Ray tracing in anisotropic media with singularities

Abstract

Singularities often cause trouble in tracing rays in inhomogeneous anisotropic media. The ray-tracing algorithms can break down in the vicinity of the singularities because the medium becomes nearly degenerate and the right-hand sides of the ray-tracing equations yield indefinite expressions. We propose a modified ray-tracing approach, which is numerically stable and yields correct results in all types of singularities and their vicinities.We demonstrate the applicability and efficiency of this approach using various numerical examples. We discuss the possibility of the splitting of a ray when crossing a singularity.