We study properties of S waves generated by a point source in a homogeneous transversely isotropic medium and propagating in directions close to a kiss singularity which coincides with the symmetry axis of the medium. Comparing an exact and ray solutions in the far field we show that the zeroth-order ray approximation fails for these directions. The wavefield of the S waves is not composed only of two split S waves, as is usually assumed, but contains also their interaction. The interaction wave appears in times between arrivals of the split S waves, it can be of high frequency and it can be detected in the near field but also in the far field. The split S waves are described by the zeroth-order ray approximation, the interaction wave can be successfully reproduced by the first-order ray approximation. In analogy to the near-field wave, which appears in the vicinity of a source, we call the interaction wave as the "near-singularity wave", because it is prominent only in the vicinity of the S-wave singularity. The near-singularity wave is a non-geometrical wave, being described by higher-order ray approximations and neglected by the geometrical ray theory.
Anisotropy, Green tensor, near-field wave, near-singularity wave, ray theory, S-wave splitting, S-wave singularity, S-wave coupling.
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