Numerical modeling of seismic waves with a 3-D, anisotropic scalar-wave equation

By systematically defining the orientation and amount of velocity anisotropy at every point in a computational grid, and modifying the scalar-wave equation to accommodate directionally dependent velocity coefficients, scalar waves may be numerically synthesized in heterogeneous anisotropic 3-D structure by finite-differencing. The use of an intermediate, local, rotated coordinate system associated with each grid point allows the anisotropy orientation to conform spatially with 3-D structure, stress orientations, or any other correlate of the anisotropy. Both travel times and amplitudes in anisotropic media may differ significantly from those in the corresponding isotropic media. Under some conditions, the seismic response of an anisotropic flat-layered medium is nearly identical to, and may be confused with, that of a symmetrical isotropic structure. In general, these alternate interpretations can be evaluated by obtaining independent data from different recording configurations.