Inverse Solutions for Two-Dimensional Elastic Waves in a Nonhomogeneous Medium

Abstract

An inverse procedure has been developed to obtain an exact solution for the travel time of seismic rays transmitted through a nonhomogeneous medium in which the seismic velocity depends only on depth from the surface. If the nonhomogenity is in the form of distinct, horizontal layers (graded material), then the procedure of ensuring continuous displacement and stress across the interface between homogeneous layers is straight forward but involves a considerable amount of algebra. However, if the nonhomogeneous medium has a continuous variation of properties (gradient material), then the problems are reduced to Abel's integral equation.