Abstract

Parameters associated with the presence of inclusions (cracks or vugs) significantly influence seismic responses. The T-matrix method is used to define approximate anisotropic effective elastic stiffness tensors for media with inclusions. This allows 3D, three-component, eighth-order staggered-grid finite-difference modeling to simulate the seismic responses of anisotropic media with high inclusion density, various aspect ratios, spatial distributions and orientations of inclusions, and fluid content. The model parameters are chosen to represent aligned inclusions ranging from vertical cracks to vugs in a carbonate reservoir encased in clastics. The magnitude of anisotropy increases with increasing inclusion density for P- and S-waves. Cracks in a high-velocity carbonate reduce the stiffnesses and correspondingvelocities; this results in smaller contrasts with the surrounding (lower-stiffness) clastics and, hence, smaller reflection coefficients. S-wave splitting and the anisotropy of VPVS are clearly visible. The aspect ratio of the spatial distribution of the cracks potentially produces larger anisotropy than the crack aspect ratio, especially at large crack density. The crack distribution has little effect on stiffnesses parallel to the cracks but a large effect perpendicular to the cracks. As the crack orientation moves farther from vertical, changes in the resulting seismograms are more systematic in the direction parallel to the crack strike than perpendicular to it. The seismic signatures resulting from variations of the inclusion parameters are significant and easily visible in the data. This is a computational basis for obtaining more accurate, complete, and quantitative characterizations of inclusions.

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