements of shear wave splitting from P-S converted waves from the same dataset (Ata and Michelena, 1995). In this work, we use P-wave data to see if the data can yield the same information using azimuthal variation of P-wave AVO responses. Results obtained from the azimuthal P-wave AVO analysis corroborate the results previously obtained using P-S converted waves. This analysis with field data is an example of the high potential of P-waves to detect fracture effects on seismic wave propagation.

Source Radiation Patterns In Cased Boreholes

2019-04-12T20:32:14Z

Source Radiation Patterns In Cased Boreholes Rao, Rama V.N.; Turpening, Roger M.; Nafi, M. Toksoz Source radiation from open and cased boreholes are well documented. The effect of an unbonded casing on the radiation patterns of volume, radial stress and axial stress sources in a borehole has received less attention and is modeled and analyzed here in the context of performing single well imaging. Radiation patterns were evaluated using a global matrix approach and wavenumber integration. 'While a borehole with a bonded casing has a single propagating mode at low frequencies, the stoneley mode, the borehole with unbonded casing has three propagating modes. Of the two additional modes that are due to the unbonded casing, one is present mainly in the cross-section of the casing and has a phase speed close to the speed of longitudinal waves in steeL Because of its large phase speed (~ 5400 m/s), this mode radiates into almost all formations and influences the radiation pattern of all source types. Test data and the predicted radiation patterns were used to identify the annulus material behind the casing.

Rapid 3-D Raytracing For Optimal Seismic Survey Design

2019-04-10T18:05:22Z

Rapid 3-D Raytracing For Optimal Seismic Survey Design Zhang, Jie; Lavely, Eugene; Toksoz, M. Nafi A useful approach to optimal seismic survey design is to simulate the seismic response for a suite of a priori subsurface models and shot-receiver templates. The response can be used to evaluate many criteria such as subsurface coverage, target resolution, noise sensitivity, aquisition footprint, data redundancy, long-wavelength statics resolution, and others. A key requirement for practical implementation is the use of an accurate and rapid simulation method. For most cases survey optimization for a highly detailed 3D model would not be useful because (1) such information is often not available, (2) some of the conclusions may not be robust to small changes in the model, and (3) simulation of generally varying complex models would be prohibitively expensive. Instead, a more useful model class for survey design would be 3D models with constant velocity layers separated by arbitrary (and possibly complex) interfaces. The models may be from conjecture or previous seismic surveys. We present a rapid 3D raytracing method optimized for the computation of reflection and refraction wavefronts from a point source in this model class. We demonstrate that the method simulates wave phenomena such as diffraction and head wave propagation. The approach is extremely fast since it avoids traveltime expansion in the volume between interfaces, and solves a simple 2D problem on each interface. Other methods require local propagators (even in constant velocity regions), whereas our approach enables large jumps of wavefronts from interface to interface. The calculation of 3D reflection or refraction traveltimes for a model with an arbitrary interface from one source to any number of receivers requires less than 1 sec of CPU time on a DEC 3000/500 workstation. We briefly review how our new method can be used to facilitate survey resolution computations. We also develop a method for estimating an efficient source-receiver distribution for resolving an assumed 3D structure. To design the receiver distribution, we calculate continuous traveltime slices at the surface from a given source template and plot the RMS curvatures of the wavefronts. The spatial density of the receiver coverage should be in proportion to the locally-varying magnitude of the RMS curvature. Similarly, to determine the optimal source distribution, we sum the RMS curvatures of the wavefront traveltimes due to each source in the entire survey area. In the same way, the magnitude of the curvatures suggests the most important areas for source locations. Zhang, Jie; Lavely, Eugene; Toksoz, M. Nafi

Shear-Wave Tomographic Images Of An Oil Reservoir At MIT's Michigan Test Site

2019-04-12T20:32:12Z

Shear-Wave Tomographic Images Of An Oil Reservoir At MIT's Michigan Test Site Zhang, Jie; Turpening, Roger; Chauvelier, Chantal; Morgan, F. Dale; Toksoz, M. Nafi; Queen, John; Cox, Dale We conducted a P- and S-wave crosswell survey with Conoco's orbital vibrator source and three-component receivers at M.LT.'s Michigan Test Site. The receiver and source wells bracket a known oil reservoir. Applying a nonlinear crosswell traveltime tomography method, we reconstruct the velocity structures in the oil reservoir using P- and S-wave data separately. The P-wave tomogram shows a similar image to the one by Matarese (1993), and it does not present much velocity variations in the oil producing zone. However, the S-wave tomogram clearly shows the image of the reservoir zone, which is characterized with low velocities in a pinnacle reef. The S-wave velocities in the reservoir are about 20% lower than those of the surrounding carbonates.

Borehole Acoustics and Logging and Reservoir Delineation Consortia

2019-04-12T20:32:21Z

Borehole Acoustics and Logging and Reservoir Delineation Consortia Burns, Daniel R. Research activity in the Borehole Acoustics and Logging/Reservoir Delineation Consortia continue to focus on the development of geophysical methods to detect and characterize geological conditions which control fluid flow in a reservoir. This report presents a summary of our results from the past year. Three major areas of research are presented: subsurface fracture characterization, modeling and imaging of complex structures, and reservoir logging applications.

Nonlinear Refraction Traveltime Tomography

2019-04-12T20:32:21Z

Nonlinear Refraction Traveltime Tomography Zhang, Jie; Toksoz, M. Nafi We identify a few unique issues that are important for performing a nonlinear refraction traveltime tomography effectively. These include accuracy of traveltime and raypath calculation for a turning ray and physical information in a refraction traveltime curve. Consequently, we develop a shortest path raytracing method with an optimized node distribution that can accurately calculate refraction traveltimes and raypaths in any velocity model. We find that minimizing misfit of refraction traveltimes with the least-squares criterion does not account for the whole physical meaning of a refraction traveltime curve. We therefore pose a different nonlinear inverse problem that explicitly minimizes misfits of both traveltimes (integrated slownesses) and traveltime gradients (apparent slownesses). As a result, we enhance the resolution of the tomographic inversion as well as the convergence speed. We regularize our inverse problem with the Tikhonov method as opposed to applying ad hoc smoothing to keep the inversion stable. The use of the Tikhonov regularization avoids solving an ill-posed problem and allows us to invert an infinite number of unknowns. We apply this tomographic technique to image the shallow velocity structure at a coastal site near Boston, Massachusetts. The results are consistent with a local boring survey.

Imaging Hydraulic Fractures: Source Location Uncertainty Analysis At The UPRC Carthage Test Site

2019-04-10T18:05:22Z

Imaging Hydraulic Fractures: Source Location Uncertainty Analysis At The UPRC Carthage Test Site Li, Yingping; Zhu, Xianhuai; Cheng, Arthur C. H.; Toksoz, M. Nafi Hydraulic fracturing is a useful tool for enhancing gas and oil production. High-resolution seismic imaging of the fracture geometry and fracture growth process is the key in determining optimal spacing and location of wells and in improving reservoir performance for increased production rate. In this paper, we address how accurately the sources along a fracture zone at different depths can be determined for given velocity models, geophone array geometry configurations, and location of monitor wells. We apply a theory of uncertainty analysis to estimate microearthquake location uncertainties in both relative and absolute senses. To estimate the location uncertainties, we used the velocity models, two geophone arrays in two monitor wells, and the location of the fracture well, and an assumed fracture orientation of an upcoming hydraulic fracturing experiment by Union Pacific Resources Company (UPRC) and its partners at Carthage Field, Panola, Texas. We calculated the 95% confidence regions, in both absolute and relative senses, for five hypothetical sources along an assumed strike of a target fracture zone at three different depths. The semimajor and semiminor axes of the relative error ellipses for these epicenters are typically estimated to be 12 and 5 ft, respectively, and the relative depth uncertainty is derived at about 6 ft. The absolute location uncertainties are at least 3 to 10 times larger than the relative location uncertainties. The high-precision relative source locations result in a relative measurement error about 4-15% in measuring the fracture length. The location ambiguity from two-station locations is discussed and arrival azimuthals is proposed to to be used for removing such location ambiguity. The location uncertainty analysis is expected to be generalized as a practical tool in optimal designing of a two-well seismic monitoring system for high-resolution imaging of hydraulic fractures.

1995 Data Acquisition Program At The Michigan Reservoir Delineation Research Facility

2019-04-12T20:32:21Z

1995 Data Acquisition Program At The Michigan Reservoir Delineation Research Facility Turpening, Roger; Chauvelier, Chantal; Queen, John; Cox, V. Dale 1995 was the most active year in recent history at the test site. Although the initial year of 1983 saw more work, we were still basking in the glow of the modern "oil boom"; the downsizing crash was ahead of us. In 1983, working around the clock, we recorded 13 VSPs, a suite of logs, a reverse VSP, borehole gravity survey, and a 3-D survey in two months of field time. In 1995, a single, four-man Conoco crew worked ten to twelve hour days, for 70 days, and recorded a massive cross-well, orbital vibrator data set-clearly a Herculean task. This paper outlines the pre-survey planning that took place in anticipation of that effort. In addition, we document the single well data acquisition efforts of Conoco, Inc. and Lawrence .Berkeley Laboratory (LBL), and the dipole logging work of Halliburton Energy Services. These data are in the handling stages and processing has not yet begun.

Multiple Multipole Expansions For Elastic Scattering: An Aid To Understanding The Problems In "No-Record" Areas

2019-04-09T16:14:26Z

Multiple Multipole Expansions For Elastic Scattering: An Aid To Understanding The Problems In "No-Record" Areas Imhof, Matthias G. This paper presents a new approach to solving scattering of elastic waves in two dimensions. Wavefields are often expanded into an orthogonal set of basis functions. Unfortunately, these expansions converge rather slowly for complex geometries. The new approach enhances convergence by summing multiple expansions with different centers of expansion. This allows irregularities of the boundary to be resolved locally from a nearby center of expansion. Mathematically, the wavefields are expanded into a set of non-orthogonal basis functions. The incident wavefield and the fields induced by the scatterers are matched by evaluating the boundary conditions at discrete matching points along the domain boundaries. Due to the non-orthogonal expansions, more matching points are used than actually needed, resulting in an overdetermined system which is solved in the least squares sense. Since there are free parameters such as the location and number of expansion centers as well as the kind and orders of expansion functions used, numerical experiments are performed to measure the performance of different discretizations. An empirical set of rules governing the choice of these parameters is found from these experiments. The resulting algorithm is a general tool to solve relatively large and complex two-dimensional scattering problems.

A Time-Domain Finite-Difference Method With Attenuation By A Recursive Algorithm

2019-04-10T23:56:54Z

A Time-Domain Finite-Difference Method With Attenuation By A Recursive Algorithm Cheng, Ningya; Cheng, Arthur C. H.; Toksoz, M. Nafi A recursive algorithm to incorporate attenuation into a time-domain finite-difference calculation is developed. First, a rheological model of the generalized Maxwell body is chosen. The discrete relaxation frequency and the peak strength of these Maxwell bodies are jointly determined by fitting to an arbitrary Q law in the frequency band of the interest. A conjugate gradient technique and a randomly chosen starting model are used to determine optimum fitting. Examples of constant and frequency dependent Q models are shown. Second, in order to include the attenuation into a finite-difference staggered-grid scheme, the convolution integral of stress and strain is evaluated directly. The convolution integral can be expressed recursively. This is possible because the time-domain viscoelastic modulus function is exponential. The implementation of 1-D wave propagation in a constant Q medium is shown as a example. At the distance of 50 wavelengths and with three relaxation frequencies, the finite-difference results are in very good agreement with the analytic solutions.

An Amplitude And Traveltime Calculation Using A Higher-Order Parabolic Equation

2019-04-10T23:56:53Z

An Amplitude And Traveltime Calculation Using A Higher-Order Parabolic Equation Cheng, Ningya; House, Leigh; Fehler, Michael C. A higher-order parabolic equation is used to compute the traveltime (phase) and the amplitude in constant density acoustic media. This approach is in the frequency domain, thereby avoiding the high frequency approximation inherent in the Eikonal equation. Intrinsic attenuation can be naturally incorporated into the calculation. The error at large angles of propagation caused by the expansion of the square root operator can be virtually eliminated by adding more terms to the expansion. An efficient algorithm is obtained by applying the alternate direction method. Our results are in excellent agreement with the finite element approach for the range-dependent wedge-shaped benchmark problem. The amplitude and the phase are calculated for a syncline and the Marmousi models.

Modeling Of Elastic Wave Propagation On Irregular Triangular Grids Using A Finite-Volume Method

2019-04-11T08:20:45Z

Modeling Of Elastic Wave Propagation On Irregular Triangular Grids Using A Finite-Volume Method Nolte, Bertram We present a finite-volume method for the modeling of wave propagation on irregular triangular grids. This method is based on an integral formulation of the wave equation via Gauss's theorem and on spatial discretization via Delaunay and Dirichlet tessellations. We derive the equations for both SH and P-SV wave propagation in 2-D. The method is of second-order accuracy in time. For uniform triangular grids it is also second-order accurate in space, while the accuracy is first-order in space for nonuniform grids. This method has an advantage over finite-difference techniques because irregular interfaces in a model can be represented more accurately. Moreover, it may be computationally more efficient for complex models.

Reservoir Delineation Research

2019-04-12T20:32:13Z

Reservoir Delineation Research Gibson, Richard L., Jr. This report describes work performed by the Reservoir Delineation Consortium during the past year. We have made progress in the areas of theoretical analysis of wave propagation, data analysis, and significant field work at the Michigan test site. Research on wave propagation focused on developing new algorithms for rapid and flexible calculation of full waveform synthetic seismograms. These methods provide the modeling tools for surface seismic, crosshole, single hole experiments and data interpretation. Initial progress on a finite volume method is summarized, and simulations using parabolic equations, attenuation modeling, and elastic wave simulations with multiple multipole methods are also examined in this report. New work in the area of data processing and analysis is represented by hydraulic fracturing imaging via source location methods and nonlinear refraction imaging. The past year (1995) has been one of the most active in our entire experience with the Michigan test site, and a summary report documents the crosshole survey, single well imaging experiments and dipole logging performed recently. This introduction to the report describes first the wave propagation research, including a summary statement providing our motivations for continued research in this area. Briefly, while there are many algorithms currently available for modeling tasks, each of them has its own limitations and advantages in regard to both accuracy and speed. Given a strong incentive for accurate and efficient inversion or migration algorithms, there is a continuing need for improving the modeling routines that serve as the basis for data analysis. Following this motivation is a brief summary of each of the reports mentioned above. The overview concludes with a summary of the field work results and the two papers on data processing tasks.

Dynamic Streaming Currents From Seismic Point Sources In Homogeneous Poroelastic Media

2019-04-12T20:32:12Z

Dynamic Streaming Currents From Seismic Point Sources In Homogeneous Poroelastic Media Haartsen, Matthijs W.; Toksoz, M. Nafi In a porous medium saturated with a fluid electrolyte, mechanical and electromagnetic disturbances are coupled. The coupling is electrokinetic in nature since it is due to an excess of electrolyte ions that exist in an electric double layer near the grain surfaces within the material. Mechanically-induced streaming currents generated by point sources in homogeneous, isotropic porous media are presented. The electrically-induced streaming current is shown to be second-order in the electrokinetic coupling coefficient and can be neglected. This decouples the mechanical behavior from the electromagnetic behavior with respect to the induced fluxes and simplifies the analysis of the relative fluid flow and dynamic streaming current. We used Biot theory to calculate the amount of induced relative flow by the solution to Green's function. The transport coefficients-conductivity, dynamic permeability, and the electrokinetic coupling coefficient-and their sensitivity with respect to porosity, dc permeability, and frequency changes are evaluated. Conductivity decreases with increasing dc permeability. It has a k[subscript 0][superscript -1/2] dependence when grain surface conductances are more important than the bulk fluid phase conductivity. Stationary phase relative flow and streaming current solutions are calculated for an explosive and vertical point source acting on the bulk and a volume injection source acting on the fluid. The streaming currents are induced both by P and S waves. The streaming current decreases with increasing fluid conductivity. This is consistent with the decrease of the diffuse double layer thickness and ζ-potential. The porosity effect on the streaming current induced by S waves is different from the currents induced by the P waves. The porosity affects the bulk moduli of the solid. Its effect, combined with the frame bulk modulus and compressibility of the saturating fluid, determines the streaming current amplitude induced by a P wave versus porosity. The increase in streaming current amplitude induced by S waves with increasing porosity is due to the decrease of the shear frame modulus with increasing porosity. The streaming current behavior with respect to dc permeability is found to differ for sources applied to the elastic frame and volume injection sources.

Electroseismic Investigation Of The Shallow Subsurface: Field Measurements And Numerical Modeling

2019-04-09T15:32:44Z

Electroseismic Investigation Of The Shallow Subsurface: Field Measurements And Numerical Modeling Mikhailov, Oleg V.; Haartsen, Matthijs W.; Toksoz, M. Nafi Electroseismic phenomena in porous media, first observed almost 60 years ago (Ivanov, 1939), were recently "rediscovered" due to their potential to detect zones of high fluid mobility and fluid chemistry contrasts in the subsurface (Thompson and Gist, 1993; Haartsen et al., 1995). However, a limited number of field studies of these phenomena reported in the literature were not able to support the results with an explicit comparison to theoretical predictions. In this paper, we demonstrate that electroseismic phenomena in porous media can be observed in the field, explained, and modeled numerically, yielding a good agreement between the field and the synthetic data. We first outline the design of our field experiment and describe the procedure used to reduce noise in the electroseismic data. Then, we present and interpret the field data, demonstrating how and where different electroseismic signals originated in the subsurface. Finally, we model our field experiment numerically and demonstrate that the numerical results correctly simulate arrival times, polarity, and the amplitude-versus-offset behavior of the electroseismic signals measured in the field.

Experimental Studies Of Electrokinetic Conversions In A Fluid-Saturated Porous Medium

2019-04-12T20:32:21Z

Experimental Studies Of Electrokinetic Conversions In A Fluid-Saturated Porous Medium Zhu, Zhenya; Toksoz, M. Nafi The electrokinetic effect in a fluid-saturated porous rock is defined as the coupling and conversion between seismic and electric energies. When seismic waves propagate through a fluid-saturated formation and cause a pore fluid-flow relative to the solid matrix, the motion of the cations in the fluid- flow forms a streaming electrical current and induces an electromagnetic wave at any discontinuous interface of the formation or stationary electric potential inside the homogeneous formation. Another conversion of energies opposite to the seismoelectric conversion is when an alternating electric field induces a relative fluid-flow in a fluid-saturated porous rock where fluid-flow can generate an electroseismic wave in the rock. In this paper we study the electrokinetics in porous sandstone and man-made porous models at high frequencies. A P-wave or S-wave transducer excites different acoustic wave modes in a cylinder, layer, or borehole model. Our experiments observe and record the radial or stationary seismoelectric signals induced at the interface or inside the formation. Some relative experiments have confirmed the reliability of the electrokinetic phenomenon observed in our experiments and the mechanism that is different from the piezoelectric effect. The results show that the seismoelectric signal induced by the extensional or flexural wave in the sandstone cylinder is a stationary local electric potential. The seismoelectric signal induced at the interface of the layer model is an electromagnetic wave which can be received within the fluid-filled porous medium. Experimental measurements performed in a borehole model by means of vertical seismic profiling (VSP) and single borehole logging show it is possible to conduct seismoelectric measurements in a deep borehole of petroleum formation. Measurements of electrokinetics can thus provide an effective means for estimating parameters in a fluid-saturated porous formation.

Off-Center Monopole And Dipole Sources In Fluid-Filled Boreholes

2019-04-10T23:56:53Z

Off-Center Monopole And Dipole Sources In Fluid-Filled Boreholes Tadeu, Antonio J. B.; Toksoz, M. Nafi; Kausel, Eduardo A variety of seismic testing techniques rely on the use of seismic sources, detectors, or both, placed at some depth below the ground surface; these are often installed within fluid-filled boreholes. The interpretation of the records obtained in the course of such explorations requires a thorough understanding of how waves propagate in the borehole and its immediate vicinity. Depending on the distance between the source and the receiver as well as their placement and orientation relative to the axis of the borehole, it is known that very complex wave patterns may arise. In this paper, analytical-numerical solutions are used to study the wave-field elicited by monopole or dipole sources within a fluid-filled cylindrical cavity drilled through an unbounded homogeneous elastic medium. This model is used to assess the effects of a source-receiver tool, placed in an off-centered and/or tilted position inside the fluid-filled borehole, on the propagation of both axisymmetric and non-axisymmetric wave modes.

Effects Of A Borehole Environment And Residual Hydrocarbon On Stoneley Wave Amplitude And Reflectivity

2019-04-10T23:56:53Z

Effects Of A Borehole Environment And Residual Hydrocarbon On Stoneley Wave Amplitude And Reflectivity Tao, Guo; Cheng, C. H. In recent years, borehole Stoneley wave amplitude and reflectivity have been used for estimating formation permeability based on the strong correlation between Stoneley wave attenuation, reflectivity and formation fluid conductivity. There are other factors, however, that may cause substantial Stoneley attenuation and reflection in a borehole environment. To make better use of Stoneley measurements for formation permeability estimation, it is desirable to identify and quantify those causes of Stoneley attenuation and reflection that do not directly result from formation permeability. In this study, a simplified Biot-Rosenbaum model developed by Tang et at. (1991) is adopted to systematically model Stoneley attenuation and reflection in various borehole environments and formation configurations. By changing pore fluid, formation porosity, lithology, bed boundaries and thickness in the modeling, the sensitivity of Stoneley wave propagation to these conditions are quantitatively assessed. It is found that the presence of a light hydrocarbon in the formation, especially a natural gas residual in the immediate vicinity of the borehole wall, even with only 5% contained in pore fluid, may also cause substantial Stoneley attenuation and reflection. This phenomenon, on the other hand, can be used to evaluate a nonfractured, low permeability gas reservoir when combined with shear wave velocity data. For the full gas-saturated zone, Stoneley wave reflection may be observed even when the permeability is as low as a few milliDarcies. Compared to the effects of pore fluid, the effects due to lithology contrasts at the boundaries and the changes of nonfracture porosity are insignificant in the cases studied here. For a residual gas-bearing zone of moderate permeability, Stoneley wave attenuation and reflection may be observed if the zone is thicker than 0.5 meter.

Flexural Waves In An Anisotropic Hard Formation Borehole Model

2019-04-12T20:32:21Z

Flexural Waves In An Anisotropic Hard Formation Borehole Model Zhu, Zhenya Y.; Cheng, Arthur C. H.; Toksoz, M. Nafi To investigate the propagation of flexural waves in a borehole surrounded by an azimuthally anisotropic hard formation, we made an ultrasonic borehole model of Delabole slate with very strong anisotropy. The axial and azimuthal acoustic fields generated by a dipole source were measured in the fluid-filled borehole. The results show that there are three dominant wave modes: fast and slow flexural waves and one we call a "flexural Stoneley wave. The phase velocities of the fast and slow flexural waves are lower than and close to those of the fast and slow shear waves of the formation, respectively. The phase velocity of the "flexural Stoneley" wave is higher than that of the borehole fluid. Regardless of the polarization of the dipole source, the particle motions of the fast and slow flexural waves are linear and in the direction of the fast and slow shear waves, respectively. The "flexural Stoneley" wave, similar to the normal Stoneley wave generated by a monopole source, is a tube wave with low frequency and high amplitude. Its main particle motion is in the horizontal plane perpendicular to the borehole axis. If the formation is azimuthally anisotropic, its particle motion is linear only when the source polarization is in the same direction as the fast and slow shear waves, and is elliptic everywhere else. Dipole acoustic well logging could be an effective and potential means for determining the anisotropy of a formation.

Estimation Of Nonorthogonal Shear Wave Polarizations And Shear Wave Velocities From Four-Component Dipole Logs

2019-04-12T20:32:21Z

Estimation Of Nonorthogonal Shear Wave Polarizations And Shear Wave Velocities From Four-Component Dipole Logs Nolte, Bertram; Cheng, Arthur C. H. Polarizations of split shear waves and flexural borehole waves are most commonly estimated from four-component data using the rotation technique of Alford (1986). This method is limited to the case of the two polarizations being orthogonal to each other. We present a method that is able to handle the case of nonorthogonally polarized waves and, moreover, is computationally more efficient than Alford's technique. Our method is based on the eigenvalue decomposition of an asymmetric matrix and a least-squares minimization of its off-diagonal components. In the case of orthogonally polarized waves, our method will yield exactly the same results as the Alford rotation. We apply our method to a cross-dipole shear-wave logging data set from the Powder River Basin in Wyoming and find that independently rotated source-receiver sets are very consistent with each other in anisotropic sections. After the rotation we compare two methods for estimating the phase velocities of fast and slow waves-a semblance method and homomorphic processing (Ellefsen et al., 1993). We find homomorphic processing to be more reliable due to the dispersive nature of flexural waves.

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2019-04-10T23:56:53Z

Cheng, Arthur C. H. This is the second year we have combined the work of the Logging and Reservoir Delineation groups at the Earth Resources Laboratory. In the first part of this report, we present work related to logging and petrophysics, including the ongoing work of electroseismics. This summary describes briefly the contributions of each paper in this group. Most of our focus in logging the past year was in understanding the physics of dipole logging in an azimuthally anisotropic medium, and the processing algorithms used in characterizing such a medium. In Nolte and Cheng (Paper 2), we analyzed a cross-dipole data set in extreme detail. We found that the Alford-type rotation appears to be stable in the anisotropic region of the data. The extra degree of freedom we used by allowing the principal axes to be nonorthogonal did not affect the results significantly. Furthermore, the rotation angles are consistent for all seven independently rotated source-receiver pairs. Velocities, on the other hand, are another matter. We used both the semblance method and the homomorphic method to estimate the fast and slow shear wave velocities from the rotated traces, and compared our results with those provided by the contractor. We also obtained estimates of velocity anisotropy from cross-correlation of the principal traces after the rotation. Although all of the processing shows similar variations in the velocities over our interval of interest, the actual velocities varied more than 10 percent. This is probably the result of the large dispersion of the flexural waves. More analysis is necessary to determine the most robust method of obtaining the shear wave velocities. Paper 3 (Zhu et al.) deals with laboratory dipole logging measurements in a rock sample with both fast and slow shear wave velocities higher than the acoustic velocity of water. The authors show evidence of a Stoneley wave that may be coupled to the flexural waves. Since we really do not have a well-understood theory for such a condition, more work needs to be done to see if any new information can be obtained from this "flexural Stoneley" mode. In an area where we have a better understanding of the underlying theory, Tao and Cheng (Paper 4) investigated the effects of gas-saturation, lithology, and borehole environment in the determination of permeability from Stoneley waves. This work combined the previous work in our group of Xiao-Ming Tang, Xiaomin Zhao, and Kazuhiko Tezuka, among others. The results indicated that small amounts of gas can significantly affect Stoneley wave dispersion and attenuation. Moreover, in a gas-saturated reservoir, the Stoneley wave sensitivity to permeability is increased significantly, so that permeability as low as a few millidarcies can be detected effectively. The vertical extent of the permeable zone (as opposed to a fracture) needs to be around 0.5 meters for effective detection. Tadeu et al. (Paper 5) deals with the numerical modeling of full waveform and dipole logs using mode summation techniques. Their method is capable of modeling tool ex-centering and other geometrical effects. The next series of papers (Zhu and Toksiiz, Paper 6; Mikhailov et al., Paper 7; and Haartsen and Toksiiz, Paper 8), investigate the electroseismic phenomenon in detail, using theory, numerical modeling, laboratory scale modeling, and field experiments. The results demonstrate that the electroseismic effect is indeed real and observable in the field. This topic is still in the initial stages of development and we will continue the development of the electroseismic technique as a practical tool for detecting fluid flow.

Modeling Of Seismoelectric Effects In A Borehole

2019-04-12T20:31:24Z

Modeling Of Seismoelectric Effects In A Borehole Haartsen, Matthijs W.; Toksoz, M. N. We present a method to simulate the propagation of seismic and converted electromagnetic waves generated by a mechanical borehole source embedded in a layered poroelastic medium. The electroseismic conversions occur at both the borehole wall and the layer boundaries. Most studies in electroseismic effects have been modelled and tested with seismic sources and detectors (geophones and antennas) at the surface. In this paper, we investigate the case of a seismic source in a borehole and receivers either at the surface or embedded in the medium. The method is formulated as a boundary element technique (where the poroelastic displacement and relative flow Green's functions are calculated by the discrete wavenumber method. The singular properties of the Green's functions are determined analytically using static Green's functions to regularize the integrals. This is necessary to calculate the element's self interaction. The borehole is cylindrical and its axis rulls normal to the interfaces. The coupled electroseismic effects in the layered media are included by using the global matrix technique. The developed method is an extension of the model of Biot-Rosenbaum, who applied the wavenumber integration technique to investigate the effect of formation permeability on Stoneley waves, using Biot's theory to model the wave propagation effects of a homogeneous permeable formation surrounding a borehole. We extend the Biot-Rosenbaum model by including the effect of a heterogeneous permeable formation surrounding the borehole. The effect of formation permeable zones (or fractured zones) on Stoneley waves can now be investigated. The other modification is the inclusion of conversions of mechanical into electromagnetic waves at mechanical and/or electrical contrasts in the poroelastic formation. The converted electromagnetic fields are sensitive to large permeability contrasts and fluid chemistry contrasts inside a reservoir. Using the electroseismic method downhole will provide more information about permeability/permeability contrasts in the formation, as well as additional lithological information (salinity of the fluids).

Electroseismic Waves From Point Sources In Layered Media

2019-04-10T18:05:19Z

Electroseismic Waves From Point Sources In Layered Media Haartsen, Matthijs W.; Toksoz, M. N. The macroscopic governing equations controlling the coupled electromagnetics and acoustics of porous media are numerically solved for the case of a layered poro-elastic medium.It is shown that these coupled equations decouple into two equation sets describing two uncoupled wavefield pictures. That is, the PSVTM picture where the compressional and vertical polarized mechanical waves drive currents in the PSV particle motion plane that couples to the electromagnetic wavefield components of the TM mode. And the SHTE picture where the horizontal polarized rotational mechanical waves drive currents in the SH particle motion plane that couples to the electromagnetic wavefield components of the T E mode. The global matrix method is employed in computing electroseismograms in layered poro-elastic media in the PSVTM picture. The principal features of the converted electromagnetic signals are the following: (1) contacts all antennas at approximately the same time; (2) arrives at the antennas at half of the seismic traveltime at normal incidence reflected P waves; and (3) changes sign on opposite sides of the shot. The seismic pulse is shown to induce electric fields that travel with the compressional wavespeed and magnetic fields that travel with the rotational wavefield. The frequency content of the converted electromagnetic field has the same frequency content of the driving incident seismic pulse, as long as the propagation distances are much less than the electromagnetic skin depth. Snapshots in time and converted electromagnetic amplitudes versus seismic point source-antenna offset-are calculated for contrasts in mechanical and/or electrical medium property. Conversion happens there where the seismic wavefront passes a contrast in medium properties due to generated imbalances in current across the contrast. The TM component amplitude radiation pattern away from the interface shows similarities with an effective electric dipole radiation pattern, or its dual, an effective magnetic current loop radiation pattern centered right beneath the source at the contrast's depth. The TM mode amplitudes decay rapidly with traveled distance and suggest the importance of a Vertical Electroseismic Profiling geometry to enhance recording of the converted electromagnetic signal by positioning the antennas closer to the target (contrast) of interest.

Scattering Of Acoustic And Elastic Waves Using A Hybrid Multiple Multipole Expansions-Finite Element Technique

2019-04-10T18:05:19Z

Scattering Of Acoustic And Elastic Waves Using A Hybrid Multiple Multipole Expansions-Finite Element Technique Imhof, Matthias G. In this paper, two different methods to solve scattering problems in acoustic or elastic media are coupled to enhance their usefulness. The multiple multipole (MMP) expansions are used to solve for the scattered fields in homogeneous regions which are possibly unbounded. The finite element (FE) method is used to calculate the scattered fields in heterogeneous but bounded scatterers. As the MMP method requires, the different regions and methods are coupled together in the least squares sense. For some examples, the scattered fields are calculated and compared to the analytical solutions. Finally, the seismograms are calculated for a scattering problem with several scatterers, and complex geometries. Thus, the hybrid MMP-FEM technique is a very general and useful tool to solve complex, two-dimensional scattering problems.

3-D Traveltime Modeling With Application To Seismic Imaging And Tomography

2019-04-12T20:31:21Z

3-D Traveltime Modeling With Application To Seismic Imaging And Tomography Matarese, Joseph R. Fast algorithms exist for performing traveltime modeling, even in three dimensions. These algorithms have the nice property that the computational time and memory requirements scale linearly with the number of grid points used represent subsurface velocities in discrete form. While traveltime modeling is typically used to predict first arrival times, later arrivals can also be simulated through the incorporation of a priori reflector information. For two-dimensional seismic imaging and tomography applications, the traveltime modeling algorithms presented here greatly expedite solution and can be readily deployed on distributed-memory parallel computers. Three-dimensional applications present a greater challenge, but by coupling an understanding of algorithm complexity with the promise of faster computers having greater quantities of physical memory, one can begin to predict future capabilities.

A Comparison Of Scattering From 2-D And 3-D Rough Interface

2019-04-10T18:05:19Z

A Comparison Of Scattering From 2-D And 3-D Rough Interface Cheng, Ningya; Schultz, Craig A.; Toksoz, M. Nafi In this paper we compared scattered waves from 2-D and 3-D interface structures. The modeling technique is the 3-D time domain finite difference method. The scheme is second-order accurate in time and fourth-order accurate in space. It is implemented on a massively parallel nCUBE computer. In order to investigate the characteristics of 2-D and 3-D rough surface scattering, we consider an acoustic-elastic boundary, which is described by a Gaussian autocorrelation function. The F-K analysis of reflected signals shows that 2-D scattering generates similar amounts of forward and back scattering, while in the 3-D case, more forward and less back scattering. The 3-D effects also show larger reflected energy than the 2-D case, especially near the normal incident. The out-of-plane scatterings are clearly demonstrated on the F-K spectra in the 3-D case. In the 2-D simulations, we have to keep in mind that it tends to overestimate the amount of backscattering energy.

Acoustic Wave Backscattering In A Random Inhomogeneous Ocean Sediment

2019-04-12T20:31:19Z

Acoustic Wave Backscattering In A Random Inhomogeneous Ocean Sediment Shi, Weiqun The backscattering of sound by inhomogeneities of the ocean sediment may provide a remarkable effect on underwater acoustic wave propagation. It may also be used as a means of remotely estimating complicated sediment properties. In this paper, a theoretical model of acoustic waves backscattered from an inhomogeneous sediment is formulated based on the Born approximation. The model not only contains the formal homogeneous bottom case but is also extended to the more realistic stratified bottom case. A complex wavenumber, in which an attenuation coefficient is introduced, reveals significant changes of the penetration depth within the sediment. The model predicts that for the stratified bottom, the backscattering strength is rapidly oscillating and decreases sharply at small grazing angles owing to the refraction of the waves caused by the sound velocity gradient. In order to reduce the number of independent variables, Biot's theory is applied to relate three-dimensional density fluctuations to sound speed fluctuations through porosity. A transverse-isotropic model is also developed to access the three-dimensional sound speed fluctuation spectrum. Geoacoustic surface and cross-hole tomographic data acquired from different sites characterizing sandy and silty bottoms are used to obtain three-dimensional sediment volume inhomogeneities. Backscattering strengths are evaluated for those bottom cases. The results agree with intuition and other published data.

Seismic Delineation Of A Geothermal Reservoir

2019-04-12T20:31:22Z

Seismic Delineation Of A Geothermal Reservoir Lee, Jung Mo; Gibson, Richard L., Jr.; Toksoz, M. Nafi; Cameli, Gian Mauro; Batini, Fausto; Dini, Ivano Surface seismic reflection surveys and VSP's have been extensively carried out in the Monteverdi area, within the Larderello region. Calibration of these seismic observations with data from numerous deep wells allowed the interpretation of the 2-D traverses so that a good geologic-structural reconstruction for the whole area was achieved. Many important reflectors were detected inside the Metamorphic basement by VSP's acquired in several wells in the area. These reflections were attributed to changes in petrophysical characteristics of the medium, particularly changes in fracture density, rather than to contrasts in lithology. Since at this time the main goal of the exploration in the Larderello region is the location of producing layers inside the basement, a major effort was applied to acquiring and modeling numerous VSP's in existing wells. In particular, a multioffset VSP was carried out in the COLLA 2 well with the specific goal of detecting fractured horizons within the reservoir of the Monte:verdi area. Because of the three-dimensionality of the seismic wave propagation in such a complicated geological structure, the standard onedimensional VSP modeling is not reliable. Therefore, 2-D and 3-D methods of modeling were applied. The modeling of the VSP data predicts important reflections at the depths corresponding to the main fractured zones intersected by drilling. These fractured zones should show subhorizontal distribution and thickness of tens of meters.

Source Characterization Of Microearthquakes Induced By Hydraulic Fracturing With Empirical Green's Function

2019-04-10T18:05:12Z

Source Characterization Of Microearthquakes Induced By Hydraulic Fracturing With Empirical Green's Function Li, Yingping; Cheng, C. H.; Toksoz, M. Nafi In this paper, we retrieved relative source time functions (RSTF) and estimated the source parameters for microearthquakes (M= -1.9 to -2.6) induced by hydraulic injection at Fenton Hill, New Mexico, using an empirical Green's function (EGF) method. Seismic waveform of a small event in seismic doublets or multiplets (Gelle and Meuller, 1980), defined as co-located events with similar focal mechanisms, within a hydraulic fracture zone, is treated as the EGF and is deconvolved from that of a larger event in the doublets or multiplets to retrieve the relative source time function. Time domain analysis of the RSTFs reveals the source complexity of the induced microearthquakes. The azimuthal variation of the RSTF indicates that the rupture propagates to the northwest, which is consistent with the growth direction of the hydraulic fracture zone determined by Li and Cheng (1995) with a seismicity temporal-spatial distribution pattern. The source duration of the induced events ranges from 2 to 8 ms and the source radii are estimated to be 4 to 12 meters. Values of stress drops are from 1 to 19 bars. Significant variation of the stress drops may reflect the heterogeneity of the stress field in the hydraulic fracture zone and its vicinity and indicate that the stress field heterogeneity extends down to a few meters.

Imaging Geometry And Growth Rate Of A Hydraulic Fracture Zone By Locating Induced Microearthquakes

2019-04-10T18:05:18Z

Imaging Geometry And Growth Rate Of A Hydraulic Fracture Zone By Locating Induced Microearthquakes Li, Yingping; Cheng, C. H. The hydraulic fracturing technique has become an important tool in the enhancement of hydrocarbons recovery, geothermal energy extraction, and solid waste disposal. The characterization of geometry parameters and growth rate of a hydraulic fracture zone is an important task for monitoring and assessing subsurface cracks. In this paper, we develop a location approach to determine the precise hypocenter locations for a cluster of seismic events induced by hydraulic fracturing. Two techniques were used in our location scheme: waveform correlation and grid search methods. The waveform correlation method allows us to obtain more accurate differential arrival times among events within in a cluster.. The grid search method is suitable when dealing with a nonlinear location problem. We applied our method to seismic waveform data from a hydraulic fracturing experiment at the Los Alamos Hot Dry Rock geothermal site and determined hypocenter locations for 157 induced microearthquakes. The maximum absolute and relative location errors were estimated to be 30-39 meters and 3-9 meters, respectively. Among the 157 events, 147 microearthquakes occurred in a tight cluster of a dimension of 40 meters, roughly defining a vertical hydraulic fracture zone. The length, height, and width of the hydraulic fracture zone were measured to be 40, 35 and 5 meters, respectively. The orientation of the fracture zone is estimated at about N400W. Analysis of the temporal-spatial pattern of the induced microseismicity revealed that the fracture zone grows significantly in a two-hour period during the hydraulic injection. Using seismicity distribution in time and space in this period, we determined that the fracture zone grows toward the northwest along the fracture zone strike with a growth rate of 0.1-0.2 meters per minute.

Analysis Of Microseismic Location Accuracy For Hydraulic Fracturing At The DWTI Site, Jasper, Texas

2019-04-10T18:05:10Z

Analysis Of Microseismic Location Accuracy For Hydraulic Fracturing At The DWTI Site, Jasper, Texas Rieven, Shirley; Rodi, William This report presents the results of a feasibility study designed to assess whether microseismic location techniques can provide enough accuracy and precision to enable a high resolution study of the spatial distribution of microseismic events induced during a hydraulic fracture experiment. We calculated the 90% confidence regions for six synthetic microevent 'clusters' along the azimuth of a hydraulic fracture produced during Atlantic Richfield's 1993 Fracture Technology Field Demonstration Project in Jasper, Texas. Examination of the confidence regions for the absolute locations indicates that microseismic events can be confidently located for areas near the monitoring wells but away from the plane intersecting the two observation points. We determined that the resolution for events located at the ends of the fracture is poor but improves dramatically nearer the wells. The minimum dimensions of the 90% confidence regions for events within our study area are approximately 8 ft in the northwest-southeast direction, 3 ft in the northeast-southwest direction, and 3 ft in depth.

Determination Of The Orientation Of Open Fractures From Hydrophone VSP

2019-04-10T18:05:18Z

Determination Of The Orientation Of Open Fractures From Hydrophone VSP Lee, Jung Mo; Toksoz, M. Nafi Open fractures are of interest in many areas such as ground water contamination, hazardous waste disposal, oil and gas recovery, and geothermal energy extraction. In borehole geophysics and engineering, fractures are usually located by acoustic borehole televiewer logging, however, not all of the observed fractures are permeable. The caliper log, on the other hand, provides the information about the change of borehole diameter, but increasing diameter does not prove the existence of open fractures. Nor can the combination of these two methods-televiewer logs and caliper logs-provide direct information about open fractures. However, tube waves, generated by P- and/or S-waves in hydrophone vertical seismic profiling (VSP) or cross-well seismic profiling section can detect open fractures intersecting the borehole. A new technique is developed to determine the orientation of open fractures using the normalized ratios of an S-wave-generated tube wave to a P-wave-generated tube wave. The fracture orientations determined by this method represent the average over the fracture planes for large radii, generally on the order of a meter. Numerical tests show that, given a good experiment design, a set of two independent measurements of these ratios with polarization information, or a set of three independent measurements without polarization information, provides a unique solution. The developed technique is stable in the presence of noise. This technique is applied to hydrophone VSP data from the Kent Cliffs test well in southeastern New York state. The orientations of the three major fractures which generate primary tube waves in the seismic profiling sections are obtained. The results agree well with the orientations measured from the borehole televiewer images in general. Any discrepancy may be attributed to the difference between the sampling size of this method and the borehole televiewer, to the deviation of rays from the straight lines due to inhomogeneity, and/or to possible BH-wave motion due to anisotropy and lateral inhomogeneity.

Polarization Of Flexural Waves In An Anisotropic Borehole Model

2019-04-09T16:15:12Z

Polarization Of Flexural Waves In An Anisotropic Borehole Model Zhu, Zhenya; Cheng, C. H.; Toksoz, M. Nafi Two modes of flexural waves can be generated by a dipole source in an anisotropic borehole. Their velocities are related to those of the fast and slow shear waves in the formation. The particle motions and the polarization diagrams of the fast and slow flexural waves are measured in borehole models made of phenolite materials with transverse isotropy or orthorhombic anisotropy. The experimental results show that the particle motion of the fast flexural wave is linear and in the same direction as that of the fast shear wave in the formation. The polarization direction of the fast flexural wave coincides with that of the fast shear wave and is independent ofthe direction of the dipole source. The particle motion of the slow flexural wave is nonlinear and elliptic. Its polarization direction and variation are dependent on the anisotropic material and the source direction. This means that the slow flexural wave is a more complicated wave mode rather than the simple mode where the particle motion generated by a dipole source is in the direction of the slow shear wave. The polarization characteristics of the fast flexural wave can be applied to determine the principal axis of an anisotropic formation by in-line and cross-line logging data.

Decomposition And Particle Motion Of The Acoustic Dipole Log In Anisotropic Formation

2019-04-09T16:53:23Z

Decomposition And Particle Motion Of The Acoustic Dipole Log In Anisotropic Formation Cheng, Ningya; Cheng, C. H. For linear wave propagation in anisotropic media, the principle of superposition still holds. The decomposition of the acoustic dipole log is based on this principle. In the forward decomposition inline and crossline acoustic dipole logs at any azimuthal angle the projection of measurements is along the principal direction of the formation. In the inverse decomposition the measurements along the principal direction can be constructed from the orthogonal pair of inline and crossline acoustic dipole log. The analytic formulas for both forward and inverse decompositions of the dipole laaa sss-saog are derived in this paper. The inverse decomposition formula is the solution in the least-square sense. Numerical examples are demonstrated for the acoustic dipole log decomposition in isotropic and anisotropic formations. The synthetic dipole log is calculated by the 3-D finite difference method. The numerical examples also show that the inverse decomposition formula works very well with noisy data. This inverse decomposition formula will be useful to process the field acoustic logging data in anisotropic formations. It can provide the direction of the formation anisotropy as well as the degree of anisotropy. Because acoustic dipole logging is in the near field distance, the particle motion is complicated. The particle motion is linearly polarized only in the principle direction. The initial particle motion with a dipole source at an arbitrary azimuthal angle tends to point in the fast shear wave direction. However, it will be difficult to use this information to find a stable estimation of a fast shear wave direction.

Measurements Of Shear-Wave Azimuthal Anisotropy From Ultrasonic Dipole Data

2019-04-10T18:05:12Z

Measurements Of Shear-Wave Azimuthal Anisotropy From Ultrasonic Dipole Data Tao, Guo; Cheng, Ningya; Zhu, Zhenya; Cheng, C. H. Four methods for analyzing azimuthal anisotropy from dipole logging data are described and attempted in this paper. These techniques are based on the phenomena of flexural wave splitting in anisotropic materials and are analogous to the techniques used for vertical seismic profiling (VSP) data processing. The laboratory measured dipole data obtained with a scaled tool and a scaled borehole drilled in an anisotropic material (phenolite) are employed to simulate the flexural modes propagating in transversely isotropic (TI) formation with symmetry axis perpendicular to the borehole, and to examine and compare these methods. Amplitude and particle motion analyses of the laboratory data demonstrate that, under the conditions of our laboratory measurements and numerical simulation, only the polarization direction of the fast flexural mode is consistent in accordance with the fast principal direction of the anisotropic material. The slower mode, which is much easier to excite and is of much larger amplitude than the fast mode, turns out to be subject to interferences and is complicated; it has not been well-understood. The particle motion of this guided mode is highly elliptical, and its polarization direction always changes irregularly with the source orientations. The first three methods used in VSP data processing-the linear-transform technique, the technique of rotating the data matrix in the time domain, and the technique of rotating the propagator matrix in the frequency domain-do not work well for the case of flexural modes. The fourth method-determining the eigen-direction of a TI material by identifying the the polarization with polar energy spectrum-works best for the data used in this study.

Borehole Seismic Source Radiation In Layered Isotropic And Anisotropic Media: Boundary Element Modeling

2019-04-12T20:31:26Z

Borehole Seismic Source Radiation In Layered Isotropic And Anisotropic Media: Boundary Element Modeling Dong, Wenjie; Bouchon, Michel; Toksoz, M. N. An algorithm based on the boundary element method is established for modeling seismic source radiation from open or cased boreholes in layered transversely isotropic (TI) media. The axis of symmetry of TI layers is assumed to be parallel to the borehole axis. Under this assumption, the problem is significantly simplified because the element discretization of the borehole remains one dimensional. For fluid-filled open boreholes, three equivalent sources on each element are required to represent the boundary effects on the inner fluid and the outer solid. The three boundary conditions for a f1uidsolid interface set up a system of equations for the equivalent sources on all elements. Once the sources are known, displacements in the solid and pressure in the fluid are obtained. For fluid-filled and cased boreholes, the method treats borehole fluid, casing, and cement as a cylindricaliy layered isotropic medium. In this case, the boundary conditions to be satisfied at the borehole wall are four (continuity of the normal and tangential displacements and stresses). The implementation of the method is illustrated through a few examples.

Solute Transport In Heterogeneous Porous Media

2019-04-10T18:05:21Z

Solute Transport In Heterogeneous Porous Media Zhao, Xiaomin; Toksoz, M. Nafi Solute mass transport in porous media is strongly correlated with pore fluid flow. The analysis of solute transport is an effective means for studying medium heterogeneities. In this study, we discuss the effects of heterogeneity on the tracer transport. Assuming steady fluid flow, we have simulated tracer transport in various permeability heterogeneities. The results show that the tracer distribution is very closely correlated with the medium heterogeneity, and anisotropy in tracer transport exists when there is permeability lineation and large permeability contrast between low- and high-permeability regions. An important feature by which the tracer transport differs from the fluid flow field is that the tracer transport tends to smear the effects of a thin non-permeable layer (or small permeability barriers) through diffusion into the low-permeability layer, while the fluid flow cannot penetrate the low-permeability layer. In addition, the modeling results also show that the tracer transport strongly depends on the tracer source dimension, as well as the flow source dimension.

Electrokinetics Of A Fluid-Saturated Rock Sample: Laboratory Experiments

2019-04-12T20:31:27Z

Electrokinetics Of A Fluid-Saturated Rock Sample: Laboratory Experiments Zhu, Zhenya; Toksoz, M. N. The conversion between seismic and electromagnetic energies was discovered in a fluidfilled porous formation. When seismic waves propagate through a fluid-saturated porous formation, relative motion between the pore fluid and the solid matrix is generated and cation motion in the fluid is formed. The streaming electric current induces electromagnetic waves in the formation. There is an opposite phenomenon, i.e., the conversion of electric energy into acoustic energy in the porous formation. The electroseismics in porous sandstone samples are investigated by ultrasonic experiments in our laboratory. A compressional or a shear transducer excites an acoustic wave in the water-saturated sample and the electric signals generated on the surface are measured by an electrode. The relationship between the electric potential and acoustic wave or the conductivity of water-saturated rocks is studied. The electro-seismic conversion in rock samples is also investigated. Electroseismics could provide an effective means for estimating the fluid-saturated porous formation.

Nonlinear Semblance Processing For The Evaluation Of An Acoustic Altered Zone Around The Borehole

2019-04-10T18:05:21Z

Nonlinear Semblance Processing For The Evaluation Of An Acoustic Altered Zone Around The Borehole Tezuka, Kazuhiko This paper describes a simple method to evaluate an acoustic altered zone around the borehole using an array of sonic waveforms. The method is based on a semblance velocity analysis and a nonlinear travel time window is introduced. On the assumption that a velocity gradient of the altered zone may be linear, the nonlinear travel time window is calculated as a function of averaged velocity and a normalized velocity gradient. The method is applied to the synthetic acoustic data calculated by finite difference modeling. Case studies with several altered formation models confirmed that this method is a good estimator of the velocity gradients around the borehole.

Stoneley Wave Propagation Across Borehole Permeability Heterogeneities

2019-04-12T21:17:25Z

Stoneley Wave Propagation Across Borehole Permeability Heterogeneities Zhao, Xiaomin; Toksoz, M. N.; Cheng, C. H. An important application of borehole acoustic logging is the determination of formation permeability using Stoneley waves. Heterogeneous permeable structures, such as fractures, sand-shale sequences, etc., are commonly encountered in acoustic logging. The purpose of this study is to investigate the effects of the permeability heterogeneities on the borehole Stoneley wave propagation. We have studied the effects of formation permeability heterogeneities on the Stoneley wave propagation when the heterogeneity changes in radial and azimuthal directions (Zhao et al, 1993). To further study the problem of acoustic logging in heterogeneous porous formations, we study the case where the formation permeability varies in the borehole axial and radial directions. This is a very important problem because vertical heterogeneity variations are commonly encountered in acoustic logging applications. Using the finite difference approach, such heterogeneities as random heterogeneous permeability variations, multiple fracture zones, permeable (sand) - non-permeable (shale) sequences, can be readily modeled, and the results are presented. Our numerical simulation results show that the continuous permeability variations in the formation have only minimal effects on the Stoneley wave propagation. Whereas the discontinuous variation (e.g., permeable sand and non-permeable shale sequences) can have significant effeces on the Stoneley wave propagation. However, when the Stoneley wavelength is considerably large compared to the scale of heterogeneity variations, the Stoneley wave is sensitive only to the overall fluid transmissivity of the formation heterogeneity, To demonstrate the effects of heterogeneity on the Stoneley wave propagation. an experimental data set (Winkler et aI., 1989) has been modeled using a randomly layered permeability model. The heterogeneous permeability model results agree with the data very well, while the data disagree with the results from homogeneous permeability models. The numerical technique for calculating Stoneley wave propagation across permeability heterogeneities has been applied to interpret the acoustic logging data across a heeerogeneous fraceure zone (paillet. 1984). The modeling technique, in conjunction with a variable permeability model, successfully explains the non-symmetric patterns of the Stoneley wave attenuation and reileceion at the top and bottom of the fracture zone, while it is difficult to explain these patterns using a homogeneous permeable zone model. The technique developed in this study can be used as an effective means for characterizing permeability heterogeneities using borehole Stoneley waves.

Fast Inversion Of Formation Permeability From Stoneley Wave Logs Using A Simplified Blot-Rosenbaum Model

2019-04-12T20:31:27Z

Fast Inversion Of Formation Permeability From Stoneley Wave Logs Using A Simplified Blot-Rosenbaum Model Tang, X. M.; Cheng, C. H. This paper describes a fast algorithm for estimating formation permeability from Stoneley wave logs. The procedure uses a simplified Biot-Rosenbaum model formulation. The input to the inversion is the Stoneley wave spectral amplitudes at each depth and receiver, the borehole fluid properties (velocity and density), the borehole caliper log, the formation density and porosity (from log data), and the compressional and shear velocities for the interval of interest. The model uses the borehole caliper and elastic properties to compute the Stoneley wave excitation (that is, predicted amplitude without permeability effects) as a function of frequency, and the porosity and permeability to compute the fluid flow amplitude reduction. This method also uses a reference depth of known permeability and compares amplitude variations at other depths relative to the reference depth. The permeability value obtained from the inversion represents the best fit over all receivers and all relevant frequencies. A processing example is shown to demonstrate the ability of this technique to extract formation permeability from Stoneley wave logs.

Experimental Study Of The Flexural Waves In The Fractured Or Cased Borehole Model

2019-04-10T18:05:21Z

Experimental Study Of The Flexural Waves In The Fractured Or Cased Borehole Model Zhu, Zhenya; Cheng, C. H.; Toksoz, M. N. The ultrasonic logging is performed with dipole transducers in aluminum and lucite borehole models to study the propagation of the flexural waves in a fractured or cased borehole. The experimental results show that the flexural wave is much more sensitive to a horizontal fracture than to a vertical one. The propagation of flexural waves in a borehole with an inclined fracture is related to both the polarization of the flexural wave and the direction of the fracture. The experimental results show that a very strong low-frequency flexural wave can be generated by a dipole source in a cased borehole and it propagates with the shear wave velocity of the formation. High-frequency waves generated by a dipole source propagate with the compressional wave and flexural wave velocities of the casing. Dipole acoustic well logging could be an effective means for determining horizontal and declined fractures and measuring the formation shear wave velocity in a cased borehole.

Acoustic Wave Propagation In And Around A Fluid-Filled Borehole Of Irregular Cross-Section

2019-04-10T18:05:20Z

Acoustic Wave Propagation In And Around A Fluid-Filled Borehole Of Irregular Cross-Section Peng, Chengbin; Cheng, C. H. Boreholes with 10% or more ellipticity are not uncommon. In this paper, we consider the coupling of an incident elastic wave into a borehole of irregular cross-section and investigate the cross-mode coupling phenomenon in sonic well logging in the presence of borehole irregularity. The mode-matching method is used. Different from its original formulation, we employ the Reichel et al. algorithm to obtain the discrete least square approximation by trigonometric polynomials, a technique closely related to the fast Fourier transform (FFT). Our method not only yields great accuracy but also gains computational speed. Our study shows that the pressure in the borehole fluid is sensitive to the irregularity of the borehole cross-section, it is larger if the incident wave is along the effective minor axis and smaller if the incident wave is along the effective major axis. In the frequency range of a typical borehole experiment, the solid displacement in the formation is much less affected by the borehole irregularity. In an elliptical borehole, a monopole source excites dipole wave trains that are characteristic of the tube waves, and a centered dipole source excites monopole wave trains that are characteristic of the flexural waves.

Untitled

2019-04-12T20:31:20Z

Tezuka, Kazuhiko; Cheng, C. H.; Tang, X. M. This paper describes a propagator matrix formulation for the problem of the Stoneley wave propagation in an irregular borehole. This is based on a simple one-dimensional theory that is possible for the low frequency Stoneley wave, because it is a guided wave with no geometrical spreading in the borehole. The borehole and the surrounding formation are modeled by multi-layers discretized along the borehole axis, then the propagator matrices at each boundary are calculated. The mass balance boundary condition is introduced to express an interaction of the Stoneley wave at the interfaces which include radius changes. We have used the method to investigate the reflection and the transmission characteristics of the Stoneley wave with several models. The results are consistent with the results obtained by other existing modeling methods such as the finite difference method and the boundary integral method. The calculation speed is much faster than those of the other methods. We have applied the method to the field data to simulate the synthetic iso-offset records and have compared them with the actual field records. The results show a good agreement in the major reflections due to the washout zones and an important disagreement in the reflections related to the fractures. This result suggests the possibility of distinguishing the fracture induced reflections from others. Through this study, we found that the proposed method is efficient in modeling the low frequency Stoneley wave propagation in the irregular borehole, especially in simulating the synthetic iso-offset records, which provide helpful information in the evaluation of fractures.

Borehole Wave Propagation In Isotropic And Anisotropic Media III: Anisotropic Formation

2019-04-10T18:05:21Z

Borehole Wave Propagation In Isotropic And Anisotropic Media III: Anisotropic Formation Cheng, Ningya; Cheng, C. H.; Toksoz, M. N. In this paper we extend the 3-D finite difference method to simulate wave propagations in an anisotropic medium. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point force source in the transversely isotropic medium. The finite difference synthetics are compared with ultrasonic lab measurements in a scaled borehole drilled along the X axis in an orthorhombic phenolite solid. Both monopole and dipole logs agree well. The 3-D time domain finite difference method is applied to the fluid-filled borehole wave propagation problems in the anisotropic formation. The following results are obtained: 1. In a borehole drilled along the Z axis in a phenolite formation, the monopole log shows the P wave travelling with velocity v[subscript zz]. There are no shear-pseudo-Rayleigh wave arrivals. The dipole log is dominated by the single slow flexural mode. 2. In a borehole drilled along the Y axis in a phenolite formation, the monopole log shows the P wave travelling with velocity v[subscript yy]. There are shear-pseudo-Rayleigh wave arrivals shown on the monopole seismograms between the P and Stoneley waves due to the shear wave anisotropy. The anisotropy also causes the shear wave splitting in the dipole log. The two shear wave arrivals correspond to the fast and the slow flexural modes. 3. The disagreement between the shear wave velocity from the Stoneley wave inversion and the direct shear wave log velocity from field data is beyond the errors in the measurements. It is shown that the formation permeability is not the cause of the discrepancy. From the estimated "shear/pseudo-Rayleigh" phase velocities in the array full waveform log and the 3-D finite difference synthetics in the anisotropic formation, the discrepancy can be explained as shear wave anisotropy.

Borehole Wave Propagation In Isotropic And Anisotropic Media II: Isotropic Formation

2019-04-09T17:56:14Z

Borehole Wave Propagation In Isotropic And Anisotropic Media II: Isotropic Formation Cheng, Ningya; Cheng, C. H.; Toksoz, M. N. In this paper we apply the 3-D finite difference method to simulate borehole wave propagations in an isotropic formation. The scheme is tested in a fluid-filled borehole surrounded by the homogeneous elastic formation. The finite difference synthetics results are in good agreement with the discrete wavenumber solutions for both monopole and dipole sources in hard as well as soft formation. These tests also show the good performance of Higdon's absorbing boundary condition for the body waves as well as the guided waves. In the isotropic borehole formation, the following results are obtained: 1. Off-centered dipole sources generate almost the same waveforms as the centered dipole source. The slight amplitude differences are due to the different values of the excitation function at the different source positions. The off-centered monopole shows a larger Stoneley wave than the centered one. 2. In an elliptic borehole, where the source is in line with the minor axis of ellipse, the dipole waveforms have similar waveforms to the circular borehole with the same radius as the minor axis. This corresponds to the odd flexural mode. The waveform similarity demonstrates that the odd flexural mode is insensitive to the major axis. When the dipole is in line with the major axis of the ellipse, the waveforms shift to the low frequency range. The waveforms are dominated by the even flexural mode. 3. For a borehole near a horizontal bed, the monopole log can be used to detect it by using refracted P waves from the bed boundary. Because a dipole is a directional source, when it is parallel to the bed, there is little effect of the bed on the waveforms, and when it is perpendicular to the bed, there are strong flexural wave interferences. For a borehole which penetrates a 45 degree tilted layer interface, the monopole log has less reflection and transmission than the horizontal interface. The dipole log also transmits less flexural waves across the tilted boundary than the horizontal one. The horizontally layered formation seismograms clearly show the two flexural modes in the different layers. There are no clear flexural wave reflections in both cases.

Report Summary

2019-04-12T20:31:27Z

Report Summary Cheng, C. H. This report contains the results of work completed during the twelfth year of the Borehole Acoustics and Logging Consortium in the Earth Resources Laboratory at M.LT. This year we have achieved one of our major goals in numerical modelling. We have completed a code for modelling elastic wave propagation in a borehole in a generally anisotropic and heterogeneous formation in three dimensions. This opens up a lot of possibilities in terms of modelling full waveform and shear wave logging. Along the same trend, we have continued to develop our numerical modelling of permeable zones. We are able to simulate Stoneley wave propagation in zones with varying vertical permeability. This allows us to match the field observations better. Another application of numerical flow modelling is to model tracer transport in heterogeneous media. This has applications in environmental as well as enhanced oil recovery areas. Another area we have addressed is the influence of borehole geometry on the full waveform and dipole wavefield. We have looked at the effects of a borehole with an irregular cross-section on the full waveform, and we have also effectively modelled a borehole with a vertically varying radius, such as in the case of washouts. We can model the scattered Stoneley waves from these washouts and the results compare well with data. On the field data Side, we have a paper dealing with the estimation of permeability from Stoneley waves. This case study was done in a water well. We have processed a number of other data sets during the past year, and some of the results will be discussed at the Annual Meeting. On the more theoretical side, we have a paper on the radiation of a borehole source into a layered or transversely isotropic medium. This work is done using the Boundary Element method. We also have a paper addressing the possibility of using non-linear semblance to better process the full waveform array data. The idea is to estimate velocity changes (increases) away from the borehole. In the laboratory we have examined the effects of fractures (vertical, horizontal, and inclined) on flexural wave propagation. We have also begun to investigate the electroseismic coupling in porous rocks, with an eye on the possibility of coupling acoustic and electric logs to better delineate permeability/fluid changes in the field. More detailed descriptions of the papers follow.

Borehole Wave Propagation In Isotropic And Anisotropic Media I: Finite Difference Method

2019-04-12T20:31:21Z

Borehole Wave Propagation In Isotropic And Anisotropic Media I: Finite Difference Method Cheng, Ningya; Cheng, C. H.; Toksoz, M. N. In this paper we developed a 3-D finite difference method to simulate wave propagations in an isotropic medium. The wave equation is formulated into the first-order hyperbolic equations by using velocity and stress and then discretizing it on a staggered grid. The 3-D time domain finite difference scheme is second order accurate in time and fourth order accurate in space. The grid dispersion and anisotropy are analyzed and the stable condition of the scheme is obtained. Higdon's absorbing boundary condition is discussed and generalized to the anisotropic medium. The scheme can provide realistic 3-D wave propagation simulation by the use of a parallel computer. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point explosion source in the acoustic medium and a point force source in the elastic medium. The finite difference method accurately models not only the far field P and S waves, but also the near field term. It demonstrates that the second-order Higdon's absorbing boundary condition works very well in an acoustic and elastic medium.

Location Of Microearthquakes Induced By Hydraulic Fracturing

2019-04-12T20:32:12Z

Location Of Microearthquakes Induced By Hydraulic Fracturing Rodi, William; Li, Yingping; Cheng, C. H. This paper examines the problem of locating microearthquakes induced by hydraulic fracturing using seismic arrival time data. In addition to the use of absolute arrival times measured for individual events, we consider the use of differential arrival times amongst a set of two or more seismic events as a means of constraining their locations relative to one another. Differential arrival times can be measured very accurately using cross-correlation techniques and are less sensitive than absolute arrival times to subsurface velocity structure. We have developed an algorithm which combines relative event location techniques with conventional absolute location techniques and applied it to a set of 19 microearthquakes recorded during a hydraulic fracturing experiment conducted as part of the Los Alamos Hot Dry Rock project. We find that the events, except for a few outliers, delineate a planar zone 30 meters in dimension, presumably a fracture plane. This example shows that the use of differential arrival times improves the accuracy of locating microearthquake clusters and that the relative locations of events within the cluster are better determined than their absolute locations. The results also suggest the need for directional data from three-component stations or better station geometry to further improve location accuracy.

Optimal Absorbing Boundary Conditions For Finite Difference Modeling Of Acoustic And Elastic Wave Propagation

2019-04-10T18:05:09Z

Optimal Absorbing Boundary Conditions For Finite Difference Modeling Of Acoustic And Elastic Wave Propagation Peng, Chengbin; Toksoz, M. N. An optimal absorbing boundary condition is designed to model acoustic and elastic wave propagation in 2D and 3D media using the finite difference method. In our method, extrapolation on the artificial boundaries of a finite difference domain is expressed as a linear combination of wave fields at previous time steps and/or interior grids. The acoustic and elastic reflection coefficients from the artificial boundaries are derived. They are found to be identical with the transfer functions of two cascaded systems: one is the inverse of a causal system and the other is an anticausal system. This method makes use of the zeros and poles of reflection coefficients in a complex plane. The optimal absorbing boundary condition designed in this paper yields about 10 dB smaller in magnitude of reflection coefficients than Higdon's absorbing boundary condition, and around 20 dB smaller than Reynolds' absorbing boundary condition. This conclusion is supported by a simulation of elastic wave propagation in a 3D medium on an nCUBE parallel computer.

Tube Waves, Seismic Waves And Effective Sources

2019-04-11T04:49:19Z

Tube Waves, Seismic Waves And Effective Sources Burridge, Robert; Kostek, Sergio; Kurkjian, Andrew L. A simple asymptotic analysis, based on the smallness of the ratio of the borehole radius to the wavelength, reveals the interaction between tube waves and seismic waves. The pressure field in a tube wave acts as a secondary source of seismic waves and conversely an incoming seismic wave excites a tube wave. The asymptotic analysis leads to a characterization of these sources in terms of the solution to two-dimensional elastostatic problems. These may be solved exactly when the borehole has an elliptical cross-section even in an anisotropic formation. Also the borehole need not be straight provided that its radius of curvature is large compared with a wavelength.

Dynamic And Static Green's Functions In Transversely Isotropic Elastic Media

2019-04-10T18:05:09Z

Dynamic And Static Green's Functions In Transversely Isotropic Elastic Media Dong, Wenjie; Schmitt, Denis P. Concise and numerically feasible dynamic and static Green's functions are obtained in dyadic form by solving the wave equation and the equilibrium equation with general source distribution in transversely isotropic (TI) media. The wave and equilibrium equations are solved by using an extended version of the Kupradze method originally developed for isotropic media. The dynamic Green's function is expressed through three scalar quantities characterizing the propagation of SH and P-SV waves in a transversely isotropic medium. The 2-D inverse Laplacian operator contained in previous Green's function expressions is eliminated without limiting to special cases and geometries. The final dyadic form is similar to that of the isotropic dyadic Green's function, and therefore lends itself to easy analytical and numerical manipulations. The static Green's function has the same dyadic form as the dynamic function except that the three scalars must be redefined. From the dynamic Green's function, displacements due to vertical, horizontal, and explosive sources are explicitly given. The displacements of the explosive source show that an explosive source in a TI medium excites not only the quasi-P wave, but also the quasi-SV wave. The singular properties of the Green's functions are also addressed through their surface integrals in the limit of coinciding receiver and source. The singular contribution is shown to be -1/2 when the static stress Green's function is integrated over a half elliptical surface.

Calculation Of Conical (Mach) Wave Displacement Fields Radiated By Borehole Sources In Slow Formations And Inhomogeneous Media

2019-04-12T21:17:26Z

Calculation Of Conical (Mach) Wave Displacement Fields Radiated By Borehole Sources In Slow Formations And Inhomogeneous Media Gibson, Richard L., Jr. Stationary phase solutions for the radiation patterns of borehole sources are commonly used to study the far-field seismic wavefields produced in crosshole or reverse VSP experiments, but they break down when the formation shear wave velocity is less than the tube wave velocity in the source borehole. This is because the tube wave, not the primary source, radiates the dominant shear wave signal in the form of large amplitude conical waves, which are also called Mach waves. I model this effect by considering the tube wave to be a moving secondary point source generated by the primary source of acoustic energy. A discretization of the source well allows a numerical solution of the integral equation which yields the displacement field by a general source distributed in space and time. The time at which each point source in the discretization emits energy is determined by the group velocity of the tube wave, while the radiation of the individual sources is characterized by the stress field induced by the tube wave at the borehole wall. An integration along the borehole of these point sources then yields the observed Mach wave arrivals. Since this method involves the summation of shear wave ray arrivals from the many point sources along the borehole, the method is called the Ray Summation Method (RSM). Comparison of RSM results with full waveform synthetic seismograms computed with the discrete wavenumber method confirms the accuracy of this method. Unlike the discrete wavenumber method, however, the use of ray tracing in the RSM allows computation of the Mach wave arrivals for inhomogeneous layered media as well as homogeneous models, including the waves generated by reflections of the Mach waves at interfaces and from the reflections of the tube wave itself. The interactions of the conical waves with interfaces can show unusual patterns of arrivals which would not be predicted from ordinary point source behavior.

Cased Borehole Effect On Downhole Seismic Measurements

2019-04-12T20:31:12Z

Cased Borehole Effect On Downhole Seismic Measurements Peng, Chengbin; Cheng, C. H.; Toksoz, M. N.; Zhu, Zhenya Approximate and exact formulations are presented for the interaction of an incident wave with a cased borehole. In the approximate method, the borehole coupling theory is used to compute pressure in the fluid at a low frequency. The results are simple and explicit. They are useful in the study of cased borehole coupling and as well as borehole radiation. In the exact method, elastic potentials in each annulus are represented as a superposition of fundamental solutions to the Helmholtz equations. Continuity of displacements and stresses across layer boundaries are used to determine unknown coefficients. The global matrix method is employed to simultaneously compute these coefficients in individual layers. This method is advantageous over the Thomson Haskell propagator matrix method in handling evanescent waves. Our results show that, in a cased borehole, the borehole effects on downhole seismic measurements are more significant than those in an open borehole, especially when the formation is soft and the casing is steel. For hard formations and frequency below 1 kHz, cased borehole influence on downhole geophone measurement is minimal, while at high frequencies, large discrepancies occur, especially at grazing incidence. For soft formations, both the pressure in the fluid and the solid displacement on the borehole wall show strong dependence on frequency and incidence angle, even at very low frequencies. Strong resonance occurs in the fluid for an SV incidence at angle δ = cos[superscript -1]β/C[subscript T] where CT is the tube wave velocity in a cased borehole. This resonance is prominent even at a very high frequency and large incidence angle because the tube wave velocity is raised well above the formation shear velocity by the steel pipe. This behavior is very different from that in an open borehole. At a particular angle of incidence of a plane P wave, the pressure in the fluid is near zero at low frequencies. This angle is dependent on the casing thickness and can be computed exactly. In general the casing behaves like a shield in such a way that the amplitude of both pressure in the fluid and solid motion on the borehole wall are reduced compared to those in an open borehole.

Acoustic Logging In Randomly Stratified Formations

2019-04-10T18:05:08Z

Acoustic Logging In Randomly Stratified Formations Tang, X. M.; Cheng, N. Y.; Cheng, C. H.; Toksoz, M. N. The propagation of borehole acoustic waves in the presence of various types of heterogeneous formations is investigated by modeling them as stratified media with varying velocity-depth distributions. Two types of formations are modeled, using translational and cyclic random models, respectively. Borehole acoustic wavefields for the heterogeneity formation models are simulated using finite-difference techniques. The wavefield modeling results show that the borehole acoustic waves can be significantly affected by the formation heterogeneities. Specifically, the scattering due to heterogeneity can cause significant amplitude attenuation and travel time delay for the transmitted waves. The borehole guided waves are also sensitive to the formation heterogeneity. The effects of the random formation heterogeneity on the borehole acoustic waves are controlled by two factors: the degree of heterogeneity variation and the heterogeneity scale length relative to the wavelength.

Propagation Of Flexural Waves In An Azimuthally Anisotropic Borehole Model

2019-04-10T18:05:09Z

Propagation Of Flexural Waves In An Azimuthally Anisotropic Borehole Model Zhu, Zhenya; Cheng, C. H.; Toksoz, M. N. Flexural waves generated by a dipole source have been studied theoretically and used to estimate the shear parameters of a formation. The basic principles and main properties of flexural waves propagating in a borehole are reviewed in this paper. A mono/dipole transducer made of a PZT piezoelectric tube is used for laboratory experiments in borehole models. The radiation pattern of the dipole source is measured in a water tank. In order to simulate the hard and soft formations, measurements are performed in borehole models made of aluminum and lucite, respectively. Experimental results are in good agreement with the theoretical dispersion characteristics. Measurements are also performed with the transducers in an azimuthally anisotropic borehole model made of Phenolite XX-324. Both fast and slow flexural waves with different velocities are generated by a dipole source in the model. The flexural waves are related to the fast or slow shear waves in the anisotropic material. Experimental results show that the flexural wave splits into a fast and a slow component in an azimuthally anisotropic borehole; therefore, dipole acoustic well logging could be an effective means for estimating a formation's anisotropy.

Stoneley Wave Propagation In Heterogeneous Permeable Porous Formations

2019-04-10T18:05:08Z

Stoneley Wave Propagation In Heterogeneous Permeable Porous Formations Zhao, Xiaomin; Toksoz, M. N.; Cheng, C. H. The propagation of borehole Stoneley waves is strongly correlated with permeability of the formation. Previous studies primarily focused on the situation where the permeability is homogeneously distributed in the formation. In many in-situ situations, however, the permeability distribution of the formation is heterogeneous, due to effects such as a damaged zone around the borehole, random variation of the formation permeability, and layering, etc. This study investigates the effects of formation permeability heterogeneity on Stoneley wave propagation. Using the theory of dynamic permeability and a finite difference technique in cylindrical coordinates, dynamic pore fluid flow in an arbitrarily heterogeneous porous medium surrounding the borehole is modeled. The effects of the flow on the borehole Stoneley waves are calculated. The calculations were performed on various types of permeability heterogeneities. For a formation having random permeability variation with various heterogeneity scale lengths (smaller than the scale of the borehole), the Stoneley wave attenuation and dispersion are only slightly higher than those calculated with a constant permeability (mean value of the random distributions). For a formation with permeability linearly increasing or decreasing away from the borehole, the Stoneley wave behaviors are also similar to those calculated with a constant permeability. Significant effects are found for a damaged zone case where the zone has much higher permeability than the virgin formation. The attenuation exhibits a peak and the Stoneley wave velocity is significantly decreased in the frequency range from 0 to 3 kHz. These features, if measured from the data, can be used as a diagnostic of the borehole condition.

Fourth-Order Finite Difference Acoustic Logs In A Transversely Isotropic Formation

2019-04-10T18:05:08Z

Fourth-Order Finite Difference Acoustic Logs In A Transversely Isotropic Formation Cheng, N. Y.; Cheng, C. H.; Toksoz, M. N. In this paper we present a finite difference scheme for seismic wave propagation in a fluid-filled borehole in a transversely isotropic formation. The first-order hyperbolic differential equations are approximated explicitly on a staggered grid using an algorithm that is fourth-order accurate in space and second-order accurate in time. The grid dispersion and grid anisotropy are analyzed. Grid dispersion and anisotropy are well suppressed by a grid size of 10 points per wavelength. The stability condition is also obtained from the dispersion analysis. This finite difference scheme is implemented on the nCUBE2 parallel computer with a grid decomposition algorithm. The finite difference synthetic waveforms are compared with those generated using the discrete wavenumber method. They are in good agreement. The damping layers effectively absorbed the boundary reflections. Four vertically heterogeneous borehole models: a horizontal layered formation, a borehole with a radius change, a semi-infinite borehole, and a semi-infinite borehole with a layer, are studied using the finite difference method. Snapshots from the finite difference results provide pictures of the radiating wavefields.

Report Summary

2019-04-12T20:31:20Z

Report Summary Cheng, C. H. This report contains the results of work completed during the eleventh year of the Borehole Acoustics and Logging Consortium in the Earth Resources Laboratory at M.LT. We continued our trend toward more general borehole acoustics instead of just full waveform logging. In this report we have papers related to borehole radiation as well as reception patterns, as well as more theoretical work on the Green's function of an anisotropic medium. The borehole reception pattern paper is the continuation of the work from last year, where we dealt with the receiver pattern in an open borehole. This year the work is extended to include cased boreholes. On the subject of borehole radiation, this year we have two papers dealing with the radiated seismic wavefield away from a borehole. The interest is in the areas of downhole sources as applied to single hole imaging, measurement while drilling, reverse vertical seismic profiling, as well as cross borehole tomography. In all these areas how the source energy is coupled into the borehole under different situations is of tremendous interest. On the more traditional full waveform acoustic logging side, we have a paper dealing with logging in a randomly heterogeneous formation, and one on the effect of permeability heterogeneity on the measured Stoneley wave velocity and attenuation. We also have a paper on the ultrasonic modeling of shear wave logging in an azimuthally anisotropic formation. On the numerical side, we have one paper on a fourth-order staggered-grid finite difference formulation of full waveform logging in a transversely isotropic formation with vertically varying properties, and one on the formulation of an optimal absorbing boundary condition for finite difference elastic wave propagation algorithms. Finally, as a continuation of previous work, we are working to improve our algorithm to location microearthquakes generated by hydraulic fracturing and thus provide a better location of the fracture in a three-dimensional space. A more detailed summary of the papers follows.

Tube Wave Generation At A Layer Boundary For An Incident Compressional Plane Wave

2019-04-11T03:52:22Z

Tube Wave Generation At A Layer Boundary For An Incident Compressional Plane Wave Peng, Chengbin; Toksoz, M. Nafi An approximate theory for the scattering of an incident plane P wave into tube waves in a fluid-filled borehole drilled through two homogeneous half-spaces is proposed in this paper. This theory is in excellent agreement with the zero frequency formulation (White, 1983) for frequencies below hundreds of Hertz (in the range of conventional crosshole or VSP experiments) and finite difference simulation at high frequencies. At low frequency the excited tube wave is found to be independent of the borehole radius and shows stronger sensitivity to the formation shear velocity contrast across the layer boundary. The sensitivity towards the compressional velocity perturbation is opposite to that of the shear wave and density such that little tube wave can be generated if the compressional and shear velocities are both increased or decreased accordingly. Unlike the tube wave excited in the borehole when an incident plane wave hits a fracture, the reflected and transmitted tube waves generated at a layer boundary show opposite polarities.

Borehole Effects On Downhole Seismic Measurements

2019-04-12T21:17:25Z

Borehole Effects On Downhole Seismic Measurements Peng, Chengbin; Cheng, C. H.; Toksoz, M. N. An exact formulation for borehole coupling, which is valid for all frequencies and all azimuthally symmetric and nonsymrnetric components, is given in this paper. The borehole effects on downhole measurements are studied in detail as functions of frequency, incidence angle and polarization of an incident wave as well as geophone orientation. We found that correction of the borehole effect for downhole measurements should be made for frequencies above 500 Hz in a hard formation. In a soft formation, if the incidence angle is well away from the resonance angle for a SV incidence, no borehole correction is needed for frequencies below 300 Hz; while for frequencies above 300 Hz, the borehole can cause severe problems on downhole measurements. The borehole can also significantly alter the particle motion direction such that horizontal components rotation from data itself is unreliable for experiments with frequencies above 1 kHz in the hard formation and around 500 Hz in the soft formation.

Numerical Simulation Of The Acoustic And Elastic Wavefields Radiated By A Source In A Fluid-Filled Borehole Embedded In A Layered Medium

2019-04-10T18:05:08Z

Numerical Simulation Of The Acoustic And Elastic Wavefields Radiated By A Source In A Fluid-Filled Borehole Embedded In A Layered Medium Bouchon, Michel We present a method of calculation to simulate the propagation of acoustic and elastic waves generated by a borehole source embedded in a layered medium. The method is formulated as a boundary element technique where the Green's functions are calculated by the discrete wavenumber method. The restrictive assumptions are that the borehole is cylindrical and that its axis runs normal to the layer interfaces. The method is used to generate synthetic acoustic logs and to investigate the wavefield radiated into the formation. The simulations considered display the Stoneley wave reflections at the bed boundaries and show the importance of the diffraction which takes place where the borehole wall intersects the layer interfaces.

Radiation Patterns Of Compressional And Shear Transducers At The Surface Of An Elastic Half Space

2019-04-10T18:05:09Z

Radiation Patterns Of Compressional And Shear Transducers At The Surface Of An Elastic Half Space Tang, X. M.; Zhu, Zhenya; Toksoz, M. N. The radiation patterns of an elastic wave field generated by circular plane compressional and shear transducers are derived using the method of steepest descent. These patterns contain both effects of the elastic half space and the amplitude modulation due to the finite dimension of the piston source. Behaviors of radiation patterns of the generated compressional and shear waves are shown for low, medium, and high frequencies. Laboratory experiments have been performed to measure radiation patterns of compressional and shear transducers. Theory and experiment are found to be in good agreement.

Experimental And Finite Difference Modelling Of Borehole Mach Waves

2019-04-12T20:31:20Z

Experimental And Finite Difference Modelling Of Borehole Mach Waves Cheng, N. Y.; Zhu, Zhenya; Cheng, C. H.; Toksoz, M. N. A series of model experiments are done in the ultrasonic laboratory to study the radiation of downhole sources in a variety of formations. Three models are used in the experiments. They are a lucite model, a lucite model with free glass pipe in the center, and a glass cased soil model. In addition, the finite difference modelling technique is used to simulate the wave propagation in these models and the results of the laboratory and numerical experiments are compared. In the lucite borehole model the waveforms recorded in the experiment agree very well with the finite difference synthetics. The snapshots of the wavefield from finite difference simulation show the radiation pattern of the P and S wave in the lucite formation. These patterns are consistent with the theoretical calculations. In the lucite model with the free glass pipe, the finite difference synthetics are also in good agreement with the experimental observations, especially for the conical P-wave arrival. The angle between the wavefront of the conical P wave and the borehole axis observed from the snapshot agrees with the theory. In the cased soil model the arrival time of the finite difference synthetics is in good agreement with the lab measurements. The relative amplitudes of the P wave and Mach wave are not correctly modelled because of no intrinsic attenuation in the finite difference calculation. The Mach cone angle from the snapshot agrees with the theoretical prediction. Finally the finite difference method is used to simulate the Mach wave propagation in the formation with two horizontal layers. In the two slow formation layers case, Mach wave generated in the first layer reflected back from and transmitted through the boundary and another Mach wave is generated at the second layer when the Stoneley wave travels into the second layer. In the one slow and the one fast formation layer case, the Mach wave generated in the slow formation is reflected back at the boundary and leaked into the fast formation layer. There is no Mach wave in the fast formation layer.

Crack Models For A Transversely Anisotropic Medium

2019-04-12T20:31:19Z

Crack Models For A Transversely Anisotropic Medium Cheng, C. H. A commonly used model for a transversely anisotropic crack rock is that by Hudson (1980, 1981). This model is based on a simplified analysis of a thin circular crack, with displacement and stress conditions specified on the boundary. These papers have a second order correction in addition to the first order term in porosity/crack density. In this paper we compare the results of Hudson with those of Anderson et al. (1974) and Cheng (1978) using the long wavelength static approximation and the ellipsoidal crack model first proposed by Eshelby (1957). We showed that the Hudson model and those based on the complete Eshelby theory agree for small aspect ratio cracks and small crack densities, as expected, provided the weak inclusion version of Hudson's model (1981) is used. For larger crack densities but small aspect ratios, Hudson's first order term agrees with the Eshelby solution. The expansion in the second order term in crack density is an asymptotic series and not a uniformly converging series. Thus there is no general statement one can make about the accuracy of the second order expansion that is valid for a variety of situations. A new expansion based on the Pade approximation is proposed which is identical to Hudson's expansion up to second order in density. This expansion avoids some of the problems associated with Hudson's second order expansion such as increasing moduli with crack density at relatively small crack densities.

A Short Note On Permeability Anisotropy In Heterogeneous Porous Media

2019-04-10T20:48:49Z

A Short Note On Permeability Anisotropy In Heterogeneous Porous Media Zhao, Xiaomin; Toksoz, M. Nafi This paper presents some new results of theoretical modeling on permeability anisotropy in heterogeneous porous media. It is shown that the lineation of heterogeneities results ·in permeability anisotropy. However, to produce strong anisotropy, the permeability contrast between the lineated high permeability region and the background must be very high. We demonstrate this using two examples. The first is the fracture model in which the background has negligible permeability compared to the fractures. In the second example the fractures are replaced by impermeable stripes and the background has high permeability. In both cases permeability anisotropy with an order of magnitude difference is produced. These results compare well with the results of laboratory experiments performed to evaluate permeability anisotropy.

Dynamic Fluid Flow In Heterogeneous Porous Media And Through A Single Fracture With Rough Surfaces

2019-04-12T20:30:53Z

Dynamic Fluid Flow In Heterogeneous Porous Media And Through A Single Fracture With Rough Surfaces Zhao, Xiaomin; Cheng, C. H.; Tang, Xiaoming; Toksoz, M. Nafi This study investigates the frequency-dependence of fluid flow in heterogeneous porous media using the theory of dynamic permeability and a finite-difference method. Given a permeability distribution, the dynamic permeability is applied locally to calculate the frequency-dependence of fluid flow at each local point. An iterative Alternating Direction Implicit finite-difference technique is applied to calculate the flow field in the frequency domain. We compare the flow through a 2-D heterogeneous porous medium and that through an equivalent homogeneous medium and find that the two media do not behave equivalently as a function of frequency. At very low-frequencies, the heterogeneous medium is less conductive than the homogeneous medium, However, in the transition region from quasi-static to dynamic regimes, the former medium becomes more conductive than the latter medium, with the ratio of the former flow over the latter flow reaching a maximum in this region. The larger the scale, or the higher the degree of the heterogeneity, the higher this maximum is. This finding is important for studying the interaction of a borehole stoneley wave with a heterogeneous porous formation. The finite-difference technique is also applied to simulate frequency-dependent flow through a single fracture with rough surfaces. It is shown that the flow exhibits strong frequency-dependence even for small fractures with contacting surfaces. The amount of flow through the fracture is reduced by the surface roughness .

Transient Fluid Flow In Heterogeneous Porous Media

2019-04-12T20:31:19Z

Transient Fluid Flow In Heterogeneous Porous Media Zhao, Xiaomin; Toksoz, M. Nafi A stable Alternating Direction Implicit finite-difference algorithm is used to model transient fluid flow in heterogeneous porous media. In connection with the laboratory system for pressure transient testing of core permeability, the effects of permeability heterogeneities on the characteristics of the pressure transient were investigated. The results show that the early portion of the pressure transient is sensitive to the heterogeneity, while the late time portion is primarily controlled by the effective permeability of the sample. As in the steady flow case, lineation in permeability distribution produces anisotropy in measured permeability. Particularly, in the case of lineated fractures, where the background permeability is small, such anisotropy can produce an order of magnitude difference in permeability.

Modeling The Drag Forces Of Porous Media Acoustics

2019-04-12T20:31:19Z

Modeling The Drag Forces Of Porous Media Acoustics Pride, Steve The drag forces controlling the amount of relative flow induced in a fluid-saturated porous material by a mechanical wave are modeled here from first principles. Specifically, analytical expressions are derived for the drag force in material models that possess variable-width pores; Le., pores that have widths that vary with distance along their axis. The dynamic (complex, frequency-dependent) permeability determined for such a variable-width pore model is compared to estimates made using the models of Johnson, Koplik, and Dashen (JKD) and of Biot. Both the JKD model and the Biot model underestimate the imaginary part of the dynamic permeability at low frequencies with the amount of discrepancy increasing with the severity of the convergent/divergent flow; Le., increasing with the magnitude of the maximum pore-wall slope relative to the channel axis. It is shown how to modify the JKD model to obtain proper low-frequency behavior; however, even with this modification, discrepancies still exist near the transition frequency that separates viscous-force-dominated flow from inertial-force-dominated flow. The amount of discrepancy is again a function of the severity of the convergent/divergent flow (maximum pore-wall slope).

Borehole Stoneley Wave Propagation Across Permeable Structures: Comparison Between Theory And Experiment

2019-04-12T20:31:21Z

Borehole Stoneley Wave Propagation Across Permeable Structures: Comparison Between Theory And Experiment Zhu, Zhenya; Tang, Xiaoming; Cheng, C. H.; Toksoz, M. N. The attenuation of borehole Stoneley waves across a permeable structure (e.g., fractures or fracture zone) is correlated with the permeability of the structure. Using a simplified Biot theory, the structure can be modelled as a permeable porous layer intersecting the borehole. In order to study the effect of such a structure on Stoneley waves and to evaluate the theoretical model, we performed laboratory experiments using ultrasonic borehole models. The porous layer model is made of fine-grained sands with high permeability and porosity. The experiments are carried out with three saturant fluids: water, alcohol, and glycerol. The iso-offset Stoneley waveforms are recorded by moving the source and receiver across the porous layer. In this way, robust estimates of Stoneley wave transmission coefficients are obtained. The experimental transmission coefficients are compared with the theoretical coefficients calculated using the borehole and permeable zone parameters. There is good agreement between theoretical results and experimental results. For low viscosity fluid water and ethyl alcohol, the agreement is very good. For high viscosity fluid, glycerol, the agreement is fair with the experimental Stoneley attenuation higher than the theoretical value.

Estimation Of Formation Parameters Using Full Waveform Acoustic and Shear Wave Logs

2019-04-12T20:31:20Z

Estimation Of Formation Parameters Using Full Waveform Acoustic and Shear Wave Logs Cheng, N. Y.; Cheng, C. H. A combination of borehole Stoneley waves from full waveform acoustic logs and direct shear wave logs was used to estimate formation permeability and shear wave velocity. Data sets used here were collected by Area's array full waveform acoustic logging tool and shear wave logging tool. The P- and S-wave velocities of the formation are determined by threshold detection with cross-correlation correction from the full waveform and the shear wave log, respectively. The full waveform acoustic logging data are also processed using the Extended Prony's method to estimate the borehole Stoneley wave phase velocity and attenuation as a function of frequency. Two different borehole models are considered for the inversion of Stoneley wave velocity and attenuation data. They are the isotropic elastic and the porous isotropic borehole models. Inversion parameters include shear wave velocity and formation permeability. Inverted shear wave velocities and permeabilities are compared with the shear wave log and the core permeability measurements, respectively, for an integrated interpretation and possible identification of shear wave anisotropy.

Acoustic Waveform Logging - Advances In Theory And Application

2019-04-10T18:05:04Z

Acoustic Waveform Logging - Advances In Theory And Application Cheng, C. H.; Pennington, W. D.; Paillet, F.L. Full-waveform acoustic logging has made significant advances in both theory and application in recent years, and these advances have greatly increased the capability of log analysts to measure the physical properties of formations. Advances in theory provide the analytical tools required to understand the properties of measured seismic waves, and to relate those properties to such quantities as shear and compressional velocity and attenuation, and primary and fracture porosity and permeability of potential reservoir rocks. The theory demonstrates that all parts of recorded waveforms are related to various modes of propagation, even in the case of dipole and quadrupole source logging. However, the theory also indicates that these mode properties can be used to design velocity and attenuation picking schemes, and shows how source frequency spectra can be selected to optimize results in specific applications. Synthetic microseismogram computations are an effective tool in waveform interpretation theory; they demonstrate how shear arrival picks and mode attenuation can be used to compute shear velocity and intrinsic attenuation, and formation permeability for monopole, dipole and quadrupole sources. Array processing of multi-receiver data offers the opportunity to apply even more sophisticated analysis techniques. Synthetic microseismogram data is used to illustrate the application of the maximum-likelihood method, semblance cross-correlation, and Prony's method analysis techniques to determine seismic velocities and attenuations. The interpretation of acoustic waveform logs is illustrated by reviews of various practical applications, including synthetic seismogram generation, lithology determination, estimation of geomechanical properties in situ, permeability estimation, and design of hydraulic fracture operations.

Report Summary

2019-04-10T18:05:04Z

Report Summary Cheng, C. H. This report contains the results of work completed during the tenth year of the Borehole Acoustics and Logging Consortium in the Earth Resources Laboratory at M.l.T. This is the first year that the Consortium has been known under this name, and the first year where the focus of research is evolving to encompass more than just acoustic logging. In this year's report, we have included papers on the wavefield interaction with a borehole, downhole source radiation, flow in porous media, as well as full waveform logging. As we have indicated when we decided to change the name of the Consortium, we will be doing research related to elastic wave propagation and interaction with the borehole and the interpretation of the results. Thus we will be interested in projects from petrophysics to full waveform logging, to single hole imaging and measurement while drilling, to crosshole tomography. In this report we lead off with a comprehensive review of the theory and application of full waveform acoustic logging, followed by a paper on the combined interpretation of full waveform and shear wave logs. We also have a paper on testing our permeable zone model using ultrasonic model experiments. A major portion of this report is devoted to the modeling of fluid flow in fractures and porous rocks. There are papers using both the theoretical and the numerical approach to this problem. There is also a paper on the crack models for anisotropic media. On the borehole acoustics side there are two papers dealing with the interaction of an incoming wavefield with the borehole. One of the papers deals with the displacements and stress around and inside a borehole caused by an incident plane wave (P or S) in the formation. The other concerns the conversion of an incident body wave at a layer boundary intersecting a borehole and the conversion into tube or Stoneley wave energy. Both of these results are important in three component downhole measurements. There are also theoretical, numerical, and ultrasonic model papers on the radiation pattern of downhole sources. A summary of all the papers in this report follows.

Seismic Imaging Of The Velocity Structure And The Location Of A Hydrofrac In A Geothermal Reservoir

2019-04-10T18:05:05Z

Seismic Imaging Of The Velocity Structure And The Location Of A Hydrofrac In A Geothermal Reservoir Block, Lisa V.; Cheng, C. H.; Fehler, Michael C.; Phillips, W. Scott The Los Alamos Hot Dry Rock Reservoir is an experimental geothermal project in north-central New Mexico. A fractured zone was created within otherwise impermeable igneous and metamorphic rock by injecting water into a borehole under high pressure, at about 3.5 km depth. During the injection process, the seismic waves created by the fracturing events were recorded by seismometers located in four nearby boreholes. A subset of the arrival times from these microearthquakes is iteratively inverted for the three-dimensional P-wave and S-wave velocity structures and the hypocenter parameters, using the separation of parameters technique. The inversion results indicate that the P-wave and S-wave velocities decrease by at least 20% within the fractured zone. Also, the hypocenters are rotated into a more compact distribution, elative to the initiallocations found using a homogeneous velocity model, suggesting that the hypocenter locations are significantly improved.

Modeling Fluid Flow In Heterogeneous And Anisotropic Porous Media

2019-04-10T19:22:03Z

Modeling Fluid Flow In Heterogeneous And Anisotropic Porous Media Zhao, Xiaomin; Toksoz, M. Naft Permeability distribution in reservoirs is very important for the flow of water or oil and gas. In this study, the effects of various heterogeneous permeability distributions on the flow field are simulated using the finite difference technique. We have simulated the flow for two types of heterogeneous distributions, one is Gaussian and the other is self-similar or fractal, the latter being much rougher than the former. The results show that the flow is not sensitive to the roughness of the distribution. In the case of lineated heterogeneities, anisotropy in the flow properties occurs. The anisotropy is not very significant if the lineated highly permeable regions are surrounded by less permeable regions. However, in the case of lineated fractures, where the background permeability is small, the flow is very sensitive to the direction of the lineation, such anisotropy can produce orders of magnitude difference in permeability. Furthermore, it is shown that the degree of anisotropy depends on the connectivity of the fractures. The anisotropy decreases with decreasing connectivity.

Simulated Annealing Determination Of Shear Wave Travel Time

2019-04-12T20:30:54Z

Simulated Annealing Determination Of Shear Wave Travel Time Cheng, C. H.; Foley, Jack The method of simulated annealing is introduced to obtain relative moveouts between different depths from an iso-offset section. This method has been shown to be more consistent than conventional picks based on peaks, troughs, or zero crossings especially in situations where the signal-to-noise ratio is low or the wavelet is emergent. This method also provides a means of quantifying the relative confidence in each pick over the entire depth of the well. The method has been applied to the data obtained by the ARCO shear wave logging tool and compared favorably with more conventional estimates of shear wave slowness and was shown to be robust, even in areas of weak arrivals.

Homomorphic Processing Of Acoustic Logging Data

2019-04-11T01:22:22Z

Homomorphic Processing Of Acoustic Logging Data Ellefsen, K. J.; Burns, D. R.; Cheng, C. H. A new processing method, which we developed for the guided waves generated during acoustic logging, accurately estimates the wavenumber when only a few seismograms are available or when the seismograms are irregularly spaced. The estimates of the attenuation coefficient are seemingly accurate when many seismograms are available but are inaccurate when only a few seismograms are available. The new method does not generate any spurious estimates as the Prony-based method does.

The Equivalent Force System Of A Monopole Source In A Fluid-Filled Open Borehole

2019-04-10T18:05:04Z

The Equivalent Force System Of A Monopole Source In A Fluid-Filled Open Borehole Ben-Menahem, Ari; Kostek, Sergio The elastodynamic body-wave field outside a fluid-filled open borehole due to a monopole source in the fluid, is reduced to the radiation-field due to a suitable equivalent force system (EFS) in the absence of the borehole, consisting of a monopole plus a vertical dipole. Theoretical seismograms of the EFS displacements in the solid are shown to be in excellent agreement with those obtained from the exact solution to the fluid-filled open borehole problem.

Secondary Shear Waves From Source Boreholes

2019-04-10T18:05:05Z

Secondary Shear Waves From Source Boreholes Meredith, J . A.; Cheng, C. H.; Toksoz, M. N. The purpose of this paper is to synthesize the most important results of the thesis work of Meredith (1990) concerning radiation from seismic sources in boreholes. Previous studies of radiation from sources in boreholes have been far-field studies and have neglected the explicit contribution of the borehole. In general, this is fine for P-wave radiation and for S-wave radiation into high velocity rocks. However, tube waves "leak" shear conical waves (Mach waves) which propagate when the tube wave velocity is greater than the shear wave velocity of the surrounding medium. These Mach waves are of high amplitude because of the dominance of the tube wave and radiate away from the borehole in a fixed conical shape. The shape of the cone is dependent on the shear wave velocity of the medium and the tube wave velocity. This paper defines the conditions under which these Mach waves exist and thoroughly describes them in a physical sense and less so in a mathematical sense. Finally, the relationship of Mach waves to data sets is examined and how Mach waves may be confused with receiver borehole tube waves. To keep the presentation simple, radiation from axial or torsional sources or radiation from empty boreholes is omitted in this paper but fully addressed in Meredith (1990).

Characterizing Surface Roughness From Pressure-Joint Closure Measurements Using Inversion Procedure

2019-04-12T20:31:12Z

Characterizing Surface Roughness From Pressure-Joint Closure Measurements Using Inversion Procedure Zhao, Xiaomin; Toksoz, M. Nafi An inversion procedure has been formulated to estimate the surface roughness of a joint (fracture) from the measured pressure-closure data. A gamma distribution for the local minima (or maxima) on a topography profile was used to account for the skewness in the measured distribution of the asperities. By using the distribution, the average height [bar over z] and the standard deviation a of the profile can also be characterized. An inversion procedure was formulated based on the modification of the theory proposed by Brown and Scholz (1985) and has been successfully tested with synthetic data. The inversion finds average height [bar over z][subscript 1], standard deviation σ, and average aperture. These three parameters characterize the surface roughness and aperture of a fracture and are the topography parameters governing permeability, electric conductivity and other transport properties of the fracture. Pressure-closure data from laboratory measurement of a rough and a smooth joint were also inverted to find the joint properties. The results agree with the profile measurement quite well. The variations of transport properties of a fracture with pressure are also studied.

Modeling Of Elastic Wave Propagation In A Fluid-Filled Borehole Excited By A Piezoelectric Transducer

2019-04-12T20:31:19Z

Modeling Of Elastic Wave Propagation In A Fluid-Filled Borehole Excited By A Piezoelectric Transducer Kostek, Sergio Acoustic logging is an important geophysical method for obtaining relevant information concerning rock properties in formations traversed by boreholes. Typically, the formation parameters that are measured are the compressional, shear, and Stoneley wave slownesses, which are related to important petrophysical parameters such as porosity, permeability, etc. Theoretical waveform modeling has played an important role in helping to understand the complex wave pattern setup in the borehole, and many processing algorithms have come out of this improved understanding. However, in the presence of formation inhomogeneities and borehole irregularities, which are the most common situations found in practice, no satisfactory modeling scheme has yet been presented. Furthermore, source and receivers have been treated as idealized pointwise transducers, with isotropic radiation patterns. As new applications of full waveform acoustic logs arise, such as sonic imaging, cross-well tomography, etc., a better understanding of the wave phenomena including excitation, propagation, scattering, and detection is necessary for inverting the recorded wavefield. In this paper a velocity-stress finite-difference model is presented for a cylindrical piezoelectric transducer in a borehole. The transducer may be free-flooded or capped, and a variety of support and auxilliary structures may be included. The borehole may be irregular and the surrounding formation inhomogeneous. The model is two-dimensional in that azimuthal symmetry is assumed. The description of the tranducer is a full elasto-electromagnetic one, including transverse isotropy in the elastic, dielectric, and piezoelectric parameters, and dissipation in the piezoelectric material. The borehole propagation portion of the model is verified by comparison with a standard transform technique. Predictions of the model for a piezoelectric cylinder radiating into a fluid medium are compared to experimental results with excellent agreement. The radiation patterns of a bare transducer near resonance frequencies are quite anisotropic. Acoustic waveforms in a borehole excited by a finite sized cylindrical transducer are displayed and are quite different from those excited by an ideal point pressure source. The effect of borehole loading upon the impedance of the transducer is shown to be small.

Effects Of A Logging Tool On The Stoneley Wave Propagation In Elastic And Porous Formations

2019-04-10T18:05:04Z

Effects Of A Logging Tool On The Stoneley Wave Propagation In Elastic And Porous Formations Tang, X. M.; Cheng, C. H. A detailed study is carried out to investigate the effects of an acoustic logging tool on the propagation characteristics of Stoneley waves in both elastic and porous formations. In an elastic formation, the presence of the tool in the borehole reduces the Stoneley velocity and enhances the Stoneley wave excitation. When intrinsic attenuation due to formation and bore fluid anelasticity is present, the tool reduces Stoneley attenuation due to fluid and increases the attenuation due to formation. For a permeable porous formation, the simplified Biot-Rosenbaum model of Tang et al. (1990) is modified to incorporate the effects of the tool on the Stoneley propagation. The presence of the tool increases the sensitivity of the Stoneley waves to the formation flow properties. Specifically, the dispersion of Stoneley velocity due to formation permeability is increased and the attenuation of the Stoneley waves is more pronounced, compared with the results without the tool. Consequently, in the determination of formation flow properties using Stoneley wave measurements, the effects of permeability may be better estimated using a tool with large diameter.

Modeling Borehole Stoneley Wave Propagation Across Permeable In-Situ Fractures

2019-04-09T15:51:38Z

Modeling Borehole Stoneley Wave Propagation Across Permeable In-Situ Fractures Tang, X. M.; Cheng, C. H.; Paillet, F. L. The characterization of hydraulic transmissivity of permeable fracture reservoirs is a very important task in the exploration of water resources and hydrocarbons. Previous studies that model the permeable structure as a single fluid-filled fracture failed to explain the observed significant Stoneley wave attenuation across the permeable structure. In this paper, the structure is modeled as a permeable fracture zone and synthetic Stoneley wave seismograms in the vicinity of the structure are calculated. The results show that Stoneley waves can be strongly attenuated or even eliminated without significant reflection, because of the dissipation of wave energy into the permeable zone. Several field cases are also modeled and the theoretical results are compared with the field data. It is shown that low- and medium-frequency Stoneley waves (1 kHz data from Moodus, Conneticut, and 5 kHz data from Monitoba, Canada) are very sensitive to the permeability of the fractures and can be used to assess permeability from in-situ logging data, if the fracture porosity and zone thickness can be measured. At high frequencies, however, Stoneley waves are not very sensitive to permeability but are mainly affected by the sum of the fracture openings expressed as the product of fracture zone thickness and porosity in the fracture zone. This finding is demonstrated by a logging data set (Monitoba, Canada) obtained using high-frequency Stoneley waves at 34 kHz.

Borehole Stoneley Wave Propagation Across Heterogeneous And Permeable Structures

2019-04-12T20:31:12Z

Borehole Stoneley Wave Propagation Across Heterogeneous And Permeable Structures Tang, X. M.; Cheng, C. H. This study investigates the propagation of borehole Stoneley waves across heterogeneous and permeable structures. By modeling the structure as a zone intersecting the borehole, a simple one-dimensional theory is formulated to treat the interaction of the Stoneley wave with the structure. This is possible because the Stoneley wave is a guided wave, with no geometric spreading as it propagates along the borehole. The interaction occurs because the zone and the surrounding formation possess different Stoneley wavenumbers. Given appropriate representations of the wavenumber, the theory can be applied to treat a variety of structures. Specifically, four types of such structures are studied, a fluidfilled fracture (horizontal or inclined), an elastic layer of different properties, a permeable porous layer, and a layer with permeable fractures. The application to the fluid-filled planar fracture shows that the present theory is fully consistent with the existing theory and accounts for the effect of the vertical extent of an inclined fracture. In the case of an elastic layer, the predicted multiple reflections show that the theory captures the wave phenomena of a layer structure. Of special interest are the cases of permeable porous zones and fracture zones. The results show that, while Stoneley reflection is generated, strong Stoneley wave attenuation is produced across a very permeable zone. This result is particularly important in explaining the observed strong Stoneley attenuation at major fractures, while it has been a difficulty to explain the attenuation in terms of the planar fracture theory. In addition, by using a simple and sufficiently accurate theory to model the effects of the permeable zone, a fast and efficient method is developed to characterize the fluid transport properties of a permeable fracture zone. Tills method may be used to provide a useful tool in fracture detection and characterization.

Report Summary

2019-04-11T01:22:22Z

Report Summary Cheng, C. H. This report contains the results of work completed during the ninth year of the Full Waveform Acoustic Logging Consortium in the Earth Resources Laboratory at M.LT. During the past year, we have started the evolution from purely full waveform acoustic logging to more problems dealing with the broader perspective of borehole acoustics. As of April 1, 1991, tills Consortium will be known as the Borehole Acoustics and Logging Consortium. Our research in the past year reflects the beginning of tills change. We have continued to work on the problem of logging in fractured formations. We have developed a method of calculating the reflection and transmission of Stoneley wave energy through a variety of different elastic and permeable formations using a onedimensional wave equation approximation for the Stoneley wave. By doing so, we are able to model isolated fractures, fracture zones, and porous zones. Tills method matches the field data from fracture zones much better than the isolated fracture approach. We have started to work in the area of source radiation from the borehole and the resulting radiation pattern observed in the formation. Tills is for applications in crosshole tomography as well as single hole imaging. As a part of tills work, we are studying the piezoelectric response of transducers. On a more microscopic level, we are also studying the crack and fracture surfaces in core samples, how the roughness of the surface is affecting seismic and flow measurements. This allows us to relate in situ seismic velocities and attenuation to petrophysical parameters which are the actual objectives of many geophysical measurements. There are two papers dealing with the processing of full waveform data, and a paper on the seismic imaging of a hydrofrac using travel time information. A summary of all the papers in this report follows.

Modelling Of Downhole Seismic Sources II: An Analysis Of The Heelan/Brekhovskikh Results And Comparison Of Point Source Radiation To Radiation From Boreholes

2019-04-10T18:05:05Z

Modelling Of Downhole Seismic Sources II: An Analysis Of The Heelan/Brekhovskikh Results And Comparison Of Point Source Radiation To Radiation From Boreholes Meredith, J. A.; Cheng, C. H.; Toksoz, M. N. The work of Heelan (1952, 1953a,b) was one of the first studies of wave propagation from a cylindrical boundary. Heelan attempted to model the radiation emanating from a cylindrical shot hole filled with dynamite. To do so he applied a constant stress to a finite length of an empty infinite cylindrical cavity embedded in an infinite elastic, homogeneous medium. The stresses he considered were axial, torsional, and radial stresses. The radial and axial stresses were required to be proportional to each other and of the same duration. To date Heelan's work has been referenced in over 100 articles and 15 different journals including recent works (Paulsson, 1988) . His results have also been compared with results from the reciprocity theorem (White, 1953, 1960) and played an integral part of important books including those by Brekhovskikh (1960, 1980) and White (1965, 1983). His fundamental contributions were the description of shear wave lobes, the famous four-leaved rose, generated from a radial source in a borehole and that the radiation patterns for an axial source and a torsional source in a borehole have the same geometries as the point axial and torsional sources in infinite media. Despite the importance of this work, Heelan's results have been criticized by Jordan (1962) who dismissed the work as mathematically unsound and Abo-Zena (1977) who devoted an appendix of his 1977 paper to criticizing Heelan's results. The main point of contention has been the use of contour analysis in his first paper (Heelan, 1953a). Although Heelan's work did not include a fluid-filled borehole which is a crucial omission for our purposes, his work may nonetheless be seen as a starting point for the modelling of downhole seismic sources. For instance, Lee and Balch (1982) developed radiation patterns for fluid boreholes which were simple extensions of Heelan's results. Additionally, one particular application of Heelan's theory is in the preliminary development of downhole seismic Sources that often require dry holes until the electronics can be properly shielded. For that reason, an exhaustive examination of the mathematics and physics that went into Heelan's first paper was undertaken to determine if his formulation was correct. The fundamental basis of Heelan's work was a variant of the Sommerfeld integral, an integral of cylindrical waves, in which he unfortunately did not specify the contour. To overcome this obstacle of an unknown contour a parallel method suggested by Brekhovskikh (1960, 1980) was implemented. Brekhovskikh used the Weyl integral, an integral over plane waves, to duplicate Heelan's results for the radial and torsional stresses. However he does no justification of the extensive algebra or analysis involved and does not include the effects of axial stress. Thus in this paper, we have completed and elucidated the work that Brekhovskikh initiated and moreover indirectly verified that Heelan's results were correct. Additionally, we found that Abo-Zena's and Heelan's initial formulations were equivalent. The only difference was in a reversal of the separation of variables procedure necessary to replicate this work and also in Abo-Zena's USe of the Laplace transform where Heelan used the Fourier transform. However, Abo-Zena's results do extend Heelan's by allowing the source function to vary over the distance in which it is applied. The far field results of Abo-Zena and Heelan are equivalent (White, 1983) only if a 1/μ correction is applied to Abo-Zena's results. The first half of this paper is very involved mathematically but much of the algebra is relegated to Appendix A. Having verified that Heelan's results were correct we then proceed to compare Heelan's results with well established point source representations known in the literature (White, 1983) and also with radiation patterns from point sources and stress sources in a fluid-filled borehole (Lee and Balch, 1982). These comparisons will help us isolate the propagation effects of the fluid and the geometrical effect of the borehole. One unique aspect to our approach will be the consideration of radiation from boreholes surrounded by varying lithologies instead of just the Poisson solid as is commonly done. The lithologies to be considered include a soft sediment (Pierre shale) and two more indurated sediments, Berea sandstone and Solenhofen limestone. By following this approach we show that the effect on the radiation magnitude can be substantial due to changes in lithology in addition to isolating the relative effects of the borehole and the fluid.

Modelling Of Downhole Seismic Sources I: Literature Review, Review Of Fundamentals, Impulsive Point Source In A Borehole

2019-04-10T18:05:04Z

Modelling Of Downhole Seismic Sources I: Literature Review, Review Of Fundamentals, Impulsive Point Source In A Borehole Meredith, J. A.; Cheng, C. H.; Toksoz, M. N. This paper represents the first of a two paper sequence comprising a multi-faceted introduction to the numerical and analytical modelling of seismic sources in a borehole. Part one will present a literature review and a review of the fundamental mathematical descriptions of wave propagation outside a borehole. By listing the mathematical descriptions here we can show the equivalence and interrelationships of many treatments presented in the literature. Part one will conclude with an outline of the familiar discrete wavenumber technique as applied to modelling radiation outside a borehole from a point source inside a borehole. Part two will attempt to isolate the effects of the fluid-filled borehole on the radiation of a borehole source by comparing radiation patterns for three cases: a point source in an infinite medium, a stress applied to the wall of an empty borehole (Heelan's (1953) result) and a point source in a fluid-filled borehole (Lee and Balch, 1982). Heelan's results will also be analyzed and defended against criticism of them brought by Jordan (1962) and Abo-Zena (1978). The literature review will be thorough and will include the work done directly on modelling downhole seismic sources and the comparatively larger amount of work done on modelling sources for acoustic logging purposes which is directly applicable. Different authors publishing work on seismic sources have made widely different symmetry assumptions ranging from no symmetry to axisymmetry to symmetry along the z axis. These differences hamper the ability to directly compare results between the different treatments. Compounding the differences in symmetry are the use of different time dependencies ([superscript -iwl], [superscript iwl]) and the use of different Hankel function or modified Bessel function strategies. Therefore, the mathematical fundamentals of wave propagation in a borehole from the different symmetry systems are presented here in a consistent notation and are related to each other and treatments in the literature to help eliminate duplication of effort. Finally, wave propagation outside a borehole is examined using synthetic seismograms. For the synthetic seismograms, a point source inside the borehole is used as a source and the synthetics are calculated using the discrete wavenumber method. The synthetic seismograms are measured along vertical arrays of point receivers placed outside the borehole and for lithologies of Pierre shale, Solenhofen limestone, and Berea sandstone. The method and the resulting seismograms are outlined in this paper along with a brief description of the discrete wavenumber technique.

Lithologic Cycles And Paleo Fluid Flow Channels In Old Oceanic Crust From Geophysical Logs At ODP Site 418A

2019-04-12T20:31:12Z

Lithologic Cycles And Paleo Fluid Flow Channels In Old Oceanic Crust From Geophysical Logs At ODP Site 418A Burns, D. R.; Thompson, D. R.; Cheng, C. H. Using some new processing of the multichannel sonic (MCS) log data from Site 418A, the resulting P, S, and Stoneley wave velocity estimates and apparent attenuation were integrated with the natural gamma, spectral gamma, resistivity, neutron, density, and caliper logs and core lithology information for interpretation of lithologic cycles and possible paleo fluid flow intervals. These data indicate the presence of multiple breccia or rubble zones in the lower portions of the borehole. These zones are interpreted as the last stages of eruptive cycles as described by Hyndman and Salisbury (1984). The results of permeability (packer) tests and temperature gradient measurements at Sites 395A and 504B indicate that fluid flow in the crust at those sites is localized to brecciated zones which occur below massive flow basalts. By analogy, the breccia zones interpreted at Site 418A may have acted as fluid flow channels at an earlier time. Six major paleo fluid flow zones are interpreted at Site 418A. These breccia zones have low velocities (P, S, and Stoneley), increased apparent attenuation, and an increase in gamma activity. These intervals are interpreted as permeable pathways which may have been altered by the second stage of oxidizing alteration as described by Holmes (1988). Breccia units occur just below massive basalt flow units. The massive basalt flow units are also easily identified in the MCS data. The resistivity log data suggest that each major eruptive cycle trend is made up of several smaller sub-cycles. The MCS data provides much insight into the variations in lithology in ODP boreholes. The trace energy provides a stable measure of apparent attenuation which may be related to alteration, fracturing, or permeability (if there are open fractures). Velocity estimates for P, S, and Stoneley waves provide useful information about lithologic variability if interpreted in detail.

Permeability Estimation From Velocity Anisotropy In Fractured Rock

2019-04-12T20:31:19Z

Permeability Estimation From Velocity Anisotropy In Fractured Rock Gibson, Richard L., Jr.; Toksoz, M. Nafi Cracks in a rock mass subjected to a uniaxial stress will be preferentially closed depending on the angle between the fracture normal vectors and the direction of the applied stress. If the prestress fracture orientation distribution is isotropic, the effective elastic properties of such a material after application of the stress are then transversely isotropic due to the overall alignment of the cracks still open. Velocity measurements in multiple directions are used to invert for the probability density function describing orientations of crack normals in such a rock. This is accomplished by expanding the crack orientation distribution function into generalized spherical harmonics. The coefficients in this expansion are functions of the crack density and the crack aspect ratio distribution. The information on fracture distribution obtained from the velocity inversion allows an estimation of the anisotropic permeability of the fractured rock system. Permeability estimates are based on the number of cracks open of each aspect ratio, and the contribution of a given crack is weighted by the cosine of the angle between the crack and the direction of the applied pressure gradient. This approach yields a prediction of permeability as a function of the angle from the uniaxial stress axis. The inversion for crack orientation is applied to ultrasonic velocity measurements on Barre granite, and permeability predictions for this sample are presented. The inversion results are good and reproduce velocity measurements well, and the permeability predictions show some of the expected trends. Initial comparisons of the predictions with available permeability data, however, show deviations suggesting that further information on partial crack closure and connectivity of cracks should be included in the permeability model.

Inversion For Permeability From Stoneley Wave Velocity And Attenuation

2019-04-12T20:31:11Z

Inversion For Permeability From Stoneley Wave Velocity And Attenuation Cheng, N. Y.; Cheng, C. H.; Toksoz, M. N. The in situ permeability of a formation is obtained by the inversion of Stoneley wave phase velocity and attenuation, which are evaluated by applying the Extended Prony's method to the array sonic logging data. The Maximum Likelihood inversion is used together with logarithmic parameterization of the permeabilities. Formation shear wave velocity is also inverted for. This process is tested on both synthetic and field data. Logarithmic parameterization contributes to rapid convergence of the algorithm. Permeabilities estimated from field data are in good agreement with core measurements.

Finite Difference Modelling Of Acoustic Logs In Vertically Heterogeneous Biot Solids

2019-04-12T20:30:54Z

Finite Difference Modelling Of Acoustic Logs In Vertically Heterogeneous Biot Solids Stephen, Ralph A.; Cheng, N. Y.; Cheng, C. H. This paper discusses the results of tests carried out on a finite difference formulation of Biot's equations for wave propagation in saturated porous media which vary in range and depth (Stephen, 1987). A technique for modeling acoustic logs in two dimensionally varying Biot solids will give insight into the behavior of tube waves at permeable fractures and fissures which intersect the borehole. The code agrees well with other finite difference codes and the discrete wavenumber code for small porosity in the elastic limit of Biot's equations. For large porosity (greater than one per cent) in the elastic limit or for the acoustic limit, good agreement is not obtained with the discrete wavenumber method for vertically homogeneous media. The agreement is worst for amplitudes of the pseudo-Rayleigh wave. The amplitude of the Stoneley wave and the phase velocities of both waves could be acceptable for some applications. An example is shown of propagation across a horizontal high porosity stringer in a Berea sandstone. Reflections from the stringer are observed but given the inaccuracies of the pseudo-Rayleigh waves for vertically heterogeneous media the amplitudes for the stringer model are questionable. We propose a three stage approach for further work: 1) Use the Virieux scheme instead of the Bhasavanija scheme for the finite difference template. The Virieux scheme has been shown in other studies to be more accurate for liquid-solid interfaces. 2) Run the present code for lower frequency sources to emphasize Stoneley waves and diminish pseudo-Rayleigh waves. Stoneley waves are most sensitive to permeability variations which are the primary objective of Biot wave studies. 3) Develop a finite difference code for Biot media with the fluid-solid boundary conditions specifically coded. This code would be suitable for studying constant radius boreholes in vertically varying Biot media.

Acoustic Wave Propagation In A Fluid-Filled Borehole With A Horizontal Fracture

2019-04-10T18:05:07Z

Acoustic Wave Propagation In A Fluid-Filled Borehole With A Horizontal Fracture Tang, X. M.; Cheng, C. H.; Toksaz, M. N. The propagation of guided waves in a fluid-filled borehole with an open horizontal fracture is investigated both theoretically and experimentally. The fracture is modeled as a fluid layer that separates the domain of propagation into two regions. For the solution of the problem, we use a hybrid method to generate wave modes in the two regions. The modes are then summed to match the boundary conditions at the fracture surfaces. A singularity problem arises in matching the surface conditions and is regularized using a physical model based on the conservation of mass. Using the theory developed in this study, we study the transmission and reflection characteristics of borehole guided waves (Le., Stoneley and pseudo-Rayleigh waves) due to the fracture. At low frequencies, the effects of a fracture on the Stoneley wave are dominated by the fluid flow into the fracture. As frequency increases, mode conversion at the fracture becomes significant. Above the cut-off frequency of the pseudo-Rayleigh wave, part of the incident Stoneley wave is converted to pseudo-Rayleigh waves, which is demonstrated by synthetic microseismograms. The pseudo-Rayleigh wave is substantially affected by the fracture. Because this wave requires the formation shear strength to sustain its propagation, even a thin fracture with zero shear strength can significantly attenuate the wave amplitude and produce strong reflection. This effect is more pronounced towards the cut-off frequencies than away from the frequencies. Consequently, the lack of pseudo-Rayleigh energy across a fracture may be used as a sensitive indicator in fracture detection and characterization. Ultrasonic experiments have been performed to measure the transmission of guided waves across laboratory borehole fracture models. For the Stoneley waves, we performed the experiment below the cut-off frequency of the pseudo-Rayleigh wave and the experimental results are in good agreement with the theory. For the pseudo-Rayleigh wave, we performed the experiment in a higher frequency range. The experiment has verified the substantial effects of a fracture on this wave mode. The weak early arrivals of the transmitted waves have also been observed for thin as well as thick fractures. This confirms the theoretical prediction that the transmission of the pseudo-Rayleigh wave is the smallest towards the cut-off frequencies. The measured transmission coefficients agree with theoretical results. In summary, we have presented an analysis on the guided wave propagation across a borehole horizontal fracture. The wave characteristics in the vicinity of a fracture as described in this study may be used to provide useful information for the detection and characterization of borehole fractures using acoustic logging techniques.

Dynamic Permeability And Borehole Stoneley Waves: A Simplified Biot-Rosenbaum Model

2019-04-10T18:05:04Z

Dynamic Permeability And Borehole Stoneley Waves: A Simplified Biot-Rosenbaum Model Tang, X. M.; Cheng, C. H.; Toksoz, M. N. Stoneley waves in permeable boreholes are diagnostic of formation permeability because their propagation is affected by the dynamic fluid flow at the borehole wall. We characterize this flow using the concept of dynamic permeability. We examined the applicability of the dynamic permeability to porous media by applying it to a single fracture case and found that it agrees excellently with the fracture conductivity derived from an exact solution. In dealing with the interaction of a Stoneley wave with a porous formation, we decompose the problem into two parts. The first is the interaction of the Stoneley with an equivalent elastic formation without fluid flow. The second is the interaction with the flow that is governed by the dynamic permeability. In this manner, we obtained a simple model for the Stoneley propagation in permeable boreholes. We compared the Stoneley wave attenuation and dispersion characteristics from this model with those from the complete model of the Biot-Rosenbaum theory in the case of a hard and a soft formation, respectively. We found that the results from both models agree very well for a hard formation, although they differ at higher frequencies for a soft formation because of the increased solid compressibility. The theoretical predictions from this simple model were also compared with recently published laboratory data of Stoneley wave measurements, performed at both low- and high-frequency regions of Biot theory. The simple model and experiment are in excellent agreement. Because of the simplicity of the model, it can be easily applied to problems concerning Stoneley propagation in permeable boreholes, especially to an inverse problem to extract formation permeability from Stoneley wave measurements.

Effects Of Anisotropy Upon The Normal Modes

2019-04-12T20:31:18Z

Effects Of Anisotropy Upon The Normal Modes Ellefsen, K. J.; Cheng, C. H.; Toksoz, M. N. The effects of anisotropy upon elastic wave propagation along a fluid-filled cylindrical borehole are determined. The wave equation is solved in the frequency-wavenumber domain with a variational method, and the solution yields the phase velocities, group velocities, pressures, and displacements for the normal modes. These properties are studied for two cases: a transversely isotropic model for which the borehole has several different orientations with respect to the symmetry axis and an orthorhombic model for which the borehole is parallel to the intersection of two symmetry planes. The normal modes for these two cases show several significant effects which do not exist when the solid is isotropic or transversely isotropic with its symmetry axis parallel to the borehole: 1. The phase velocities for the quasi-pseudo-Rayleigh, both quasi-flexural, and both quasi-screw waves do not exceed the phase velocity of the slowest qS-wave. (The phase velocities of the leaky modes, which were not investigated, will exceed this threshold. ) 2. The two quasi-flexural waves have different phase and group velocities; the differences are greatest at low frequencies and diminish as the frequency increases. The two quasi-screw waves behave similarly. 3. The greater the difference between the phase velocities of the qS-waves, the greater the difference between the phase velocities of the quasi-flexural waves at all frequencies. The two quasi-screw waves behave similarly. 4. Near the limiting qS-wave velocity, the difference between the phase velocities of the two quasi-flexural waves is greater than that for the two quasi-screw waves. 48 Ellefsen et al. 5. For the slow quasi-flexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the slow qS-wave. 6. For the fast quasi-flexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the fast qS-wave. 7. For the slow quasi-screw wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned along two mutually perpendicular directions which are rotated 45° with respect to the polarizations of both qS-waves. 8. For the fast quasi-screw wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned along two mutually perpendicular directions which are parallel with the polarizations of both qSwaves. (In this list, the qS-waves are those plane waves whose wavenumber vectors are parallel to the borehole.) Despite these significant effects, the general characteristics of the phase and group velocities, pressures, and displacements are similar (but not identical) to those that would exist if the solid were isotropic or transversely isotropic with its symmetry axis parallel to the borehole. This result is expected because the models are only slightly anisotropic.

Estimating A Shear Modulus Of A Transversely Isotropic Formation

2019-04-09T16:09:04Z

Estimating A Shear Modulus Of A Transversely Isotropic Formation Ellefsen, K. J.; Cheng, C. H.; Toksoz, M. N. A method to estimate c[subscript 66], which is a shear modulus of a transversely isotropic formation (with its symmetry axis parallel to the borehole), is developed and tested. The inversion for c[subscript 66] is based upon a cost function which has three terms: a measure of the misfit between the observed and predicted wavenumbers, a measure of the misfit between the current estimate for c[subscript 66] and the initial guess of its value, and penalty functions which constrain the estimate for c[subscript 66] to physically acceptable values. The inversion is applied to synthetic data for fast and slow formations, and the estimates for c[subscript 66] are within 5% of their correct values and are well resolved. The inversion is applied to field data from a formation which consists mostly of siltstone. All estimates for c[subscript 66] are significantly higher than for c[subscript 44] , and the S-wave anisotropy generally ranges from 19 to 24%.

Report Summary

2019-04-10T18:05:07Z

Report Summary Cheng, C. H. This report contains the results of work completed during the eighth year of the Full Waveform Acoustic Logging Consortium in the Earth Resources Laboratory at M.I.T. During the past year, we were able to accomplish many of the goals we had set out to do. We have concentrated our efforts in understanding logging in fractured and anisotropic media, so as to enable us to infer for the properties of the media from full waveform acoustic logs. For logging in fractured media, we have developed the theory of scattering of Stoneley wave by a horizontal fracture, as well as transmissions through the fracture and attenuation by the fracture. We have also developed the theory for the case when the fractures are small compared to the wavelength of the rock and we have an effective anisotropic medium. In the case of a horizontally layered medium such as a shale, we can invert for the degree of shear wave anisotropy using the Stoneley wave velocity. In the area of logging in permeable formations, we have developed a much sim plified theory that gives similar results as the Biot-Rosenbaum theory. We have also coded the latter for finite-difference modelling. We have developed an inversion algorithm which gives formation permeability from Stoneley wave phase velocity and attenuation. The algorithm gives good results when compared with core permeability measurements. On other related topics, in petrophysics we have a report on the estimation of formation permeability from velocity anisotropy measurements. We have also extended our research away from the borehole to a crosshole situation. We have calculated the near and far field radiation pattern in the formation from a point source inside the borehole. This knowledge is critical in the application of diffraction tomography to crosshole measurements. The following is a summary of the papers in this report.

Velocity Anisotropy Of Two Deep Crystalline Samples

2019-04-10T18:05:03Z

Velocity Anisotropy Of Two Deep Crystalline Samples Mendelson, Jim; Toksoz, M. N. Using ultrasonic velocity measurements taken over a multiplicity of directions we show that samples exhibit weak to moderate anisotropy of seismic velocities. We further define the anisotropic geometry with high resolution scanning electron microscopy. Our data indicate that one sample, a granite, is transversely anisotropic, and that the presence of fine to moderately fine microcracks is the most important factor effecting the velocities. We model the angular velocity dependence using 5 elastic constants and show that all 9 observed velocities fit these predictions to within 0.1 km/s. We are unable to obtain similar fits to a second sample, a mica-schist, in the same fashion. SEM observations indicate this rock displays orthorhombic symmetry. We made additional velocity measurements in order to calculate 9 elastic constants, and found that the predicted angular velocity dependence agreed much better with our velocity observations.

Pore Geometry And Permeability Modeling From Pressure Dependence Of Transport Properties In Sandstone

2019-04-10T18:05:06Z

Pore Geometry And Permeability Modeling From Pressure Dependence Of Transport Properties In Sandstone Bernabe, Yves In this paper, a model of the pore geometry of sandstones is proposed. Three categories of pores are considered: large spherical pores at 4-grain vertices, tube-like throats at 3-grain edges and narrow sheet-like throats at 2-grain faces. Tube-like and sheet-like throats control the transport properties whereas nodal pores dominate the storing capacity. Tube-like throats tend to enhance permeability and improve accessibility to the storage pore space. Exploiting the fact that these different types of pores .respond very differently to pressure, it is possible to evaluate the volume fraction of each category of pores in the framework of a simple capillary model. This approach was applied to data from the literature. Satisfactory fit was obtained for most of the sandstones considered. The exceptions seemed to be associated with high clay content which was not accounted for by the model.

Theoretical Models Relating Acoustic Tube-Wave Attenuation To Fracture Permeability - Reconciling Model Results With Field Data

2019-04-12T20:31:13Z

Theoretical Models Relating Acoustic Tube-Wave Attenuation To Fracture Permeability - Reconciling Model Results With Field Data Cheng, C. H.; Tang, X. M.; Paillet, F . L. Several recent investigations indicate that tube-wave amplitude attenuation in acoustic full-waveform logs is correlated with permeability in fractured rocks. However, there are significant differences between predictions based on theoretical models for tubewave propagation and experimental waveform amplitude data. This investigation reviews the results of existing theoretical models for tube-wave attenuation in fractured rock and compares model predictions with acoustic full-waveform data where extensive independent fracture-permeability data are available from straddle-packer permeability tests. None of the tube-wave models presented in the literature predicts attenuation at fracture apertures as small as those producing attenuation in the field; and most models predict tube-wave reflections, which are rarely measured at frequencies greater then 5 kHz. Even the unrealistic assumption that all of the tube-wave energy loss is caused by viscous dissipation in fracture openings does not result in predicted apertures being as small as those indicated by packer permeability measurements in most situations. On the basis of these results, it is concluded that plane-fracture models cannot account for the measured tube-wave attenuation where natural fractures intersect fluidfilled boreholes. However, natural fractures are fundamentally different from plane parallel passages. This difference appears to explain the small equivalent flow apertures and lack of reflections associated with fractures in waveform-log data. Permeable fracture openings modeled as irregular tubes embedded between asperities along the fracture face are predicted to produce significant tube-wave attenuation when tube diameters exceed 1.0 cm, but arrays of such tubes conduct fluid flow equivalent to that through plane fractures less than 2 mm in effective flow aperture. Although the theory predicts some reflection from simple cylindrical passages, scattering from irregular distributions of natural fracture openings probably accounts for the infrequency with which coherent tube-wave reflections occur in field data.

Multi-Shot Processing For Better Velocity Determination

2019-04-10T18:05:06Z

Multi-Shot Processing For Better Velocity Determination Mendelson, Jim We develop a linear programming inversion scheme to estimate lithology from well log data. The inversion described severely limits the dependence on core retrieval, and makes accurate mapping of new parameters possible. There are no limitations on the number of input well logs or output lithologic fractions. Because the method uses an L-I norm error measure, it should be more ·robust than otherwise similar techniques. Other advantages of the technique include the straightforward imposition of inequality constraints, and strictly positive volume fraction results. As specific examples we apply the method in a variety of geologic situations, and compare our results to those achieved via coring. We also test the new method against conventional least squares inversion algorithms. While both methods perform well, the linear programming inversion yields improved results when formation petrophysical properties are not known accurately.

Multi-Shot Processing For Better Velocity Determination

2019-04-12T20:31:13Z

Multi-Shot Processing For Better Velocity Determination Thompson, Delaine; Burns, Dan We perform a technique called multi-shot processing on a section of 12-channel sonic logs in order to better resolve compressional and shear velocities. The data are from the ODP Leg 102 cruise, which occupied drill site 418A near the Bermuda Rise in 1985. Multi-shot processing has been done on a 9 meter section of this data, using different combinations of numbers of shots vs. numbers of receivers in an attempt to compare the vertical resolution and stability of this processing method. The method is stable only with certain shot-to-receiver subarray combinations. This paper demonstrates that the optimum combinations using this set of data are 4 shots with 6 receivers apiece, and 3 shots with 8 receivers each. While a combination using 5 shots with 4 receivers is possible, the method produces spurious results. This may be because of spatial aliasing over too few receivers, or it may be a result of poor outside control over the entire experiment (ship heave, etc.). It is hoped that an optimum subarray combination can be used to resolve velocities over shorter array lengths using the redundancy in the sonic data. This would result in a greater ability to characterize fracturing and alteration in the oceanic crust, since velocity variations have been shown to correlate with fracture zones.

The Full Waveform Acoustic Log Inversion Problem

2019-04-10T18:05:06Z

The Full Waveform Acoustic Log Inversion Problem Garcia, G. H.; Cheng, C. H. This paper presents the full waveform acoustic log inversion problem for a multisource - multireceiver tool logging a cylindrical fluid-filled borehole. The problem is formulated in the frequency-depth domain. A priori knowledge about the source array spectra and the borehole formation parameters (velocity, attenuation, density) is taken Into account. It is shown that the inversion problem can be formulated as a Separable Nonlinear Least Squares (SNLS) problem with separable nonlinear equality constraints. The case where the source is known and parameterized is studied with synthetic data and an inversion for V[subscript p], V[subscript s], V[subscript f] and P[subscript b] is implemented and studied.

Evaluation And Prediction Of Shear Wave Velocities In Soft Marine Sediments

2019-04-10T18:05:05Z

Evaluation And Prediction Of Shear Wave Velocities In Soft Marine Sediments Meredith, J . A.; Wilkens, R. H.; Cheng, C. H. Shear wave velocities from full waveform acoustic logs were determined at DSDP Site 613 using the spectral ratio inversion method. Discrete shear wave velocities for a 350 meter interval at 0.5-2 meter depth increments were calculated. Shear wave velocities were not evaluated for the upper 130m of the log because of data recording problems. The sediments of Site 613 represent a progression from carbonaceous-siliceous oozes through partial lithification and cementation. A method for predicting shear wave velocities using Wood's equation, the bulk moduli of water and carbonate grains, the P-wave velocity and porosity from well logs will be described. The predictions of this method provided a theoretical maximum value for the shear wave velocity to compare with the inversion results. In general, the method works well for shear wave velocities greater than 800 m/s. The inverted data fall just below the predicted theoretical maximum value from Wood's equation and agree quite well with the trends. Below this velocity threshold, trends with depth and Poisson's ratio and the divergence of the inversion itself seem to indicate incorrect behavior.

Permeability Estimation From Velocity Anisotropy In Fractured Rock

2019-04-11T03:23:08Z

Experimental Verification of Acoustic Waveform and VSP Seismic Tube Wave Measurements of Fracture Permeability

2019-04-10T18:05:03Z

Experimental Verification of Acoustic Waveform and VSP Seismic Tube Wave Measurements of Fracture Permeability Paillet, Frederick L.; Cheng, C. H.; Hsieh, Paul A variety of established and experimental geophysical techniques was used to measure the vertical distribution of fracture permeability in a 229-meter deep borehole penetrating schist and quartz monzonite near Mirror Lake, New Hampshire. The distribution of fractures in the borehole was determined by acoustic borehole televiewer and other geophysical logs. Fracture permeability was estimated by application of two experimental methods: (1) Analysis of tube-wave-amplitude attenuation in acoustic full-waveform logs; and (2) interpretation of tube waves generated in vertical seismic profiles. Independent information on fracture permeability was obtained by means of packer-isolation flow tests and flowmeter measurement of vertical velocity distributions during pumping in the same borehole. Both experimental methods and packer-isolation-flow tests and flowmeter data indicated a single, near horizontal zone of permeability intersecting the borehole at a depth of about 45 meters. Smaller values of transmissivity were indicated for other fractures at deeper depths, with details of fracture response related to the apparent volume of rock represented by the individual measurements. Tube-wave amplitude attenuation in full-waveform acoustic logs, packer-isolation flow tests, and flowmeter measurements during pumping indicated transmissivity values for the upper permeability zone within the range of 0.6 to 10.0 centimeters squared per second. Vertical seismic-profile data indicated a relative distribution of fracture permeability in agreement with the other methods; however, the calculated values of transmissivity appeared to be too small. This disagreement is attributed to oversimplification of the model for fracture-zone compressibility used in the analysis of vertical seismic-profile data.

Full Waveform Inversion of P Waves for V[subscript s] and Q[subscript p]

2019-04-11T01:22:14Z

Full Waveform Inversion of P Waves for V[subscript s] and Q[subscript p] Cheng, C. H. We present an indirect method of determining shear wave velocities from full waveform acoustic logs based on the inversion of the spectral ratio of the P-wave trains at two source-receiver separations. This method simultaneously inverts for the formation shear wave velocity and compressional wave attenuation. The P-wave response is calculated by means of branch-cut integration. This method is useful in "soft" formations where the shear wave velocity is lower than the acoustic velocity of the borehole fluid and thus there are no refracted shear wave or pseudo-Rayleigh wave arrivals. The method is shown to give good estimates of formation shear wave velocity in both synthetic and field data. The inversion algorithm is sensitive to local minima; care must be taken to avoid them.

Estimating The Elastic Moduli Of Transversely Isotropic Formations

2019-04-12T20:30:47Z

Estimating The Elastic Moduli Of Transversely Isotropic Formations Ellefsen, K. J.; Cheng, C. H. Using acoustic logging data, we develop a method of estimating the horizontal shear modulus C[subscript 66]) of a transversely isotropic formation with its axis of symmetry parallel to that of the borehole. The data for the inversion are the wavenumbers, at every frequency, of the guided waves. The inversion minimizes the difference between these observed wavenumbers and those calculated by a forward model. The final estimates of the elastic moduli are constrained by the a priori estimates of their values and by the requirement to keep the stiffness tensor positive definite. The inversion produced similar results when it was applied to synthetic data from hard and soft formations. The estimate for the shear modulus, C[subscript 66], was fairly accurate because this parameter is moderately well resolved. The estimates for C[subscript ll] and C[subscript 13] are inaccurate because they are poorly resolved by the data. Tight constraints on the fluid modulus prevent this parameter from changing. much. The inversion did not attempt to estimate either C[subscript 33] or C[subscript 44] because they can be determined from the refracted P - and S-waves or the flexural wave.

Stoneley Wave Propagation In A Fluid-Filled Borehole With A Vertical Fracture

2019-04-09T17:28:42Z

Stoneley Wave Propagation In A Fluid-Filled Borehole With A Vertical Fracture Tang, X. M.; Cheng, C. H.; Toksoz, M. N. The propagation of Stoneley waves in a fluid-filled borehole with a vertical fracture is investigated both theoretically and experimentally. The borehole propagation excites fluid motion in the fracture and the resulting fluid flow at the fracture opening perturbs the fluid-solid interface boundary condition at the borehole wall. By developing a boundary condition perturbation technique for the borehole situation, we have studied the effect of this change in the boundary condition on the Stoneley propagation. Cases of both hard and soft formations have been investigated. It has been shown that the fracture has minimal effects on the Stoneley velocity except in the very low frequency range in which the Stoneley velocity drastically decreases with decreasing frequency. Significant Stoneley wave attenuation is produced because of the energy dissipation into the fracture. In general, the effects of the fracture are more important in the low frequency range than at higher frequencies. The quantitative behavior of these effects depends not only on fracture aperture and borehole radius, but also on the acoustic properties of the formation and fluid. Ultrasonic experiments have been performed to measure Stoneley propagation in laboratory fracture borehole models. Aluminum and lucite were used to simulate a hard and a soft formation, respectively. Array data for wave propagation were obtained and were processed using Prony's method to give velocity and attenuation of Stoneley waves as a function of frequency. In both hard and soft formation cases, the experimental results were found to agree well with the theoretical predictions. The important result of this study is that, we have found a quantitative relationship between the Stoneley propagation and the fracture character in conjunction with formation and fluid properties. This relationship can be used to provide a method for estimating the characteristics of a vertical fracture by means of Stoneley wave measurements.

Wave Propagation In A Fluid-Filled Fracture-An Experimental Study

2019-04-11T01:22:19Z

Wave Propagation In A Fluid-Filled Fracture-An Experimental Study Tang, X. M.; Cheng, C. H. A laboratory experimental study has been carried out to investigate the mode trapping characteristics of a fluid-filled fracture between two elastic solids. Using a small circular cylindrical receiver of 2.7 mm diameter, we were able to measure the wave motion directly inside a 2.8 mm thick fracture and to obtain array data for the propagating waves. The data was processed using Prony's method to give velocity of the wave modes as a function of frequency. The experimental results agree with the theoretical predictions quite well. Specifically, in a "hard" (aluminum) fracture where the shear velocity of the solid is greater than the fluid velocity, four normal modes were detected in the frequency range up to 2.4 MHz. Whereas in a "soft" (lucite) fracture where the shear velocity is smaller than the fluid velocity, four leaky-P modes were detected in the same frequency range. In both cases, a fundamental mode analogous to Stoneley waves in a borehole was detected. In particular, the velocity of this mode approaches zero in the low frequency limit, as indicated by the theory and confirmed by the experiment in a low frequency range down to 25 kHz.

Guided Waves In Slight, Azimuthally Anisotropic Formations

2019-04-12T20:30:49Z

Guided Waves In Slight, Azimuthally Anisotropic Formations Ellefsen, K. J.; Cheng, C. H. A method of calculating dispersion curves for guided waves in slight, azimuthally anisotropic formations is developed with perturbation theory. The fluid is assumed to be inviscid, the formation perfectly elastic and homogeneous, and the ·borehole wall cylindrical. The first step is calculating the elastic moduli for a transversely isotropic formation whose moduli are close to those for the azimuthally anisotropic formation. The perturbative method then uses the particle displacements for a guided wave in the transversely isotropic formation and the difference between the elastic moduli in the two formations to determine a first order correction to the wavenumber. These corrections are used to calculate the perturbation in the phase velocity. To test the method, the elastic moduli of an isotropic formation were pe~turbed to make it transversely isotropic. The exact dispersion curves and those estimated by the perturbative method are very close. The perturbative method was used to calculate dispersion curves for guided waves in two different geologic settings - a formation with aligned, vertical cracks and another with a tilted bed. In both examples the dispersion curves for the guided waves appear similar to typical dispersion curves for either isotropic or transversely isotropic formations. At low frequencies, the phase velocities of the tube waves closely match the velocities predicted by Rice's formula.

Applications Of Perturbation Theory To Acoustic Logging

2019-04-12T20:30:50Z

Applications Of Perturbation Theory To Acoustic Logging Ellefsen, K. J.; Cheng, C. H. For guided wave propagation in boreholes, perturbation theory is used to calculate (1) the partial derivative of the wavenumber or frequency with respect to an elastic modulus or density, (2) group velocity, and (3) the effect of a borehole with a slightly irregular cross section upon the phase velocity. The method, which is developed for a fluid-filled, cylindrical borehole through a transversely isotropic formation, relates perturbations in formation properties (i.e., elastic moduli, densities, and interface locations) and wave properties (i.e., wavenumber and frequency) for guided waves with any azimuthal order number. Velocity perturbations, which are calculated for three common cross sections of irregular boreholes, show several general characteristics. The tube and pseudo-Rayleigh waves, which have no azimuthal dependence, completely smooth the effects of the irregularity making the velocity perturbation independent of the wave's orientation. The perturbations for the tube wave are small because it is a Stoneley wave, but those for the pseudo-Rayleigh wave are much larger because the borehole shape affects the multiply-reflected part of this wave. The velocity perturbations for the flexural and screw waves are similar in character to those for the pseudo-Rayleigh wave, but because these waves are directional, they can interact with the irregularity to amplify or diminish the velocity perturbation.

Report Summary

2019-04-09T15:24:24Z

Report Summary Cheng, C. H. This report contains the results of work completed during the seventh year of the Full Waveform Acoustic Logging Consortium in the Earth Resources Laboratory at M.LT. During the past year, we have been concentrating on the problem of logging in fractured and anisotropic media. We have developed theories for wave propagation in boreholes in these media. One of the theories is for the propagation and attenuation of Stoneley waves across a horizontal fracture and along a vertical fracture. The theory has been checked against laboratory data obtained from scale models. The theoretical predictions and experimental results agree very well. We have also developed a theory for calculating the phase and group velocities of guided wave modes, including non-axisymmetric modes such as the flexural and screw modes, in a borehole embedded in a general, weakly anisotropic medium. This addresses the effects of logging in holes drilled into tilted blocks, non-horizontally drilled into sedimentary sequences, and drilled into formations with vertical fractures. We used a perturbation method based on Hamilton's Principle to calculate these velocities. We have generated techniques of inverting for the relevent parameters in these media such as the different elastic moduli and the degree of anisotropy from the full waveform logs. This year we have begun applying some of the techniques we have developed over the past years to logs in the field. In one example, we compare the shear wave velocity obtained in soft sediments by our inversion technique to those based on the difference between measured P-wave velocity and that predicted using Wood's equation. The results give us some handle on the limitations and accuracies of our technique. In another example, we restacked array data in various combinations to obtain a better depth resolution for the velocities picked from array data without sacrificing the use of a larger number of receivers to enhance the signal to noise ratio. In a third paper, we apply a general inversion to a number of different logs to obtain the lithology in a marine environment. Another paper deals with the implications of the differences in hydraulic conductivity estimated from Stoneley wave attenuation and packer tests in the field. Another focus of the past year's research is rock physics. Specifically, the relationship between permeability, velocity, including anisotropy, and pore geometry. The aim is to interpret measured velocities in terms of pore sizes and shapes, and then to use these pore geometries to model the flow properties of the rocks. The following is a summary of the papers in this report.

Transverserly Isotropic Saturated Porous Formations: II. Wave Propagation And Application To Multipole Logging

2019-04-12T21:17:24Z

Transverserly Isotropic Saturated Porous Formations: II. Wave Propagation And Application To Multipole Logging Schmitt, D. P. The wavefields generated by monopole and dipole sources in a fluid filled borehole embedded in multilayered transversely isotropic saturated porous formations are studied. The layers are modeled following Biot theory modified in accordance with homogenization theory. It allows to take into account a transversely isotropic skeleton and/or a transversely isotropic complex permeability tensor. Their axes of symmetry are assumed to coincide, parallel to the vertical axis of the borehole. A general formulation, valid for any order of multipole source and based on the Thomson Haskell method, allows to take into account any combimi.tion of elastic and saturated porous layers, either isotropic or transversely isotropic. The presence of an external fluid layer is also possible. The study focuses on the modes behavior. It is achieved through the computation of dispersion and attenuation curves, sensitivity coefficients with respect to the stiffness constants of the skeleton(s), and full waveform synthetic microseismograms using the discrete wavenumber method. In the simple hole model with an impermeable borehole wall, whatever the type of the formation (fast or slow), the behavior of the modes is analogous to that in the presence of simple elastic formations with body wave attenuations added. The phase velocity of the Stoneley wave generated by a monopole source is sensitive to the horizontally propagating SH-wave velocity. Such a coupling decreases with increasing frequency and stiffness of the formation. The low frequency part of the zero-th order (Le., flexural) mode generated by a multi(di)pole source measures the vertically propagating SV-wave velocity. The shear wave anisotropy may then be evaluated. With a fast formation, the vertically propagating SV-wave velocity can also be obtained from the low frequency (high velocity) part of the pseudo-Rayleigh mode generated by the monopole source. The anisotropy of the complex permeability tensor cannot be detected. Moreover, only the attenuation of the vertically propagating P wave is sensitive to the only vertical permeability. Any anelastic (anisotropic) attenuation will supersede the latter. When the borehole wall is permeable, the fluid flow which takes place at the interface refers to the horizontal mobility (I.e., horizontal permeability/saturant fluid viscosity). Assuming greater horizontal velocities, the decrease of the Stoneley wave phase velocity and the increase of its low frequency attenuation are enhanced. The shear wave transverse isotropy cannot be anymore detected and any estimation of the horizontal permeability based on Stoneley wave characteristics may become questionable with a high anisotropy degree of the skeleton. However, detection of permeability variation may still be reasonably performed. In the presence of an invaded zone, whatever the boundary conditions at the borehole wall, Stoneley wave integrates the properties of the inner layer in the entire frequency range. This coupling phenomenon increases with increasing thickness and decreasing body wave velocities of the inner layer. As a result, both estimations of the shear wave transverse anisotropy and the permeability of the virgin formation from the Stoneley wave characteristics are ill posed. Of course, such a result hold true in a cased borehole, whatever the quality of the bonding. In any of the multilayered configuration, the low frequency part of both the flexural mode and the pseudo-Rayleigh mode, when it exists, measures the characteristics of the vertically propagating SV wave of the virgin formation. Such an interesting information may be however difficult to extract.

Transverserly Isotropic Saturated Porous Formations: 1. Theoretical Developments And (Quasi) Body Wave Properties

2019-04-12T20:30:50Z

Transverserly Isotropic Saturated Porous Formations: 1. Theoretical Developments And (Quasi) Body Wave Properties Schmitt, D. P. Using the results of homogenization theory, the constitutive equations for an anisotropic porous formation saturated by a Newtonian viscous fluid are derived. The transverse isotropy situation is investigated in terms of partial stresses in both phases. It allows to take into account a transversely isotropic skeleton and/or a transversely isotropic complex permeability tensor whose axes of symmetry are assumed to coincide. The wavenumbers equations are solved as part of a cylindrical geometry and general solutions for the displacement potentials in each phase are presented. Four dispersive and dissipative waves propagate in a transversely isotropic saturated porous formation: two quasi compressional waves, a quasi SV wave and aSH wave. All three quasi body waves approach the isotropic P[subscript 1] wave, slow P[subscript 2] wave, and S wave only as the degree of anisotropy of both the skeleton and the complex permeability tensor vanishes. Simple analytical formuale are derived for vertical and horizontal propagations. The SH-wave only excites the horizontal permeability, whatever its angle of propagation with respect to the vertical. The velocities and attenuations of these four waves are studied as a function of the only transversely isotropic permeability, the anisotropy of the skeleton, and the anisotropy of the mass coupling coefficient. Whatever the frequency, the quasi P[subscript 1]-wave, quasi SV-wave and SH-wave velocities are primarily governed by the anisotropy of the skeleton. Contrary, the quasi slow P[subscript 2] wave velocity is mostly representative of the complex permeability tensor transverse isotropy. At very high frequencies, when the inertial forces in the saturated porous formation are dominant, an anisotropy of the mass coupling coefficient leads to slightly different quasi BV-wave velocities along the principal directions, contrary to the pure elastic situation. For the quasi PI wave and the quasi BV wave, the degree of anisotropy of the strongly frequency dependent attenuation induced by the two phase character of the material is more important than that of the velocity.

Laboratory Studies Of The Acoustic Properties Of Samples From The Salton Sea Scientific Drilling Project And Their Relation To Microstructure And Field Measurements

2019-04-11T01:22:08Z

Laboratory Studies Of The Acoustic Properties Of Samples From The Salton Sea Scientific Drilling Project And Their Relation To Microstructure And Field Measurements Tarif, P. A.; Wilkens, R. H.; Cheng, C. H.; Paillet, F . L. Compressional and shear wave velocities were measured at confining pressures up to 200 MPa for twelve core samples from the depth interval of 600 to 2600 m in the California State 2-14 borehole. Samples were selected to represent the various lithologies, including clean, heavily cemented sandstones, altered, impermeable claystones, and several intermediate siltstones. Velocities measured at ultrasonic frequencies in the laboratory correspond closely with velocities determined from acoustic waveform logs and vertical seismic profiles. The samples exhibit P-wave velocities around 3.5 km/sec at depths above 1250 m, but increase to nearly 5.0 km/sec at 1300 m in depth. Further increases with depth result in compressional wave velocity increasing to nearly 6.0 km/sec. These increases in velocities are related to systematic variations in lithology, microstructure and hydrothermal alteration of originally clay-rich sediments. Scanning electron microscope observations of core samples confirm that local core velocities are determined by the combined effects of pore size distributions, and the proportion of clays and alteration minerals such as epidote present in the form of pore fillings and veins.

Elastic Wave Diffraction Of A Piston Source And Its Effect On Attenuation Measurement

2019-04-12T20:28:07Z

Elastic Wave Diffraction Of A Piston Source And Its Effect On Attenuation Measurement Tang, X. M.; Toksoz, M. N.; Cheng, C. H. The radiation of an elastic wave field from a plane piston source is formulated using the representation theorem, in which the Green's function for an elastic half space is employed. On the basis of this formulation, we derive the radiated elastic wave field for both compressional and shear wave sources. We study the diffraction of elastic waves incident on a receiver that is coaxially aligned with the source. We present a procedure in which both numerical and asymptotic techniques are employed to allow us to evaluate the diffraction effects in any frequency range of interest. We compare the elastic diffraction with the acoustic diffraction and find that they are different in the near field of the piston source due to the coupling between shear and com pressional components in the elastic case. In the far field, however, the elastic diffraction approaches the acoustic diffraction. With the help of ultrasonic laboratory measurements, we test the theoretical results and find that the theory and experiments agree well. An important result of this study is that in attenuation measurements with pulse propagation techniques where spectral ratio relative to a standard sample or ratio of samples of the same material but of different lengths is used, it is necessary to correct for diffraction effects. In the attenuation measurement using spectral ratio of a sample and a standard reference sample, the attenuation can be overestimated, while in the attenuation measurement using a spectral ratio of samples of different lengths, the attenuation can be significantly underestimated, if corrections for diffraction effects are not made.

Viscous Attenuation Of Acoustic Waves In Suspensions

2019-04-11T01:22:20Z

Viscous Attenuation Of Acoustic Waves In Suspensions Gibson, Richard L. Jr.; Toksoz, M. Nail A model for attenuation of acoustic waves in suspensions is proposed which includes an energy loss due to viscous fluid flow around spherical particles. The expression for the complex wavenumber is developed by considering the partial pressures acting on the solid and fluid phases of the suspension. This is shown to be equivalent to the results of the Biot theory for porous media in the limiting case where the frame moduli vanish. Unlike earlier applications of the limiting case Biot theory, however, a value for the attenuation coefficient is developed from the Stokes flow drag force on a sphere instead of attempting to apply a permeability value to a suspension. If the fluid and solid particle velocities have harmonic time dependence with angular frequency w, the attenuation in this model is proportional to w2 at low frequencies and approaches a constant value at high frequencies. The predicted attenuation is very sensitive to the radius and density of the spherical particles. Accurate modeling of observed phase velocities from suspensions of spherical polystyrene particles in water and oil and successful inversion for kaolinite properties using attenuation and velocity data from kaolinite suspensions at 100 kHz show that this viscous dissipation model is a good representation of the effects controlling the propagation of acoustic waves in these suspensions. Attenuation predictions are also compared to amplitude ratio data from an oil-polystyrene suspension. The viscous effects are shown to be significant for only a limited range of solid concentration and frequency by the reduced accuracy of the model for attenuation in a kaolinite suspension at 1 MHz.

Geophysical Well-Log Analysis In Characterizing The Hydrology Of Crystalline Rocks Of The Canadian Shield

2019-04-10T20:20:14Z

Geophysical Well-Log Analysis In Characterizing The Hydrology Of Crystalline Rocks Of The Canadian Shield Paillet, F . L. A full suite of geophysical logs, including nuclear, electric, acoustic transit-time, acoustic waveform, and acoustic televiewer logs, and high-resolution flowmeter measurements have been used to investigate the lithologic and hydrologic properties of three igneous plutons located on the southern margin of the Canadian shield. Geophysical logs were used to identify lithologic boundaries, determine the properties of unfractured granitic or gabbroic rocks, interpret and calibrate the results of surface geophysical surveys, and characterize permeable fracture zones that could serve as conduits for fluid migration. Nuclear and acoustic transit-time logs provided good quantitative correlation with changes in lithology. Electric logs yielded consistent qualitative correlations, with lower resistivities associated with more mafic lithologies. Lithologic contacts indentified on logs generally confirmed the results of surface electromagnetic, seismic, and gravity surveys. All major fracture zones intersected by boreholes were clearly indicated by the geophysical logs. Electric, epithermal-neutron, and acoustic transit-time logs gave the most consistent indications of fracturing, but the lithologic responses associated with some thin mafic intrusions were difficult to distinguish from possible fractures, and some steeply-dipping fractures were not indicated by conventional acoustic transit-time logs. Electric and neutron log response is attributed to the effect of clay minearl alteration products in the vicinity of fractures. This alteration may be indirectly related to permebaility, but no direct relationship between resistivity or neutron attenuation and permeability appears to exist. Tube-wave attenuation determined from acoustic waveform logs was related to the transmissivity of equivalent infinite, plane fractures; these results agree qualitatively, and possibly quantitatively with packer isolation and injection tests if the combined effects of differing scales of investigation and borehole enlargements in fracture zones are taken into account. Tube-wave attenuation in waveform logs also compares well with the permeability distributions determined from tube-wave generation in vertical seismic profiles. Comparison of conventional geophysical logs, acoustic televiewer images of the borehole wall, and fracture frequency distributions measured on core samples indicates that many fractures are completely sealed and have no effect on log response, whereas many more apparently sealed fractures have been slightly opened during drilling, and do provide some log response. High resolution flowmeter meaurements of natural flow in boreholes and comparison of packer isolation tests with log data indicate that a relatively few individual fractures often provide a large proportion of fracture zone transmissivity in the immediate vicinity of the borehole, and that the orientation of these fractures may not coincide with fracture zone orientation. These results indicate that the scale problem in relating borehole logs to regional configuration of fracture flow systems may be the most important consideration in the appplication of geophysical well logging to the characterization of ground water flow in crystalline rock bodies.

Fracture Detection And Characterization

2019-04-09T18:17:04Z

Fracture Detection And Characterization Toksoz, M. Nafi; Guler, Fatih The effects of fractures on full waveform acoustic logs are studied on the basis of field observations, available theoretical models, and a series of ultrasonic laboratory experiments. Results from diffusion models applicable to fine microfractures and finite difference models of isolated fractures are reviewed. Laboratory experiments are carried out with fine microfractures around the borehole in a Lucite model, and isolated single fractures in aluminum models. Cases of horizontal and inclined (45°) fractures are studied as a function of fracture aperture and frequency of Stoneley waves. A vertical fracture model is also studied. Results indicate that the effect of different fractures are manifested differently on P, S, pseudo-Rayleigh, and Stoneley waves. Micro-fractures surrounding a borehole attenuate Stoneley waves most strongly. Vertical fractures attenuate Stoneley waves more strongly than other phases in the wave train. Horizontal and inclined fractures have a greater effect on P and S waves than on Stoneley waves.

A Dynamic Model For Fluid Flow In A Borehole Fracture

2019-04-10T19:18:27Z

A Dynamic Model For Fluid Flow In A Borehole Fracture Tang, X. M.; Cheng, C. H. The attenuation of Stoneley waves by a borehole fracture are closely related to fluid flow in the fracture. We consider the dynamic response of a viscous fluid in a horizontal fracture to the oscillating pressure excitation of Stoneley waves at the fracture opening. A dynamic model has been developed to describe the fluid motion in the fracture. This model relates both viscous shear effects at the fracture surface and the acoustic wave propagation in the fracture fluid. The dynamic conductivity is derived to characterize the fluid conduction in the fracture. This model is applied to study Stoneley wave attenuation across a borehole fracture, and is found to agree well with laboratory fracture modeling data.

Acoustic Logging Guided Waves In Transversely Isotropic Formations

2019-04-09T16:14:26Z

Acoustic Logging Guided Waves In Transversely Isotropic Formations Ellefsen, K. J.; Cheng, C. H.; Schmitt, D. P. We have studied the velocity dispersion of guided waves in transversely isotropic formations. Theoretical velocity dispersion curves were calculated with elastic constants based on laboratory and field measurements and compared to dispersion curves for isotropic formations having the same vertical po and S-wave velocities. The symmetry axis for the transverse isotropy was parallel to the borehole. The differences between the phase velocities for the transversely isotropic and isotropic formations depend on the type of wave, its frequency, and the amount of anisotropy, and can be as high as 7 to 10 percent. The changes in the phase velocity due to changes in the elastic constants of the formation (c[subscript 11], C[subscript 1]3, C[subscript 33], C[subscript 44], and C[subscript 66]) and the bulk modulus of the borehole fluid (⋋) vary with frequency. In a hard formation, the tube wave's velocity is sensitive to C[subscript 66] at low frequencies, to C[subscript 44] at high frequencies, and to ⋋ at all frequencies. The pseudo-Rayleigh wave is affected by C[subscript 44] near its cutoff frequency and by ⋋ at high frequencies. The flexural wave, which is generated by a shear wave logging tool, is similarly affected by C[subscript 44] at low frequencies and by ⋋ at high frequencies. As the formation becomes soft, the effect of the elastic constants upon the phase velocity gradually changes. Like a hard formation, the tube wave's velocities in a moderately soft formation are primarily affected by C[subscript 66] and ⋋ at low frequencies, but the influence of C[subscript 44] is much greater at high frequencies. Since array processing methods can accurately estimate the velocity dispersion of the guided waves over a wide range of frequencies, some elastic constants can be estimated. In a hard formation, the refracted P- and S-wave velocities uniquely determine C[subscript 33] and C[subscript 44], and an inversion can be used to estimate C[subscript 66] and ⋋. In a moderately soft formation, the refracted P-wave velocity determines C[subscript 33], the flexural wave from the shear wave logging tool determines C[subscript 44], and the tube wave's velocity dispersion can be used to estimate C[subscript 66] and ⋋.

Application Of Rayleigh's Principle To Guided Waves In A Borehole

2019-04-11T01:22:19Z

Application Of Rayleigh's Principle To Guided Waves In A Borehole Ellefsen, K. J.; Cheng, C. H. The Lagrangian for guided waves in a completely general borehole model is presented. Rayleigh's principle is used to derive the first order perturbations in wavenumber and frequency due to slight perturbations in the physical properties of the model. The principle is also used to calculate perturbations in frequency due to perturbations in wavenumber. These formulas are applied to a fluid-filled borehole through an infinite, transversely isotropic formation, for which the axis of symmetry is aligned with the borehole, to calculate (1) partial derivatives of wavenumber and velocity at constant frequency, (2) partial derivatives of frequency and velocity at constant wavenumber, and (3) group velocity. These formulas are also applied to a formation with general anisotropy to calculate the velocity dispersion.

Full Wave Logging In An Irregular Borehole

2019-04-10T07:13:24Z

Full Wave Logging In An Irregular Borehole Bouchon, Michel; Schmitt, Denis We present a boundary integral equation formulation for the problem of wave propagation in a borehole of irregular cross-section. The method consists in representing the wave field diffracted at the borehole-rock interface by the radiation from a distribution of surface sources applied along the borehole wall. The wave field in the borehole fluid and in the elastic rock are then expressed using the discrete wavenumber method. The application of the boundary conditions at discretized locations along the borehole wall leads to a linear system of equations. The inversion of this system yields the required source distribution. We have used the method to investigate the effect of changes in borehole diameter on the pressure wave field inside the borehole. The results show that when the change is smooth, the records obtained ahead of the discontinuity location are not affected by its presence. In the case of a steep variation, however, a significant amount of the Stoneley wave energy is reflected. When the borehole diameter is different at the source and at the receiver levels, the microseismograms obtained are somewhat of an average between the ones that would be recorded in boreholes of constant radius equal to the radius at the source and at the receiver. The presence of small-scale fluctuations in borehole diameter reduces the amplitude of the Stoneley wave and decreases its velocity and the pseudo-Rayleigh wave velocity.

Estimating Phase Velocity And Attenuation Of Guided Waves In Acoustic Logging Data

2019-04-10T07:12:57Z

Estimating Phase Velocity And Attenuation Of Guided Waves In Acoustic Logging Data Ellefsen, K. J.; Cheng, C. H. Phase velocity and attenuation of guided waves have been estimated from acoustic logging data recorded by a receiving array. The method uses data from multiple sources and successive depths yielding more accurate estimates than could be obtained with data from one source and one depth. The inversion requires two steps: (1) all traces are transformed into the frequency domain with a fast Fourier transform, and (2) at each frequency a modification of Prony's method is used to estimate the guided waves' characteristics which include amplitude, attenuation coefficient, and wavenumber (which yields the phase velocity). An important assumption underlying this technique is that the formation, borehole fluid, and tool are homogeneous along the receiving array. Application of this method to synthetic data shows that the phase velocity and attenuation of the tube and pseudo-Rayleigh waves are accurately estimated at many frequencies. With noisy synthetic data, the phase velocities are correctly determined, but the attenuation estimates, being sensitive to noise, are accurate only when the amplitudes are high. Using data from multiple sources and successive depths suppresses the noise effects and improves both estimates. The amplitude estimates are important because they roughly indicate the reliability of the velocity and attenuation estimates. From laboratory and field data, the velocities for the guided waves are accurately predicted even when the amplitudes are low. The attenuation estimates are good when the amplitudes are high but degrade as the amplitudes diminish.

Report Summary

2019-04-11T01:22:17Z

Report Summary Cheng, C. H. This report contains the results of work completed during the sixth year of the Full Waveform Acoustic Logging Consortium in the Earth Resources Laboratory at M.LT. Over the last six years, our work have evolved from simply modelling an open borehole in an isotropy, elastic formation to the study of logging under more complicated, realistic conditions, especially those that may be encounted in production and development environments. In the past year, we have modelled elastic wave propagation in a transversely isotropic formation, in a formation where the borehole is irregular in radius, across an open fracture, and in a transversely isotropic porous formation, where the horizontal and vertical permeabilities are different. All of these situations are rather common in the field. It is important for us to understand how these complications mayor may not affected our interpretation of the full waveform acoustic logs, and how large an error we are likely to make if our interpretation is based on a isotropy, elastic model of the formation. Just as importantly, we need to learn to identify these situations in the field, so that we can make the appropriate corrections to our interpretation. In data analysis, we have refined the Extended Prony's Method to calculate the dispersion and attenuation of the guided waves in the borehole, and have applied the technique to both laboratory and field data with success. We have also studied the sensistivity of the guided waves to a transversely anisotropic formation. These sensistivities are critical in the inversion of the dispersion and attenuation obtained by the Extended Prony's Method for the actual elastic and anelastic properties of the formation. In a continuation of last year's work, we have studied the attenuation of solid particles in a viscous fluid, applicable to the study of both drilling muds and unconsolidated sands. We have studied the diffraction of a cylindrical transducer and its effect on the measurement of attenuation in laboratory experiments using the spectral ratio technique. We are also continuing in our effort of scale model experiments to mimic field situations which are not readily modelled by analytic or numerical methods. A field study and comparison of velocities from core measurement, borehole compensated sonic log, full waveform acoustic log, and VSP in the Salton Sea Scientific Drilling Program is included in this report. Also included is an extended abstract on an effort to map fractures in the Canadian Shield using borehole geophysical techniques. The following is a summary of the papers in this report.

Ultrasonic Laboratory Study of Full Waveform Acoustic Logs in Boreholes with Fractures

2019-04-12T20:30:49Z

Ultrasonic Laboratory Study of Full Waveform Acoustic Logs in Boreholes with Fractures Toksoz, M. N.; Guler, Fatih A set of ultrasonic experiments was carried out to determine the effects of horizontal and vertical fractures on full waveform acoustic logs. Boreholes of 1 cm diameter were drilled in aluminum blocks. Measurements were made with horizontal fractures of 0.05 mm, 1.0 mm, 2.5 mm, and 4.5 mm width and a vertical fracture of 1.0 mm width. The horizontal fractures of even the smallest thickness significantly attenuate the P, S, and pseudo-Rayleigh waves. The Stoneley waves are the least attenuated, and attenuation increases with increasing fracture width. The vertical fracture attenuates Stoneley waves most significantly. Both scattering and fluid flow playa role in attenuation. The results may qualitatively be extended to inclined open fractures, where we expect strong attenuation of P and S waves and moderate attenuation of Stoneley waves.

A Method of Measuring Acoustic Wave Attenuation in the Laboratory

2019-04-12T20:30:44Z

A Method of Measuring Acoustic Wave Attenuation in the Laboratory Tang, X. M.; Toksoz, M. N.; Tarif, P. The measurement of attenuation is performed by directly determining the attenuation operator (or the impulse response of the medium) in the time domain. In this way, it is possible to separate the attenuation operator from other non-attenuation effects, e.g. reflections. The Wiener filtering technique, or the damped least-squares, is used to calculate the attenuation operator. For the damped least squares, we have corrected for the effect due to the addition of the damping constant using a perturbation method. Numerical tests are carried out to illustrate the technique. The geometric beam spreading of ultrasonic waves generated by a source of finite size can strongly affect the result of attenuation measurements. Corrections are made by equating the received signal to the average pressure over the receiver surface. The technique is used to measure ultrasonic attenuation in water, glycerol and mud. The measurement in water offers a test of the corrections made for the geometric beam spreading. The measurement in glycerol and mud shows that, in the frequency range of 0.2-1.5 MHz, the attenuation of glycerol increases rapidly with frequency, whereas the attenuation of mud is proportional to frequency, exhibiting a constant Q behavior. The measurements show that the technique used here is an effective approach to the measurement of attenuation.

An Object-Oriented System for Full Waveform Data Processing

2019-04-12T20:30:48Z

An Object-Oriented System for Full Waveform Data Processing Larrere, Marc A new approach to the processing of sequences of full waveform acoustic logs is investigated. The rationale for this approach is primarily based on the observation that processing and interpretation tasks strongly depend on each other. Hence, a system that incorporates geologic knowledge in data processing naturally and uses processing results for petrophysical evaluation can improve the overall geological interpretation. The implementation of such ideas requires the use of a versatile computer environment, allowing numeric and symbolic processing. The new generation of Lisp machines satisfies these characteristics. An interactive environment for the processing of sequences of acoustic signals was designed using object-oriented programming. The package includes a novel method for acoustic full waveform signal matching that uses dynamic time warping. The system is tested on synthetic data and field data are processed.

Well-to-Well Log Correlation Using Knowledge-Based Systems and Dynamic Depth Warping

2019-04-10T16:49:28Z

Well-to-Well Log Correlation Using Knowledge-Based Systems and Dynamic Depth Warping Lineman, D. J.; Mendelson, J. D.; Toksoz, M. N. We present a novel system for well-to-well log correlation using knowledge-based systems and dynamic depth warping techniques. This approach overcomes a major drawback inherent in previous methods, namely the difficulty in correlating missing or discontinuous rock units. The system has three components: (1) A Dynamic Programming algorithm to correlate the logs and to find the minimum-cost or "best" match; (2) A set of "rules" to guide the correlation; (3) A data base that contains the logs and other relevant geologic and seismic information. The Dynamic Programming algorithm calculates the cost of correlating each point in the first well with each of the points in the second well. The resulting matrix of dissimilarity contains cost information about every possible operation which matches the well logs. The cost of matching the two wells is measured by the difference in the log values. The dynamic programming approach allows correlation across geologic structures, thinning beds, and missing or discontinuous units. A path finding algorithm then traces through the matrix to define a function which maps the first well onto the second. The minimum cost path is the optimal correlation between the wells. The system's database contains the well logs themselves and other relevant data including information about the geologic setting, seismic ties, interpreted lithologies, and dipmeter information. Rules operating on the data affect the dynamic programming and path finding algorithms in several ways: (1) Seismic ties or marker beds define a point in the warping path, thereby removing calculations over large portions of the search space; (2) Dipmeter results and knowledge of geologic structure further constrain the path to certain global areas and save calculation time; (3) The system assigns weights to different logs based on log quality and sensitivity; (4) Knowledge of the paleoenvironment allows the program to choose a set of rules (model) which accounts for changes in sediment type or thickness within a field. For example, when the program is operating in a deltaic environment, it will correlate the shales before attempting to correlate the sands. We demonstrate the method with synthetic examples in which the program successfully correlates across geologic structures and pinch-outs. We also applied the program to field examples from two widely separated oil provinces. In both cases, the automated correlation agreed very well with correlations provided by geologic experts.

Estimating Phase Velocity and Attenuation of Guided Waves in Acoustic Logging Data

2019-04-11T01:22:17Z

Estimating Phase Velocity and Attenuation of Guided Waves in Acoustic Logging Data Ellefsen, K. J.; Cheng, C. H.; Duckworth, G. L. Phase velocity and attenuation of guided waves have been estimated from multireceiver, full waveform, acoustic logging data using the extended Prony's method. Since a formation affects velocity and attenuation, estimating these quantities is important in evaluating the formation properties. The estimation is performed using an array processing technique which requires two steps: (1) the traces for all receivers are transformed into the frequency domain, and (2) for each frequency the extended Prony's method is used to determine the presence of a guided wave propagating past the array of receivers. The guided wave properties estimated by the Prony's method include amplitude, attenuation, and phase change which is related to phase velocity. An important assumption in this array processing technique is that the formation, borehole fluid, and tool are homogeneous along the receiving array. For synthetic data, the phase velocities and attenuation of the tube wave and two modes of the pseudo-Rayleigh wave are accurately estimated over many frequencies, with the exception that the low amplitude of the second mode causes its attenuation estimate to be somewhat less accurate. For laboratory data, very good estimates of the phase velocities of the tube wave and three modes of the pseudo-Rayleigh wave are obtained. Since the materials used in the laboratory experiment had very large quality factors, the attenuation could not be estimated. For field data, the dispersion of the tube wave and the velocity of the pseudo-Rayleigh wave at its cutoff are very close to those predicted by another, independent method. Accurate attenuation estimates could not be made because the data are noisy and consist of only eight traces.

Velocity Analysis of Multi-Receiver Full Waveform Acoustic Logging Data In Open and Cased Holes

2019-04-11T03:09:42Z

Velocity Analysis of Multi-Receiver Full Waveform Acoustic Logging Data In Open and Cased Holes Block, Lisa V.; Cheng, C. H.; Duckworth, Gregory L. Average semblance and maximum-likelihood spectral analyses are applied to synthetic and field full waveform acoustic logging data to determine formation velocities. Of particular interest is the ability of these methods to resolve the P and shear/pseudo Rayleigh arrivals in data from poorly-bonded cased boreholes. In synthetic open-hole data the velocity analyses yield results within 4% of the true velocities. Results from synthetic well-bonded cased hole data are generally as good as those from the open hole data. However, if the formation P-wave velocity is within roughly 10% of the plate velocity of the steel pipe (about 5.3-5.5 km/s), then there may be a resonance effect that appears to slow down the P wave slightly (on the order of 6%). For cased-hole models with no steel/cement bonding (the free-pipe situation), the measured P-wave velocities are typically 6 to 8% less than the actual formation velocities. If the formation S-wave velocity is greater than about 2.5 km/s, the S-wave velocity estimate may also be 6 to 8% low. Furthermore, increasing the thickness of either the cement layer or the fluid layer between the pipe and the cement further decreases the formation velocity estimates. Also, if the P-wave velocity is within roughly 15% of the velocity of the steel arrival, the P wave may not be resolved by the semblance method unless the data is first low-pass filtered. Initial tests show that this filtering process may adversely affect the final P-wave velocity estimate, but the details of this type of approach have not been studied. The P wave is resolved. by spectral analysis of the original, unfiltered data. For cased-hole models with no cement/formation bonding (the unbonded-casing situation), formation S-wave velocities are estimated to within 3% relative error, and the formation P-wave velocity is estimated to within 2% error in a slow formation. However, for P-wave velocities between 3.4 km/s and 5.94 km/a, the P wave cannot be resolved by spectral analysis, and it is resolved by the semblance method only in the model with the low velocity (3.4 km/s).

Determining Shear Wave Velocities in Soft Marine Sediments

2019-04-11T01:22:14Z

Determining Shear Wave Velocities in Soft Marine Sediments Meredith, J . A.; Cheng, C. H.; Wilkens, R. H. The inversion technique presented in this volume (Cheng, 1987) that simultaneously inverts full waveform acoustic logs for shear wave velocity (V[subscript 3]) and compressional wave attenuation (Q[subscript p]) was applied to selected full waveform acoustic logs taken in soft sediments from Deep Sea Drilling Project Site 613. Besides V[subscript 3] and Q[subscript p], the sensitivity of the inversion to perturbations in the fixed parameters, P-wave velocity (V[subscript p]), fluid velocity (V[[subscript f]), borehole diameter, bulk density (P[subscript b]), and borehole fluid attenuation (Q[subscript f]), were tested. Our study shows that the inversion technique is most sensitive to the estimate of V[subscript p] because the inversion is based on the P leaky mode energy portion of the spectrum. The Poisson's ratio, however, which primarily controls the amplitude of the waveforms, is rather stable with different estimates in V[subscript p]. The inversion technique is less sensitive to small perturbations in borehole diameter, P[subscript b], V[subscript f], and Q[subscript f] The shear wave velocities inferred from these inversions correlate well with the attendant velocity logs run at Site 613 and the diagenetic changes identified by shipboard stratigraphers. For example, there is an increase in both V[subscript p] and V[subscript 3] at the diagenetic boundary between siliceous nannofossil oozes and porcellanite. This boundary is responsible for a sharp seismic reflector in a USGS. seismic line run nearby. Over the depth interval that we analyzed, from 390.0 to 582.0 meters below sea floor, we determined shear wave velocities ranging from 0.74 to 1.06 km/sec corresponding to compressional wave velocities from 1.70 to 2.20 km/sec.

Experimental Determination of Elastic Anisotropy of Berea Sandstone, Chicopee Shale and Chelmsford Granite

2019-04-11T01:22:09Z

Experimental Determination of Elastic Anisotropy of Berea Sandstone, Chicopee Shale and Chelmsford Granite La, Tien-when; Coyner, Karl B.; Toksoz, M. Nafi We use the ultrasonic transmission method to measure P-, SH-, and SV-wave velocities for Chelmsford Granite, Chicopee Shale, and Berea Sandstone in different directions up to 1000 bars confining pressure. The velocity measurements indicate that these three rocks are elastically anisotropic. The stiffness constants, dynamic Young's moduli, dynamic Poisson's ratios, and dynamic bulk moduli of these three rocks were also calculated. These elastic constants, together with velocity measurements, suggest that: (1) Elastic anisotropy is due to the combined effects of pores/cracks and mineral grain orientation. (2) Elastic anisotropy decreases with increasing confining pressure. The residual anisotropy at higher confining pressure is due to mineral grain orientation.

Sandstone Pore Aspect Ratio Spectra from Direct Observations and Velocity Inversion

2019-04-10T20:28:01Z

Sandstone Pore Aspect Ratio Spectra from Direct Observations and Velocity Inversion Burns, D. R.; Cheng, C. H.; Wilkens, R. H. Measurements of pore shapes from Scanning Electron Microscope (SEM) images for three sandstone samples (the Navajo Sandstone, the Weber Sandstone, and the Kayenta Sandstone) are compared to the aspect ratio spectra obtained from inverting laboratory velocity versus pressure data using the method of Cheng and Toksoz (1979). The results indicate that the inversion method is in very good agreement with the observations at high aspect ratios ( ex > 0.0 1). At low aspect ratios the agreement is very good for the clean Navajo Sandstone sample, but poor for the Weber and Kayenta samples which contain clay. The Navajo sample is composed chiefly of quartz with significant pressure dissolution apparent along grain contacts resulting in smooth, flat cracks between grains. The Weber and Kayenta samples have rougher crack surfaces as well as tapered pore edges, indicating that asperities ,and non-elliptical pore shapes may result in an over estimation of low aspect ratio cracks by velocity inversion. The presence of degraded feldspars may also play a role.

Physical Properties of a Set of Sandstones, III: the Effects Of Fine Grained Pore Filling Material on Compressional Wave Velocity

2019-04-12T20:28:06Z

Physical Properties of a Set of Sandstones, III: the Effects Of Fine Grained Pore Filling Material on Compressional Wave Velocity Wilkens, R. H.; Simmons, G.; Wissler, T. M.; Caruso, L. We have used aspect ratio modeling to explain the measured compressional wave velocities of twenty different dry sandstone samples with varying clay contents at a single confining pressure of 0.5 kbar. Velocities of the sandstones range between 3.1 km/sec and 5.7 km/sec. Measured porosities are between 6% and 33%, clay contents between 2% and 30%. Pores were described using three simple type classifications. The pore type distributions of the samples were quantified by point counting polished impregnated thin sections using a scanning electron microscope. A representative aspect-ratio was assigned to each of the three categories of pore type. Velocities were modeled using these aspect ratios weighted by the observed distribution of the porosity types. Agreement between theoretical and measured velocities is generally within 10%. The modeling suggests that the effects of clays in sandstone pores is to reduce the sample porosity without reducing the non-framework (void + clay) volume. Thus, for a given porosity, clay rich samples contain greater non-framework volume, which in turn lowers velocity. The model derived from the dry measurements can be used to successfully approximate empirical relationships for saturated samples of velocity-porosity-clay content taken from the literature.

Laboratory Measurements of Attenuation in Rocks at Ultrasonic Frequencies

2019-04-11T01:22:09Z

Laboratory Measurements of Attenuation in Rocks at Ultrasonic Frequencies Gonguet, Christophe; Coyner, Karl B.; Toksoz, M. Nafi The spectral ratio method is used to calculate the quality factor (Q) in porous rock samples at ultrasonic frequencies (0.3 - 1.5 MHz). The data were collected using the pulse transmission technique with aluminum used as a high Q standard. The data set consists of dry, water and benzene saturated rocks at differential pressures from zero to one kilobar. Two sandstones, Berea and Kayenta, Bedford limestone, and Webatuck dolomite are studied. Water and benzene were chosen as pore fluid saturants to contrast the effects of two different pore fluids (density, compressibility, viscosity, dielectric constant, and wetting properties) at ultrasonic frequencies. The main features observed are: 1) The quality factor Q increases with increasing confining pressure; at low pressures the rate of increase is larger. 2) Q for saturated samples is generally lower than for dry samples. 3) The introduction of a fluid saturant into a dry rock increases S-wave attenuation more than P-wave attenuation. 4) In general, given the measurement error and the fact that these results are preliminary, the differences in attenuation between the two fluid saturations, water and benzene, are not large. Nevertheless, we observe that benzene-saturated attenuations are slightly higher than water-saturated values, particularly at lower pressures (less than 500 bars) for the P-wave.

The Effects of Confining Pressure and Fluid Saturation on Ultrasonic Velocities in Rocks

2019-04-12T20:30:43Z

The Effects of Confining Pressure and Fluid Saturation on Ultrasonic Velocities in Rocks Coyner, Karl B.; Cheng, C. H. Laboratory measurements of ultrasonic p- and S-wave velocities were made as a function of confining pressure for vacuum dry, benzene-, and water-saturated samples of Westerly granite, Bedford limestone, and Weber, Navajo, Berea, and Kayenta sandstones. The measurements indicate: 1) water-saturated bulk moduli are higher than benzene-saturated values, 2) fluid-saturated shear moduli are always greater than or equal to dry values, and 3) water-saturated shear moduli for the sandstones are higher than benzene values at low pressure while lower than both benzene and dry values at higher pressure, Indicating that an apparent water-softening effect Is concentrated In the shear modulus. Modelling of the velocity measurements with the Blot (1956a) and Gassmann (1951) equations for static effective bulk modulus indicates that it underestimates the increase in bulk modulus and velocities caused by fluid saturation. Inertial effects of the pore fluid as treated by Blot (1956a, 1956b) are also shown to give minimal improvement to predicted velocities, which are underestimated. Velocity measurements are modelled with the Cheng-Kuster-Toksoz ellipsoidal pore and crack model using the inversion technique developed by Cheng (1978). Fits of dry and benzene-saturated velocities are shown along with pore aspect ratio distributions at zero pressure. Water-saturated velocity data and measured porosity reductions with pressure are compared with predictions of the model.

Petroleum Source Rock Logging

2019-04-12T20:30:42Z

Petroleum Source Rock Logging Mendelson, James Regional distributions of organic content are an important aid in developing basin evolution and hydrocarbon generation models. An approach to evaluate hydrocarbon source rocks using resistivity, sonic, density, neutron and natural gamma ray logs is developed. Organic matter, as a constituent in sedimentary rocks, has a relatively low density, slow velocity, and is high in hydrogen content. Source rocks generally have low water content, and often exhibit abnormally high concentrations of uranium. These effects combine to make an in-situ estimation of organic content plausible. Evolution of kerogen to bitumen, oil, and gas systematically affects the above properties and it is possible to obtain a qualitative assessment of the state of maturation of a known source bed. In this thesis logs and core data from wells in two separate oil provinces are used to test the methods of predicting total organic carbon content from log data. Two approaches are followed. The first method treats the organic matter as a rock constituent and calculates the log responses as a function of organic content. Two (rock and organic matter) and three (rock matrix, water and organic matter) component models are tested. This approach suffers because of the uncertainties of the physical properties of the organic matter. For each log type (I.e. sonic, gamma, resistivity, ...) log values are correlated with the laboratory measured total organic content. Bivariate regression helps to illustrate the efficacy of the models. In the second method, multivariate equations based on linear combinations of individual correlation coefficients are obtained. The importance cf combining several logs which are organic content predictors is demonstrated. These equations can be used to predict total organic carbon content using only log data, in different parts of an oil province.

Inversion of Travel Time for Velocity Using Multi-Spacing Sonic Tools

2019-04-12T21:17:23Z

Inversion of Travel Time for Velocity Using Multi-Spacing Sonic Tools Paternoster, Benoit J. Spatial resolution of sonic logs is greatly affected by the minimum spacing between receivers. Improvements can be made, however, when the spatial sampling of the formation is less than the minimum spacing. This paper proposes a recursive least squares inversion of travel times based on the Kalman filter. This formulation emphasizes the noise.content of the data as a factor limiting resolution. Synthetic data as well as real data processing is presented here.

Detection and Characterization of Fractures from Generation of Tube Waves

2019-04-09T16:46:32Z

Detection and Characterization of Fractures from Generation of Tube Waves Hardin, Ernest; Toksoz, M. Nafi Field testing has been conducted to evaluate a model which predicts the permeability and orientation of a permeable zone, in a deep water well in crystalline rock. Tube waves are generated by seismic P-waves incident on a fracture intersecting the borehole, a process observed in vertical seismic profiling (VSP). The behavior is explained by fluid exchange between the fracture and borehole, and the observed efficiency of conversion is theoretically related to fracture permeability. Additionally, fracture orientation may be obtained from multiple-source-offset VSP surveys. Conventional temperature, caliper, resistivity and televiewer logs show the presence of fractures and their orientation, and provide indirect evidence of associated flow. Open fractures are simultaneously sampled over the full borehole depth by hydrophone VSP methods. The tube wave generation model produces results which compare favorably to independent estimates of fracture parameters.

Tube Wave Attenuation and In-Situ Permeability

2019-04-11T02:51:18Z

Tube Wave Attenuation and In-Situ Permeability Hsui, Albert T.; Jinzhong, Zhang; Cheng, C. H.; Toksoz, M. N. The measurement of in-situ permeability is very important in exploration and production logging. Observed data show that tube wave attenuation in full waveform acoustic logs is correlated with formation permeability. It is postulated that attenuation is due to fluid flowing away from the borehole into the formation. In this paper we investigate the theoretical relationship between tube wave attenuation and permeability using two different models. The first is a simple model of a borehole with absorbing walls, and the second is a borehole with a Biot porous medium in the formation. Both models give qualitatively similar results. Tube wave attenuation increases with increasing permeability. Attenuation also increases with increasing frequency and porosity. We have also investigated the relative effects of intrinsic formation attenuation (anelasticity) and permeability on the attenuation of tube waves. Intrinsic attenuation was introduced into the models by means of complex velocities. It is found that in rocks with low to medium permeability (less than 100 millidarcies), intrinsic attenuation is the major contributor to tube wave attenuation. However, in high permeability (greater than 100 millidarcies) rocks, fluid flow associated with in-situ permeability is as important as intrinsic attenuation in controlling tube wave attenuation. In either case, if one can estimate the intrinsic formation attenuation from the other parts of the full waveform (such as the P wave or the psuedo-Rayleigh wave), an estimate of the permeability of the formation can be obtained. We tested the models using published data on core permeability and tube wave amplitudes. By assuming an average value of intrinsic attenuation appropriate to the formations under study, we obtained a good agreement between theory and data.

Effects Of Layer Boundaries On Fwal And Dip Estimation (Oblique Events)

2019-04-12T20:27:44Z

Effects Of Layer Boundaries On Fwal And Dip Estimation (Oblique Events) Paternoster, Benoit; Larrere, Marc Data recorded by the full waveform acoustic logging tool EVA shows events generated at acoustic layer boundaries. These can be interpreted as reflections on and transmissions through interfaces. Ray modelling shows that these events are very sensitive to the dip. After processing of an iso-offset section designed to enhance and separate such events, two sections are interpreted and the dip angles of the interfaces are estimated.

Asymmetric Modes of Elastic Wave Propagation in a Fluid-Filled Borehole

2019-04-12T20:27:59Z

Asymmetric Modes of Elastic Wave Propagation in a Fluid-Filled Borehole Jinzhong, Zhang; Cheng, C. H. A numerical investigation of asymmetric modes of elastic wave propagation in a fluid-filled borehole is treated in this paper. The dispersion curves of guided waves (called flexural waves) and synthetic microseismograms are presented. The guided waves are found to be highly dispersive, with the phase velocities decreasing from the formation shear wave velocities in both hard and soft formations. They have much lower cut-off frequencies than the pseudo-Rayleigh waves in axisymmetric modes of propagation. We found that under conditions of low frequency (2-3 kHz) and long source-receiver separation (3-4 m), the flexural wave is the prominent arrival in a microseismogram generated with an asymmetric source, traveling with a phase velocity equal to the formation shear wave velocity, while the compressional wave arrival before that is generally suppressed. The results of this study may be meaningful for designing a shear wave logging tool.

Energy Partitioning and Attenuation of Guided Waves in a Radially Layered Borehole

2019-04-12T07:33:07Z

Energy Partitioning and Attenuation of Guided Waves in a Radially Layered Borehole Burns, D. R.; Cheng, C. H.; Toksoz, M. N. Recently published results (Tubman et al., 1984; Baker,. 1984) indicate that synthetic full waveform acoustic logs generated in cased or damaged boreholes differ significantly from those generated in an open hole with the same formation parameters. In particular, the guided waves appear to be the most affected by such radial layering. In order to gain some understanding of these effects, the amplitude response and energy distribution of the pseudo-Rayleigh and Stoneley waves are studied for the cased and invaded borehole models. The expressions derived by Cheng et al. (1 982) are used to calculate partition coefficients (partial derivatives of phase velocity with respect to body wave velocities) for the guided wave modes. The attenuation of the guided wave can then be represented by the sum of the layer attenuation values weighted by their respective partition coefficients. The results indicate that the attenuation of the Stoneley wave is dominated by the fluid attenuation at all frequencies in fast formations, both in the open hole geometry and in the presence of casing or invaded zones. In a slow formation, the Stoneley wave attenuation becomes more sensitive to the shear wave attenuation of the formation at higher frequencies in both the open and cased hole situations. For the pseudo-Rayleigh wave, the introduction of casing reduces the effect of the fluid attenuation, while the presence of an invaded zone reduces the effect of the formation shear attenuation. Plots of the partition coefficients indicate that the casing and invasion layers are most important over a limited frequency range which is related to the thickness of the layer. Radial displacement curves illustrate the depth of penetration of the various frequency components of the pseudo-Rayleigh wave.

A Numerical Investigation of Head Waves and Leaky Modes in Fluid-Filled Boreholes

2019-04-12T20:30:42Z

A Numerical Investigation of Head Waves and Leaky Modes in Fluid-Filled Boreholes Paillet, Frederick L.; Cheng, C. H. Although synthetic borehole seismograms routinely can be computed for a wide range of borehole conditions, the physical nature of shear and compressional head waves in fluid-filled boreholes is poorly understood. This paper presents a series of numerical experiments designed to provide insight into the physical mechanisms controlling head wave propagation in boreholes. These calculations demonstrate the existence of compressional normal modes equivalent to shear normal modes, or pseudo-Rayleigh waves, with sequential cutoff frequencies spaced between the cutoff frequencies for the shear normal modes. Major contributions to head wave spectra are shown to occur in discrete peaks at frequencies just below mode cutoff for both compressional and shear modes. This result is confirmed by calculations with synthetic waveforms at frequencies corresponding to mode cutoff, and by branch cut integrals designed to yield independent spectra for the compressional mode. In the case of soft formations where shear velocity falls below acoustic velocity in the borehole fluid, leaky compressional normal modes attain properties similar to those observed for shear normal modes in the hard rock case. This result is formally related to a fluid-fluid waveguide with undamped compressional normal modes in the limit of vanishing shear velocity. Synthetic waveforms demonstrate that high amplitude arrivals, traveling at velocities less than the acoustic velocity of the borehole fluid, and at frequencies above a few kilohertz represent the Airy phase of the compressional mode and not a tube wave. Comparison of synthetic waveforms with waveforms obtained in soft sea sediments indicates that the predicted Airy phase arrivals are present in the experimental data.

Full Waveform Acoustic Logging - From Theory To Applications

2019-04-12T20:30:41Z

Full Waveform Acoustic Logging - From Theory To Applications Toksoz, M. N.; Cheng, C. H. This report contains results from the third year of the Full Waveform Acoustic Logging Consortium and rock physics studies at M.J.T. This year marks the completion of the first phase of the project which has been directed primarily to the understanding of the basic theoretical aspects of acoustic waves in a borehole. With such a background we are ready to emphasize applications as well as to undertake special problems which require new and different theoretical approaches. As examples of the latter, we can mention uncentered tools, vertical fractures around boreholes, thinly bedded formations and anisotropy. The third year studies fall into four general areas: theoretical aspects of wave propagation in the borehole, applications to the characterization of formations, integrated log analysis and physical properties of sedimentary rocks relevant to logging. There are fifteen papers in this report which discuss individual topics in detail. In this introduction we summarize the major points and also list the potential applications of full waveform acoustic logs and future directions of our research.

Static Deformation of Fluid-Saturated Rocks

2019-04-12T20:28:05Z

Static Deformation of Fluid-Saturated Rocks Coyner, Karl The static strain response of porous solids to combinations of confining stress and pore pressure is explained both theoretically and experimentally. The theoretical analysis is a synopsis of linear elasticity principles for porous media taken mainly from Biot (1941), Gassmann (1951), Biot and Willis (1956), and Geertsma (1957). From this analysis the conclusion is made that the "effective stress" of Terzaghi (1923, 1925), which is the difference between hydrostatic confining stress and pore pressure for strain properties, has no theoretical or experimental significance for the static strain response of intact rocks. The Terzaghi effective stress cannot account for the intrinsic bulk strain of minerals, a component of strain response important in consolidated sediments and rocks but not in muds and soils, for which the Terzaghi relation was originally intended. Effective stress "laws" for static deformation proposed by Nur and Byerlee (1971), Garg and Nur (1973), Robin (1973), and Carroll (1979) are shown only to be reformulations of linear elasticity relations. The effective stress so defined has no intrinsic physical meaning. Experimental bulk strain measurements on a suite of rocks as a function of hydrostatic confining stress and pore pressure are presented. Equilibrium strain at any combination of confining stress and pore pressure is predicted on the basis of 1) the zero pore pressure or drained jacketed stress-strain relation, and 2) the unjacketed stress-strain relation. Unjacketed strain measurements with a confining pressure fluid are emphasized as a means of directly measuring the intrinsic modulus of aggregate minerals in rocks. A technique is outlined for experimentally obtaining pore volume or porosity as a function of confining stress from finely digitized unjacketed and jacketed strain data by a straightforward application of linear elasticity principles incrementalized over small data steps. An argument is made, based on the linear elasticity analysis for strain response, that the differential hydrostatic stress, or what is commonly called effective stress, predicts many physical properties exclusive of bulk strain because of 1) the large intrinsic moduli of minerals, and 2)the definition of a stress as a force per unit area is maintained during deformation because of the small strains normally encountered in consolidated rocks and sediments.

Application of Full Waveform Acoustic Logging Data to the Estimation of Reservoir Permeability

2019-04-11T03:23:05Z

Application of Full Waveform Acoustic Logging Data to the Estimation of Reservoir Permeability Mathieu, F.; Toksoz, M. N. Development of borehole geophysics has recently focused on reservoir characterization. Within this effort, extensive full waveform acoustic surveys have demonstrated a correlation between the occurance of open fractures and attenuation of Stoneley waves. A relationship is obtained here between fracture permeability and attenuation of Stoneley waves, on the basis of a physical mechanism. This mechanism involves an energy transfer under the form of a fluid flow inside permeable formations. It is applied to the cases of a single open fracture, a multi-fractured medium and a homogeneous porous medium. Theoretical results show the effects of frequency, borehole radius, permeability, fracture density and porosity on attenuation. The single fracture theory is applied to observed attenuation data due to isolated large open fractures: the theoretical fracture apertures obtained compare favorably to values determined from packer tests.

Field Test of a Low-Frequency Sparker Source for Acoustic Waveform Logging

2019-04-12T07:14:31Z

Field Test of a Low-Frequency Sparker Source for Acoustic Waveform Logging Paillet, Frederick L. Low-frequency acoustic-energy sources for waveform logging have important applications in: 1) Verifying theoretical calculations; 2) generating tube waves in large-diameter boreholes; and 3) providing larger sample volumes in cases where borehole effects are important. A new low-frequency source was fabricated by modifying an existing acoustic-waveform logging system to discharge multiple capacitors in series with an automobile spark plug. The sparker source was tested in boreholes of 15- and 8-centimeter diameter in homogeneous granite containing isolated fractures. The sparker source produced repeatable waveforms with frequencies centered on 5 kilohertz in the 8-centimeter-diameter borehole, and 7 kilohertz in the 15-centimeter-diameter borehole, compared to frequencies near 15 kilohertz for the same system using a low-frequency magnetostrictive source. The lower-frequency sparker source excited consistently measurable tube waves, in agreement with theory. Test results also confirmed that lower-source frequencies greatly decreased sensitivity to borehole effects. Observed differences in frequency content and extent of shear-mode excitation in the two different diameter boreholes are probably related to differences in mode-excitation functions. The data confirm theoretical predictions that optimum shear-mode excitation occurs for source frequencies near normal-mode cutoff. Reflection of low-frequency tube waves appears to be an effective means for distinguishing between isolated open fractures and intervals containing extensive alteration around nearly impermeable fractures.

Analysis of Full Waveform Acoustic Logging Data in "Soft" Formations

2019-04-11T02:51:17Z

Analysis of Full Waveform Acoustic Logging Data in "Soft" Formations Barton, C.; Cheng, C. R.; Toksoz, M. N. Direct recording of formation shear wave travel time is not possible in "soft" formations where the shear velocity is lower than the borehole fluid velocity. The borehole Stoneley wave is quite sensitive to changes in formation shear wave properties and may be used to indirectly determine shear velocity. This paper presents a method to calculate formation shear velocity through inversion of the dispersion equation for the propagation of borehole Stoneley waves. The Stoneley wave group velocity and effective attenuation are also computed in this data analysis.

Applications of Finite Difference Synthetic Acoustic Logs

2019-04-11T02:51:17Z

Applications of Finite Difference Synthetic Acoustic Logs Stephen, R. A.; Pardo-Casas, F. Finite difference synthetic acoustic logs are suitable for studying wave propagation in vertically varying boreholes and in boreholes with continuously varying properties. Snapshots for the traditional smooth bore in a homogeneous rock show the standard phases in the borehole (compressional and shear head waves, pseudo-Rayleigh waves, and Stoneley waves), and also display the complex wave interaction which occurs in the rock. If a simple gradient in elastic parameters and density replaces the sharp interface the shear head wave and pseudo-Rayleigh wave are strongly attenuated. Also, off-centered receivers, washouts and horizontal fissures can have significant effects on amplitudes. A thorough understanding of these effects by forward modelling is essential in order to avoid pitfalls in interpretation and in order to design robust schemes for obtaining elastic properties and attenuation from acoustic logs. Stephen, R. A.; Pardo-Casas, F.

The Study of Wave Propagation in a Borehole Using the Finite Difference Method

2019-04-12T20:29:38Z

The Study of Wave Propagation in a Borehole Using the Finite Difference Method Pardo-Casas, Federico; Cheng, C. B.; Stephen, Ralph A. Synthetic microseismograms of elastic wave propagation in a fluid-filled borehole were generated using both the finite difference technique and the discrete wavenumber summation technique. For the finite difference calculations, the solid-liquid borehole boundary was handled as a sharp boundary using a second order Taylor expansion of the displacements. and additionally, a rigid solid-liquid sharp interface is used to model the existence of the logging tool. A heterogeneous formulation was used to handle variations in formation properties. The finite difference grid has absorbing boundaries on two sides and axes of symmetry on the remaining two sides. A grid size no less than 10 points per wavelength was used. The results from the finite difference modeling were compared with the synthetic microseismograms generated by the discrete wavenumber summation method. A detailed comparison between the microseismograms generated by the two methods showed that the body waves (refracted P and S waves) are identical, while the guided waves showed a slight difference in both phase and amplitude. These differences are believed to be due to the dispersion generated by the finite difference method. We have studied the depth of investigation of the retracted body waves in an invaded or damaged borehole using the conventional ray theory approach and compared the results to those obtained by the finite difference method. The results show that the minimum source-receiver separation necessary to observe the unaltered formation depends on both the velocity gradient and the lowest and highest velocity of the damaged zone. Such an investigation shows us the importance of the length of the logging tool to be able to "see" past the damaged and invaded zone, and thus enables us to measure the true formation properties, as well as to estimate the depth of the damaged or invaded zone.

Nullerical Studies of Body Wave Amplitudes in Full Waveform Acoustic Logs

2019-04-12T07:14:28Z

Nullerical Studies of Body Wave Amplitudes in Full Waveform Acoustic Logs Zhang, Jinzhong; Cheng, C. H. The amplitudes of P and S head waves in a full waveform acoustic log microseismogram are studied numerically as a function of borehole and formation parameters. The technique used is contour integration around the respective branch cuts in the complex wavenumber plane (Tsang and Rader, 1979). The results showed that the P wave amplitude depends on the Poisson's ratio, but the S wave amplitude does not. The well accepted geometric spreading factor for P and S waves in the "far field" is only valid for a limited range of source-receiver spacings, and the onset of "far field" depends on the Poisson's ratio as well as the wavelength. The wave shape factor I[subscript e] for the P wave as defined by Lebreton et al. (1978) has a direct relationship to in situ attenuation.

Determination of Formation Properties in Cased Boreholes Using Full Waveform Acoustic Logs

2019-04-12T20:28:08Z

Determination of Formation Properties in Cased Boreholes Using Full Waveform Acoustic Logs Tubman, Kenneth M.; Cheng, C. H.; Toksoz, M. Nafi Wave propagation in bonded and unbonded cased boreholes is examined through the calculation cif synthetic full waveform acoustic logs. The models consist of a central fluid borehole surrounded by a number of fluid and solid annuli. Waveforms calculated for a variety of formation and cement parameters demonstrate that the first arrivals observed on full waveform acoustic logs in well bonded cased holes are those of the formation and not the casing. Waves refracted along the casing are generally too small to be observed. The presence of the steel and cement can make the determination of formation velocities more difficult than in an open hole. The formation body wave arrivals are decreased substantially if the cement velocities are near or greater than the formation velocities. A fluid layer between the steel and the cement essentially frees the pipe from the cement. The steel arrival then becomes a large, ringing signal which obscures the formation arrival. The presence of this layer is a more important factor than its thickness in causing such behavior. If the fluid layer is between the cement and the formation, the cement can damp out the ringing of the pipe. If a thick cement layer is bonded to the pipe and the fluid layer is thin. the casing arrival is small and the formation arrivals are discernible. A thinner cement layer results in the observation of a body wave that has a velocity that is an average of the steel and cement velocities.

Dispersion Curves and Synthetic Microseismograms in Unbonded Cased Boreholes

2019-04-09T16:09:22Z

Dispersion Curves and Synthetic Microseismograms in Unbonded Cased Boreholes Tubman, Kenneth M.; Cole, Stephen P.; Cheng, C. H.; Toksoz, M. N. The dispersion relations and impulse response. are calculated for a geometry consisting of an arbitrary number of coaxial annuli surrounding a central cylinder. The annuli may be either solid or fluid. The formulation allows any number of solid and fluid layers in any sequence. The only restrictions are that the central cylinder is fluid and the outermost layer is solid. A propagator matrix method is used to relate stresses and displacements across layer boundaries. Fluid layers are handled by directly relating the displacements and stresses across these layers. A number of examples of dispersion curves and synthetic waveforms are given. The speciflc geometries used are those for a pipe not bonded to the cement and for the pipe well bonded to the cement but with the cement not bonded to the formation. The addition of an intermediate fluid layer can have a large effect on the calculated waveforms. More surprisingly, this additional layer may have only minor effects, indicating possible difficulties in establishing its presence. It the fluid layer lies between the steel and the cement (free pipe situation), the first arrival is from the steel. This is the case even for a very thin layer, or microannulus. If the fluid layer is between the cement and the formation,. the thicknesses of the cement and fluid layers become important in determining what will be the first arrival as well as the nature of the microseismogram. An intermediate fluid layer is shown to have the additional effect of introducing another Stoneley wave mode. This mode has only a small amount of energy and so it does not contribute significantly to the calculated· microseismograms.

Full Waveform Acoustic Logging - Where We Are, Where We Are Going

2019-04-11T01:22:09Z

Full Waveform Acoustic Logging - Where We Are, Where We Are Going Toksoz, M. Nafi; Cheng, C. H.; Garcia, Gilles We have now completed the second year of the Full Waveform Acoustic Logging Consortium. During these two years, we have developed a good understanding of seismic wave propagation in a borehole through both theoretical modelling and data interpretation. If we were to make a simple statement about the full waveform acoustic log, it would be that the method has far greater potential for determining formation properties than we ever had envisioned. But the problem is complicated and utilizing the data effectively requires sophisticated theoretical analyses and new approaches to data acquisition and interpretation. In this introductory chapter of the second annual report of the Consortium, we give some examples to illustrate the potential of full waveform acoustic logs and problems associated with the interpretation of the data. Based on these assessments, we also identify some topics that will receive priority in our research in the coming years.

The Effects Of High Pressure-High Temperature On Some Physical Properties Of Ocean Sediments

2019-04-12T07:14:28Z

The Effects Of High Pressure-High Temperature On Some Physical Properties Of Ocean Sediments Morin, Roger; Silva, Armand J. A series of laboratory experiments was conducted with four ocean sediments, two biogenic oozes and two clays. Permeability and thermal conductivity were directly measured as a function of porosity and the testing program was designed to identify any dependence of these physical properties upon hydrostatic pressure and temperature. The results show no discernible effect of pressure, within the range of 2 to 60 MPa, upon the permeability of any of the samples. Temperature effects, from 22' to 220', upon this property are accounted for by applying a viscosity correction to the permeating seawater. Previous investigations have suggested the existence of a pressure-induced and/or a temperature-induced breakdown of the adsorbed water which surrounds clay particles, thereby promoting an increase in sediment permeability. Our experimental findings cannot confirm this phenomenon and fail to provide a satisfactory solution to the confiicting data which now exist between the pore water velocities inferred from non-linear thermal profiles of ocean sediments and those fluid velocities derived from Darcy's Law and laboratory permeability data. The effects of sizeable variations in pressure and temperature upon sediment thermal conductivity are found to closely refiect the behavior of the conductivity of the liquid phase alone under these same changes in environmental conditions. This is not surprising, due to the relatively narrow range of high porosities encountered in this study. Empirical equations are developed which allow sediment thermal conductivity to be calculated as a function of temperature and void ratio. A hydrostatic pressure correction term is also presented.

Detection Of Subsurface Fractures And Permeable Zones By The Analysis Of Tube Waves

2019-04-09T16:14:41Z

Detection Of Subsurface Fractures And Permeable Zones By The Analysis Of Tube Waves Beydoun, W. B.; Cheng, C. H.; Toksoz, M. N. In Vertical Seismic Profiling tube waves are generated by compressional waves impinging on subsurface fractures or permeable zones. The amplitude of tube waves is dependent upon the formation permeability, the length of the fracture, and on the source frequency. The generation of tube waves is formulated theoretically and the relative effects of these parameters are studied individually. Field examples are shown for open fractures in granite. From tube wave amplitudes normalized to P-wave amplitudes, calculated permeabilities are on the order of 400 millidarcys.

Frequency and Scale Effects in the Optimization of Acoustic Waveform Logs

2019-04-12T07:14:26Z

Frequency and Scale Effects in the Optimization of Acoustic Waveform Logs Paillet, Frederick L. Previously formulated scaling laws relating acoustic waveforms in boreholes to frequency, tool size and borehole diameter were investigated by repeated logging of the same test interval with different frequencies, and by logging adjacent boreholes of different diameters with the same logging system. Acoustic source frequency bands were centered on approximately 15, 20 and 34 kilohertz. Borehole diameters were Band 17 centimeters for test intervals located at depths ranging from 100 to 400 meters in granite. Test intervals included zones of homogeneous rock and fracture zones that were independently characterized with acoustic televiewer logs and core from the B centimeter borehole. The high frequency transducer produced waveforms dominated by the tube wave mode in the B centimeter borehole, but by a complicated interference pattern produced by the superposition of three normal modes in the 17 centimeter borehole. The two lower frequency transducers produced waveforms in the 17 centimeter diameter borehole with power spectra dominated by the first normal mode. Various methods for picking shear arrivals produced shear velocities in close agreement with known values for all cases except for the data obtained with the high frequency transducer in the 17 centimeter diameter borehole. This result was attributed to the effects of mode superposition and enhanced attenuation of higher frequencies. Tube wave amplitudes constructed from the data obtained with the higher frequency transducer in the B centimeter borehole provided the most unambiguous indication of open fractures. The superior quality of these amplitude logs was attributed to the strong excitation of tube waves, as opposed to the primary excitation of the first normal mode by the two lower frequency transducers in the 17 centimeter borehole.

Acoustic Character Of Hydraulic Fractures In Granite

2019-04-11T02:51:16Z

Acoustic Character Of Hydraulic Fractures In Granite Paillet, Frederick I. Hydraulic fractures in homogeneous granitic rocks were logged with conventional acoustic-transit-time, acoustic-waveform, and acoustic-televiewer logging systems. Fractured intervals ranged in depth from 45 to 570m. and logs were made both before and after the fractures were induced. Unambiguous identification of almost all induced fractures was made on the three types of logs, with depth alignments verified through identification of nearby natural fractures. Most televiewer images of the induced fractures indicate the presence of discontinuous hairline fractures parallel to or splaying from the main fractures. Induced fractures also were similar in orientation to nearby natural fractures. All but the two most steeply dipping hydraulic fractures produced small apparent decreases in compressional velocity. Waveforms that propagated across hydraulic fractures at depths greater than 100 m had negligible shear anomalies and tube-wave attenuation. These results indicate that the hydraulic fractures at these depths were slightly open within a few centimeters or less of the borehole wall, and did not produce a measurable increase in permeability. Two induced fractures at depths of less than 100 m had more pronounced shear anomalies, indicating that these fractures may not have fully reclosed upon pressure release at the end of the fracture experiment.

Inversion Of Travel Time For Velocity

2019-04-11T02:51:17Z

Inversion Of Travel Time For Velocity Willis, M.E. Common source velocities and borehole compensated (BC) estimates have been used to obtain formation velocity estimates from full waveform acoustic logs (Willis and Toksoz, 1982). With both of these methods the receiver separation of the tool dictates the depth resolution of the velocities determined. This paper presents a method to 1) increase the depth resolution of the velocity estimates, and 2) remove the effects of a changIng borehole radius upon the velocity estimates through formal inversion of arrival times and travel time moveouts. Results obtained by the inversion of full waveform acoustic log travel times appear quite promising. The velocity estimates on synthetic arrival times are slightly more noisy than those obtained using the standard BC technique. The most significant aspect of synthetic arrival times is that they generally appear to be unbiased. The BC technique is biased around formation boundaries and is especially biased for thin layers.

P And S Wave Velocity Determination

2019-04-10T20:56:59Z

P And S Wave Velocity Determination Willis, M. E.; Toksoz, M.N. There are three general methods that can be used to determine formation velocities from full waveform logs. The first approach is to make use of the data from the entire waveform. This type of velocity analysis is performed either in the frequency domain (i.e. f-k analysis or the two station method) or in the time domain (I.e. velocity spectral analysis). The second approach is to identify the P wave pulses on individual traces and to determine delay times between traces. In conventional acoustic logging this technique has been used successfully to determine the compressional wave velocities. The third approach' is to use the phase velocity of the gUided waves (Pseudo-Rayleigh) to determine the shear velocity. Each of these approaches have certain advantages and limitations depending on the tool characteristics (number of records, frequency response), formation properties (high or low shear velocity), and computation times required. The effect of these parameters upon each method of velocity determination is presented.

Approximate Effects of Off-Center Acoustic Sondes and Elliptic Boreholes Upon Full Waveform Logs

2019-04-12T07:14:30Z

Approximate Effects of Off-Center Acoustic Sondes and Elliptic Boreholes Upon Full Waveform Logs Willis, M. E.; Toksoz, M. N.; Cheng, C. H. Full waveform acoustic well logging has become instrumental to hydrocarbon exploration because of its ability to determine in situ velocity information for P and S waves as well as the attenuation (or absorption) of seismic energy. It is therefore important that the factors infuencing these logs be understood. In addition to formation properties, Poisson's ratio, the borehole environment, and tool centering can affect the full waveform acoustic logs. These latter factors are evaluated through modeling of elliptic boreholes and de-centralized tools in the borehole.

Finite Difference Synthetic Acoustic Logs

2019-04-09T16:38:59Z

Finite Difference Synthetic Acoustic Logs Stephen, R. A.; Pardo-Casas, F.; Cheng, C. H. Synthetic seismograms of elastic wave propagation in a fluid-filled borehole were generated using both the finite difference technique and the discrete wavenumber summation technique. The latter is known to be accurate for both body and surface (guided) waves. The finite difference grid has absorbing boundaries on two sides and axes of symmetry on the remaining two sides. A grid size no less than 10 points per wavelength was used. The far absorbing boundary was located at a distance of five to 10 radii from the borehole. Two types of solid-liquid interfaces were investigated: 1) a velocity gradient using the heterogeneous formulation, and 2) a sharp boundary using a second order Taylor expansion of the displacements. The results from the finite difference modeling were compared with the synthetic seismograms generated by the discrete wavenumber summation method. No comparison the heterogeneous formulation and the discrete wavenumber method has been made. The second order approximation to the solid-liquid interface produced seismograms that compared 'well with the discrete wavenumber seismograms. A detailed comparison between the seismograms generated by the two methods showed that the body waves (refracted P and S waves) are identical. while the guided waves showed a slight difference in both phase and amplitude. These differences are believed to be due to the approximations introduced in the fluid-solid interface, the absorbing boundary at the edge of the grid, and the grid and time step sizes involved. Owing. to the fact that they are interface waves, the guided waves, especially the higher modes, are much more sensitive to the above mentioned approximations.

Effects of Casing on Full Waveform Acoustic Logs

2019-04-11T02:51:16Z

Effects of Casing on Full Waveform Acoustic Logs Tubman, Kenneth M.; Cheng, C. H.; Toksoz, M. Nafi A general expression is derived for the dispersion relations and the impulse response of a radially layered borehole. The. model geometry consists of a central fluid cylinder surrounded by an arbitrary number of solid annuli. A Thomson-Haskell type propagator matrix is used to relate stresses and displacements across the layers. Although the model is completely general, the geometries considered here are restricted to those of a cased hole. Layers of steel, cement, and an infinite, outermost layer of a formation surround the fluid layer. Synthetic seismograms containing all body and interface waves are calculated for a variety of model parameters. Formation body wave arrivals are relatively unaffected by the presence of a casing. They may, however, be hard to identify if the cement velocities are close to or larger than those of the formation. The Stoneley and pseudo-Rayleigh wave arrivals are predominantly influenced by the casing parameters. They respond to the combined effects of the steel, the cement, and the formation.

Determination of Shear Wave Velocities in "Slow" Formations

2019-04-12T20:28:08Z

Determination of Shear Wave Velocities in "Slow" Formations Cheng, C. H.; Toksoz, M. Nafi Direct determination of formation shear wave travel time is impossible in "slow" formations where the shear wave velocity is lower than the borehole fluid (mud) velocity. However, the Stoneley waves in these formations are very sensitive to changes in formation shear wave properties and can be used to indirectly determine the formation shear velocity, In addition, the P wave packet is highly dependent on the Poisson's ratio and thus can be used to estimate the shear velocity once the P wave velocity is known. These phenomena are demonstrated with both numerical and field examples.

Seismic Waves in a Borehole - A Review

2019-04-11T01:22:08Z

Seismic Waves in a Borehole - A Review Toksoz, M. N.; Cheng, C. H.; Willis, M. E. The propagation of seismic waves in an open borehole is reviewed. The principal wave types are the refracted P and S waves and the two guided waves - pseudo-Rayleigh and Stoneley. The dispersion properties of the guided waves are analyzed. An efficient method of computing synthetic microseismograms is described. The relative effects of the borehole. fluid and formation properties on the propagation characteristics of the different wave types are discussed.

Determination of Shear Wave Velocity and Attenuation From Waveforms in Low Velocity Formations

2019-04-12T20:28:05Z

Determination of Shear Wave Velocity and Attenuation From Waveforms in Low Velocity Formations Toksoz, M. Nafi; Wilkens, R. H.; Cheng, C. H. In boreholes where formation shear velocity is lower than borehole fluid velocity neither refracted shear waves nor pseudo-Rayleigh waves can propagate. When frequency response of the sonde does not extend to low frequencies (e.g. 2 kHz) Stoneley waves are not excited efficiently. In such cases refracted P, leaking modes (PL) and fluid waves become dominant phases on a full waveform acoustic log. The P wave velocity can be determined from the first arrivals. Then, using synthetic microseismograms and a waveform matching technique, formation shear wave velocity and attenuation can be determined. This method· is demonstrated using data from a well in the Baltimore Canyon Trough area of the Atlantic margin.

Detection of Open Fractures with Vertical Seismic Profiling

2019-04-12T20:28:02Z

Detection of Open Fractures with Vertical Seismic Profiling Beydoun, W. B.; Cheng, C. H.; Toksoz, M. N. In Vertical Seismic Profiling surveys tube waves are generated by compressional waves impinging on subsurface fractures or permeable zones. The problem of generation of these waves by a non-normal incident P wave for an inclined borehole intersecting a tilted parallel wall fracture is formulated theoretically. The amplitude of tube waves depends on the permeability, the length of the fracture, and on the frequency. The relative effects of these parameters are studied individually. The problem is also formulated for a thin oblate ellipsoidal (penny-shaped) fracture. The results for the two fracture models are compared and contrasted. Field data from Tyngsboro, Massachusetts are shown for open fractures in granite. From tube wave amplitudes normalized to P wave amplitudes, calculated permeabilities are on the order of one hundred millidarcys.

A comparison of LWD and wireline dipole sonic data

2019-04-11T06:24:50Z

A comparison of LWD and wireline dipole sonic data Briggs, Victoria; Rao, Rama V. N.; Grandi, Samantha K.; Burns, Daniel R.; Chi, Shihong Data measured by both wireline and LWD tools in the same borehole are compared. Discrepancies in shear velocities as calculated from the data are on average around 5% and discrepancies between compressional velocities are less than 3%. The consistency of the bias between logs suggest it is related to the calculation of velocity. Comparison of industry and ERL velocity processing show excellent agreement and give an example of possible spread of velocity data due to processing chain. A short section of data in an unconsolidated zone shows velocity differences of just over 10% with an opposite trend to the over all bias. Dispersion analysis of the waveforms show this is consistent with a damaged zone surrounding the borehole wall caused by drilling.

Effects of source mismatch on multipole Logging

2019-04-10T19:51:48Z

Effects of source mismatch on multipole Logging Byun, Joongmoo; Toksoz, M. Nafi; Rao, Rama V. N. The effects of mismatched multipole sources were investigated. Multipole sources considered here are those that they are constructed of monopoles with appropriate sign combination. To simulate mismatched dipole and quadrupole sources, we made the amplitude of one of monopoles smaller than those of the other monopoles. The dipole and quadrupole component were obtained with four monopole receiver array system by subtracting or adding appropriate responses. Mismatched dipole source excites nondipole modes in addition to the flexural mode. The strongest of these is the Stoneley mode, whose amplitude increases with increasing mismatch. Similarly, mismatched quadrupole sources produce nonquadrupole modes such as the Stoneley mode in addition to the screw mode. The amplitude of the Stoneley mode increases with mismatch. However, we can obtain the flexural mode by A-C and the screw mode by A-B+C-D processing, respectively. The Stoneley mode, which has the same amplitude at the same radial position from the borehole axis, is cancelled out by A-C and A-B+C-D processing as long as the tool is placed at the center of the borehole.

Effects of tool eccentricity on wave dispersion properties in borehole acoustic logging while drilling

2019-04-11T06:24:53Z

Effects of tool eccentricity on wave dispersion properties in borehole acoustic logging while drilling Zheng, Yibing; Toksoz, M. Nafi In this paper, a finite element approach is applied to study the dispersion properties of non-leaky acoustic waves inside boreholes with off-centered LWD (logging while drilling) tools. Both soft and hard formation cases are studied with focus on phase velocity dispersions of Stoneley, dipole and quadrupole modes. When an LWD tool is off-centered, the dispersion curve of the Stoneley mode shifts to the lower phase velocity compared with that of a centered-tool condition. Meanwhile, the dipole dispersion curve splits into two curves with different phase velocities. This splitting phenomenon is also observed with the quadrupole mode. The splitting and shifting of the dipole mode are greater than those of the quadrupole mode. These new observations are important for interpreting acoustic LWD data accurately.

Experimental Studies of Multipole Acoustic Logging with Scaled Borehole Models

2019-04-11T06:24:54Z

Experimental Studies of Multipole Acoustic Logging with Scaled Borehole Models Zhu, Zhenya; Rao, Rama V. N.; Burns, Daniel R.; Toksoz, M. Nafi A scaled multipole acoustic tool is built for laboratory measurements at ultrasonic frequencies in borehole models. The source with four separate transducers generate monopole, dipole, and quadrupole waves by different combination of the transducers. Each receiver has two separate transducers and six receivers which records twelve acoustic components of the multipole waves propagating along a borehole. The experimental results in the borehole models show the center frequency of the multipole waves responding in a soft formation is lower than in a hard formation. The monopole system can measure the P-wave and S-wave in hard formation, but no S-wave or slow shear wave in soft formation. In a dipole system, flexural and hexapole modes in both the soft and hard formations can be observed. These dispersive modes propagate at velocities that are slightly slower than the formation shear velocity. The quadrupole system records the screw waves in soft and hard formations, which also propagate slower than the formation shear velocities. in the soft anisotropic formation, no slow screw wave is recorded.

3-D Finite Di erence Modeling for Borehole and Reservoir Applications

2019-04-12T15:20:25Z

3-D Finite Di erence Modeling for Borehole and Reservoir Applications Krasovec, Mary L.; Burns, Daniel R.; Willis, Mark E.; Malcolm, Shihong; Toksoz, M. Nafi ERL's in-house nite difference code (Krasovec et al., 2003) has undergone several upgrades in the past year. Most notably, a stretched grid can now be used to greatly reduce the amount of RAM memory needed by certain types of models. Improvements have been made in the GUI front end, allowing more freedom and ease in building the model, source or source array, and receiver array. The finite difference code has contributed to several different research projects at ERL in the past year. A few of these projects, including borehole seismics, reservoir delineation, and source mechanics, are shown in this report.

Finite-Difference Simulations of Time Reversed Acoustics in a Layered Earth Model

2019-04-12T15:20:20Z

Finite-Difference Simulations of Time Reversed Acoustics in a Layered Earth Model Lu, Rongrong; Toksoz, M. Nafi Traditionally an earthquake is located by using the arrival times of P and S phases. This uses only a limited portion of the information on a seismogram. A large part of the information carried by the waveform is not used. In this study we investigate the applicability of the Time Reversed Acoustics (TRA) technique, and thus the whole waveform of the recorded signal, for earthquake locations and source characterization. The basic concept involved in TRA is the fundamental symmetry of time reversal invariance. Injecting the recorded signal, with time running backwards, reconstructs the whole wave field within the medium and can focus the wave field to the source. TRA has emerged as an important technique in acoustics with applications to medicine, underwater sound, and many other disciplines. The objective of this paper is to demonstrate the feasibility of applying TRA to seismological data by means of simulating the relevant features using a finite-difference approach. The following subjects are investigated: (1) Locating the earthquake hypocenter; (2) finding the source space-time function; and (3) characterizing the direction of fault rupture during an earthquake. The results show that the TRA technique can focus back to the source reasonably well in a layered earth model and can recover the source time function. The results also show that TRA has a good tolerance to noise. For efficient applications, calculation time can be reduced by generating a medium response library. The source location and source time function can then be determined by convolving the medium response library with the time-reversed signals recorded at the seismic stations.

S-wave Splitting Analysis: Covariance Matrix Method and Preliminary Application

2019-04-10T07:26:14Z

S-wave Splitting Analysis: Covariance Matrix Method and Preliminary Application Li, Xu; Sze, Edmond; Burns, Daniel R.; Toksoz, M. Nafi From polarization analysis on a covariance matrix, a method of S-wave splitting analysis is developed, which processes 3-component recordings simultaneously, rather than just 2 horizontal components as done traditionally. Thus not only orientation, but also dip information of fractures can be resolved. The synthetic test results show that this method is stable even for noise levels as high as 100% (S/N=1). If time window sizes are larger than roughly twice the time delay between the fast and slow S waves, the results are always reasonable even with noise levels up to 50%.The method is applied to 12 microseismic events recorded from a producing reservoir. The preliminary results suggest that stress-aligned fractures strike in NE-SW direction in the reservoir. The dips of the fractures are primarily vertical. The time difference between the fast and slow shear waves is about several tens of milliseconds per kilometer.

Fluid Flow Modeling in Fractures

2019-04-12T15:20:25Z

Fluid Flow Modeling in Fractures Sarkar, Sudipta; Toksoz, M. Nafi; Burns, Daniel R. In this paper we study fluid flow in fractures using numerical simulation and address the challenging issue of hydraulic property characterization in fractures. The methodology is based on Computational Fluid Dynamics, using a finite-volume based discretization scheme. Steady-state, viscous, laminar flow simulations for a Newtonian fluid are carried out in both 2D and 3D fracture models. In 2D, flow is analyzed in single fractures, series and parallel combination of fractures, inclined fractures, intersecting fractures, mixed networks, and in real (rough-surface) fractures. In 3D, flow is simulated in both uniform and variable aperture fracture models. To characterize each fracture model with an equivalent hydraulic aperture, equations are derived for all possible scenarios followed by comparison and validation with results derived from flow simulation. Based on the fracture models analyzed, the following are some of the important findings: 1) For fractures connected in series, the equivalent hydraulic aperture is a weighted harmonic mean of cubed apertures of all fractures. 2) For fractures connected in parallel, the equivalent flow is simply the sum of all flows through individual fractures. 3) If a fracture is inclined with respect to the axis of pressure gradient, then the amount of flow will be reduced by a factor of cosine of the inclination angle. 4) Any network of randomly intersecting fractures can be replaced by a single fracture to give flow equivalence; the aperture of that equivalent fracture will roughly be close to the aperture of the fracture in the network that cuts across the boundaries (inlet and outlet) in the most continuous fashion and have the smallest inclination (with respect to the pressure gradient axis). 5) For hydraulic characterization purposes, fluid flow in fractures can be sufficiently modeled using both Stokes and Navier-Stokes equations for flow Reynolds number upto approximately 100.

Seismic Scattering Attributes to Estimate Reservoir Fracture Density: A Numerical Modeling Study

2019-04-11T06:24:57Z

Seismic Scattering Attributes to Estimate Reservoir Fracture Density: A Numerical Modeling Study Pearce, Frederick Douglas We use a 3-D finite difference numerical model to generate synthetic seismograms from a simple fractured reservoir containing evenly-spaced, discrete, vertical fracture zones. The fracture zones are represented using a single column of anisotropic grid points. In our experiments, we vary the spacing of the fracture zones from 10-meters to 100-meters, corresponding to fracture density values from 0.1- to 0.01-fractures/meter, respectively. The vertical component of velocity is analyzed using integrated amplitude and spectral attributes that focus on time windows around the base reservoir reflection and the scattered wave coda after the base reservoir reflection. Results from a common shot gather show that when the fracture zones are spaced greater than about a quarter wavelength of a P-wave in the reservoir we see 1) significant loss of amplitude and coherence in the base reservoir reflection and 2) a large increase in bulk scattered energy. Wavenumber spectra for integrated amplitude versus offset from the time window containing the base reservoir reflection show spectral peaks corresponding to the fracture density. Frequency versus wavenumber plots for receivers normal to the fractures separate backscattered events that correspond to spectral peaks with positive wavenumbers and relatively narrow frequency ranges. In general, backscattered events show an increase in peak frequency as fracture density is increased.

Fracture Detection using Amplitude versus Offset and Azimuth Analysis of a 3D P-wave Seismic Dataset and Synthetic Examples

2019-04-12T15:20:24Z

Fracture Detection using Amplitude versus Offset and Azimuth Analysis of a 3D P-wave Seismic Dataset and Synthetic Examples Minsley, Burke J.; Willis, Mark E.; Krasovec, Mary L.; Burns, Daniel R.; Toksoz, M. Nafi Amplitude versus offset (AVO) analysis of seismic reflection data has been a successful tool in describing changes in rock properties along a reflector. This method is extended to azimuthal AVO (AVOA) in order to characterize vertically aligned fractures within a reservoir, which can be important fluid migration pathways. AVOA analysis is performed on synthetic data using a least squares inversion method to investigate the effects of varying acquisition geometry, amount of noise, and fracture properties. These tests show that it is possible to detect the fractured layer and determine the fracture strike orientation under typical acquisition conditions. This method is also applied to field data collected during an Ocean Bottom Cable (OBC) survey. These data include a broad offset-azimuth range, which is important for the AVOA analysis. The fracture location and strike orientation recovered from the field data analysis are well correlated with borehole information from this area. Based on an understanding of AVOA behavior under synthetic conditions, this technique provides an effective methodology for describing the spatial variability of a fractured reservoir using 3D seismic data.

Comparison Of Scattered Energy Using Point Scatterers Versus Full 3D Finite Difference Modeling

2019-04-12T15:20:14Z

Comparison Of Scattered Energy Using Point Scatterers Versus Full 3D Finite Difference Modeling Willis, Mark E.; Zhang, Yang; Burns, Daniel R. We present results of 3D numerical modeling using a series of simple point scatterers to create synthetic seismic shot records collected over regular, discrete, vertical fracture systems. The background medium is taken to be constant velocity. The model contains a series of point scatterers delineating the top tip and bottom tip of each vertical fracture. We use these results to gain an understanding of some of the features seen in full 3D elastic modeling of vertical fractures. We compare our results to those of Willis et al (2003) and Willis et al (2004) for their 5 layer model with 50m spacing between discrete, vertical fractures. Our modeling shows that a series of back scattered events with both positive and negative moveouts are observed when the shot record is oriented normal to the direction of fracturing. When the shot record is both located in the middle of the fractured zone and is oriented normal to the direction of fracturing, a complicated series of beating is observed in the back scattered energy. When the shot record is oriented parallel to the fracturing, ringing wavetrains are observed which moveouts similar to reflections from many horizontal layers. The point scattering models are, in general, very consistent with the full 3D elastic modeling results.

Spatial Orientation And Distribution Of Reservoir Fractures From Scattered Seismic Energy

2019-04-12T15:20:18Z

Spatial Orientation And Distribution Of Reservoir Fractures From Scattered Seismic Energy Willis, Mark E.; Rao, Rama V. N.; Burns, Daniel R.; Byun, Joongmoo; Vetri, Laura Expanded details and additional results are presented using a new method (Willis et al, 2003) for determining the reflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations made from 3D finite difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fractures impart a ringing coda type signature to any seismic energy which is transmitted through or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1) the difference in angle between the orientation of the fractures and the acquisition direction, 2) the fracture spacing, 3) the wavelength of the illuminating seismic energy, and 4) the compliance, or stiffness, of the fractures. This coda energy is greatest when the acquisition direction is parallel to the fractures, the seismic wavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. The method uses surface seismic reflection traces to derive a transfer function which quantifies the change in an apparent source wavelet propagating through a fractured interval. The transfer function for an interval with low scattering will be more spike-like and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. When a 3D survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows the identification of subsurface areas with high fracturing and the orientation (or strike) of those fractures. The method was calibrated with model data and then applied to a field with a fractured reservoir giving results which agree with known field measurements.

Singularity analysis: a tool for extracting lithologic and stratigraphic content from seismic data

2019-04-12T15:20:15Z

Singularity analysis: a tool for extracting lithologic and stratigraphic content from seismic data Lyons, William J.; Herrmann, Felix; Grotzinger, John P. In this work, we test an amplitude-independent method of seisimic data analysis designed to extract lithologic information about stratigraphic horizons. We apply the method of singularity characterization in an attempt to determine the sharpness of lithologic boundaries. We infer the sharpness of the boundary based upon a fractional integration of the seismic trace. The order of fractional integration is taken to represent the abruptness of the lithologic transition responsible for a given reflector. We find that the method output behaves in a geologically reasonable manner which suggests that our method is responding to lithologic variations along boundaries responsible for prominent reflectors in the data.

3−D Surface Topography Boundary Conditions in Seismic Wave Modelling

2019-04-10T19:47:51Z

3−D Surface Topography Boundary Conditions in Seismic Wave Modelling Hestholm, Stig; Ruud, Bent New alternative formulations of exact boundary conditions for arbitrary three{dimensional (3−D) free surface topographies on seismic media have been derived. They are shown to be equivalent with previously published formulations, thereby serving as a verification of the validity of each set of formulations. The top of a curved grid represents the free surface topography while the grid's interior represents the physical medium. We assume the velocity{stress version of the viscoelastic wave equations to be valid in this grid before transforming the equations to a rectangular grid. In order to do the numerical discretization we apply the latter version of equations for seismic wave propagation simulation in the interior of the medium. The numerical discretization of the free surface topography boundary conditions by second−order finite−differences (F−Ds) is shown in detail, as well as spatially unconditional stability of the resulting system of equations. The F−D order is increased by two for each point away from the free surface up to eight, which is the order used in the interior. We use staggered grids both in space and time and the second-order leap-frog and Crank-Nicholson methods for wave field time propagation. We simulate point sources at the surface of a homogeneous medium, with a plane surface containing a hill and a trench, respectively. The main features of these general cases are outlined. Then, we present results using parameters typical of teleseismic earthquakes and explosions with a 200 × 100 km[superscript 2] area of real topography from southwestern Norway over a homogeneous medium. A dipping plane wave simulates a teleseismic P−wave incident on the surface topography. Results show clear conversion from P− to Rg− (short period fundamental mode Rayleigh) waves in the steepest and/or roughest topography, as well as attenuated waves in valleys and fjords. The codes are parallellized for simulation on fast supercomputers to model higher frequencies and/or larger areas than before.

Quantitative tools for seismic stratigraphy and lithology characterization

2019-04-10T21:08:47Z

Quantitative tools for seismic stratigraphy and lithology characterization Herrmann, Felix Seismological images represent maps of the earth's structure. Apparent bandwidth limitation of seismic data prevents successful estimation of transition sharpness by the multiscale wavelet transform. We discuss the application of two recently developed techniques for (non-linear) singularity analysis designed for bandwidth limited data, such as imaged seismic reflectivity. The first method is a generalization of Mallat's modulus maxima approach to a method capable of estimating coarse-grained local scaling/sharpness/Hölder regularity of edges/transitions from data residing at essentially one single scale. The method is based on a non-linear criterion predicting the (dis)appearance of local maxima as a function of the data's fractional integrations/differentiations. The second method is an extension of an atomic decomposition technique based on the greedy Matching Pursuit Algorithm. Instead of the ordinary Spline Wavelet Packet Basis, our method uses multiple Fractional Spline Wavelet Packet Bases, especially designed for seismic reflectivity data. The first method excels in pinpointing the location of the singularities (the stratigraphy). The second method improves the singularity characterization by providing information on the transition's location, magnitude, scale, order and direction (anti-/causal/symmetric). Moreover, the atomic decomposition entails data compression, denoising and deconvolution. The output of both methods produces a map of the earth's singularity structure. These maps can be overlayed with seismic data, thus providing us with a means to more precisely characterize the seismic reflectivity's litho-stratigraphical information content.

An Experimental Study of Turbidite Channel Deposits: Implications for Channel Evolution and Sandstone Deposits

2019-04-11T06:24:52Z

An Experimental Study of Turbidite Channel Deposits: Implications for Channel Evolution and Sandstone Deposits Buttles, James; Minsley, Burke J.; Schweller, Will; Grotzinger, John P. Gaining a detailed understanding of turbidite bed sequences is important for the characterization of sandstone reservoir properties, correlation of well cores, and geological interpretation. Many factors influence the internal structure of sandstone reservoirs: source material, source location in time, transport processes, basin geometry, fan channel development and evolution to name a few. Sandstone deposits associated with channel complexes are easy to find but difficult to develop. Here, we conduct tank experiments of scaled sediment-laden turbidity currents traversing a submerged channel to: (1) establish a state-of-the-art data collection and data processing system that has the potential to gain a unique understanding of the processes and deposits that build submarine fan environments; and (2) to use the facility to demonstrate how the interaction of a depositive turbidity current with a sinuous channel may influence the geometry, spatial relationships and grain size sorting of sandstone deposits. Our data shows the construction of prominent levees, asymmetric levee growth, continuous channel overspill, enhanced channel overspill downstream of bend corners, and lobate-shaped lobe deposits. Our preliminary results are qualitative, but indicate that channel wavelength, bend curvature, and bend peak-to-peak amplitude may have strong controls on down-channel and cross-channel depositional patterns, deposit thickness and grain size sorting.

Experimental Studies of Electrical Fields on a Breaking Rock Sample

2019-04-11T06:24:51Z

Experimental Studies of Electrical Fields on a Breaking Rock Sample Zhu, Zhenya; Morgan, Frank Dale; Marone, Chris J.; Toksoz, M. Nafi When a rock sample is pressed by a force, the pressure on the crystal lattice generates an electrical field around the quart grains due to the piezoelectric effect. If a rock is saturated by conductive fluid, the relative motion between the pore fluid and the matrix solid generates an electromagnetic field due to seismoelectric conversion, and the permeating of fluid into new microcracks made by the pressure changes the fluid distribution and the natural potential level. In this paper, we measure the electrical fields on dry and water-saturated Westerly granite cylinder samples during their breaking. Experimental results show that there are two kinds of mechanisms that generate two kinds of electrical fields during rock breaking: (1) Pressure, or rock breaking, generates an electrical potential on the dry rock surface due to piezoelectric effect; and (2) the potential on a dry sample due to a piezoelectric effect is small, and its polarization depends on the characteristic and orientation of quartz grains around the measurement point. Experiments with water-saturated granite samples record two electrical fields: An electromagnetic wave due to seismoelectric conversion, and the dc or low-frequency electrical potential due to the piezoelectric effect, which is an important indicator of rock breaking.

The propagation and linkage of normal faults: Insights from the Strathspey-Brent-Statfjord fault array, northern North Sea

2019-04-10T20:30:53Z

The propagation and linkage of normal faults: Insights from the Strathspey-Brent-Statfjord fault array, northern North Sea McLeod, Aileen E.; Dawers, Nancye H.; Underhill, John R. Through examination of the scaling relations of faults and the use of seismic stratigraphic techniques, we demonstrate how the temporal and spatial evolution of the fault population in a half-graben basin can be accurately reconstructed. The basin bounded by the >>62 km long Strathspey-Brent-Statfjord fault array is located on the western flank of the Late Jurassic age northern North Sea rift basin. Along-strike displacement variations, transverse fault-displacement folds and palaeo- fault tips abandoned in the hangingwall all provide evidence that the fault system comprises a hierarchy of linked palaeo-segments. The displacement variations developed while the fault was in a pre-linkage, multi-segment stage of its growth have not been equilibrated following fault linkage. Using the stratal architecture of syn-rift sediments, we date the main phase of segment linkage as latest Callovian - Middle Oxfordian (10-14 M.yr. after rift initiation). A dense sub-population of faults is mapped in the hangingwall to the Strathspey-Brent-Statfjord fault array. The majority of these faults are short, of low displacement and became inactive within 3-4 M.yr. of the beginning of the extensional event. Subsequently, only the segments of the proto- Strathspey-Brent-Statfjord fault and a conjugate array of antithetic faults located 3.5 km basinward continued to grow to de fine a graben-like basin geometry. Faults of the antithetic array became inactive approximately 11.5 M.yr. into the rift event, concentrating strain on the linked Strathspey-Brent-Statfjord fault; hence, the basin evolved into a half-graben. As the rift event progressed, strain was localised on a smaller number of active structures with increased rates of displacement. The results of this study suggest that a simple model for the linkage of 2-3 fault segments may not be applicable to a complex multi-segment array.

Diffusive MASS NMR Studies of Transport in Porous Materials

2019-04-12T15:20:16Z

Diffusive MASS NMR Studies of Transport in Porous Materials Liu, Yun; Leu, Gabriela; Cory, David G.; Sen, Pabitra NMR methods are widely used to probe the structure and fluid dynamics of porous materials including such diverse materials as cheese and chocolate, cosmetics and pharmaceuticals, solvents in resins and soft matter, biological tissue, and for oil exploration. NMR measurements are uniquely suited to these studies since it records the correlation of changing local magnetic fields over a time scale of ms to seconds. The local magnetic fields are established by local variations in the bulk magnetic susceptibility of the sample (and so are directly tied to the sample's local structure). The fluctuation in field that a spin sees is due to molecular transport (including molecular diffusion) through these local fields, and so reports on the length scales of structures and impediments to transport. In the past this information has primarily been employed via empirical relations that relate bulk measurements of relaxation times or diffusion to some microscopic property (pore size, throat size, S/V, and surface relaxivity, etc.). These empirical relationships, while useful, hide the underlying complexity of spin dynamics in confining geometries. We have developed a new set of methods to provide a means of systematically varying the reflective time scale of the measurement and thus the reflective length scale. This new handle permits a detailed, microscopic picture of the structure and dynamics.

Subsurface Imaging with Reverse Vertical Seismic Pro les

2019-04-12T15:20:15Z

Subsurface Imaging with Reverse Vertical Seismic Pro les Krasovec, Mary L.; Coates, Richard; Toksoz, M. Nafi A novel imaging process, referred to as vector image isochron (VII) migration, is specifically designed to reduce artifacts caused by arrays with limited apertures. By examining the assumptions behind generalized Radon transform (GRT) migration, a new approach is found which identities and suppresses array artifacts, based on the array geometry and the migration earth model. The new method works in four steps: 1) The conventional image is broken down according to the orientation of imaged planes within the image space, forming a vector image of the earth; 2) the earth model and the geometry of the arrays are used to derive vector image isochrons, which define the shape of reflection events in the vector image space; 3) the vector image is transformed by summing along the isochrons so that it depends on subsurface location and reflector orientation, rather than imaged plane orientation. This process is referred to as vector image isochron (VII) transformation; and 4) the transformed vector image is collapsed to a scalar image by summing over reflector orientations. The VII imaging method is derived in both 2D and 3D with the assumption that at least one of the arrays, source or receiver, is oriented horizontally. The surface array can have any distribution along the surface. The other array can have any orientation, although in this paper it will be assumed to be either another surface array or a vertically oriented downhole array. Downhole surveys in deviated wells, or in multiple wells, can be imaged with VII migration, at the likely cost of more computation time. The VII imaging method is tested on field data acquired in 1998 by MIT and several industry partners. The dataset is a 3D reverse vertical seismic profile (RVSP) over a hydrocarbon-bearing pinnacle reef in the northern Michigan reef trend. The survey exhibited two features of note: 1) A new, strong, downhole vertical vibrator, and 2) a random distribution of surface receiver locations. Due to adverse conditions, a large portion of the surface spread had to be abandoned. The reduced spatial coverage presents a challenge to the new migration method, but also limits the extent of the migrated image, precluding an evaluation of the reflectiveness of the random receiver spread. The limited nature of the receiver array also causes artifacts in the image which resemble migration "smiles". These are partially suppressed by limiting the dip aperture of the migration, but this also limits the reflector dips that can be imaged. The new VII imaging scheme, on the other hand, removes the artifacts without diminishing dipping reflectors. The VII images show more continuity along reflectors than images made with the conventional method.

Wavelet domain linear inversion with application to well logging

2019-04-11T06:24:51Z

Wavelet domain linear inversion with application to well logging Kane, Jonathan; Herrmann, Felix; Toksoz, M. Nafi Solving linear inversion problems in geophysics is a major challenge when dealing with non-stationary data. Certain non-stationary data sets can be shown to lie in Besov function spaces and are characterized by their smoothness (differentiability) and two other parameters. This information can be input into an inverse problem by posing the problem in the wavelet domain. Contrary to Fourier transforms, wavelets form an unconditional basis for Besov spaces, allowing for a new generation of linear inversion schemes which incorporate smoothness information more precisely. As an example inversion is performed on smoothed and subsampled well log data.

Simultaneous least squares deconvolution and kriging using conjugate gradients

2019-04-11T06:24:53Z

Simultaneous least squares deconvolution and kriging using conjugate gradients Kane, Jonathan; Rodi, William; Toksoz, M. Nafi Least squares deconvolution is a method used to sharpen tomographic images of the earth by undoing the bandlimiting effects imposed by a seismic wavelet. Kriging is a method used by geoscientists to extrapolate and interpolate sparse data sets. These two methodologies have traditionally been kept separate and viewed as unrelated fields of research. We demonstrate the connection between these methods by deriving them both as examples of linear inversion. By posing the methods in this way we can define a joint inverse problem in which observed values of reflectivity in wells are used to improve deconvolution, and, conversely, seismic data is used to help extrapolate well data. Solving this joint problem involves the solution of large sparse sets of linear equations. Due to the structure of the problem, the conjugate gradients method is ideal to perform the solution. Preliminary results show that convergence to a solution for a 3-D problem is fast and accurate, requiring only a few iterations. This methodology can be of great use to interpreters by sharpening the post stack image as well as helping to tie seismic data to wells.

The effect of stresses on the sound velocity in rocks: Theory of Acoustoelasticity and Experimental Measurements

2019-04-11T06:24:51Z

The effect of stresses on the sound velocity in rocks: Theory of Acoustoelasticity and Experimental Measurements Huang, Xiaojun; Burns, Daniel R.; Toksoz, M. Nafi The theory of acoustoelasticity provides direct link between the change of elastic wave velocities and residual stresses in solids. The general theory of acoustoelasticity is reviewed. A number of experimental measurements of the effect of stresses on the sound velocities in various types of rocks are compiled and compared to the acoustoelastic theory. The theory of acoustoelasticity agrees within 1% of error with experiments for stress levels that are representative for in-situ reservior conditions. With the measurements of Nur and Simmons, acoustoelastic theory is found to agree with Sayers's microcrack model within 2% of error, much smaller than experimental error which was 10%. We may safely conclude that the theory of acoustoelasticity is a macroscopic version of the microcrack model and applicable to in-situ rocks.

Determination of Near-Surface Anisotropy From Surface Electromagnetic Data

2019-04-12T15:20:15Z

Determination of Near-Surface Anisotropy From Surface Electromagnetic Data Al-Dajani, AbdulFattah; Morgan, Frank Dale; Toksoz, M. Nafi; Repperty, Philip Ground penetrating radar (GPR) signatures, such as reflection moveout, are sensitive to the presence of azimuthal anisotropy. Azimuthal anisotropy can occur as an intrinsic property of the medium and/or due to the presence of fractures. In such cases, the GPR normal moveout (NMO) velocity, along different orientations of common-midpoint (CMP) gathers, varies with azimuth. This fact is well known in surface reflection seismology. The azimuthal variation of the NMO velocity in an arbitrary medium is elliptical. Considering the analogy between seismic wave propagation in surface seismology and GPR sounding, we can transfer some of the ideas between both fields, including the ellipticity of the NMO velocity in a fractured medium. Here, we discuss briefly GPR reflection moveout in azimuthally anisotropic media. Our study focuses on the transverse mode of electromagnetic wave propagation in which the polarization is normal to the incidence plane of the CMP gathers. A field data example is presented in which three GPR CMP gathers are acquired along three different azimuths, 60° apart, over a fractured medium. Our data analysis demonstrates the azimuthal variation of the GPR NMO velocity, which is utilized to invert for the local orientation of the fracture system in the near surface. The results obtained from the field example agree with the information obtained from geology and near surface studies. This work has important applications in imaging near surface geologic structures and in the determination of tectonic-induced fractures in the near surface.

Towards a Quantitative Understanding of Bed Structure by Turbidity Currents

2019-04-11T06:24:50Z

Towards a Quantitative Understanding of Bed Structure by Turbidity Currents Kudrolli, Arshad; Blanchette, Francois; Brenner, Michael P.; Bush, John W. M. We are currently carrying out a series of experiments and theoretical calculations with the goal of creating a quantitative model for the structure of beds created by turbidity currents. Our research project operates on three different levels: first, on the largest scale, Jim Buttles and his colleagues in Earth and Planetary Sciences have a laboratory scale model of turbidity current deposition, where they can study both the dynamics and end-product of turbidity current flows. Our ultimate goal is to create a quantitative model for the beds they deposit. On a smaller scale, we are carrying out a set of experiments aimed at uncovering the essential mechanisms of particle deposition/layering in a bed caused by turbidity currents. These experiments are designed to be smaller scale counterparts of small "pieces" of the ERL turbidity current bed experiment. Finally, we are carrying out a theoretical investigation of how particle segregation/layering occurs in the beds laid down by turbidity currents. The ultimate goal of this research is to provide a modeling tool that will help interpret seismic data on turbidity currents. Although our research is still in its preliminary stages, we believe that coupling an understanding of how particle layering occurs as a function of the properties of the particle/fluid flow, with the state of the art understanding of the flow structure of turbidity currents will give a powerful tool for "guessing/deducing" bed structures that are below seismic resolution. The close coupling of this modeling effort with a laboratory scale model of a turbidite bed means that we will be able to test the model quantitatively in the laboratory. Another goal of the ongoing research is to discover physical laws which improve quantitative modeling of turbidity currents. In particular, the models of erosion by turbidity currents are ad hoc; the experiments we are planning will be designed to test these models, and stimulate theoretical improvements.

Executive Summary

2019-04-12T15:20:14Z

Executive Summary Burns, Daniel R. Our research results for the past year are divided into two major areas: 1) the quantification and prediction of reservoir heterogeneity and 2) the use of borehole measurements to quantify fluid flow related properties. As we look towards the future of instrumented reservoirs and downhole sensors, it is clear that these areas of research will begin to overlap in many ways. This overlap is evident in several of the papers presented in this report. One example is the migration of reverse VSP data (Krasovec et al, 2001), which develops a methodology with applications into reservoir imaging using downhole sensors as well as monitoring with acoustic emissions. Another example is the measurement of seismoelectric effects in boreholes (Zhu and Toksoz, 2001), which has great potential for reservoir monitoring. Other applications presented this year, such as Herrmann (2001) and Lyons et al. (2001), developed out of scaling analysis studies on well log data and now provide a promising method for extracting lithologic heterogeneity information from seismic reflection data. We are also extending our interest into new areas of measurement, such as NMR imaging (Leu et al., 2001), in order to develop a better understanding of the physics of fluid flow in porous media. We also continue our research philosophy of integrating theory, laboratory measurements, and field data analysis in all areas of reservoir science.

Interferometric imaging of multiples in an RTM approach

2019-04-11T06:24:52Z

Interferometric imaging of multiples in an RTM approach Malcolm, Alison E.; de Hoop, Maarten V. It is well known that reverse-time migration is capable of correctly imaging multiply scattered energy. To do this, one of the interfaces from which the waves scatter must be included in the background velocity model. In a one-way framework this requirement is avoided by iteratively forming images of higher-order scattered waves. These techniques use an image made with singly scattered waves to estimate the locations of some of the reflection points in a multiply-scattered wave, from which the location of an additional scattering point is determined through standard imaging techniques. This removes the requirement that a single multiple-generating interface be identified. Here we extend this technique to reverse-time migration using results from several recent studies linking standard and extended imaging conditions to interferometry. This results in a method to generate images with multiply-scattered waves using the full-waveform imaging techniques of reverse-time migration and the iterative imaging formulations of scattering series in a one-way framework.

A field expansions method for scattering by periodic multilayered media

2019-04-11T06:24:53Z

A field expansions method for scattering by periodic multilayered media Malcolm, Alison E. The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein is described a Boundary Perturbation Method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than Finite Difference and Finite Element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Bruno & Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original Field Expansions method, this approach is extremely efficient and spectrally accurate.

Effects of surface scattering in full-waveform inversion

2019-04-10T20:16:40Z

Effects of surface scattering in full-waveform inversion Bleibinhaus, Florian; Rondenay, Stephane In full-waveform inversion of seismic body waves, often the free surface is ignored on grounds of computational efficiency. Asynthetic study was performed to investigate the effects of this simplification. In terms of size and frequency, the test model and data conform to a real long-offset survey of the upper crust across the San Andreas fault. Random fractal variations are superimposed on a background model with strong lateral and vertical velocity variations ranging from 1200 to 6800 m/s. Synthetic data were computed and inverted for this model and different topographies. A fully viscoelastic time-domain code was used to synthesize the seismograms, and a viscoacoustic frequency-domain code was utilized to invert them. The inversion was focused on early arrivals, which are dominated by P-waves but also contain strong P-Rayleigh wave conversions from the near-field of the receiver. Resulting waveform models show artifacts and a loss of resolution from neglecting the free surface in the inversion, but the inversions are stable, and they still improve the resolution of kinematic models. The extent of deterioration depends more on the subsurface than on the surface structure. Inversion results were improved at no additional expense by introducing a weak contrast along a staircase function above shots and receivers.

Array-conditioned deconvolution of multiple component teleseismic recordings

2019-04-12T15:20:20Z

Array-conditioned deconvolution of multiple component teleseismic recordings Chen, C. -W.; Rondenay, Stephane; Miller, D. E.; Djikpesse, H. A. We investigate the applicability of an array-conditioned deconvolution technique, developed for analyzing borehole seismic exploration data, to teleseismic receiver functions and data preprocessing steps for scattered wavefield imaging. This multichannel deconvolution technique constructs an approximate inverse filter to the estimated source signature by solving an overdetermined set of deconvolution equations, using an array of receivers detecting a common source. We find that this technique improves the efficiency and automation of receiverfunction calculation and data preprocessing workflow. We apply this technique to synthetic experiments and to teleseismic data recorded in a dense array in northern Canada. Our results show that this optimal deconvolution automatically determines and subsequently attenuates the noise from data, enhancing P-to-S converted phases in seismograms with various noise levels. In this context, the array-conditioned deconvolution presents a new, effective and automatic means for processing large amounts of array data, as it does not require any ad-hoc regularization; the regularization is achieved naturally by using the noise present in the array itself.

Asymmetric source acoustic LWD for the improved formation shear velocity estimation

2019-04-12T15:20:15Z

Asymmetric source acoustic LWD for the improved formation shear velocity estimation Chen, Tianrun; Wang, Bing; Zhu, Zhenya; Toksoz, Daniel R. Most acoustic logging while drilling (LWD) tools generate a single pure borehole mode (e.g., dipole or quadrupole) to estimate the formation shear velocity. We propose an approach where multipole modes are generated simultaneously and used to obtain a better shear estimation. This approach uses an asymmetric source with arrays of receivers distributed azimuthally around the tool to generate and identify signals from different modes. We investigate such an approach using both synthetic and laboratory data. The laboratory data are collected from a scale-model LWD tool with one active source transducer mounted on the side of the tool. Four sets of receiver arrays, each separated by 90 degrees azimuthally, are used to isolate monopole, dipole and quadrupole modes by coherently adding and subtracting received arrivals. A method is then apply to perform dispersion analysis on these arrivals. With least square fitting, formation shear velocities are estimated from both dipole and quadrupole modes' arrivals. We find that, by averaging the estimates obtained independently from dipole and quadrupole modes, we can reduce the uncertainty and improve the confidence of the estimation for the formation shear velocity.

Kinematic redatuming by two source interferometry

2019-04-11T06:02:36Z

Kinematic redatuming by two source interferometry Poliannikov, Oleg V. Interferometry is a method of redatuming physical sources to receiver locations. Under idealized assumptions stacking the cross correlogram of the two common receiver gathers yields a bandlimited Green's function between the receivers. Geometrically this process amounts to isolating a physical source, which generates a path containing both receivers, and canceling the common part. In this paper, we show that in order to recover the travel time between two receivers, one could creatively use rays from more than one physical source. With this approach redatuming is possible even in situations where the conventional interferometry fails.

Interferometric correlogram-space analysis

2019-04-12T21:43:33Z

Interferometric correlogram-space analysis Poliannikov, Oleg V.; Willis, Mark E. Seismic interferometry is a method of obtaining a virtual shot gather from a collection of physical shot gathers. The set of traces corresponding to two common receiver gathers from many physical shots is used to synthesize a virtual shot located at one of the receivers and a virtual receiver at the other. An estimate of a Green's function between these two receivers is obtained by first cross-correlating corresponding pairs of traces from each of the shots and then stacking the resulting cross-correlograms. In this paper, we study the structure of cross-correlograms obtained from a VSP acquisition geometry using surface sources and down-hole receivers. The model is purely acoustic and contains flat or dipping layers and/or point inclusions that act as di ffractors. Results of a semblance-based moveout scan of the cross-correlograms are used to identify the potential geometry of the reflectors. This new information allows improvements in the quality of the trace at the virtual receiver by either rejecting those moveouts or enhancing them before the stack is performed.

An improved method for hydrofracture induced microseismic event detection and phase picking

2019-04-10T14:01:12Z

An improved method for hydrofracture induced microseismic event detection and phase picking Song, Fuxian; Kuleli, Huseyin Sadi; Toksoz, M. Nafi; Ay, Erkan; Zhang, Haijiang The ability to detect small microearthquakes and identify their P and S phase arrivals is a key issue in hydrofracture downhole monitoring because of the low signal-to-noise ratios. We apply an array-based waveform correlation approach (matched filter) to improve the detectability of small magnitude events with mechanisms and locations similar to a nearby master event. After detecting the weak events, we use a transformed spectrogram method to identify the phase arrivals. We have tested the technique on a downhole monitoring dataset of the microseismic events induced by hydraulic fracturing. We show that, for this case, one event with a signal-to-noise ratio around 6dB, which is barely detectable using an array-stacked short-time average/long-time average (STA/LTA) detector under a reasonable false alarm rate, is readily detected on the array-stacked correlation traces. The transformed spectrogram analysis of the detected events improves P and S phase picking.

Frequency-Domain Finite-Difference Acoustic Modeling with Free Surface Topography using Embedded Boundary Method

2019-04-12T15:20:02Z

Frequency-Domain Finite-Difference Acoustic Modeling with Free Surface Topography using Embedded Boundary Method Li, Junlun; Zhang, Yang; Toksoz, M. Nafi In this paper, we present a method to model acoustic wave propagation in the frequencydomain in the presence of free surface topography using the embedded boundary method. The advantage of this method is to solve for the pressure field at each frequency on regular finite difference grids but with sub-cell resolution (up to 2nd order accuracy) for the irregular free surface. The topographic free surface condition is implemented in 2nd order accuracy, as in the regular domain so that global 2nd order accuracy is guaranteed. We use the level set method to obtain the projection points and normal directions corresponding to the ghost points in the scheme in the irregular domain. The computational cost for solving the modified sparse matrix for the pressure field increases very little compared to that for a flat surface. We have benchmarked our solver with a 2-D Gaussian hill model and simulated wave propagating in a modified Canadian foothills model. This solver can be used as the forward engine in the full waveform inversion, and we are working underway to perform full waveform inversions with real land survey data with considerable presence of surface topography.

Recursive Imaging with Multiply-Scattered Waves Using Partial Image Regularization: A North Sea Case Study

2019-04-12T21:44:50Z

Recursive Imaging with Multiply-Scattered Waves Using Partial Image Regularization: A North Sea Case Study Malcolm, Alison E.; de Hoop, Maarten V.; Ursin, Bjorn As more resources are directed toward reverse-time migration an accurate velocity model, including strong reflectors, is necessary to form a clear image of the subsurface. This is of particular importance in the vicinity of salt, where singly-scattered waves are often not ideal for imaging the salt flanks. This has led to interest in processing doubly-scattered waves (also called duplex or prismatic waves) for imaging salt flanks and thus improving the location of salt boundaries in a velocity model. We present a case study in which we use doubly-scattered waves in a two-pass one-way method to image salt flanks in a North Sea data set. By working in the one-way framework we are able to separately construct images with singly, doubly, and triply scattered waves. We illustrate a multi-step imaging process that includes multiply-scattered waves by using an imaged reflector to fix one (or more) of the scattering points, allowing for multiply-scattered energy from several reflectors, potentially with poor continuity, to be included without picking each reflector individually. With this method we are able to image the flank of a North Sea salt body.

Surface-wave eikonal tomography in a scattering environment

2019-04-10T13:15:56Z

Surface-wave eikonal tomography in a scattering environment Verdel, Arie; Gouedard, Pierre; Yao, Huajian; van der Hilst, Robert D. Surface waves are of increasing interest in seismic prospecting. Traveltime tomography based on dispersion measurements is often used to process surface-wave data, but it has limitations due to the a priori information it requires. The surface-wave eikonal tomography proposed here does not require such a priori information. In complex scattering environments, picking arrivals is difficult because the waveforms are complicated. Working in narrow frequency bands makes it even more difficult as it spreads arrivals in time and introduces overlap. We present here a neighborhood-based cross-correlation picking method that overcomes this difficulty, which then allows for reliable calculation of 2D phase-velocity variation through the eikonal equation.

Using SVD for improved interferometric Green’s function recovery.

2019-04-12T15:20:01Z

Using SVD for improved interferometric Green’s function recovery. Melo, Gabriela; Malcolm, Alison E.; Mikessel, Dylan; van Wijk, Kasper Seismic interferometry is a technique used to estimate the Green’s function (GF) between two receiver locations, as if there were a source at one of the locations. By crosscorrelating the recorded seismic signals at the two locations we generate a crosscorrelogram. Stacking the crosscorrelogram over sources generates an estimate of the inter-receiver GF. However, in most applications, the requirements to recover the exact GF are not satisfied and stacking the crosscorrelograms yields a poor estimate of the GF. For these non-ideal cases, we enhance the real events in the virtual shot gathers by applying Singular Value Decomposition (SVD) to the crosscorelograms before stacking. The SVD approach preserves energy that is stationary in the crosscorrelogram, thus enhancing energy from sources in stationary positions, which interfere constructively, and attenuating energy from non-stationary sources that interfere distructively. We apply this method to virtual gathers containing the virtual refraction artifact and find that using SVD enhances physical arrivals. We also find that SVD is quite robust in recovering physical arrivals from noisy data when these arrivals are obscured by or even lost in the noise in the standard seismic interferometry technique.

Detecting medium changes from coda by interferometry

2019-04-11T06:02:37Z

Detecting medium changes from coda by interferometry Poliannikov, Oleg V.; Malcolm, Alison E. In many applications, sequestering CO[subscript 2] underground for example, determining whether or not the medium has changed is of primary importance, with secondary goals of locating and quantifying that change. We consider an acoustic model of the Earth as a sum of a smooth background velocity, isolated velocity jumps and random small scale fluctuations. Although the first two parts of the model can be determined precisely, the random fluctuations are never known exactly and are thus modeled as a realization of a random process with assumed statistical properties. We exploit the so-called coda of multiply scattered energy recorded in such models to monitor for change and to localize and quantify that change, by examining the shape and frequency content of correlations of the coda produced by different parts in the medium. These ideas build upon past work in time-reversal detection methods that have often been limited to theoretical regimes in which the scales of scattering and reflection are strictly separated. This results in an application of time-reversal detection methods to non-theoretical regimes in which the separation of scales is not strictly satisfied, opening up the possibility, discussed here, of using such techniques to monitor CO[subscript 2] sequestration sites for leakage.

Downhole microseismic monitoring of hydraulic fracturing: a full-waveform approach for complete moment tensor inversion and stress estimation

2019-04-12T15:20:01Z

Downhole microseismic monitoring of hydraulic fracturing: a full-waveform approach for complete moment tensor inversion and stress estimation Song, Fuxian; Toksoz, M. Nafi; Li, Junlun Downhole microseismics has gained in popularity in recent years as a way to characterize hydraulic fracturing sources and to estimate in-situ stress state. Conventional approaches only utilize part of the information contained in the microseismic waveforms such as the P/S amplitude ratio and/or P first motion polarity to determine the microearthquake focal mechanisms and infer stress state. Thus, additional con-straints like double-couple assumption must be made to stabilize the inversion for conventional methods. The situation becomes even worse for downhole monitoring where only limited azimuthal coverage is available. In this study, we have developed a full-waveform based approach to invert for complete moment tensor. We use the discrete wavenumber integration approach as the fast forward modeling tool to calculate the synthetic waveforms for one-dimensional layered velocity models. By matching full three-component waveforms across the array, a stable moment tensor solution can be obtained without imposing additional constraints. We also derive the source radius from the far-field displacement spectrum with the Madariaga’s model and determine the stress drop afterwards. We test our method on a downhole microseismic dataset from hydraulic fracturing treatments in East Texas. The result indicates the existence of the isotropic component in some events. A clear difference is observed that non-double-couple events tend to have smaller stress drops, which is consistent with other studies. The derived fracture plane direction also agrees with that derived from multiple event location.

Focal Mechanism Determination Using High Frequency Waveform Matching and Its Application to Small Magnitude Induced Earthquakes

2019-04-10T21:23:37Z

Focal Mechanism Determination Using High Frequency Waveform Matching and Its Application to Small Magnitude Induced Earthquakes Li, Junlun; Zhang, Haijiang; Kuleli, Huseyin Sadi; Toksoz, M. Nafi We present a new method using high frequency full waveform information to determine the focal mechanisms of small, local earthquakes monitored by a sparse surface network. During the waveform inversion, we maximize both the phase and amplitude matching between the observed and modeled waveforms. In addition, we use the polarities of the first P-wave arrivals and the average S/P amplitude ratios to better constrain the matching. An objective function is constructed to include all four criteria. An optimized grid search method is used to search over all possible ranges of source parameters (strike, dip and rake). To speed up the algorithm, a library of Green’s functions is pre-calculated for each of the moment tensor components and possible earthquake locations. Optimizations in filtering and cross-correlation are performed to further speed the grid search algorithm. The new method is tested on a 5-station surface network used for monitoring induced seismicity at a petroleum field. The synthetic test showed that our method is robust and efficient to determine the focal mechanism when using only the vertical component of seismograms in the frequency range of 3 to 9 Hz. The application to dozens of induced seismic events showed satisfactory waveform matching between modeled and observed seismograms. The majority of the events have a strike direction parallel with the major NE-SW faults in the region. The normal faulting mechanism is dominant, which suggests the vertical stress is larger than the horizontal stress.

Imaging the Soultz Enhanced Geothermal Reservoir Using Double-Difference Tomography and Microseismic Data

2019-04-12T20:58:45Z

Imaging the Soultz Enhanced Geothermal Reservoir Using Double-Difference Tomography and Microseismic Data Concha, Diego Alvaro Pinero We applied the double-difference tomography method to image the P and S-wave velocity structure of the European Hot Dry Rock geothermal reservoir (also known as the Soultz Enhanced Geothermal System) at Soultz-sous-Forets, France. We used absolute, differential catalog and differential cross-correlation times obtained from the reservoir’s September and October 1993 hydraulic stimulations along with starting event locations obtained using Joint Hypocenter Determination and Collapsing methods. The stimulations produced over 12000 microseismic events of which we chose 8930 for further analysis. We obtained high accuracy crosscorrelation differential times and then performed a double-difference tomographic inversion to jointly invert for velocity structure and event locations. It is shown through a detailed analysis of model and data residuals vs smoothing weight, ray path derivative weighted sums, and a synthetic checkerboard test that the double-difference inversion is able to produce interpretable results despite the poor source-receiver geometry employed in the study. The results show that velocity structure for S-waves correlates well with seismicity and show the expected low velocity zones at depths between 2900 and 3600 meters, where fluid was believed to have infiltrated the reservoir. P-wave velocity structure shows less of a correlation with seismicity and shows low velocity zones at shallow depths where no water was believed to have entered the reservoir. Between 2900 and 3600 meters the P-wave velocity structure shows high velocity zones near the injection well. The results also show the NNW-SSE trend of event location clusters and velocity structure which lines up with the maximum horizontal stress orientation. Lastly, we show that using the double-difference tomographic method to relocate events produces locations that come close to rivaling those of collapsing methods.

Estimate the Effective Elastic Properties of Digitized Porous Rocks by Inverting the Cracks Unresolved

2019-04-11T06:24:26Z

Estimate the Effective Elastic Properties of Digitized Porous Rocks by Inverting the Cracks Unresolved Zhang, Yang; Toksoz, M. Nafi Current imaging technique such as micro X-ray CT can provide us detailed 3D micro-structures of porous rocks that can be used in numerical simulation so as to predict elastic properties of rocks saturated with different fluids. However, limited by the resolution the imaging process can provide, we usually lose the small features of rocks such as cracks and micro-pores, consequences of which can cause over-predicted effective elastic properties of porous rocks. In this paper, we present an inversion scheme to estimate the lost cracks during imaging process with Monte-Carlo algorithm. This method combines numerical simulation with theoretical models – the differential effective media model and Kuster-Toksöz model. Compared to the traditional inversion algorithms solely based on theoretical models, the algorithm presented in this paper utilizes the micro-structures of porous rocks resolved and takes the advantages of computational results from the digitized rocks, which in fact provides us much information of rocks and limits our inversion space for cracks. At end, we demonstrate the capability of this method on predicting the elastic properties of Berea sandstones measured in laboratory.

Modeling of acoustic wave scattering from a two-dimensional fracture

2019-04-11T06:24:27Z

Modeling of acoustic wave scattering from a two-dimensional fracture Chen, Tianrun; Fehler, Michael; Brown, Stephen; Zhang, Yang; Fang, Xinding; Burns, Daniel R.; Wang, Ping In this paper, we model the acoustic scattering from a two dimensional fracture that is simulated by two different physical models. We calculate the scattering from the fractures with different properties based on these two models.

Sensitivity analysis of fracture scattering

2019-04-11T06:24:25Z

Sensitivity analysis of fracture scattering Fang, Xinding; Fehler, Michael; Chen, Tianrun; Burns, Daniel R. The understanding of seismic scattering of a finite fracture is very important in reservoir fracture characterizations, but the analytical solution of this problem is not available. Thus, in this paper, we present an approach for numerical study of the seismic response of a finite fracture.

Experimental studies of streaming potential and high frequency seismoelectric conversion in porous samples

2019-04-10T10:34:11Z

Experimental studies of streaming potential and high frequency seismoelectric conversion in porous samples Zhu, Zhenya; Toksoz, M. Nafi; Zhan, Xin Streaming potential across a porous medium is induced by a fluid flow due to an electric double layer between a solid and a fluid. When an acoustic wave propagates through a porous medium, the wave pressure generates a relative movement between the solid and the fluid. The moving charge in the fluid induces an electric field due to the seismoelectric conversion. In order to investigate the streaming potential and the seismoelectric conversion in the same rock sample, we conduct quantitative measurements with cylindrical and plate samples of Berea sandstone 500 saturated by NaCl solutions with different conductivities. We measure the electric voltage (streaming potential) across a cylinder sample in solutions with different conductivities and under different pressures. In a solution container, we measure the seismoelectric signals induced by acoustic waves at different frequencies and solution conductivities. We calculate the quantitative coupling coefficients of the seismoelectric conversion at DC and high frequencies with samples saturated by solutions with different conductivities. According to the streaming potentials, we calculate the theoretical coupling coefficients at the DC and high frequency range. The experimental and theoretical results are compared quantitatively and their differences are discussed.

Passive Seismic Tomography Using Induced Seismicity at a Petroleum Field in Oman

2019-04-12T21:43:34Z

Passive Seismic Tomography Using Induced Seismicity at a Petroleum Field in Oman Kindy, Fahad; Zhang, Haijiang; Sarkar, Sudipta; Toksoz, M. Nafi; Kuleli, Huseyin Sadi; Al-Kindy, Fahad A borehole network consisting of 5 monitoring wells was used to monitor the induced seismicity at a producing petroleum field for a period of about 11 months. Nearly 5400 microseismic events were analyzed and utilized in imaging the reservoir based on a new doubledifference (DD) seismic tomography. The DD tomography method simultaneously solves for event locations and Vp, Vs, and Vp/Vs models using absolute and differential P, S and S-P arrival times. Microseismicity in the field was primarily caused by compaction of the reservoir in and above the gas bearing formation and was distributed along the two major northeastsouthwest (NE-SW) faults in the field. The model resolution analysis based on the checkerboard test and the resolution matrix showed that the central part of the model was relatively well resolved for the depth range of 0.7 to 1.1 km. Clear velocity contrasts were imaged across most parts of the two NE-SW faults. Vp/Vs ratio estimations from the tomographic inversion were low (<1.75) in the shallow depth range, likely due to lithology and gas content, whereas they were large (>1.75) in the deeper part of the model, likely due to fluid saturated formation. In this study seismic tomography showed a great potential for reservoir imaging and property estimation using induced seismicity.

A Numerical Study of the Effects of Wave-Induced Fluid Flow in Porous Media: Linear Solver

2019-04-10T07:36:57Z

A Numerical Study of the Effects of Wave-Induced Fluid Flow in Porous Media: Linear Solver Zhang, Yang; Song, Limin; Deffenbaugh, Max; Toksoz, M. Nafi In this paper, we present a computational method to simulate wave propagation in porous rocks saturated with Newtonian fluids over a range of frequencies of interest. The method can use a digital representation of a rock sample where distinct material phase and properties at each volume cell are identified and model the dynamic response of the rock to an acoustic excitation mathematically with a coupled equation system: elastic wave equation in solid matrix and viscous wave equation in fluid. The coupled wave equations are solved numerically with a rotated-staggered-grid finite difference scheme. We simulate P-wave propagation through an idealized porous medium of periodically alternating solid and fluid layers where an analytical solution is available and obtain excellent agreements between numerical and analytical solutions. The method models the effect of pore fluid motion on the rock dynamic response more accurately with a linearized Navier-Stokes equation than with the viscoelastic model of the generalized Maxwell body, a low frequency approximation commonly used to overcome the difficulty of modeling frequency-dependent fluid shear modulus in time domain.

Pore Scale Modeling of Rock Properties and Comparison to Laboratory Measurements

2019-04-12T15:54:38Z

Pore Scale Modeling of Rock Properties and Comparison to Laboratory Measurements Zhan, Xin; Schwartz, Larry; Smith, Wave; Toksoz, M. Nafi; Morgan, Frank Dale The microstructure of a porous medium and the physical characteristics of the solid and fluid phases determine the macroscopic transport properties of the medium. The purpose of this paper is to test numerical calculations of the geometrical and transport properties (electrical conductivity, permeability, specific surface area, and surface conductivity) of porous, permeable rocks, given their 3D digital microtomography (μCT) images. We focus on μCT data for a 23.6% porosity sample of Berea Sandstone 500 (BS500) with 2.8 micron resolution. Finite difference methods are used to solve the Laplace and Stokes equations for electrical and hydraulic conductivities. We show that the permeability and formation factor are well correlated using a hydraulic radius computed from the digitized image. Electrical transport in the BS500 sample is complicated by the presence of clays. A three phase conductivity model, which includes the double layer length and counter-ion mobility, is developed to compute interface conductivity from the μCT image and measured values of the cation exchange capacity (CEC). Our calculations compare well with the laboratory measurements on cm[superscript 3] core samples. Finally, we examine the influence of image size and image resolution on our numerical results.

Fracture quality images from 4D VSP and microseismic data at Jonah Field, WY.

2019-04-12T21:43:34Z

Fracture quality images from 4D VSP and microseismic data at Jonah Field, WY. Willis, Mark E.; Willis, Kent M.; Burns, Daniel R.; Shemeta, Julie; House, Nancy J. Natural and induced fractures provide the only means of production in tight gas sand reservoirs. The objective of this work is to locate and characterize natural and induced fractures from the analysis of scattered waves recorded on 4-D (time lapse) VSP data in order to optimize well placement and well spacing in these gas reservoirs. Using synthetic seismic data, we have previously shown that it is possible to characterize the quality of fracturing based upon the amount of scattering of seismic energy from hydraulic fractures. We show this concept applied to a field dataset from the Jonah Field in Wyoming. The time lapse (4D) VSP data from this field are imaged with a migration algorithm using shot travel time tables derived from the first breaks of the 3D VSPs and receiver travel time tables based on the microseismic and perf shot arrival times. We create images of the fracture planes through two of the hydraulically fractured wells in the field. The scattered energy shows correlation with the locations of the microseismic events and azimuthal scattering which is different from the azimuthal reflectivity of the reservoir. This gives us more confidence that we have separated the scattered signal from simple formation reflectivity. Variations of the scattered energy along the image planes suggest differences in the quality of the fractures in three distinct zones.

Improved Methods for Hydrofrac Event Detection and Phase Picking

2019-04-10T10:34:34Z

Improved Methods for Hydrofrac Event Detection and Phase Picking Cornish, Bruce; Quirein, John; Ay, Erkan; Pei, Donghong; Zannoni, Steve; Song, Fuxian; Kuleli, Huseyin Sadi; Todreas, M. Nafi; Zhang, Haijiang The ability to detect small microseismic events and identify their P and S phase arrivals is a key issue in hydraulic fracture monitoring because of the low signal-to-noise ratios. We propose a array-based waveform correlation approach to detect small magnitude events with similar mechanisms and locations as a nearby master event. For the phase picking part, a transformed spectrogram method is used to identify the weak P arrivals. We have applied the technique to a downhole monitoring dataset of the microseismic events induced by hydraulic fracturing. The results show a better phase identification.

Model-guided Geosteering for Horizontal Drilling

2019-04-12T15:54:39Z

Model-guided Geosteering for Horizontal Drilling Song, Fuxian; Toksoz, M. Nafi Horizontal drilling is an important development in the petroleum industry and it relies heavily on guiding the drill bit with the aid of sonic logging, i.e. geosteering. The quality of sonic imaging depends heavily on the effective suppression of borehole waves and enhancement of weak reflection signal. To this end, we propose an approach to image the near-borehole structure using acoustic logging data. We model the borehole wave propagation using log-derived velocities. The modeled borehole waves are removed from the raw data, leaving reflected signals for imaging interfaces. We tested this method with three sets of data. First we calculated synthetic waveforms for a horizontal well with an interface parallel to the borehole using the 3D finite difference method. The processing result with our method clearly shows the parallel reflecting interface. Next, we conducted an ultrasonic laboratory measurement in a borehole with a parallel Lucite-water boundary. In this case, the interface was also visible in the final image. Finally, we applied this method to a field dataset. In the field dataset, the acoustic logging data were continuously recorded along the well, which enabled us to reject the borehole modes in both common shot gather and common offset gather. The large amount of common offset gather data also allowed us to apply migration to the data. The migrated image of the near-borehole structure is in good agreement with available geological and petrophysical information of that field.

Seismoelectric measurements on artifical porous media and Berea sandstone

2019-04-12T15:18:56Z

Seismoelectric measurements on artifical porous media and Berea sandstone Schakel, Menne D.; Zhu, Zhenya; Toksoz, M. Nafi Seismic to electromagnetic wave conversion has been proposed as a possible exploration method. We present laboratory measurements of the conversion of an acoustic wave into electric potential, which occurs at a fluid/porous-medium interface. The conversion is measured for artificial porous media and Berea sandstone. Recorded electric potentials are smaller for large grain samples. We also show variability of the conversion over a time span of 120 hours.

Interferometric correlogram-space analysis

2019-04-12T15:18:54Z

Interferometric correlogram-space analysis Poliannikov, Oleg V.; Willis, Mark E.; Mashele, Bongani Jabulani Seismic interferometry is a method of obtaining a virtual shot gather from a collection of actual shot gathers. The set of traces corresponding to multiple actual shots recorded at two receivers is used to synthesize a virtual shot located at one of the receivers and a virtual receiver at the other. An estimate of a Green’s function between these two receivers is obtained by first cross-correlating pairs of traces from each of the common shots and then stacking the resulting cross-correlograms. In this paper, we study the structure of cross-correlograms obtained from a VSP acquisition geometry using a surface source reflected by flat or dipping layers and/or diffracted by point inclusions. The model is purely acoustic. The shape of events in the cross-correlogram space can be used to infer the location and geometry of a subsurface structure. A pilot wavelet created by a curvilinear stacking process is used as a detector of predicted events in the cross-correlogram. Results of a semblance-based velocity scan of the cross-correlograms using curvilinear stacks can be used to improve the quality of the virtual gather.

In Situ, Nonlinear Soil Response Applying an Active Source

2019-04-10T21:23:47Z

In Situ, Nonlinear Soil Response Applying an Active Source Johnson, Paul; Toksoz, M. Nafi; Morgan, Frank Dale; Pearce, Fred Soil sites have a profound effect on ground motion during earthquakes due to their low wave speeds, layered structure, and nonlinear constitutive relationship. Measurements of nonlinear soil response under natural conditions are critical to understanding soil behavior during earthquakes. Currently, quantitative measurements of nonlinear soil response are derived from laboratory experiments on small samples. In this paper, we extend laboratory methods for measuring nonlinear soil response to field-scale. We observe the in situ, nonlinear response of a natural soil formation using measurements obtained immediately adjacent to a large vibrator truck. The source generates a steady-state wavefield in the soil formation at a range of discrete source frequencies and amplitudes. Accelerometers within the source provide an estimate of the source output to the soil, and an array of 4 accelerometers adjacent to the source record the wavefield at 1.5 m spacing. We develop a homodyne analysis to extract the steady-state amplitude at each discrete source frequency and amplitude without contamination from source harmonics. Steadystate amplitude ratios are computed between the receivers and the source, and between adjacent receiver pairs within the array. Both sets of amplitude ratios show dramatic decreases in peak frequency as the source amplitude is increased. These peak frequency shifts are qualitatively similar to the nonlinear soil response observed for laboratory samples under resonance conditions. Amplitude ratios between adjacent receiver pairs suggest the nonlinear soil response persists across the receiver array and is not limited to the source-soil contact region. The magnitudes of the observed peak shifts appear to depend on their frequency, a proxy for depth, which is consistent with the confining pressure dependence of soil nonlinearity observed in laboratory experiments. Future work will include measurements of steady-state phase velocities across the array to better understand the nature of nonlinear wave propagation within natural soil formations.

Focal Mechanism Determination using High Frequency, Full Waveform Information

2019-04-11T09:46:23Z

Focal Mechanism Determination using High Frequency, Full Waveform Information Li, Junlun; Zhang, Haijiang; Kuleli, Huseyin Sadi; Toksoz, M. Nafi In this research, we use high frequency waveform information to determine the focal mechanisms of small local earthquakes at an oil reservoir. During the waveform inversion, we maximize both the phase and amplitude matching between the observed and synthetic waveforms. In addition, we use the polarities of the first P-wave arrivals and the S/P amplitude ratios to better constrain the matching between the synthetic and observed waveforms. The objective function is constructed to include all four criteria. Due to the complexity in the objective function, it is almost impossible to directly perform an inversion with derivative techniques. Instead, an optimized grid search method is used to search over all possible ranges of fault strike, dip and rake, as well as a predetermined range of earthquake locations. To speed up the algorithm, a library of Green‟s functions is pre-calculated for each of the moment tensor components and possible earthquake locations. Careful optimizations in filtering and cross-correlation are performed to further improve the grid search algorithm, such that no filtering and cross correlations are performed in searching through the parameter space of strike, dip, and rake. Consequently, speed is boosted tenfold by these optimizations in filtering and cross correlation. We apply the new method to induced seismic events in an oil reservoir. Satisfactory matching between synthetic and observed seismograms is obtained, as well as reasonable focal mechanisms, considering the local geological structure and possible causes for induced seismicity.

Asymmetric source acoustic LWD for the improved formation shear velocity estimation

2019-04-12T15:18:46Z

Asymmetric source acoustic LWD for the improved formation shear velocity estimation Chen, Tianrun; Wang, Bing; Zhu, Zhenya; Burns, Daniel R. Most acoustic LWD tools generate a single pure borehole mode (e.g., dipole or quadrupole) to estimate the formation shear velocity. We propose an approach where many borehole modes are generated and all the modes are used simultaneously to obtain a better shear estimate. In this approach we find the best fit to the dispersion characteristics of a number of modes, rather than one mode. We propose using an asymmetric source, that is a single source on one side of the tool, together with arrays of receivers distributed azimuthally around the tool to allow different modes to be identified and analyzed. We investigate such an approach using synthetic and laboratory data. The lab data uses a scale-model LWD tool with one active sources transducer mounted on the side of the tool. This source geometry generates monopole, dipole, and quadrupole modes simultaneously. Four sets of receiver arrays, each separated by 90 degrees azimuthally, are used to isolate and analyze each of these modes by adding and subtracting the signals received from different arrays. Based on the dispersion analysis and the method of least square fitting, we find that the by simultaneously using both dipole and quadrupole modes, we can reduce the residual error of the best fit shear velocity. It should be noted that higher order modes (e.g., hexapole, etc) will also be generated by an asymmetric source, and these modes could also be utilized with the appropriate azimuthal receiver configuration.

Meeting Agenda

2019-04-12T15:18:54Z

Meeting Agenda Meeting agenda for the Earth Resources Laboratory 2007 Industry Consortia Meeting.

Executive Summary

2019-04-10T16:40:51Z

Executive Summary Burns, Daniel R. ERL's research activities are focused on integrated reservoir characterization and monitoring. In order to maximize the information we can obtain from geophysical measurements, there are two overarching themes: 1. Utilize more of the data through the modeling, analysis, and inversion of the full waveforms 2. Apply multi-physics approaches to query the subsurface. Our work during the past year, which is summarized in this report, reflects these themes and points towards our vision for the future. The following sections provide a brief summary of the papers in this year’s report.

Experimental studies of reflected nearborehole acoustic waves received in borehole models

2019-04-12T15:18:37Z

Experimental studies of reflected nearborehole acoustic waves received in borehole models Zhu, Zhenya; Toksoz, M. Nafi; Burns, Daniel R. Laboratory experiments are performed with an isotropic Lucite borehole model to measure the acoustic wave fields generated by a monopole source in the borehole. The source not only generates acoustic waves propagating along the borehole, but also in the surrounding formation. If there is a reflection interface in the formation, the acoustic waves can be reflected back to the borehole. We measure the acoustic waves on the model surface to investigate the acoustic fields in the formation. Acoustic measurements record both waves reflected from an interface or fracture and those propagating in the borehole. The frequency of the reflection is higher than that of the borehole waves, and the apparent velocity of the reflection is higher than the P-wave velocity. In this paper, we extract the waves reflected from an interface—which is parallel or declined to the borehole axis—with a high-pass filter. If the apparent velocity of the acoustic wave recorded in a borehole is faster than that of the P-wave propagating along the borehole, the wave must be reflected by a surface outside of the borehole. With these measured waveforms we calculate the distance between the borehole and the reflection surface and the P-wave velocity in the direction perpendicular to the borehole axis. When the reflection is declined to the borehole axis, the reflected waves recorded at both sides of the source have different first-arrival-times and different apparent velocities. Laboratory measurements show a new method to determine an interface out of a borehole, the formation anisotropy, and the distance of a reflection.

Numerical simulation of wave-induced fluid flow in digitized porous media using a coupled model with Level Set

2019-04-10T21:23:30Z

Numerical simulation of wave-induced fluid flow in digitized porous media using a coupled model with Level Set Zhang, Yang; Nave, Jean-Christophe; Toksoz, M. Nafi In this paper, we develop a unified mathematical model with velocity as the primary variable for modeling the interaction between incompressible fluid and compressible solid. We numerically solve this problem by combining the finite different method with the level set method, which is able to easily capture the dynamic change of the interface between fluid and solid. Additionally, the zero contour of a level set function can represent the interface or boundary smoothly; this smoothness can be taken into account in numerical modeling so as to avoid the staircase boundary in the traditional finite difference method. A modified projection method is developed for solving fluid and solid sub-domain simultaneously. This method is then applied on a digitized 2D section of Berea sandstone. To obtain a level set function of the 2D section, we applied the region-based active contour method to segment the micro-tomography data.

Numerical Modeling of Transport Properties and Comparison to Laboratory Measurements

2019-04-10T13:16:04Z

Numerical Modeling of Transport Properties and Comparison to Laboratory Measurements Smith, Wave; Zhan, Xin; Schwartz, Larry; Morgan, Frank Dale; Toksoz, M. Nafi Transport properties, such as permeability and electrical conductivity, are important in many geophysical and petroleum applications. The microstructure of a porous medium and physical characteristics of the solid and the fluids that occupy the pore space determine the macroscopic transport properties of the medium. The computation of macroscopic properties from the rock microtomography is becoming an increasingly studied topic. The transport properties are especially difficult to determine at the microscopic scale. The purpose of this paper is to test the applicabilities to numerically calculate the geometrical and transport properties (electrical conductivity, permeability, specific surface area and surface conductivity) of porous, permeable rocks, given the digital CT microtomography images. To better address the relationship between geometrical properties and transport properties, we use a number of artificial low, medium- to high-porosity Finney’s (1970) sphere packs. Numerically calculated transport properties are compared with analytical and empirical equations on the Finney pack. In particular, numerically computed permeability on the Finney pack agrees well with the permeability calculated from the computed formation factor using an empirical relationship on the same structure. This illustrates the consistence of resolving different transport properties on the same structure and the possibility of multiphysics coupling in the future. We also apply all the numerical simulations on the 3D X-ray microtomography of 23.6% porosity Berea Sandstone with 2.8 micron resolution. Numerical calculations of electrical conductivity, permeability and specific surface area on mm[superscript 3] image will be compared to the laboratory measurements with those parameters on cm[superscript 3] core samples. The upscaling issue will be discussed when we compare the numerical results with laboratory measurements at a different scale. We also analyze the image resolution impact on different properties to better understand the discrepancy between numerical computations and laboratory measurements. This paper provides a complete work on the numerical simulations on different physics at different scales. Numerical calculations are compared with analytic, empirical rock physics equations and laboratory measurements.

Hydraulic fracture quality from time lapse VSP and microseismic data

2019-04-10T23:33:09Z

Hydraulic fracture quality from time lapse VSP and microseismic data House, N. J.; Shemeta, J.; Willis, Mark E.; Willis, Kent M.; Burns, Daniel R. The ability to produce from low permeability, tight gas reservoirs is directly tied to the ability to repetitively perform successful hydraulic fracturing in a series of closely spaced wells. The key question is whether the induced fractures remain open and permeable, which is in part a function of the stress field and the emplacement of proppant. We study the ability to detect and characterize hydraulic fractures from scattered seismic energy. A 3D VSP forms the reference for seismic reflectivity before hydraulic fracturing. During the hydraulic fracturing the microseismic events are recorded and then the arrival times picked and the events located. Another 3D VSP survey is recorded after the fracture treatment. The difference between the VSP surveys yields a 3D time lapse VSP dataset which contains the changes in the reflected wave field and the addition of scattered energy. The microseismic moveout times can be used to extract from the time lapse VSP data the seismic energy scattered from the induced fracture planes. We show the encouraging results from both model and field data.

Improved Green’s functions from seismic interferometry

2019-04-12T21:45:20Z

Improved Green’s functions from seismic interferometry Poliannikov, Oleg V.; Willis, Mark E. Under certain theoretical assumptions, the theory of seismic interferometry allows the construction of artificial (or virtual) sources and receivers at the locations of receivers in a physical experiment. This is done by redatuming the physical sources to be at the locations of the physical receivers. Each redatumed trace is formed by stacking the cross-correlations of appropriate recorded traces from each physical shot. For the resulting stacked traces to be a valid approximation certain requirements, like an adequate number of surface sources with a small enough spacing in the acquisition geometry, must be met. If these requirements are not met, the resulting virtual shot gather will contain artifacts. In this paper, we analyze both the sets of correlated traces (correlograms) and their stack. We observe that it is possible to reduce certain artifacts in the stacked traces by novel filtering operations. These filtering operations may have broad utility in all of seismic interferometric applications.

Locating point diffractors in layered media by spatial dynamics

2019-04-11T06:02:36Z

Locating point diffractors in layered media by spatial dynamics Poliannikov, Oleg V. We present a new approach to the problem of detecting point diffractors from active source surface seismic data. We formulate an optimization problem in the configuration space of possible collections of scatterers and construct a birth-and-death spatial dynamic, which converges to the optimal solution. By design, this dynamic does not have resolution limits typical of migration based techniques, which allows for subwavelength sensing.

Seismic Imaging and Illumination with Internal Multiples

2019-04-10T16:53:00Z

Seismic Imaging and Illumination with Internal Multiples Malcolm, Alison E.; Ursin, Bjørn; de Hoop, Maarten V. If singly scattered seismic waves illuminate the entirety of a subsurface structure of interest, standard methods can be applied to image it. It is generally the case, however, that with a combination of restricted acquisition geometry and imperfect velocity models, it is not possible to illuminate all structures with only singly scattered waves. We present an approach to use multiply scattered waves to illuminate structures not sensed by singly scattered waves. It can be viewed as a refinement of past work in which a method to predict artifacts in imaging with multiply scattered waves was developed. We propose an algorithm and carry out numerical experiments, representative of imaging of the bottom and flanks of salt, demonstrating the effectiveness of our approach.

Time Reversed Acoustics and Applications to Earthquake Location and Salt Dome Flank Imaging

2019-04-10T23:33:09Z

Time Reversed Acoustics and Applications to Earthquake Location and Salt Dome Flank Imaging Lu, Rongrong The objective of this thesis is to investigate the applications of Time Reversed Acoustics (TRA) to locate seismic sources and image subsurface structures. The back-propagation process of the TRA experiment can be divided into the acausal and causal time domain. Studying the acausal process of TRA enables us to locate the source, such as an earthquake, inside a medium. The causal domain allows us to create a new datum through the TRA-based redatuming operators and then image the subsurface structures. The source location application directly uses the retro-focusing feature of the TRA technique. An earthquake is traditionally located using the arrival times of individual phases, such as P and S. As a supplementary tool, TRA provides an opportunity to locate earthquakes using whole waveforms. In this TRA technique, we first record the full seismograms due to an earthquake at an array of stations. The traces are then time-reversed and numerically sent back into the medium at those station locations using an a priori model of the medium. The wavefield of the back-propagation is tracked and in the end energy will concentrate at a focal spot which gives the original earthquake location. Both synthetic and field experiments show the capability of the TRA technique to locate the source. TRA, combined with the idea of empirical Green’s function, also provides an alternative approach to quickly estimating the focal depth for shallow events. In several field studies, solutions from other independent methodologies confirm the validity of the results. The subsurface imaging application extends the TRA principle into a redatuming method, which allows us to image the target more effectively by bypassing the overburden – which could potentially be very complicated in certain situations – between the sources and receivers. An accurate subsurface model required by conventional imaging techniques, which can be difficult and time-consuming to obtain, is no longer the prerequisite with this data-driven, TRA-based redatuming technique. Meanwhile, by imaging from a new datum that is closer to the target, the uncertainty of the imaging operator is dramatically reduced. The applicability of imaging the salt flank with the presence of a salt canopy is investigated in both acoustic and elastic scenarios with synthetic examples. Resulting images show very good delineation of the salt edge and dipping sediments abutting the salt dome. Then with the theoretical knowledge of the technique, we apply it to a 3D field experiment. In this complex field problem, with its challenge of the 3D geometry of the salt and acquisition, together with the limitation of the single well imaging, we propose a new directional imaging approach to implementing the TRA-based redatuming algorithm. The result is consistent with previous studies in this field, given the uncertainties on positioning of steep events from surface seismic data.

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source term

2019-04-11T10:28:40Z

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source term Juanes, Ruben; Dub, Francois-Xavier We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak compatibility condition that allows for subgrid communication across element interfaces, a feature that turns out to be essential for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and deviatoric components. The method is locally conservative and employs a low-order approximation of pressure and velocity at both scales. We illustrate the performance of the method on several synthetic cases and conclude that the method is able to capture the global and local flow patterns accurately.

Multiscale Determination of In Situ Stress and Fracture Properties in Reservoirs

2019-04-11T10:28:40Z

Multiscale Determination of In Situ Stress and Fracture Properties in Reservoirs Grandi-Karam, Samantha In this thesis we address the problem of determining in situ stress and fracture properties in reservoirs using borehole logs and surface seismic reflection data. The dissertation covers four subtopics. The first is the determination of horizontal stress magnitudes from measurements in a borehole. Two types of data used are stress-induced rock failures in the borehole, known as "breakouts," and the dispersions of polarized flexural waves which propagate along the borehole. Traditionally these data are analyzed to derive stress orientations but not magnitudes. To determine the magnitude of stresses directly from breakouts, we use an iterative elastic modeling of stresses around the borehole and Mohr-Coulomb failure criterion to match the borehole deformation. As a second method we use dispersion curves of the two polarized flexural waves and their crossover points. These methods are applied to data from a well in northeastern Venezuela. The combination of these two techniques provides a complete profile of stress as a function of depth since the first method is applied at the breakout depths and the second is applied everywhere else in the borehole. Both borehole methods agree in the estimation of stress orientation and magnitude. The maximum horizontal stress is in the NNW-SSE direction, in agreement with a regional stress model calculated from the relative motions of the Caribbean and South America plates. The magnitudes of principal stresses are on average, SHmax ≃ 1.1Sv (Sv: vertical stress) and Shmin ≃ 0.9Sv (Shmin: minimum horizontal stress). This suggests strike-slip faulting, consistent with earthquake mechanisms in the region. The in situ stresses play an important role on determining the properties of fractured formation. The azimuth of SHmax determines the preferred orientation of open fractures. Surface seismic reflection data provide the means for detecting the fractures. The second contribution of this thesis is developing a method to detect discrete fractures, and to determine their orientation and average spacing. We developed a novel and practical technique, called the F-K method, based on the frequency-wavenumber (f-k ) domain analysis of seismic coda. The fractured medium targeted in this study is a network of rather regularly spaced, parallel, sub-vertical fractures, with dimensions similar to seismic wavelength. The seismic response of a fractured medium is studied by finite difference numerical models for a variety of situations where orientation, spacing, height, and fracture compliance are varied. In the direction normal to fractures, scattered waves propagate with slower apparent velocities than waves propagating along the fractures. The orientation of fractures is well constrained from the azimuthal dependence of scattering. The spectral characteristics (frequency, wavenumber and amplitude) of the backscattered waves are related to fracture properties like spacing, compliance, and height. The dominant wavenumber is very sensitive to fracture spacing. We use the F-K method to analyze a data set from the Lynx Field in Canada. Characterization of fracture properties in this field is important for development plans to maximize the gas production. In the field data, the acquisition geometry results in irregular fold, with under sampling of certain azimuths and offsets. We address the acquisition footprint issue by controlling the azimuth binning of the data and neglecting the low/irregular fold gathers in the fracture analysis. We also apply the Scattering Index (SI ) method (Willis et al., 2006) to the same data from the Lynx Field. The SI method is a robust method to detect fractures and to provide fracture orientations using multi-azimuth/multi-offset pre-stack data. In the realm of existing 3D seismic surveys, data with such acquisition characteristics are few. The fourth contribution of this thesis is therefore the conception of a post-stack version of the SI method that extends the scope of this method to practically every 3D seismic surface data set. In this version, a scattering index is computed for a fully stacked trace per CMP gather. As long as the bin contains traces parallel to the fracture strike, the stacking process of all azimuths and offsets preserves the reverberating character introduced by the fractures. The post-stack SI at a fractured location has a large value in comparison to a non-fractured location. The variations of post-stack SI values across the field reveal the distribution of highly fractured areas. Fracture strike cannot be determined in this case because it does not include the azimuthal behavior of the scattering. However, the results from the post-stack SI are helpful to identify areas of interest to focus the more specialized scattering analysis methods. We apply the F-K and SI methods to the Lynx Field seismic data and compare the results. Since spatial resolution of the two methods are different we upscale the SI maps to match the resolution of the F-K method. The combined analysis of the Lynx Field indicates that the preferred fracture orientation is N40°E, which agrees with the regional stress field. The distribution of highly fractured regions appears to be associated to the geological features, such as folds and faults. The average fracture spacing, obtained by the F-K method shows that, in the Lynx Field, fracture spacing decreases in the west side of the field where the structural dips are higher.

One-Way Wave Propagators For Velocity Analysis On Curvilinear Coordinates

2019-04-10T13:16:04Z

One-Way Wave Propagators For Velocity Analysis On Curvilinear Coordinates Budkick, Scott; van der Hilst, Robert D.; de Hoop, Maarten V. Due to present computational limitations, migration by the one-way wave equation remains an integral tool in seismic exploration. For the realistic interpretation of common image point gathers, it is necessary that migration be free from artifacts from caustics and turning waves. In order to permit situations where turning waves occur, we perform our migration on specially chosen curvilinear coordinates where waves do not travel horizontally. We present an implementation of the curvilinear one-way wave equation using a rational approximation and discuss its application in migration velocity analysis, as well as transmission and reflection tomography.

Effects of Surface Scattering in Waveform Inversion

2019-04-10T07:19:09Z

Effects of Surface Scattering in Waveform Inversion Bleibinhaus, Florian; Rondenay, Stephane In full waveform inversion of seismic body waves, the free surface is often ignored on grounds of computational efficiency. We investigate the effect of this simplification for highly irregular topography by means of a synthetic example. Our test model and data conform to a long-offset survey of the upper crust in terms of size and frequency. Random fractal variations are superimposed on a background model. We compute synthetic data for this model and different topographies, and we invert it neglecting the free surface. The resulting waveform models are relatively similar and, for the most part, show a high degree of correlation with the true model. The inversion of the irregular-topography data produces a few strong artifacts at shallow depths, but only a minor decrease in overall resolution. However, both waveform models fail to image below a strong shallow velocity contrast. The results suggest that in this part of the model the incapacity to properly reproduce the reverberations from that contrast without free surface derails both inversions.

Wave-Equation Reflection Tomography: Annihilators and Sensitivity Kernals

2019-04-10T13:16:04Z

Wave-Equation Reflection Tomography: Annihilators and Sensitivity Kernals van der Hilst, Robert D.; de Hoop, Maarten V.; Shen, Peng In seismic tomography, the finite frequency content of broad-band data leads to interference effects in the process of medium reconstruction, which are ignored in traditional ray theoretical implementations. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here,we consider inverse scattering of bodywaves to develop a method of wave-equation reflection tomography with broad-band waveform data— which in exploration seismics is identified as a method of wave-equation migration velocity analysis. In the transition from transmission to reflection tomography the usual cross correlation between modelled and observed waveforms of a particular phase arrival is replaced by the action of operators (annihilators) to the observed broad-bandwave fields. Using the generalized screen expansion for one-way wave propagation, we develop the Fréchet (or sensitivity) kernel, and show how it can be evaluated with an adjoint state method. We cast the reflection tomography into an optimization procedure; the kernel appears in the gradient of this procedure.We include a numerical example of evaluating the kernel in a modified Marmousi model, which illustrates the complex dependency of the kernel on frequency band and, hence, scale. In heterogeneous media the kernels reflect proper wave dynamics and do not reveal a self-similar dependence on frequency: low-frequency wave components sample preferentially the smoother parts of the model, whereas the high-frequency data are—as expected—more sensitive to the stronger heterogeneity.We develop the concept for acoustic waves but there are no inherent limitations for the extension to the fully elastic case.

Elastodynamic Redatumming for VSP Salt Dome Flank Imaging

2019-04-08T08:17:34Z

Elastodynamic Redatumming for VSP Salt Dome Flank Imaging Lu, Rongrong; Willis, Mark E.; Campman, Xander; Toksoz, M. Nafi In this paper we construct an application methodology for the theoretical elastodynamic redatumming work by Wapenaar (2006) to be able to approximate its use in the problem of imaging a salt dome flank using a walk away VSP (WVSP). Different from acoustic redatumming where only one quantity, the pressure, is involved, full elastodynamic redatumming requires both P-wave source and S-wave sources with different polarizations. We approximate these P-wave and S-wave sources by implementing a shooting pattern for each shot position of an ordinary WVSP acquisition. We create a synthetic WVSP dataset with modified shooting pattern for a model composed of a simplified Gulf of Mexico vertical-velocity gradient, an embedded overhanging salt dome together with a nearby salt canopy. To process these data, we first compile the raw dataset due to the shooting pattern into a new dataset which approximates common receiver gathers due to P-wave source and S-wave sources, respectively. We then apply elastodynamic redatumming to this new dataset to mimic the response between different components for downhole source and receiver pairs. The reconstructed traces show a good match to the traces in the benchmark case, which we create by firing actual downhole sources and recording the responses at all downhole receivers. Instead of a more proper, full elastic migration, we apply simple acoustic migration on individual components of the full elastic Green’s functions to produce pre-stack depth migrated images of the salt dome flank and the dipping sediments. By performing four migrations of these components, we obtain very good separate images of the subsurface using predominately either P or S wave energy. The horizontal sediments and vertical salt flank decouple and appear on separate images.

Redatumming Through a Salt Canopy – Another Salt Flank Imaging Strategy

2019-04-10T20:39:21Z

Redatumming Through a Salt Canopy – Another Salt Flank Imaging Strategy Lu, Rongrong; Willis, Mark E.; Campman, Xander; Ajo-Franklin, Jonathan B.; Toksoz, M. Nafi We describe a new short cut strategy to image the sediments and salt edge around a salt flank through an overburden salt canopy. We demonstrate its performance and capabilities on a synthetic acoustic seismic data from a Gulf of Mexico (GOM) style model. In this strategy, we first redatum the surface shots from a walk away Vertical Seismic Profile (WVSP) survey to be as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving the surface shots through the salt canopy without any knowledge of the overburden velocity structure. After redatumming, we apply reverse time prestack depth migration to the effective downhole shot records using a simple linear v(z) gradient velocity model. This first pass of migration reveals the salt dome edge quite well. Once the salt dome edge is defined, a second pass of reverse time prestack depth migration is performed with an updated velocity model that now consists of the v(z) gradient and the salt dome. The second pass migration brings out the dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank forming prismatic reflections. In this target-oriented strategy, the computationally fast redatumming process eliminates the need for the traditional complex process of velocity estimation, model building, and iterative depth migration to remove the effects of the salt canopy and surrounding overburden.

Nonlinear Soil Response in the Near-Field of a Vibrator Truck: Application to Land Seismic Surveys

2019-04-12T15:05:26Z

Nonlinear Soil Response in the Near-Field of a Vibrator Truck: Application to Land Seismic Surveys Pearce, Fred; Willis, Mark E.; Burns, Daniel R.; Toksoz, M. Nafi; Johnson, Paul The nonlinear behavior of soils can significantly modify the wavelet radiated from vibrator trucks. In this paper, we describe a field experiment designed to measure the nonlinear response of a natural soil formation in the near-field of a vibrator truck. A 267-kN (30-ton) vibrator truck performed a step-sweep through a set of 201 discrete frequencies from 50-Hz to 10-Hz, which was repeated at 11 increasing source amplitudes. Steady-state amplitude spectra for the source output measured on the vibrator truck are significantly different than amplitude spectra for receivers located immediately adjacent to the vibrator truck. Spectral ratios between the source and adjacent receivers show a systematic decrease in peak frequency as the source amplitude is increased. Near-field measurements from vibrator trucks provide a more accurate measurement of the source wavelet that includes soil nonlinearity, and may ultimately lead to a method for optimizing the transmission of energy through an arbitrary soil formation.

Numerical Modeling of Seismic Wave Propagation at the Micro-Scale in Digitized Sandstone

2019-04-09T18:59:20Z

Numerical Modeling of Seismic Wave Propagation at the Micro-Scale in Digitized Sandstone Zhang, Yang; Song, Fuxian; Toksoz, M. Nafi In this paper, we first examine the relationship between the relative particle motions of fluids and solids and the seismic signal received when compressional waves propagate through saturated porous materials. We use a rotated-staggered-grid finite difference modeling scheme to simulate elastic wave phenomena in a digitized 2D structural model obtained from micrographs of a loose beach sand. When considering ultrasonic wave propagation wave in models with explicit inclusion of granular structure, the heterogeneities of quartz and pores in size and shape lead to frequency-dependent seismic phenomena. By comparing the numerical results from models where three sources with different frequencies were used, we saw that (1) strong particle motions concentrate mostly in fluid; (2) significant variations in pressure are observed in the fluid; (3) during the dynamic process of wave propagation, relative particle motion of the fluid and solid phases induces stress concentration on the sharp tips and corner of grains; (4) coherent particle motion is generated by sources with low frequency content, while sources with higher frequencies induce disordered particle motions. Corresponding to these particle motions, less scattered energy is observed in cases with more coherent particle motion, and strong scattering is generated by disordered particle motion. Then we extend our work to a 3D digitized Fontainebleau sandstone sample. Though the size of the sample is small, we still consider a relative broad source frequency band (100 kHz – 20 MHz) so as to study the frequency dependent behavior of this sample. We notice a velocity minimum occurring at some “critical frequency” (750 kHz). Above this “critical frequency”, the velocity increases with frequency; while below this frequency, velocity goes to a low frequency value – effective medium value. The transition from low frequency to high frequency behavior can be viewed as going from wave-like to ray-like propagation. We then study the fluid effect by saturating the pores with non-viscous and viscous brine and oil. The velocities for samples saturated with fluids are generally larger than those of dry sample at frequencies below the critical one, which shows the significant effect of the compressibility of fluids. While the velocities become smaller than those of dry sample at frequencies above the critical one, which shows that the density of fluids comes into play a significant role. We see little effect of viscosity of fluids on velocity. To investigate the scale effect, we first compare the result from dynamic modeling for case with source frequency of 100 kHz to that from static modeling by using finite element method on a sub-cube selected from the original sample. Then we elongate the 3D sample in one direction by repeating the original sample five times, and compare the result from this elongated one to that from the original one at source frequency of 100 kHz. Velocities for these three cases are close to each other. Smaller velocity from static modeling might be due to the higher porosity of the selected sub-cube sample.

Effective Conductivity Modeling of a Fluid Saturated Porous Rock

2019-04-10T10:00:10Z

Effective Conductivity Modeling of a Fluid Saturated Porous Rock Zhan, Xin; Toksoz, M. Nafi The microstructure of a porous medium and physical characteristics of the solid and the fluids that occupy the pore space determine the macroscopic transport properties of the medium. The computation of macroscopic properties from the rock microtomography is becoming an increasingly studied topic. The transport properties are especially difficult to determine at the microscopic scale. In this paper, we will focus on modeling the electric conductivity from the X-ray CT microtomograhpy of a 1mm3 Fontainbleau Sandstone sample. To accomplish this, we modified the finite difference Laplace solver developed at NIST (National Institute of Standards and Technology, Gaithersburg, MD 20899-8621, U.S.A). Our modified finite difference code can calculate the effective conductivity of random materials with different levels of conductivity contrasts. The effective conductivity and the current density distribution of gas, oil and different salinity brine saturated Fontainbleau Sandstone are calculated using a two-phase model. When we compare our numerical results with experimental results from previous studies, the numerically resolved conductivity is almost 100% lower than the experimental data. This is the case for all of the previous work on the numerical computation of electric conductivity from digital images of rocks. Our explanation for this large discrepancy is due to the exclusion of the surface conductivity in the electric double layer (EDL) at the rock-electrolyte interface. Thus, we develop a three phase conductivity model to include the surface conductivity and determine the effective conductivity of the numerical grids containing the EDL from the Waxman-Smits equation. By adding the surface conductivity into our numerical modeling, the calculated conductivity from rock microtomography is much closer to the experimental data.

Electroseismic and Seismoelectric Measurements of Rock Samples in a Water Tank

2019-04-10T10:00:11Z

Electroseismic and Seismoelectric Measurements of Rock Samples in a Water Tank Zhu, Zhenya; Burns, Daniel R.; Toksoz, M. Nafi An electromagnetic wave or a seismic wave can induce seismic or electric waves due to the electrokinetic conversion based on the electric double layer in a fluid-saturated porous medium. In this paper, we observe the acoustic fields generated around the electrodes excited by an electric pulse in a water tank. The electroseismic or seismoelectric waves are measured in the water tank system to confirm that the recorded seismic or electric signals are induced in porous samples due to the electrokinetic conversions. The electroseismic and seismoelectric frequency-responses in Berea sandstone and Westerly granite samples are measured at frequency range of 15 kHz to 150 kHz. The experimental measurements show that the effects of the electric source, background noises, and electroseismic or seismoelectric conversions are separated very clearly. We calculate the electroseismic and seismoelectric normalized coupling coefficients in the rock samples and compare them with the theoretical calculation. The variation trends of the normalized coupling coefficients are in agreement with the theoretical predictions. The measurement method in this paper could be used to investigate other electroseismic and seismoelectric properties for petroleum exploration applications.

Modeling and Inversion of Self Potential Data

2019-04-12T15:08:05Z

Modeling and Inversion of Self Potential Data Minsley, Burke J. This dissertation presents data processing techniques relevant to the acquisition, modeling, and inversion of self-potential data. The primary goal is to facilitate the interpretation of self-potentials in terms of the underlying mechanisms that generate the measured signal. The central component of this work describes a methodology for inverting self-potential data to recover the three-dimensional distribution of causative sources in the earth. This approach is general in that it is not specific to a particular forcing mechanism, and is therefore applicable to a wide variety of problems. Self-potential source inversion is formulated as a linear problem by seeking the distribution of source amplitudes within a discretized model that satisfies the measured data. One complicating factor is that the potentials are a function of the earth resistivity structure and the unknown sources. The influence of imperfect resistivity information in the inverse problem is derived, and illustrated through several synthetic examples. Source inversion is an ill-posed and non-unique problem, which is addressed by incorporating model regularization into the inverse problem. A non-traditional regularization method, termed “minimum support,” is utilized to recover a spatially compact source model rather than one that satisfies more commonly used smoothness constraints. Spatial compactness is often an appropriate form of prior information for the inverse source problem. Minimum support regularization makes the inverse problem non-linear, and therefore requires an iterative solution technique similar to iteratively re-weighted least squares (IRLS) methods. Synthetic and field data examples are studied to illustrate the efficacy of this method and the influence of noise, with applications to hydrogeologic and electrochemical self-potential source mechanisms. Finally, a novel technique for pre-processing self-potential data collected with arbitrarily complicated survey geometries is presented. This approach overcomes the inability of traditional processing methods to produce a unique map of the potential field when multiple lines of data form interconnected loops. The data are processed simultaneously to minimize mis-ties on a survey-wide basis using either an l[subscript 2] or l[subscript 1] measure of misfit, and simplifies to traditional methods in the absence of survey complexity. The l[subscript 1] measure requires IRLS solution methods, but is more reliable in the presence of data outliers.

Experimental Design Applied to Borehole DC Resistivity

2019-04-10T10:00:10Z

Experimental Design Applied to Borehole DC Resistivity Coles, Darrell A.; Morgan, Frank Dale This article explores various aspects of geophysical experimental design (ED) applied to single-borehole DC resistivity. For resistivity problems, an experiment or survey is defined as the set of electrode configurations used to collect a data-set. The systematic design of such surveys, whose purpose is to optimally query a target, is termed experimental design. The borehole problem is cast in cylindrical coordinates, and because only one borehole is modeled, resistivity is treated as azimuthally invariant, permitting the problem to be treated as a form of electrical resistivity tomography. The nature of the experimental design space is thoroughly explored, culminating in several novel insights into electrical resistivity tomography problems that are useful for ED. Multiple ED functions are proposed, whose distinguishing characteristic is that they can be executed serially, rather than en masse. That is, these functions are such that experiments can be designed one observation at a time, instead of the traditional approach, in which the entire experiment is designed at once. Because traditional ED approaches are fundamentally combinatoric, the size of the experimental search space is greatly reduced by our method, expediting the optimization algorithms and making experimental design a practical possibility. Several basic design strategies are explored and compared with random and standardized surveys to quantify the effectiveness of these techniques. Lastly, adaptive experimental design procedures are examined, wherein surveys are specifically adapted to a heterogeneous target. The results of this work show that ED produces real improvements in data quality, as compared with standardized and random surveys.

Optimal Experiment Design for Timelapse Tomography: Customizing Crosswell Micro-Arrays for Monitoring Applications

2019-04-08T08:17:34Z

Optimal Experiment Design for Timelapse Tomography: Customizing Crosswell Micro-Arrays for Monitoring Applications Ajo-Franklin, Jonathan B. Geophysical monitoring techniques offer the only approach capable of assessing both the spatial and temporal dynamics of subsurface fluid processes. Historically, monitoring datasets have consisted of surveys sequentially collected using acquisition geometries and sensor platforms similar to static measurements. Unfortunately, a host of logistical constraints hamper the repeatability of such surveys, particularly difficulties replicating the source/receiver geometry. Increasingly, permanent sensor arrays in boreholes and on the ocean floor are being deployed to improve the repeatability and increase the temporal sampling of monitoring surveys. Because permanent arrays require a large up-front capital investment and are difficult (or impossible) to re-configure once installed, a premium is placed on selecting a geometry capable of imaging the desired target at minimum cost. We present a simple approach to optimizing downhole sensor arrays for monitoring experiments making use of differential seismic traveltimes. In our case, we use a design quality metric based on the accuracy of tomographic reconstructions for a suite of imaging targets. By not requiring an explicit SVD of the forward operator, evaluation of this objective function scales to problems with a large number of unknowns. We also restrict the design problem by recasting the array geometry into a low dimensional form more suitable for optimization. A side effect of using these restrictive parameterizations for experiment geometry is a well-behaved objective function more amenable to local search techniques. To demonstrate the efficacy of our algorithm, we consider a series of possible designs optimization problems for a next-generation permanent tomographic monitoring system. We test two search algorithms on the design problem, the Nelder-Mead downhill simplex method and the Multilevel Coordinate Search algorithm. The complete design algorithm is tested for three crosswell acquisition scenarios relevant to continuous seismic monitoring, a 2 parameter array length optimization, a 4 parameter length/offset optimization, and a comparison of optimal multi-source designs. In the last case, we also examine trade-offs between source sparsity and the quality of tomographic reconstructions. Preliminary results suggest that high-quality differential images can be generated using only a small number of optimally positioned sources, an observation with immediate relevance to several field projects still in the development phase.

Applying Compactness Constraints to Differential Traveltime Tomography

2019-04-12T15:08:04Z

Applying Compactness Constraints to Differential Traveltime Tomography Ajo-Franklin, Jonathan B.; Minsley, Burke J.; Daley, Thomas M. Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. By performing inversions on differenced arrival time data, the properties of the timelapse feature can be directly constrained. We develop a differential traveltime tomography algorithm which selects for compact solutions i.e. models with a minimum area of support, through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously explored within the potential theory community. We compare our inversion algorithm to the results obtained by traditional Tikhonov regularization for two simple synthetic models; one including several sharp localized anomalies and a second with smoother features. We use a more complicated synthetic test case based on multiphase flow results to illustrate the efficacy of compactness constraints for contaminant infiltration imaging. We conclude by applying the algorithm to a CO[subscript 2] sequestration monitoring dataset acquired at the Frio pilot site. We observe that in cases where the assumption of a localized anomaly is correct, the addition of compactness constraints improves image quality by reducing tomographic artifacts and spatial smearing of target features.

Fracture Quality From Integrating Time-Lapse VSP and Microseismic Data

2019-04-12T15:20:17Z

Fracture Quality From Integrating Time-Lapse VSP and Microseismic Data Willis, Mark E.; Burns, Daniel R.; Lu, Rongrong; Toksoz, M. Nafi; House, Nancy J. Tight gas reservoirs are problematic to produce, often requiring multiple stages of hydraulic fracturing in order to create connected pathways through which hydrocarbons may flow. In this paper, we propose a new methodology to characterize the quality of hydraulic fractures. Using synthetic VSP and microseismic data, we test the concept that the rock volume containing open, gas filled fractures will scatter seismic energy more profusely than a volume containing closed, non-productive fractures. By measuring the amount of scattered energy in a time lapse 3D VSP study taken before and after the hydraulic fracturing episode, we hope to be able to compare the productive flow quality of different regions of the hydraulically fractured rock. The microseismic recordings allow us both to locate areas which have been hydraulically fractured and create imaging operators to extract the scattered signals from the time lapse VSP data.

Analysis of Scattered Signal to Estimate Reservoir Fracture Parameters

2019-04-12T15:20:16Z

Analysis of Scattered Signal to Estimate Reservoir Fracture Parameters Grandi, Samantha K.; Willis, Mark E.; Burns, Daniel R.; oksoz, M. Nafi We detect fracture corridors and determine their orientation and average spacing based on an analysis of seismic coda in the frequency-wave number (f-k ) domain. Fracture corridors have dimensions similar to seismic wavelengths which causes scattering. The distribution of energy in shot records in the f-k domain depends upon the orientation of the records relative to the fracture strike. In the direction normal to fractures, scattered waves propagate with slower apparent velocities than waves propagating along the fracture channels. The associated f-k spectral differences allow the identification of the preferred fracture orientation and spacing. We apply our technique to a fractured reservoir in the Lynx field, in the Canadian foothills. The estimated preferential fracture orientation is about N40 E, which agrees with regional stress measurements. The average fracture spacing is 75 m on the West side of the survey, while fractures are more sparse on the East side. We also apply the Scattering Index methodology (Willis et al., 2006) to the same data, post-stack and pre-stack. This technique has higher resolution to map fracture distribution, intensity and orientation, and therefore complements the spectral method in providing an integrated description of reservoir fractures.

Fracture Properties From Seismic Scattering

2019-04-12T15:05:05Z

Fracture Properties From Seismic Scattering Burns, Daniel R.; Willis, Mark E.; Vetri, Laura; Toksoz, M. Nafi Fractures scatter seismic energy and this energy can be analyzed to provide information about fracture direction and density. Laboratory and numerical (finite difference) models of fractures show that scattered energy varies with the seismic acquisition direction relative to the orientation of parallel fracture sets. Data acquired normal to fracture strike displays forward and backscattered energy that is canceled in the stacking process, while data acquired parallel to the fracture strike contains forward scattered and guided waves that are enhanced by stacking. The Scattering Index method estimates the fracture orientation by comparing wavelet changes in the data from azimuthal stacks. Fracture density or spacing can be estimated by spectral methods that include f-k analysis of backscattered energy or analysis of spectral notches as functions of azimuth. Application of these methods to data from a fractured carbonate field results in fracture orientation and density estimates that are consistent with borehole measurements.

A Study of Seismoelectric Signals in Measurement While Drilling (M.S. Thesis)

2019-04-12T15:08:11Z

A Study of Seismoelectric Signals in Measurement While Drilling (M.S. Thesis) Zhan, Xin An LWD acoustic wave can move the excess charge in the electric double layer along the borehole wall to generate a streaming electric field. This thesis is an experimental and theoretical investigation of the electric field induced by the multipole LWD acoustic wave. The main goal of this thesis is to understand the mechanism in the seismoelectric conversion under the LWD geometry and prove the absence of the tool mode in the LWD-acoustic-wave induced electric signals. In this experimental study, we measured the seismoelectric signals excited by an acoustic multipole source in the scaled logging-while-drilling model. We put the scaled tool in a sandstone borehole to perform LWD seismoelectric and acoustic measurements. Monopole and dipole acoustic and the induced electric signals were recorded separately under exactly the same settings. The recorded acoustic and seismoelectric signals were analyzed in both time and frequency domains using a semblance method. We found no tool mode components in the electric signals by examining both the waveforms and the time and frequency domain semblances. The underlying mechanism is the electric double layer (EDL) at the steel water interface is much weaker than the one at the formation water interface. Thus, in the LWD seismoelectric signal, there should be no component with an apparent velocity of tool mode. Since only formation acoustic modes have their corresponding components in the electric signal, we calculated the coherence of the two kinds of signals in the frequency domain. By applying the coherence curve to filter the acoustic signals, we can eliminate the tool modes and pick out the formation acoustic modes. In the theoretical study, we developed a Pride-theory-based model for the LWD-acoustic-wave induced electric field. The electric field strength is calculated at the electrode positions along the borehole wall, analogous to what was done in the experiment. The electric boundary conditions, which are the continuity of the electric field at the borehole wall and disappearance at the LWD tool surface, reveal the underlying mechanism in the LWD sismoelectric conversion which is also the basis of our lab experiment. The absence of the tool modes in the synthetic waveforms of the electric field coincides with what we have observed in the experimental study. Both the experiment and the theoretical results confirm that measuring the seismoelectric signal generated by an acoustic multipole source during the LWD process can be an effective way to eliminate the tool wave contamination on the LWD acoustic measurements. This thesis research shows that seismoelectric logging-while-drilling may be a potential new method in formation property evaluation.

Spatial Orientation and Distribution of Reservoir Fractures from Scattered Seismic Energy

2019-04-10T10:00:23Z

Spatial Orientation and Distribution of Reservoir Fractures from Scattered Seismic Energy Willis, Mark E.; Burns, Daniel R.; Rao, Rama V. N.; Minsley, Burke J.; Toksoz, M. Nafi; Vetri, Laura We present the details of a new method for determining the reflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations we have made from 3D finite difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fracture corridors impart a coda signature, which is a ringing tail of scattered energy, to any seismic waves which are transmitted through or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1) the difference in angle between the orientation of the fractures and the acquisition direction, 2) the fracture spacing, 3) the wavelength of the illuminating seismic energy, and 4) the compliance, or stiffness, of the fractures. This coda energy is the most coherent when the acquisition direction is parallel to the strike of the fractures. It has the largest amplitude when the seismic wavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. Our method uses surface seismic reflection traces to derive a transfer function which quantifies the change in an apparent source wavelet before and after propagating through a fractured interval. The transfer function for an interval with no or low amounts of scattering will be more spike-like and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. When a 3D survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows us to identify subsurface areas with high fracturing and determine the strike of those fractures. We calibrated the method with model data and then applied it to the Emilio field with a fractured reservoir giving results which agree with known field measurements and previously published fracture orientations derived from PS anisotropy. Shortened title: Fracture characterization from coda energy

A Novel Application of Time Reversed Acoustics: Salt Dome Flank Imaging Using Walkaway VSP surveys

2019-04-12T21:45:27Z

A Novel Application of Time Reversed Acoustics: Salt Dome Flank Imaging Using Walkaway VSP surveys deHoop, Maarten V.; Willis, Mark E.; Lu, Rongrong; Campman, Xander; Toksoz, M. Nafi; Zhang, Yang In this paper we present initial results of applying Time-Reversed Acoustics (TRA) technology to saltdome flank, seismic imaging. We created a set of synthetic traces representing a multilevel, walkaway VSP for a model composed of a simplified Gulf of Mexico vertical-velocity gradient and an embedded salt dome. We first applied the concepts of TRA to the synthetic traces to create a set of redatummed traces without having to perform velocity analysis, moveout corrections, or complicated processing. Each redatummed trace approximates the output of a zero-offset, downhole source and receiver pair. To produce the final salt-dome flank image, we then applied conventional, poststack, depth migration to the zero-offset section. Our results show a very good image of the salt when compared to an image derived using data from a downhole, zero-offset source and receiver pairs. The simplicity of our TRA implementation provides a virtually automated method to estimate a zero-offset, seismic section as if it had been collected from the reference frame of the borehole containing the VSP survey. GEOPHYSICS, VOL. 71, NO. 2 (MARCH-APRIL 2006); P. A7–A11, 4 FIGS. 10.1190/1.2187711

Imaging Salt Dome Flank and Dipping Sediments Using Time Reversed Acoustics

2019-04-11T00:44:52Z

Imaging Salt Dome Flank and Dipping Sediments Using Time Reversed Acoustics Lu, Rongrong; Willis, Mark E.; Campman, Xander; Ajo-Franklin, Jonathan B.; Toksoz, M. Nafi In this paper we define the theory and basic principles to move (redatum) the surface shots from a walk away VSP to be as if they had been located in the borehole. We will refer to this theory using several of the terms used in the literature including Time Reverse Acoustics (TRA), Seismic Interferometry (SI) and Virtual Source (VS) technology. Regardless of the name, the theory is built upon reciprocity and the time symmetry of the wave equation. We apply these TRA principles, together with prestack depth migration, to produce images of a modeled salt dome flank. We create a set of synthetic traces representing a multi-level, walk away VSP for a model composed of a simplified Gulf of Mexico vertical velocity gradient and an embedded overhanging salt dome. The sediment reflectors in the model dip up towards the salt dome flank. The energy from the surface shots is bent into turning rays by the linear v(z) gradient which illuminate the steeply dipping sediments and overhanging salt edges. The illuminating energy is reflected and scattered from these surfaces and then captured by the downhole VSP receivers. To simplify the processing of these data, we move (redatum) the surface shots into the borehole using our TRA or seismic interferometry principles. This removes from the seismic traces the entire, potentially complicated, path from the surface shot location to the borehole without having to perform any velocity analyses or moveout corrections. Each of these new (redatummed) traces mimics the output of a down-hole source and down-hole receiver pair. We apply prestack depth migration to these new traces to produce the final image of the beds and the salt dome flank which agree very well with the original model structure.

Computation of 3D Frequency-Domain Waveform Kernals for c(x,y,z) Media

2019-04-11T03:07:12Z

Computation of 3D Frequency-Domain Waveform Kernals for c(x,y,z) Media Nihei, Kurt T.; Ajo-Franklin, Jonathan B.; Campman, Xander; Toksoz, M. Nafi Seismic tomography, as typically practiced on both the exploration, crustal, and global scales, considers only the arrival times of selected sets of phases and relies primarily on WKBJ theory during inversion. Since the mid 1980’s, researchers have explored, largely on a theoretical level, the possibility of inverting the entire seismic record. Due to the ongoing advances in CPU performance, full waveform inversion is finally becoming feasible on select problems with promising results emerging from frequency-domain methods. However, frequency-domain techniques using sparse direct solvers are currently constrained by memory limitations in 3D where they exhibit a O(n4) worst-case bound on memory usage. We sidestep this limitation by using a hybrid approach, calculating frequency domain Green’s functions for the scalar wave equation by driving a high-order, time-domain, finite-difference (FDTD) code to steady state using a periodic source. The frequency-domain response is extracted using the phase sensitive detection (PSD) method recently developed by Nihei and Li (2006). The resulting algorithm has an O(n3) memory footprint and is amenable to parallelization in the space, shot, or frequency domains. We demonstrate this approach by generating waveform inversion kernels for fully c(x,y,z) models. Our test examples include a realistic VSP experiment using the geometry and velocity models obtained from a site in Western Wyoming, and a deep crustal reflection/refraction profile based on the LARSE II geometry and the SCEC community velocity model. We believe that our 3D solutions to the scalar Helmholtz equation, for models with upwards of 100 million degrees of freedom, are the largest examples documented in the open geophysical literature. Such results suggest that iterative 3D waveform inversion is an achievable goal in the near future.

Non-Linear Constraints with Application to Self-Potential Source Inversion

2019-04-11T04:03:18Z

Non-Linear Constraints with Application to Self-Potential Source Inversion Minsley, Burke J.; Ajo-Franklin, Jonathan B.; Dale, Frank We investigate the use of non-linear constraints for geophysical inverse problems, with specific examples applied to source inversion of self-potential data. Typical regularization methods often produce smooth solutions by introducing a quadratic term in the objective function that minimizes the L2 norm of a low-order differential operator applied to the model. In some cases, however, the properties of interest may not vary smoothly. Two alternative constraints are examined that provide inversion stability while allowing for solutions with non-smooth properties. One method, often referred to as ‘compactness’ or ‘minimum support’, seeks to minimize the area (in 2D) or volume (in 3D) occupied by non-zero model parameters. The second method, ‘total variation’, minimizes an approximation of the L1 norm of the gradient of the model. Both approaches involve a non-linear regularization functional, and must therefore be solved iteratively. We discuss the practical aspects of implementing these regularization methods and compare several examples using self-potential source inversion on a synthetic model. We also apply the compactness constraint for self-potential source inversion using a field data example.

Applying Compactness Constraints to Seismic Traveltime Tomography

2019-04-12T15:05:36Z

Applying Compactness Constraints to Seismic Traveltime Tomography Ajo-Franklin, Jonathan B.; Minsley, Burke J.; Daley, T. M. Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced seismic velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. We develop a traveltime tomography algorithm which selects for compact solutions through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously developed within the potential theory community. We emphasize the application of compactness constraints to timelapse datasets differenced in the data domain, a process which allows recovery of compact perturbations in model properties. We test our inversion algorithm on a simple synthetic dataset generated using a velocity model with several localized velocity anomalies. We then demonstrate the efficacy of the algorithm on a CO2 sequestration monitoring dataset acquired at the Frio pilot site. In both cases, the addition of compactness constraints improves image quality by reducing spatial smearing due to limited angular aperture in the acquisition geometry.

Elimination of LWD (Logging-While-Drilling) Tool Modes Using Seismoelectric Data

2019-04-10T17:18:42Z

Elimination of LWD (Logging-While-Drilling) Tool Modes Using Seismoelectric Data Zhan, Xin; Zhu, Zhenya; Chi, Shihong; Rao, Rama V. N.; Burns, Daniel R.; Toksoz, M. Nafi Borehole acoustic logging-while-drilling (LWD) for formation evaluation has become an indispensable part of hydrocarbon reservoir assessment (Tang et al., 2002; Cittá et al., 2004; Esmersoy et al., 2005). However, the detection of acoustic formation arrivals1over tool mode contamination has been a challenging problem in acoustic LWD technology. This is because the tool mode contamination in LWD is more severe than in wireline tools in most geological environments (Tang et al., 2002; Huang, 2003). In this paper we propose a new method for separating tool waves from formation acoustic waves in acoustic LWD. This method is to measure the seismoelectric 2signal excited by the LWD acoustic waves. The acoustic waves propagating along the borehole or in the formation can induce electric fields. The generated electric field is localized around the wave pulses and carried along the borehole at the formation acoustic wave velocity. The LWD tool waves which propagate along the rigid tool rim can not excite any electric signal. This is due to the effectively grounding of the drill string during the LWD process makes it impossible to accumulate any excess charge at the conductive tool – borehole fluid interface. Therefore, there should be no contribution by the tool modes to the recorded seismoelectric signals. In this study, we designed the laboratory experiments to collect simulated LWD monopole and dipole acoustic and seismoelectric signals in a borehole in sandstone. By analyzing the acoustic and electric signals, we can observe the difference between them, which are the mainly tool modes and noise. Then we calculate the similarity of the two signals to pick out the common components of the acoustic and seismoelectric signals, which are the pure formation modes. Using the seismoelectric signals as reference, we could filter out the tool modes. The method works well. To theoretically understand the seismoelectric conversion in the LWD geometry, we also calculate the synthetic waveforms for the multipole LWD seismoelectric signals based on Pride’s theory (Pride, 1994). The synthetic waveforms for the electric field induced by the LWD-acoustic-wave along the borehole wall demonstrate the absence of the tool mode, which is consistent with the conclusions we get in the experimental study.

Inversion of Shear Wave Anisotropic Parameters in Strongly Anisotropic Formations

2019-04-12T15:05:25Z

Inversion of Shear Wave Anisotropic Parameters in Strongly Anisotropic Formations Chi, Shihong; Tang, Xiaoming; Zhu, Zhenya Deepwater reservoirs use highly deviated wells to reduce cost and enhance hydrocarbon recovery. Due to the strong anisotropic nature of many of the marine sediments, anisotropic seismic imaging and interpretation can improve reservoir characterization. Sonic logs acquired in these wells are strongly dependent on well deviations. Cross-dipole sonic logging provides apparent shear wave anisotropy in deviated wells, which can be far from the truth. Although anisotropic parameters have been successfully obtained using data from wells of several deviations or using single well data based on weak anisotropy approximation, estimation of strong shear wave anisotropy from single well data remains a challenge. Using sensitivity analysis, we find Stoneley wave velocity has good sensitivity to qSV and SH wave velocities in deviated wells. We create a linear inversion scheme to estimate shear wave anisotropy using SH, SV, and Stoneley wave velocities logged in one well. We first apply the method to laboratory measurements from boreholes of various deviations relative to the symmetry axis of an anisotropic material. We then apply the method to a field data set acquired in a deviated well. We also compute the vertical and horizontal shear wave velocity logs in this well using the inverted elastic shear wave constants.

Sonic Logging in Deviated Boreholes in an Anisotropic Formation: Laboratory Study

2019-04-12T15:05:30Z

Sonic Logging in Deviated Boreholes in an Anisotropic Formation: Laboratory Study Zhu, Zhenya; Chi, Shihong; Toksoz, M. Nafi Deepwater field development requires drilling of deviated or horizontal wells. Most formations encountered can be highly anisotropic and P- and S-wave velocities vary with propagation directions. Sonic logs acquired in these wells need to be corrected before they can be applied in formation evaluation and seismic applications. In this study, we make use of a laboratory model made of an approximate transversely isotropic Phenolite to study acoustic logging in deviated wells. We drill holes at various deviations relative to the symmetry axis in the Phenolite block. Then we perform monopole and dipole sonic measurements in these holes and extract the qP, qSV, SH, and Stoneley wave velocities using the slowness-time domain semblance method. The velocities measured using monopole and dipole loggings vary with borehole deviations. We also measure the qP, qSV, and SH wave velocities using body waves at the same angles as the well deviations. We then compute the theoretical qP, qSV, SH, and Stoneley wave velocities based on an equivalent transverse isotropic model of the Phenolite. We find the qP, qSV , and SH wave velocities obtained using the body wave measurement and acoustic logging method agree with the theoretical predictions. The Stoneley wave velocities predicted by the theory also agree reasonably well with the logging measurements.

Fracture Mapping in the Soultz-sous-Forets Geothermal Field from Microearthquake Relocation

2019-04-09T15:43:11Z

Fracture Mapping in the Soultz-sous-Forets Geothermal Field from Microearthquake Relocation Michelet, Sophie; Toksoz, M. Nafi In 2003, a massive hydraulic fracturing experiment was carried out at the European Geothermal Hot Dry Rock site at Soultz-sous-Forêts, France. The two week injection of water generated a high level of microseismic activity. About 90,000 microearthquakes were triggered during and after this fluid injection. Of these, 21,000 events, detected at all stations, were located individually with a grid search algorithm to characterize the extent of the seismic zones and, ultimately, of the fracture network. The accuracy of these initial locations was around 70 meters, not sufficient to map detailed fracture patterns. We undertook a relocation effort using two different techniques: Joint Hypocenter Determination (JHD) and Multiplet analysis. The JHD technique allows for the simultaneous location of a group of events and the determination of a common set of station corrections. We added the “collapsing” method to the JHD results to further consolidate the hypocenters. This was followed by a multiplet analysis for identifying microearthquakes with similar waveforms. We found 7463 events whose seismograms correlated with a correlation coefficient of 0.8 or higher, most of which were doublets. For the relative location of the correlated events, we computed the delay in travel-time by wavelet analysis. We found that multiplets were located on small planes with lengths of a hundred to several hundred meters striking mostly along N150°E. Comparing the distribution of seismicity with fluid outflows during the fluid injection, we observed that majority of events were concentrated along the newly created fractures.

Orientation Estimation for Multiple Large Fractures by Scattering Energy

2019-04-10T09:59:44Z

Orientation Estimation for Multiple Large Fractures by Scattering Energy Zhang, Yang; Chi, Shihong; Willis, Mark E.; Toksoz, M. Nafi; Burns, Daniel R. We have done the numerical modeling of seismic response to multiple sets of vertical large fractures by using finite-difference method (FD), which can easily handle media with monoclinic anisotropy. We consider three types of fracture distributions: a set of parallel fractures, two sets of orthogonal fractures and two sets of non-orthogonal fractures intersecting at 45 degrees. We address the seismic scattering response to large fractures by using a 3-layer model and a 5-layer model, where a fractured reservoir is in the middle layer of these two models. Seismic scattered energy is analyzed by the Scattering Index (SI) method to estimate the orientation of these multiple fractures. In both models, SI indicates the correct orientation of the two orthogonal fracture sets but is ambiguous for non-orthogonal fracture sets. Information about the fracture spacing and compliance can also be extracted from the azimuthal SI in some situations. More compliant fracture sets result in higher SI values while the relationship between fracture spacing and SI depends on the source wavelength. Variations in the SI energy can be caused by fracture spacing and compliance variations, and these relationships need further investigation.

Finite Difference Modeling of Seismic Responses to Intersecting Fracture Sets

2019-04-11T04:03:17Z

Finite Difference Modeling of Seismic Responses to Intersecting Fracture Sets Chi, Shihong; Zhang, Yang; Campman, Xander; Toksoz, M. Nafi Fractured reservoir characterization is becoming increasingly important for the petroleum industry. Currentmethods for this task are developed based on effectivemedia theory, which assumes the cracks or fractures in a reservoir are much smaller than the seismic wavelength. A discrete fracturemodel has to be used for large-scale fractures. We describe an approach of using a finite difference method for modeling seismic wave propagation in rock formations with intersecting fracture sets. We then use the code to study the behavior of seismic waves, particularly scattering due to such fracture sets with various spacing and compliances. The scattering pattern due to fractures varies azimuthally. We find that converted PS and PSP waves from the bottom of the fractured layers show strong interference by the scattered waves. We observe coherent scattered waves in shot gathers parallel to the fracture orientation and significant backscattering at near offsets and forward scattering at far offsets in the gathers normal to the fracture orientation. When two sets of fractures are present, scattering becomes stronger and more complex scattered waves appear in the gathers. The scattering becomes stronger with increasing the fracture compliances and decreasing spacing (still on the order of seismic wave length). When the fracture sets are not orthogonal to each other, the gathers still show coherent scattering in the fracture orientations. Azimuthal characteristics of the scattered waves may be used to analyze fracture orientations, spacing, and relative compliance of intersecting fracture sets.

Fracture Characterization from Scattered Energy: A Case Study

2019-04-10T09:59:44Z

Fracture Characterization from Scattered Energy: A Case Study Grandi, Samantha K.; Yuh, Sung; Willis, Mark E.; Toksoz, M. Nafi We use 3D surface seismic data to determine the presence and the preferred orientation of fracture corridors in a field. The Scattering Index method is proving to be a robust tool for detecting and mapping fracture corridors. Fracture corridors largely control permeability and fluid flow in some fractured reservoirs. To apply the Scattering Index method, we compute the scattering transfer functions from the reservoir interval using prestack migrated data collected in four azimuth sectors. By measuring the azimuthal differences in the amount of scattering, we obtain maps of density of fracture corridors and their orientation across the survey area. We use geostatistical filtering to improve the spatial correlation of scattering index maps. The distribution and orientation of the final fracture corridors are interpreted considering the structure, fault network, and stress information. In the field, we observe several regions of high fracturing near the anticline’s crest and on its steepest slopes, on the southwest flank. Around well locations, fractures are oriented to the NW and NNW, which agrees with estimates of maximum stress direction from well data.

F-K Characteristics of the Seismic Response to a Set of Discrete Parallel Fractures

2019-04-11T03:07:12Z

F-K Characteristics of the Seismic Response to a Set of Discrete Parallel Fractures Zhang, Yang; Campman, Xander; Grandi, Samantha K.; Chi, Shihong; Toksoz, M. Nafi; Willis, Mark E.; Burns, Daniel R.; Vetri, Laura We model seismic wave propagation in a reservoir with discrete fracture zones using a finite difference scheme, which implements the Coates-Schoenberg formulation for fractured media. We study the variation of scattered energy in the direction perpendicular and parallel to the fracture strike. In the modeled data, we observe variations in the coherence of seismic energy and interference between backward and forward scattered energy. We then sorted data from the Emilio field in Italy in azimuthal gathers. These panels show a striking qualitative resemblance to the modeled data. We conclude that, in this case, a discrete representation of the fractures in the reservoir predicts the observation in the field data well. This supports the idea that fractures can cluster into fracture zones that scatter seismic energy. We then analyze the seismic energy on a profile in the direction perpendicular to the fracture strike. First we use estimated scattered energy in a window around the target zone to estimate the spacing between large fracture zones. The scattered energy in a later time window is shown to consist of mainly P to S scattered energy. For the estimation of smaller spacings, we rely on the smaller wavelength of these converted waves to illuminate finer structure. The result of spacing estimation is not very sensitive to the time window from which we estimate the scattered energy, because, in f-k domain, the wavenumber values of the dominant backscattered energy within successive time windows are almost the same, but frequency content drops gradually. Finally we apply this analysis to field data from Emilio Oil Field, and estimate a fracture spacing of about 40 m.

Experimental and Theoretical Studies of Seismoelectric Effects in Boreholes

2019-04-12T15:20:16Z

Experimental and Theoretical Studies of Seismoelectric Effects in Boreholes Zhu, Zhenya; Chi, Shihong; Toksoz, M. Nafi In a fluid-saturated porous formation, an impinging seismic wave induces fluid motion. The motion of fluid relative to the rock frame generates an electric streaming current. This current produces electric and magnetic fields, which are called seismoelectric and seismomagnetic fields, respectively. When there is a fracture or a discontinuity, a radiating electromagnetic wave is also generated, in addition to local fields. Seismoelectric and seismomagnetic fields depend on the amplitude, frequency, and mode of the seismic wave, as well as the formation porosity, permeability, pore size, and fluid conductivity. In this paper, we describe laboratory results of seismoelectric and seismomagnetic fields induced by an acoustic source in borehole models. We use a piezoelectric source for acoustic waves and a point electrode and a high-sensitivity Hall-effect transducer for measuring the localized seismoelectric and seismomagnetic fields in fluid-saturated rocks. The dependence of seismoelectric conversions on porosity, permeability and fluid conductivity are investigated. Three components of the seismomagnetic field are measured by the Hall-effect transducer. At a horizontal fracture, the acoustic wave induces a radiating electromagnetic wave.

Comparison of Discrete Fracture and Effective Media Representation of Fractures on Azimuthal AVO

2019-04-12T15:20:16Z

Comparison of Discrete Fracture and Effective Media Representation of Fractures on Azimuthal AVO Zhang, Yang; Chi, Shihong; Willis, Mark E.; Burns, Daniel R.; Toksoz, M. Nafi In fractured reservoir development, azimuthal AVO (AVOaz) properties of reflected PP waves from reservoir tops are often used to infer fracture properties. The fracture parameter inversion is based on either an effective media model (EMM) or a discrete fracture model (DFM). We address the differences in fracture properties that may be inferred by AVOaz based on the two models. For the DFM we focus on fractures whose length and spacing are comparable to the seismic wavelength. First, we compute the elastic parameters describing the fractured reservoir for each type of model. Then we synthesize seismic data using a finite-difference program for both sets of elastic parameters. By performing AVOaz analysis, we find that EMM and DFM predict different offsets for maximum AVOaz magnitudes. The DFM results show larger AVOaz magnitude with farther offsets, and phase changes at offsets larger than 35 degrees may indicate compliant fractures in a reservoir. For compliant fractures, the fracture strike determined using AVOaz effect based on the EMM is opposite to that from the DFM. This difference could cause incorrect estimation of fracture orientation if the EMM is used to interpret data from a reservoir with discrete fracture zones. DFM may be better suited for modeling wavelength-scale fractures.

An Experimental Study Of Seismoelectric Signals In Logging While Drilling

2019-04-09T19:24:08Z

An Experimental Study Of Seismoelectric Signals In Logging While Drilling Zhan, Xin; Zhu, Zhenya; Chi, Shihong; Rao, Rama V. N.; Toksoz, M. Nafi Acoustic logging while drilling (LWD) may be complicated because of contamination by waves propagating along the drill collar (the tool waves). In this paper we propose a new method for separating tool waves from the true formation acoustic arrivals in borehole acoustic LWD. The method utilizes the seismoelectric signal induced by the acoustic wave at the fluid-formation boundary. The basis for seismoelectric conversion is the electric double layer (EDL) that exists in most rock-water systems. EDL does not exist at the tool (conductor) water interface. Therefore, there should be no seismoelectric signals due to tool modes. In this paper, borehole monopole and dipole LWD acoustic and seismoelectric phenomena are investigated with laboratory measurements. The main thrust of the paper is the utilization of the difference between acoustic and seismoelectric signals, to eliminate the tool waves and enhance the formation acoustic signals in acoustic LWD.

Spatial Orientation And Distribution Of Reservoir Fractures From Scattered Seismic Energy

2019-04-10T09:59:44Z

Spatial Orientation And Distribution Of Reservoir Fractures From Scattered Seismic Energy Vetri, Laura; Willis, Mark E.; Burns, Daniel R.; Rao, Rama V. N.; Minsley, Burke J; Toksoz, M. Nafi We present the details of a new method for determining the reflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations we have made from 3D finite difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fractures impart a ringing coda type signature to any seismic energy which is transmitted through or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1) the difference in angle between the orientation of the fractures and the acquisition direction, 2) the fracture spacing, 3) the wavelength of the illuminating seismic energy, and 4) the compliance, or stiffness, of the fractures. This coda energy is the most coherent when the acquisition direction is parallel to the strike of the fractures. It has the largest amplitude when the seismic wavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. Our method uses surface seismic reflection traces to derive a transfer function which quantifies the change in an apparent source wavelet before and after propagating through a fractured interval. The transfer function for an interval with no or low amounts of scattering will be more spike-like and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. When a 3D survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows us to identify subsurface areas with high fracturing and determine the strike of those fractures. We calibrated the method with model data and then applied it to the Emilio field with a fractured reservoir giving results which agree with known field measurements and previously published fracture orientations derived from PS anisotropy. Shortened title: Fracture characterization from coda waves

Fracture Spacing and Orientation Estimation from Spectral Analyses of Azimuth Stacks

2019-04-12T15:05:24Z

Fracture Spacing and Orientation Estimation from Spectral Analyses of Azimuth Stacks Willis, Mark E.; Rao, Rama V. N.; Burns, Daniel R.; Toksoz, M. Nafi; Vetri, Laura Discrete, vertically aligned fracture systems impart one or more notches in the spectral ratios of stacked reflected seismic traces. This apparent attenuation is due to the azimuth dependant scattering introduced by the fractures. The most prominent notch is located at the frequency where the P wavelength is about twice the fracture spacing. The frequency location of the notches can be used to determine the fracture spacings. Azimuth stacks with an orientation parallel to the fractures tend not show these spectral notches – allowing for another way to detect the fracture orientation. An analysis of the vertical component of the 3D, ocean bottom cable seismic survey data from the Emilio field, offshore Italy, shows a prominent set of fractures with a spacing of about 30 to 40 meters with orientations that agree with previous studies.

A Novel Application of Time Reversed Acoustics: Salt Dome Flank Imaging Using Walk Away VSP Surveys

2019-04-12T15:05:20Z

A Novel Application of Time Reversed Acoustics: Salt Dome Flank Imaging Using Walk Away VSP Surveys Willis, Mark E.; Lu, Rongrong; Burns, Daniel R.; Toksoz, M. Nafi; Campman, Xander; Hoop, Martijn de In the past few years, there has been considerable research and interest in a topic known by various names, such as Time Reverse Acoustics (TRA), Time Reverse Mirrors (TRM), and Time Reverse Cavities (TRC), which exploits reciprocity and the time symmetric property of the wave equation. Very little of this work has been directed at the seismic exploration imaging problem. In fact, most of the work has had application in sonar, medical and non-destructive testing applications. Here we present some initial results of applying this technology to the seismic imaging of a salt dome flank. We create a set of synthetic traces representing a multi-level, walk away VSP for a model composed of a simplified Gulf of Mexico vertical velocity gradient and an embedded overhanging salt dome. To process these data, we first apply the concepts of TRA to the synthetic traces. This creates a set of stacked traces without having to perform any velocity analysis or complicated processing. Each of these stacked traces is equivalent to the output of a spatially coincident, or zero offset, down hole source and receiver pair. Thus we have the equivalent of a zero offset seismic section as if it were collected from down hole sources and receivers. After having applied the TRA concepts, we then apply conventional post stack depth migration to this zero offset section to produce the final image of the salt dome flank. Our results show a very good image of the salt. In fact, the image created is nearly identical to an image actually using data from down hole, zero offset source and receiver pairs. The simplicity of the TRA implementation provides a virtually automated method to create a stacked section as if it had been collected from the reference frame of the borehole containing the VSP survey.

Characterization of Induced Seismicity in a Petroleum Reservoir: A Case Study

2019-04-09T16:25:07Z

Characterization of Induced Seismicity in a Petroleum Reservoir: A Case Study Sze, Edmond; Toksoz, M. Nafi; Burns, Daniel R. Fluid production and injection in hydrocarbon and geothermal reservoirs generally results in induced seismic activity. In this paper we study the microseismic activity in a petroleum field in Oman. The microearthquake data we used are those collected by a five-station digital network in the field between 29 October 1999 and 18 June 2001. We relocated 405 high-quality microseismic events using P and S travel-times picked from waveform data by the global grid-search location method. The results reveal a complex seismic zone with a NE-SW trend. All events are located within a depth range of 0.5 to 3.5 km. Focal mechanisms of 10 events of magnitude greater than one are inverted using the wavelet-based waveform inversion method where the source parameters, data kernel, waveform data, and the inversion are all represented by wavelet expansions. The dominant style of focal mechanism is left-lateral strike-slip for events with focal depths less than 1.5 km, and dip-slip along an obliquely trending fault for those with focal depths greater than 2.0 km. The inferred focal plane is nearly vertical and has a strike of NE-SW, which is also consistent with the trend of seismicity. To determine the cause of the events, seismicity rate is correlated with gas production and fluid injection. The results show that event rate in the field is strongly correlated with gas production in the Natih formation.

Dispersive Wave Analysis – Method and Applications

2019-04-12T15:05:25Z

Dispersive Wave Analysis – Method and Applications Rao, Rama V. N.; Toksoz, M. Nafi A technique for estimating the dispersion characteristics of propagating waves as measured by an array is detailed. The technique consists of bandpass filtering the data through a filterbank and then processing the filtered waveforms non-dispersively. The results can show the dispersion of the entire time series or be parsed in time to analyze the dispersion characteristics of any section of the time series. Processing LWD field data shows that this method can extract dispersion characteristics over a broadband of frequencies and with low amplitude signals. Both the field data and laboratory scale data show that multiple modes present over the same frequency band can be identified.

Characterizing the Mechanics of Fracturing from Earthquake Source Parameter and Multiplet Analyses: Application to the Soultz-sous-Forêts Hot Dry Rock site

2019-04-11T09:01:03Z

Characterizing the Mechanics of Fracturing from Earthquake Source Parameter and Multiplet Analyses: Application to the Soultz-sous-Forêts Hot Dry Rock site Michelet, Sophie; Toksoz, M. Nafi In 2000 and 2003, two massive hydraulic fracturing experiments were carried out at the European Geothermal Hot Dry Rock site at Soultz-sous-Forêts, France. The objective was to create a dense network of enhanced permeability fractures, which would form the heat exchanger. The injection of water in the fractured rock generated a high level of microseismic activity: around 30,000 and 90,000 micro-earthquakes were triggered during the injection of 2000 and 2003 respectively. From this around 14,000 and 9,000 events were then located to characterize the extent of the stimulated zones and hence of the fracture network. Then, the source parameters of each event, like seismic moments and stress drops, were computed automatically to characterize the mechanics of the fracturing. We found for example that the total seismic moment released is proportional to the injected fluid volume. This suggests that the injection flow rate could be a means to control the earthquake strength released during the stimulation and perhaps also control the effectiveness of the stimulation. Finally, we performed a multiplet analysis of a subset of these data to identify microearthquakes having similar waveforms. Multiplets are considered to be microearthquakes that occur on the same fracture plane and therefore may represent either seismically activated structures and/or permeable fractures induced by hydraulic fracturing. We identified 350 multiplets among 1000 analyzed events. We relocated them precisely by cross-spectrum analysis and found that they belong to sub-horizontal structures, likely permeable fractures stimulated by the injection.

Temporal Integration of Seismic Traveltime Tomography

2019-04-11T09:01:03Z

Temporal Integration of Seismic Traveltime Tomography Ajo-Franklin, Jonathan B.; Urban, Jaime; Harris, Jerry M. Time-lapse geophysical measurements and seismic imaging methods in particular are powerful techniques for monitoring changes in reservoir properties. Traditional time-lapse processing methods treat each dataset as an independent unit and estimate changes in reservoir state through differencing these separate inversions. We present a general least-squares approach to jointly inverting time-varying property models through use of spatio-temporal coupling operators. Originally developed within the medical imaging community, this extension of traditional Tikhonov regularization allows us to constrain the way in which models vary in time, thereby reducing artifacts observed in traditional time-lapse imaging formulations. The same methodology can also accommodate changes in experiment geometry as a function of time thus allowing inversion of incremental or incomplete surveys. In this case, temporal resolution is traded for improved spatial coverage at individual timesteps. We use seismic traveltime tomography as a model problem although almost any geophysical inversion task can be posed within this formalism. We apply the developed time-lapse inversion algorithm to a synthetic crosswell dataset designed to replicate a CO2 sequestration monitoring experiment.

Frequency-Domain Modeling Techniques for the Scalar Wave Equation : An Introduction

2019-04-11T09:01:02Z

Frequency-Domain Modeling Techniques for the Scalar Wave Equation : An Introduction Ajo-Franklin, Jonathan B. Frequency-domain finite-difference (FDFD) modeling offers several advantages over traditional timedomain methods when simulating seismic wave propagation, including a convenient formulation within the context of wavefield inversion and a straight-forward extension for adding complex attenuation mechanisms. In this short paper we introduce the FDFD method, develop a simple solver for the scalar Helmholtz problem, and explore some possible approaches for solving large scale seismic modeling problems in the frequency domain.

A Short Note on Modeling Wave Propagation in Media with Multiple Sets of Fractures

2019-04-10T17:18:45Z

A Short Note on Modeling Wave Propagation in Media with Multiple Sets of Fractures Chi, Shihong; Campman, Xander Wave propagation and scattering in fractured formations have been modeled with finite-difference programs and the use of equivalent anisotropic media description of discrete fractures. This type of fracture description allows a decomposition of the compliance matrix into two parts: one accounts for the background medium and another accounts for the fractures. The compliance for the fractures themselves can be a sum of compliances of various fracture sets with arbitrary orientations. Non-orthorgonality of the fractures, however, complicates the compliance matrix. At the moment, we can model an orthorhombic medium (9 independent elastic constants) with the two orthogonal fracture sets. However, if the fractures are non-orthogonal, this results in more general anisotropy (monoclinic) for which we need to specify 11 independent parameters.. Theoretical formulation shows that the finite difference program can be extended to simulate wave propagation in monoclinic media with little additional computational and storage cost.

Higher Order Modes in Acoustic Logging While Drilling

2019-04-11T09:00:58Z

Higher Order Modes in Acoustic Logging While Drilling Chi, Shihong; Zhu, Zhenya; Rao, Rama V. N.; Toksoz, M. Nafi In multipole acoustic logging while drilling (LWD), the fundamental modes dominate recorded waveforms. Higher order modes may also appear and complicate the processing of LWD data. In dipole LWD measurements, the dipole tool mode is often not well separated from the flexural mode. This makes the shear wave measurement more difficult. We conducted theoretical and numerical analysis on dipole LWD logging responses. We found that hexapole mode may be present in the dipole waveforms. Laboratory dipole data show the presence of hexapole mode, which approaches asymptotically to the formation shear wave velocity. This observation supports our conclusion. We may make use of these higher order modes for accurate determination of formation shear wave velocity.

Suppressing Near-Receiver Scattered Waves from Seismic Land Data

2019-04-12T15:05:25Z

Suppressing Near-Receiver Scattered Waves from Seismic Land Data Campman, Xander; Herman, Gérard When upcoming body waves travel through a heterogeneous near-surface region, the continuity of the wavefront can be diminished by scattering. We discuss a multichannel method to predict and subtract near-receiver scattered waves, such that the continuity and trace-to-trace coherency of wavefronts increases. We apply this method to a part from a field-data set which was acquired in an area with significant near-surface scattering. We show that the method increases trace-to-trace coherency in a reflection event. Moreover, application of our method improves the results obtained from application of a dip filter only, because we remove parts of the scattered wave with apparent velocities that are typically passed by the pass-zone of the dip filter.

Effects of Saturant Conductivity on Seismoelectric Conversion

2019-04-10T07:24:31Z

Effects of Saturant Conductivity on Seismoelectric Conversion Zhu, Zhenya; Toksoz, M. Nafi When a seismic wave propagates in a fluid-saturated porous medium, a seismoelectric field can be induced in the medium due to an electric double layer at the interface between solid and fluid. The strength of the seismoelectric field depends on the characteristics of the double layer and the conductivity of the saturant fluid. In our experiments two kinds of seismoelectric fields, a radiating electromagnetic (EM) wave and a localized electric field, are induced with fractured borehole models. The amplitudes of the seismoelectric signals are recorded when the conductivity of the saturant varies from zero to 27 mS/cm. The results show that when the conductivity increases, the amplitude of the electric signals increases at a low conductivity area and decreases at a high conductivity area. In this paper we investigate the mechanisms of seismoelectric conversion. When a double layer is saturated by charges in fluid, the amplitude of seismoelectric signals is inversely proportional to the conductivity. Conversely, if it is not saturated, the amplitude is directly proportional to the conductivity.

Reservoir Simulation with the Finite Element Method Using Biot Poroelastic Approach

2019-04-09T17:52:35Z

Reservoir Simulation with the Finite Element Method Using Biot Poroelastic Approach Zheng, Yibing; Burridge, Robert; Burns, Daniel R. We are developing a finite element program for oil and gas reservoir simulation based on Biot's poroelastic theory, where a simultaneous solution is sought for both the pore pressure and strain in the solid phase. Several 2-D and 3-D cases are presented, which are compared with analytical solutions for verification of this approach. We have also applied this method to simulate surface subsidence due to gas and oil production in a subsurface reservoir. The development of this code is still in its initial stage, but the approach shows promise.

Effects of Tool Positions on Borehole Acoustic Measurements: a Stretched Grid Finite Difference Approach

2019-04-11T09:01:01Z

Effects of Tool Positions on Borehole Acoustic Measurements: a Stretched Grid Finite Difference Approach Huang, Xiaojun This dissertation made three contributions to numerical simulation and borehole acoustic logging. The first one is a novel finite difference time domain algorithm that features non- uniform grid, wavelet-based difference operator and anisotropic perfectly matched layer. This algorithm reduces numerical reflections and wave distortions introduced by grid change to a minimum by sampling the physical space with gradually varying mesh. By coordinate stretching, the algorithm discretizes the physical space with variable grid, while solving the wave equation on a uniform mesh. That approach helps retain the advantages pertaining to uniform mesh. Further improvement in efficiency is achieved without losing accuracy by the development of a wavelet-based difference operator. By using a family of compactly supported wavelet function, the wavelet- based finite difference time domain algorithm allows less grid point per wavelength. Coordinate stretching is also employed in deriving an anisotropic perfectly matched layer, superior to currently available perfectly matched layer formulation which requires field splitting, a process that results in more computer memory requirement for the storage of extra variables. Validations of the algorithm include comparison with analytical solutions, uniform grid FDTD solutions and discrete wavenumber results. The second contribution is a time domain investigation of wave propagations in the logging while drilling situation. Logging while drilling is an emerging downhole acoustic acquisition method. The investigation is focused on soft formations where formation shear velocity is slower than borehole fluid velocity, because shear velocity measurement, one of the key measurements that acoustic logging is designed to acquire, is the most problematic in soft formations. Special attention is paid to mode excitations, with respect to frequencies, tool positions and source types, in the hope to shed some light on some highly debated questions regarding tool design and data interpretation. The stretched grid finite difference algorithm is applied. The third contribution is the development of an inversion method to estimate stress magnitudes and directions from borehole acoustic measurements. It is predicted in theory that a crossover in flexural dispersion is an indicator of stress-induced anisotropy dominating over other sources of intrinsic anisotropy. The prediction is subsequently verified in a scaled-borehole experiment. We are the first ones that observe flexural dispersion crossover in field data. Using the flexural crossover as a stress signature on the borehole acoustic data, we are able to isolate stressed zones. The maximum horizontal stress direction coincides with the polarization direction of far field fast shear. The stress magnitude is related to velocity changes in the stressed state from the zero stress or hydrostatically balanced state, through a perturbation theory developed in the late 1990's. Stress directions estimated in this dissertation are consistent with focal mechanism and borehole breakout data present in the world stress map database.

Characterization of Scattered Waves from Fractures by Estimating the Transfer Function Between Reflected Events Above and Below Each Interval

2019-04-10T19:10:06Z

Characterization of Scattered Waves from Fractures by Estimating the Transfer Function Between Reflected Events Above and Below Each Interval Willis, Mark E.; Burns, Daniel R.; Rao, Rama V. N.; Minsley, Burke J. It is important to be able to detect and characterize naturally occurring fractures in reservoirs using surface seismic reflection data. 3D finite difference elastic modeling is used to create simulated surface seismic data over a three layer model and a five layer model. The elastic properties in the reservoir layer of each model are varied to simulate different amounts of vertical parallel fracturing. The presence of the fractures induces ringing wave trains primarily at times later than the bottom reservoir reflection. These ringy or scattered wave trains appear coherent on the seismograms recorded parallel to the fracture direction. While there are many scattered events on the seismograms recorded perpendicular to the direction of the fractures, these events appear to generally stack out during conventional processing. A method of characterizing and detecting scattering in intervals is developed by deconvolution to give an interval transfer function. The method is simple for the case of two isolated reflections, one from the top of the reservoir and the other from the bottom of the reservoir. The transfer function is computed using the top reflection as the input and the bottom reflection as the output. The transfer function then characterizes the effect of the scattering layer. A simple pulse shape indicates no scattering. A long ringy transfer function captures the scattering within the reservoir interval. When analyzing field data, it is rarely possible to isolate reflections. Therefore, an adaptation of the method is developed using autocorrelations of the wave trains above (as input) and below (as output) the interval of interest for the deconvolution process. The presence of fractures should be detectable from observed ringy transfer functions computed for each time interval. The fracture direction should be identifiable from azimuthal variations – there should be more ringiness in the direction parallel to fracturing. The method applied to ocean bottom cable field data at 4 locations show strong temporal and azimuthal variations of the transfer function which may be correlated to the known geology.

Fracture Density Estimation Using Spectral Analysis of Reservoir Reflections: A Numerical Modeling Approach

2019-04-11T09:00:58Z

Fracture Density Estimation Using Spectral Analysis of Reservoir Reflections: A Numerical Modeling Approach Pearce, Fred; Burns, Daniel R.; Rao, Rama V. N.; Willis, Mark E.; Byun, Joongmoo We use a 3-D finite difference numerical model to generate synthetic seismograms from a simple fractured reservoir containing evenly spaced, discrete, vertical fractures. The fractures are represented using a single column of anisotropic grid points. Analysis of seismic amplitudes and spectral characteristics were carried out on the top and base reservoir reflections as well as scattered wave coda for models with fracture spacing ranging from 0.01 to 0.1 fractures/m. Results show that the bulk scattered wave energy contained in a common shot gather increases greatly when the fracture spacing is greater than about 1/4 wavelength. Wavenumber spectra for integrated amplitude versus offset from a time window containing the base reservoir reflector show spectral peaks corresponding to the fracture spacing.

Deep Resistivity Tomographic Imaging of The Qualibou Caldera, Saint Lucia

2019-04-12T15:05:22Z

Deep Resistivity Tomographic Imaging of The Qualibou Caldera, Saint Lucia Morgan, Frank Dale; Vichabian, Yervant; Sogade, John The Qualibou Caldera has been studied since the 1970’s for possible development of geothermal power generation. In 1974 dipole-dipole resistivity measurements were performed in the area. The apparent resistivity data was plotted as contours and a single line running through Sulphur Springs was interpreted by using forward models to generate a best fit model. The data is reanalyzed using a robust 2D inversion method. The result shows a resistive body beneath Sulphur Springs, the presence of which has been debated for nearly thirty years. The data from all 2D tomograms is interpolated into 3D, which generates images showing conductive features reminiscent of hydrothermal convection plumes.

Fractured Reservoir Characterization using Azimuthal AVO

2019-04-12T15:05:20Z

Fractured Reservoir Characterization using Azimuthal AVO Minsley, Burke J.; Burns, Daniel R.; Willis, Mark E. Ordinary least squares is used to investigate the ability to detect changes in physical properties using Amplitude Versus Offset (AVO) information collected from seismic data. In order to characterize vertically aligned fractures within a reservoir, this method is extended to Azimuthal AVO (AVOA) analysis. Azimuthal AVO has the potential not only to detect fractured zones, but to spatially describe the fracture strike orientation and changes in fracture or fluid properties. Depending on the data acquisition geometry, signal-to-noise ratio, and extent of fracturing, AVOA analysis can be marginally successful. A study of the robustness and limitations of AVOA analysis is therefore first classified with synthetic data. These methods are then applied to seismic data collected during an Ocean Bottom Cable (OBC) survey over a known fractured reservoir.

Measured radiation patterns of the scale model dipole tool

2019-04-12T15:05:21Z

Measured radiation patterns of the scale model dipole tool Lu, Rongrong; Rao, Rama V. N.; Toksoz, M. Nafi The sound field of finite dipole acoustic transducers in a steel tool was investigated and their horizontal by measuring their vertical radiation patterns in water at two different frequencies. Measurements were also made with the tool in scale models representative of sonic logging conditions in the field. A Lucite borehole model was used to represent a soft formation and an Austin Chalk borehole model was used to represent a hard formation. The presence of the tool as a finite baffle for the transducer, introduces differences between the vertical and horizontal radiation patterns. In contrast to the vertical pattern, the horizontal radiation pattern has a narrower main lobe with relatively larger side lobes. The angular location of the side lobes as seen in the water measurements, do not change much in the borehole.

Finite Difference Modeling of Attenuation and Anisotropy

2019-04-11T09:00:58Z

Finite Difference Modeling of Attenuation and Anisotropy Krasovec, Mary L.; Burns, Daniel R.; Toksoz, M. Nafi A nite difference scheme which includes the effects of attenuation and anisotropy is tested for seismic reflection and borehole acoustic models. The validity of the scheme is established using a 3D homogenous isotropic model to compare results to the discrete wavenumber method. Three models are then investigated. First, reflections from a 3D at layered model are analyzed for o set and azimuthal dependence of attenuation. Second, discrete fractures are included in a 2D at layered model to examine their effect on reservoir top and bottom reflections. Third, a 3D borehole in both hard and soft formations is modeled to test the effect of attenuation on guided waves.

Structural uncertainty and geophysical data fusion: A synthetic example

2019-04-10T09:59:39Z

Structural uncertainty and geophysical data fusion: A synthetic example Kane, Jonathan; Rodi, William; Nemeth, Tamas; Mikhailov, Oleg We attempt to address two issues in seismic data processing: 1) quantifying the various forms of error that enter into the seismic data processing work-flow and relating them to uncertainty on imaged structures; and, 2) the data fusion problem, i.e. combining different sources of information, each related to seismic velocity. To begin addressing these issues a synthetic model was generated consisting of 4 tilted layers (3 interfaces), each with a different isotropic P-wave velocity. A synthetic well log was extracted from this model to be incorporated later. Synthetic shot gathers were also created. Following the standard seismic processing work-flow, stacking velocities were estimated. Uncertainty on these velocities was incorporated by under- and over-picking the velocities by ±10% and examining the effects on the final image. The stacking velocity information was then converted to interval velocity and fused with the well velocity information. Along with the under-, over-, and best picked velocities, realizations of the velocity field were created via geostatistical methods according to an assumed correlation structure. By further applying time migration and time to depth conversion, equiprobable realizations of the subsurface structure were generated along with upper and lower bounds on their locations. The realizations honor all the existing data sets and give a visual representation of the uncertainty on the spatial location of imaged structures.

An integrated well data analysis for in-situ stress estimation

2019-04-09T16:14:31Z

An integrated well data analysis for in-situ stress estimation Grandi, Samantha K.; Rao, Rama V. N.; Huang, Xiaojun; Toksoz, M. Nafi In this paper we obtain in-situ stress information based on two methods. The first one consists in matching borehole deformations to the modelling of linear poroelasticity equations around a hole in a plate that is subjected to effective compressive horizontal stresses. Knowing the formation parameters, the far field horizontal stress magnitudes can be predicted while the orientation of the minimum horizontal stress is derived from the direction of maximum elongation of the borehole cross section. The second method utilizes the crossover observed in the dispersion of polarized flexural waves to obtain the direction of maximum horizontal stress where the borehole is not deformed. For the particular field data the maximum horizontal stress runs approximately NNW-SSE. The relative principal stress magnitudes are 0.9-1.2 Sv, for the maximum horizontal stress, and 0.8-1 Sv, for the minimal horizontal stress, giving a combination of normal and strike slip tectonics. These results agree with the world stress map and the structural model of the area. The stress magnitudes are highly sensitive to the elastic parameters showing variations up to 25% for the particular data set. Careful velocity estimation, taking into account monopole as well as dipole data, is necessary to reduce uncertainties.

Effects of an Off-centered Tool on Multi-component Monopole and Dipole Logging

2019-04-12T15:05:21Z

Effects of an Off-centered Tool on Multi-component Monopole and Dipole Logging Byun, Joongmoo; Toksoz, M. Nafi Recent logging tools have monopole and dipole sources in one system, and the monopole and dipole components are acquired by adding or subtracting responses at four monopole (pressure) receiver arrays at right angles. We investigate the effects of tool eccentricity on this monopole receiver array system for three different eccentricity directions. To simulate responses at each receiver array, we use the discrete wavenumber method. An off-centered dipole source produces nondipole modes as well as the dipole mode and the responses detected at each receiver array have different features as eccentricity direction varies, showing the similar pattern for both fast and slow formation. We separate the modes included in a response and compare the amplitude of each mode to the other modes. By considering responses at each array separately, we can precisely resolve the effects associated with eccentricity direction.

Simultaneous Inversion of cross-dipole acoustic waveforms in anisotropic media for azimuthal angle and dispersion of fast and slow shear waves

2019-04-12T15:05:20Z

Simultaneous Inversion of cross-dipole acoustic waveforms in anisotropic media for azimuthal angle and dispersion of fast and slow shear waves Briggs, Victoria; Rao, Rama V. N.; Burns, Daniel R. A method to jointly invert for azimuthal angle and dispersion relations from cross-dipole data is presented. Dispersion curves from the joint inversion are compared to both Prony’s method and a simple back propagation schema and an agrrement is found. The azimuthal angle estimate is shown to differ from a frequency domain rotaion that takes no account of dispersion within the waveforms indicating the importance of joint inversion.

Crosshole Seismoelectric Measurements in Borehole Models With Fractures

2019-04-09T15:35:43Z

Crosshole Seismoelectric Measurements in Borehole Models With Fractures Zhu, Zheny; Toksoz, M. Nafi A seismic wave propagating in a fluid-saturated porous media, moves ions in the double layer between the fluid and solid and induces an electric field. When there is discontinuity (such as a fracture), the seismic wave induces a radiating electromagnetic (EM) wave. In this paper, we investigate seismoelectric fields in media with vertical and inclined fractures using cross-borehole measurements in the laboratory. Our laboratory results show that an acoustic source in a borehole generates a radiating EM wave at a vertical fracture, which is recorded by an electrode in the second borehole. The position of the fracture can be determined by the arrival times of the EM wave and acoustic wave, and the velocity of formation. The position of an inclined fracture between two boreholes can be determined by placing the acoustic source at a different depth and recording with real or synthetic arrays of acoustic receivers in the second borehole.

Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates

2019-04-11T09:49:11Z

Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates Zheng, Yibing; Huang, Xiaojun We develop new numerical anisotropic perfectly matched layer (PML) boundaries for elastic waves in Cartesian, cylindrical and spherical coordinate systems. The elasticity tensor of this absorbing boundary is chosen to be anisotropic and complex so that waves from the computational domain are attenuated in the boundary layer without reflection. The new PMLs are easy to formulate for both isotropic and anisotropic solid media. They utilize fewer unknowns in a general three-dimensional problem than the existing elastic wave PMLs using the field splitting scheme. Moreover, it can be implemented directly to the finite element method (FEM), as well as the finite difference time domain (FDTD) method. The high efficiency of these PMLs is illustrated by some numerical samples in FEM.

Fluid Flow Simulation in Fractured Reservoirs

2019-04-12T15:05:24Z

Fluid Flow Simulation in Fractured Reservoirs Sarkar, Sudipta; Toksoz, M. Nafi; Burns, Daniel R. The purpose of this study is to analyze fluid flow in fractured reservoirs. In most petroleum reservoirs, particularly carbonate reservoirs and some tight sands, natural fractures play a critical role in controlling fluid flow and hence production. Uncertainties involved in the understanding of fracture architecture and properties often propagate in the construction of reservoir flow models. The state-of-the-art reservoir simulation packages used widely in the oil industry often do not take into account the complex random geometry of real fracture systems that can vary from one grid-block to another, and sometimes even within a single grid-block. The reason for this is two-fold: there exists no technology as yet to image the micro-fractures in-situ, and most of the reservoir modeling software does not use micro-scale flow equations to model the change of flow variables. Fractures are highly conductive channels for flow among all types of porous-permeable media, Flow through them can vary widely depending on different fracture properties, such as fracture apertures, densities, asperities, etc. The objective of this study is to understand fluid flow in fractures using a finite difference approach, and to analyze the effects of fracture properties on flow mainly through visualization. Contrary to the conventional macro-scale modeling approach, micro-scale simulation is carried out. The ultimate goal is to incorporate this information into reservoir scale modeling schemes.

Frequency-Dependent Streaming Potentialsw

2019-04-11T09:01:00Z

Frequency-Dependent Streaming Potentialsw Reppert, Phillip M.; Morgan, Frank Dale; Lesmes, David P.; Jouniaux, Laurence An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 ¹m. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride’s and Packard’s models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride’s generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard’s model has one unknown model parameter while Pride’s model has four unknown model parameters, two of which can be independently determined experimentally. Pride’s additional parameters may allow for a determination of permeability.

Frequency-Dependent Electro-osmosis

2019-04-12T15:05:24Z

Frequency-Dependent Electro-osmosis Reppert, Phillip M.; Morgan, Frank Dale Electro-osmosis, the movement of a fluid with respect to solid wall when an electric field is applied tangentially to the solid wall, has been studied for many years[superscript 1]. Frequency-dependent electro-osmosis (FDE), the study of electro-osmosis when the applied electric field has a frequency component has only recently bee studied[superscript 2]. There are many potential reasons for studying frequency-dependent electro-osmosis ranging from medicine to geophysics. In medicine, electro-osmosis has been used to study a variety of human processes[superscript 3,4]. However, new areas of study may be related to electro-osmosis effects on the bodies, such as: electrical workers working in close proximity to high voltage AC electromagnetic fields, or the effects of cellular EM waves on human brains.

Acoustic Logging While Drilling (LWD): Experimental Studies with Anisotropic Models

2019-04-12T15:05:23Z

Acoustic Logging While Drilling (LWD): Experimental Studies with Anisotropic Models Rao, Rama V. N.; Zhu, Zheny; Burns, Daniel R.; Toksoz, M. Nafi A model LWD tool (0.16" ID, 0.4" OD) was built to investigate its operation in an anisotropic formation. The tool consists of a dipole source and six dipole receivers capable of operating at several hundred kHz. The formation was a block of delabole slate with a borehole of 1.27 cm diameter. In an anisotropic °uid-¯lled borehole with a dipole source and dipole receiver ori- ented along the principal directions, dipole (°exural) modes are mainly observed. Weak compression and shear refracted arrivals are also discernable when they were not ob- scured by stronger arrivals. Further, modes corresponding to fast shear direction are evident in the slow shear direction measurement. With a model LWD tool in the °uid-¯lled borehole, and oriented in the fast and slow directions, the main arrivals were the corresponding °exural modes. Modes cor- responding to the fast shear direction are no longer evident in the slow shear direction measurments. These preliminary experiments suggest that, with an LWD tool in an anisotropic formation, arrivals sensitive to formation properties can be discerned.

Wavelet Domain Geophysical Inversion

2019-04-09T18:29:55Z

Wavelet Domain Geophysical Inversion Kane, Jonathan; Herrmann, Felix; Toksoz, M. Nafi We present a non-linear method for solving linear inverse problems by thresholding coefficients in the wavelet domain1. Our method is based on the wavelet-vaguelette decomposition of Donoho (1992). Numerical results for a synthetic travel-time inversion problem show that the wavelet based method outperforms traditional least-squares methods of solution.

Geostatistically Constrained Seismic Deconvolution

2019-04-10T17:18:45Z

Geostatistically Constrained Seismic Deconvolution Kane, Jonathan; Al-Moqbel, Abdulrahman; Rodi, William; Toksoz, M. Nafi We present a method for combining seismic deconvolution and geostatistical interpolation. Both problems are posed as a single joint inverse problem in the maximum likelihood framework. Joint inversion allows for well data to improve the deconvolution results and, conversely, allows the seismic data to improve the interpolation of well data. Traditional interpolation and trace-by-trace deconvolution are special cases of the joint inverse problem. Inversion is performed on 2-D and 3-D field data sets.

A stretched grid finite-difference time-domain scheme implemented with anisotropic perfectly matched layers

2019-04-11T09:01:00Z

A stretched grid finite-difference time-domain scheme implemented with anisotropic perfectly matched layers Huang, Xiaojun; Zheng, Yibing; Burns, Daniel R.; Toksoz, M. Nafi A stable 2.5D finite difference time-domain (FDTD) scheme is developed to study wave propagation in heterogeneous media. On example is the logging while drilling configuration where small features such as the annulus between the drill pipe and the formation, only about 1/10 or even smaller than the wavelength in the steel pipe, affect the wave field significantly. The FDTD scheme proposed in this paper improves computational efficiency and accuracy from three aspects: griding, differencing, and numerical truncation. Coordinate stretching, proving to be more accurate, stable, and easy to implement, is employed to achieve variable griding. A wavelet-based differencing scheme is derived and compared with conventional FDTD schemes with spatial truncation accuracy being 2nd, 4th, 6th and 8th order. Because the wavelet-based and higher order FDTD scheme exhibits higher linear dispersion properties, it allows courser griding and is therefore more efficient. Reflections and transmission coefficients estimated from all FDTD schemes at a sharp boundary show that the wavelet-based FDTD solution outperforms the others. Efficient numerical truncation is realized by an anisotropic perfectly matched layer.

Multifractional splines: from seismic singularities to geological transitions

2019-04-12T15:05:20Z

Multifractional splines: from seismic singularities to geological transitions Herrmann, Felix; de Hoop, Martijn V. A matching pursuit technique in conjunction with an imaging method is used to obtain quantitative information on geological records from seismic data. The technique is based on a greedy, non-linear search algorithm decomposing data into atoms. These atoms are drawn from a redundant dictionary of seismic waveforms. Fractional splines are used to define this dictionary, whose elements are not only designed to match the observed waveforms but also to span the appropriate family of geological patterns. Consequently, the atom’s parameterization provides localized scale, order and direction information that reveals the stratigraphy and the type of geological transitions. Besides a localized scaling characterization, the atomic decomposition allows for an accurate denoised reconstruction of data with only a small number of atoms. Application of this approach to angles gathers allows us to track geological singularities from seismic data. Our characterization bridges the gap between the analysis of the main features within geologic processes, i.e. the geologic patterns, and the interpretation of their associated seismic response. A case study of Valhall data is presented.

Geomechanical Modeling of In-Situ Stresses Around a Borehole

2019-04-11T09:00:59Z

Geomechanical Modeling of In-Situ Stresses Around a Borehole Grandi, Samantha; Rao, Rama V. N.; Toksoz, M. Nafi In this paper, we present a modelling of the in-situ stress state associated with the severe hole enlargement of a wellbore. Geomechanical information is relevant to assure wellbore stability, i.e., to prevent damages in the formation and later on, the casing. Many of the drilling parameters, as mud weight or the optimal orientation of the borehole, require some knowledge of the mechanical behaviour of the rock. The lack of these kind of data in exploratory areas, where there are usually insufficient constraints for the geological model, increases even more the risk, hence the costs. The present model uses the concepts of poroelasticity theory to compute the stationary 2D, brittle response of the formation around a borehole that is submitted to effective compressive horizontal stresses. The numerical solution is obtained using a finite element approximation. The initial stress state at the far field was estimated combining a frictional-failure theory with the observations of dipmeter caliper in a particular borehole that presents elongations in a preferential direction. The direction and relative extension of the observed breakouts at a particular depth are modelled successfully using formation realistic parameters and dimensions, although the exact shape of the borehole (at all angles) was unknown. For the particular case study, the orientation of the breakout is NE-SW, at about 82 degrees azimuth. Therefore, the maximum horizontal stress lies at approximately 350 degrees azimuth. The ratios of horizontal principal stresses to vertical stress that best honor the observations are SHmax = 2.3Sv and Shmin = 1.7Sv. The compressive strength necessary for the rock to fail, as indicated by the caliper data under this stress field, is about 140 MPa.

Nonhyperbolic reflection moveout for orthorhombic media

2019-04-09T16:24:40Z

Nonhyperbolic reflection moveout for orthorhombic media Al-Dajani, A.; Toksoz, M. Nafi Reflection moveout in azimuthally anisotropic media is not only azimuthally dependent but it is also nonhyperbolic. As a result, the conventional hyperbolic normal moveout (NMO) equation parameterized by the exact NMO (stacking) velocity loses accuracy with increasing offset (i.e., spreadlength). This is true even for a single-homogeneous azimuthally anisotropic layer. The most common azimuthally anisotropic models used to describe fractured media are the horizontal transverse isotropy (HTI) and the orthorhombic (ORT). Here, we introduce an analytic representation for the quartic coefficient of the Taylor’s series expansion of the two-way traveltime for pure mode reflection (i.e., no conversion) in arbitrary anisotropic media with arbitrary strength of anisotropy. In addition, we present an analytic expression for the long-spread (large-offset) nonhyperbolic reflection moveout (NHMO). In this study, special attention is given to Pwave propagation in orthorhombic media with horizontal interfaces. The quartic coefficient, in general, has a relatively simple form, especially for shear wave propagation. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. In addition, the nonhyperbolic portion of the moveout for shear-wave propagation reaches its maximum along the polarization direction, and it decreases rapidly away from the direction of polarization. Hence, the anisotropy-induced nonhyperbolic reflection moveout for shear-wave propagation is significant in the vicinity of the polarization directions. In multilayered azimuthally anisotropic media, the NMO (stacking) velocity and the quartic moveout coefficient can be calculated with good accuracy using Dix-type averaging (e.g., the known averaging equations for VTI media). The interval NMO velocities and the interval quartic coefficients, however, are azimuthally dependent. This allows us to extend the nonhyperbolic moveout (NHMO) equation, originally designed for VTI media, to more general horizontally stratified azimuthally anisotropic media. Numerical examples from reflection moveout in orthorhombic media, the focus of this paper, show that this NHMO equation accurately describes the azimuthally-dependent P-wave reflection traveltimes, even on spreadlengths twice as large as the reflector depth. This work provides analytic insight into the behavior of nonhyperbolic moveout, and it has important applications in modeling and inversion of reflection moveout in azimuthally anisotropic media.

Simultaneous inversion for fast azimuth and dispersion of borehole flexural waves using cross-dipole data

2019-04-12T15:05:19Z

Simultaneous inversion for fast azimuth and dispersion of borehole flexural waves using cross-dipole data Briggs, Victoria; Huang, Xiaojun; Rao, Rama V. N.; Burns, Daniel R. This paper presents an inversion algorithm for obtaining azimuthal angle and borehole flexural wave dispersion in an anisotropic formation. The technique constructs an objective function that can be minimized using standard non-linear inversion methods, which is sensitive to both dispersion and rotation. The method is tested on both synthetic and real borehole data and gives good agreement with traditional processing.

Executive Summary

2019-04-12T15:05:19Z

Executive Summary Burns, Daniel R. During the past year, our research effort has continued to focus on borehole acoustics and reservoir characterization. The papers presented at the annual meeting, and those included in this volume, include theoretical developments as well as laboratory measurements and field data applications. Our aim is to improve our ability to estimate reservoir properties that impact production.