Ray tracing algorithms in three-dimensional laterally varying layered structures

Abstract

This chapter presents a concise review of recent methods of ray tracing and travel time computations of high-frequency seismic body wave propagating in three-dimensional laterally varying isotropic layered structures. Large attention is devoted mainly to initial value ray tracing , in which a single ray under consideration is specified by its initial point and by the initial direction of the ray at that point. The numerical, analytic and cell approaches to the solution of initial value ray tracing are discussed in detail. Particularly simple algorithms are obtained for the ray tracing in the “quadratic slowness” model, in which the quadratic slowness (1/V²) is used instead of the propagation velocity V. In Section 6, the ray tracing system is rewritten into an arbitrary curvilinear orthogonal coordinate system, and in Section 7 into a spherical coordinate system. In all these cases, the ray tracing system is supplemented by the appropriate reflection/transmission laws which allow to perform the ray tracing and the travel time computations even across arbitrary curved interfaces.