## Properties of S waves near a kiss singularity:
comparison of exact and ray solutions

**Vaclav Vavrycuk**
### Summary

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.

### Keywords

Anisotropy, Green tensor, near-field wave, near-singularity wave,
ray theory, S-wave splitting, S-wave singularity, S-wave coupling.

### Whole paper

The paper is available in
PostScript (760 kB)
and GZIPped PostScript (134 kB).

In: Seismic Waves in Complex 3-D Structures, Report 7,
pp. 307-318, Dep. Geophys., Charles Univ., Prague, 1998.

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