S-wave singularities often cause troubles to tracing of rays in inhomogeneous anisotropic media. The ray tracing algorithms can breakdown 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 kinds of singularities and their vicinities. We show applicability and efficiency of this approach on various numerical examples. We discuss a possibility of splitting of a ray when crossing a singularity.
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