## Asymptotic Green function for S waves in the kiss singularity

**Vaclav Vavrycuk**
### Summary

We have derived the far-field asymptotic formula for the S-wave elastodynamic
Green function in the kiss singularity in anisotropic media. In contrast to standard
asymptotics in regular directions the derived formula is more complex and expressed
in the form of 1-D integral. This integral is specified for the kiss singularity along the
symmetry axis in transversely isotropic media and along the fourfold symmetry axes
in the tetragonal and cubic media. The shape of the slowness surface in the singularity
is regular in transverse isotropy and the amplitude of the Green function is expressed
by means of the Gaussian curvature of this surface in the singularity. However, the shape
of the slowness surface of S waves is irregular in tetragonal or cubic media. In this case
the Gaussian curvature is not defined in the singularity. Therefore, a generalized Gaussian
curvature is introduced and the amplitude of the Green function is expressed by means of
this new quantity. For regular directions, both the generalized and standard Gaussian
curvatures yield the same value.

### Whole paper

The paper is available in
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In: Seismic Waves in Complex 3-D Structures, Report 11,
pp. 249-262, Dep. Geophys., Charles Univ., Prague, 2001.

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