## Simple anisotropic Green functions derived by higher-order ray
approximations of asymptotic ray theory

**Vaclav Vavrycuk**
### Summary

Using higher-order ray approximations, we derived exact
elastodynamic Green functions for three simple types of anisotropy. The
first type displays an orthorhombic symmetry, the other two types display
transverse isotropy. In all cases, the slowness surfaces of waves are either
ellipsoids, spheroids or spheres. All three Green functions are expressed by
a ray series with a finite number of terms. The Green functions can be
written in explicit and elementary form similar to the Stokes solution for
isotropy. In two Green functions, the higher-order ray approximations form a
near-singularity term, which is significant near a kiss singularity. In the
third Green function, the higher-order ray approximations also form a
near-field term, which is significant near the point source. No effect
connected with the line singularity was observed.

### Whole paper

The paper is available in
PostScript (668 kB)
and GZIPped PostScript (122 kB).

In: Seismic Waves in Complex 3-D Structures, Report 10,
pp. 185-202, Dep. Geophys., Charles Univ., Prague, 2000.

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