3-D Geostatistical Seismic Inversion With Well Log Constraints

Abstract

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.