Applicability of higher‐order ray theory for S wave propagation in inhomogeneous weakly anisotropic elastic media

Abstract

Modeling of S waves propagating in inhomogeneous, weakly anisotropic, elastic media creates complications for the zeroth‐order ray theory. These complications are caused mainly by the so‐called S wave coupling. If the S wave coupling is significant in the wave field, then the zeroth‐order ray theory is inapplicable. In this case, modifications of the zeroth‐order ray theory such as the coupling ray theory or the quasi‐isotropic ray theory have so far been used to reproduce the S waves correctly. We show that the failure of the zeroth‐order ray theory can also be overcome by higher‐order ray theory. If we consider not only the zeroth‐order term of the ray series but also higher‐order terms, we can obtain correct results. On a simple example of a plane S wave propagating in a weak transversely isotropic medium with a rotating axis of symmetry, we study how the accuracy of higher‐order ray theory depends on the number of higher‐order ray approximations considered in the solution.