## Anisotropic-ray-theory geodesic deviation
and two-point ray tracing
through a split intersection singularity

**Petr Bulant** **&**
**Ludek Klimes**
### Summary

We demonstrate the principal problems with tracing
the anisotropic-ray-theory S-wave rays.
While the initial-value rays can safely be traced
by solving Hamilton's equations of rays,
it is often impossible to determine the coefficients
of the equations of geodesic deviation
(paraxial ray equations, dynamic ray tracing equations)
and to solve them numerically.
As the result, we often know
neither the matrix of geometrical spreading
nor the phase shift due to caustics.
We show how surprisingly large is the number of rays
which cannot be correctly calculated
in the velocity model
with a split intersection singularity.

### Keywords

Wave propagation, elastic anisotropy, heterogeneous media,
anisotropic ray theory, geodesic deviation, KMAH index,
two-point ray tracing, S-wave singularities.

### Whole paper

The paper is available in
PDF (2460 kB !).

*Seismic Waves in Complex 3-D Structures*, **24** (2014), 179-187
(ISSN 2336-3827, online at http://sw3d.cz).