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

**Vaclav Vavrycuk**
### Summary

We have studied the properties of S waves generated by a point source
in a homogeneous, transversely isotropic, elastic medium, propagating
in directions close to that of a kiss singularity, which coincides
with the symmetry axis of the medium. We have proved analytically
as well as numerically that the ray solution can describe the S waves
correctly far from the source in all directions, including that
of the kiss singularity. We have found that, in contrast to the far-field
P wave, which can be reproduced satisfactorily by the zeroth-order ray
approximation in all directions from the source, the far-field S waves
can be reproduced satisfactorily by the zeroth-order ray approximation
only in directions far from the kiss singularity.
In directions near the kiss singularity, the first-order ray approximation
must also be considered, because the zeroth-order ray approximation
yields distorted results. The first-order ray approximation can be
of high frequency and can be detected in the far field.

### Keywords

Anisotropy, Green's function, kiss singularity, ray theory, S waves.

### Whole paper

The scanned reprint is available in
PDF 300dpi (537 kB).

*Geophys. J. int.*, **138** (1999), 581-589.

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