3-DIMENSIONAL ELASTIC MODELING BY THE FOURIER METHOD

Earlier work on three-dimensional forward modeling is extended to elastic waves using the equations of conservation of momentum and the stress-strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In addition to arbitrary compressional (or P-wave) velocity and density variation in lateral and vertical directions, elastic modeling permits shear (or S-wave) velocity variation as well. The elastic wave equation is solved using a generalization of the method for the acoustic case. Time stepping to obtain the three displacement components for the current time step is performed with second-order difference operators. This modeling scheme is implemented on a four-processor CRAY X-MP computer system using the solid-state storage device (SSD). Using parallel processing with four CPUs, a reasonable geologic model can be computed within a few hours. The modeling scheme provides a variety of seismic source types and many possible output displays.