Double-beam stacking to infer seismic properties of fractured reservoirs

Abstract

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.