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

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

The exact analytical solution for the plane S wave,
propagating along the axis of spirality
in the simple 1-D anisotropic "simplified twisted crystal" model,
is compared with four different approximate ray-theory solutions.
The four different ray methods are
(a) the coupling ray theory,
(b) the coupling ray theory with the quasi-isotropic perturbation
of travel times,
(c) the anisotropic ray theory,
(d) the isotropic ray theory.
The comparison is carried out numerically, by evaluating both
the exact analytical solution and
the analytical solutions of the equations of the four ray methods.
The comparison simultaneously demonstrates the limits of applicability
of the isotropic and anisotropic ray theories, and the superior
accuracy of the coupling ray theory over a broad frequency range.
The comparison also shows the possible inaccuracy due to the
quasi-isotropic perturbation of travel times in the equations
of the coupling ray theory.
The coupling ray theory thus should definitely be preferred
to the isotropic and anisotropic ray theories,
but the quasi-isotropic perturbation of travel times
should be avoided.
Although the simplified twisted crystal model is designed for testing
purposes and has no direct relation to geological structures,
the wave-propagation phenomena important in the comparison
are similar to those in the models of geological structures.

In additional numerical tests, the exact analytical solution is
numerically compared with the finite-difference numerical results,
and the analytical solutions of the equations of different ray
methods are compared with the corresponding numerical results
of 3-D ray-tracing programs developed by the authors of the paper.

### Keywords

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

### Whole paper

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*Studia Geophysica et Geodaetica*, **48** (2004), 675-688.

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