3-D two‐point ray tracing for heterogeneous, weakly transversely isotropic media

Abstract

A two‐point ray‐tracing technique for 3-D smoothly heterogeneous, weakly transversely isotropic media is based on Fermat’s principle and takes advantage of global Chebyshev approximation of both the model and curved rays. This approximation gives explicit relations for derivatives of traveltime with respect to ray parameters and allows use of the rapidly converging conjugate gradient method to compute traveltimes. The method is fast because, for most smoothly heterogeneous media, approximation of rays by only a few polynomials and a few conjugate gradient iterations provide excellent precision in traveltime calculation.