Pulse Propagation in a Laterally Heterogeneous Solid Elastic Sphere

Abstract

The motion of a solid elastic sphere caused by an impulsive point source has been calculated by a finite difference scheme. Results are obtained for a radially and laterally heterogeneous sphere. Both discontinuous changes in elastic parameters and density, and their continuous variation inside the sphere are treated. The results show reflection and diffraction effects. A stability analysis for the finite difference scheme in spherical co-ordinates is given. The method of solution presented here is general enough to include the actual variations in density and elastic parameters in the Earth. This includes the well-known models of radial distribution and the recently observed lateral inhomogeneity in the mantle.