## Analytical one-way plane-wave solution in the
1-D anisotropic "simplified twisted crystal" model

**Ludek Klimes**
### Summary

Analytical expressions for the exact 2x2 one--way
propagator matrix of a plane S wave, propagating along the axis
of spirality in the simple 1-D anisotropic
"simplified twisted crystal" model, are presented.
The analytical equations are
useful in testing the applicability and accuracy of various
approximate wavefield modelling methods,
especially of the coupling ray theory and of its various quasi-isotropic
approximations and various numerical implementations.

In addition to the exact analytical solution of the elastodynamic equation
in the "simplified twisted crystal" model,
the analytical solutions of the equations of the four
ray methods are given. The 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.
These four approximate solutions of the elastodynamic equation
are roughly compared with the exact solution.
Both the exact analytical solution and the analytical ray-theory
solutions in the "simplified twisted crystal" model are also helpful
in debugging computer codes for various approximate wavefield
modelling methods, especially for the coupling ray theory.

### Keywords

Anisotropy, S-wave coupling, polarization, elastic waves, exact solution.

### Whole paper

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*Studia Geophysica et Geodaetica*, **48** (2004), 75-96.

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