## Comparison of the anisotropic-ray-theory rays
and anisotropic common S-wave rays
with the SH and SV reference rays
in a velocity model
with a split intersection singularity

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

We describe the behaviour of the
anisotropic-ray-theory S-wave rays in a velocity model
with a split intersection singularity.
The
anisotropic-ray-theory S-wave
rays crossing the split intersection singularity
are smoothly but very sharply bent.
While the initial-value rays can be safely 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 a result, we often know
neither the matrix of geometrical spreading,
nor the phase shift due to caustics.
We demonstrate the abrupt changes of the geometrical spreading
and wavefront curvature
of the fast anisotropic-ray-theory S wave.
We also demonstrate the formation of caustics
and wavefront triplication
of the slow anisotropic-ray-theory S wave.

Since the actual S waves propagate approximately
along the SH and SV reference rays in this velocity model,
we compare the anisotropic-ray-theory S-wave rays
with the SH and SV reference rays.
Since the coupling ray theory is usually calculated
along the anisotropic common S-wave rays,
we also compare the anisotropic common S-wave rays
with the SH and SV reference rays.

### Keywords

Wave propagation, elastic anisotropy, heterogeneous media,
anisotropic ray theory, geodesic deviation, phase shift due to caustics,
two-point ray tracing, S-wave singularities.

### Whole paper

The reprint is available in
PDF (3309 kB).

*Stud. geophys. geod.*, **62** (2018), 57-79.