Finite-Difference Methods for Wave Propagation in an Elastic AnIsotropic Plane-Layered Medium With Orthorhombic Symmetry

P.F. Daley

ABSTRACT

This report presents a simulation system for the solution of the forward problem of elastic wave propagation in a plane-layered (orthorhombic) elastic medium. Forward modeling has become a useful tool for interpretation in exploration seismology. The method discussed here employs finite Fourier transforms to temporarily remove the x and y coordinates resulting in a coupled system of three finite-difference equations in the 3 Cartesian coordinate particle displacements in terms of depth (z) and time (t). The return to the (x,y,z,t) domain is done using a double summation over the two horizontal wavenumbers (k x , k y ). At the present time, 3-D seismic modeling realistically requires a high-performance multiprocessor computer using efficient 3-D algorithms for the geological model mentioned above. Non-geometrical wave types are minimal in this model type, but the development of the method presented here may serve as a basis from which to pursue more complicated numerical 3-D geometries.

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