## Comparison of ray methods with the exact solution
in the 1-D anisotropic "twisted crystal" model

**Petr Bulant** **,**
**Ludek Klimes** **&**
**Ivan Psencik**
### Summary

The exact analytical solution for the plane S wave,
propagating along the axis of spirality
in the simple 1-D anisotropic "twisted crystal" model,
is known. In this contribution, the exact solution and
eight ray-theory approximate solutions of different provenance
are numerically compared.
The eight approximate solutions are:
(a1) coupling ray theory solution calculated by evaluating
the analytical solution of the coupling ray theory equations,
(a2) coupling ray theory solution calculated by 3-D ray tracing package CRT,
(a3) coupling ray theory solution calculated by 3-D ray tracing package ANRAY,
(b1) zero-order quasi-isotropic approximation
to the coupling ray theory calculated by
evaluating the analytical solution of the quasi-isotropic
ray theory equations,
(b2) zero-order quasi-isotropic approximation calculated by
3-D ray tracing package ANRAY,
(c1) anisotropic ray theory solution calculated by
evaluating the analytical solution of the anisotropic
ray theory equations,
(d1) isotropic ray theory solution calculated by
evaluating the analytical solution of the isotropic
ray theory equations,
(d2) isotropic ray theory solution calculated by 3-D ray tracing package CRT.

### Keywords

Coupling ray theory, quasi-isotropic approximation,
anisotropic ray theory, isotropic ray theory,
validity conditions of ray methods.

### Whole paper

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### Expanded abstract

Bulant, P., Klimes, L. & Psencik, I.:
Comparison of ray methods with the exact solution
in the 1-D anisotropic "twisted crystal" model.
Expanded Abstracts of 70th Annual Meeting (Calgary),
pp. 2289-2292, Soc. Explor. Geophysicists, Tulsa, 2000.

In: Seismic Waves in Complex 3-D Structures, Report 8,
pp. 119-126, Dep. Geophys., Charles Univ., Prague, 1999.

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