Reformulated Kinematic and Dynamic Ray Tracing Systems for Arbitrarily Anisotropic Media

Abstract

I reformulate well-established systems for kinematic and dynamic ray tracing in 3D heterogeneous media with arbitrary anisotropy. Matrices of size 3 × 3, e.g. the Christoffel matrix, are substituted by six-component vectors, and the Christoffel matrix elements are expressed explicitly in terms of the elements of the 6 × 6 matrix of elastic coefficients, written in Voigt notation. Thereby, I find it easier to see the effects on the ray tracing systems of vanishing elastic coefficients and Christoffel matrix elements and of vanishing derivatives with respect to spatial coordinates and slowness vector components. The eigenvalue of the current wave and its derivatives with respect to the ray parameters are included explicitly, which may be favorable for ray tracing processes optimized with respect to speed. With the ANRAY program as a reference, I show that the new formulation requires less optimization than the conventional one.