## Comparison of quasi-isotropic approximations of the coupling ray
theory with the exact solution in the 1-D anisotropic
"oblique twisted crystal" model.

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

There are two different high-frequency asymptotic ray theories,
the "isotropic ray theory" assuming equal velocities of both S-wave
polarizations and the "anisotropic ray theory" assuming both S-wave
polarizations strictly decoupled. In the isotropic ray theory,
the S-wave polarization vectors do not rotate about the ray, whereas
in the anisotropic ray theory they coincide with the eigenvectors
of the Christoffel matrix which may rotate rapidly about the ray.

In weakly anisotropic models, at moderate frequencies, the S-wave
polarization tends to remain unrotated round the ray but is partly
attracted by the rotation of the eigenvectors of the Christoffel matrix.
The intensity of the attraction increases with frequency. The isotropic
and anisotropic ray theories are thus limiting cases and the gap between
them has to be filled. A ray theory providing continuous transition
between the isotropic and anisotropic ray theories is called the
"coupling ray theory".

There are many possible modifications and approximations of the
coupling ray theory. For example, the reference ray may be calculated
in different ways, the Christoffel matrix may be approximated by
its quasi-isotropic projections onto the plane perpendicular to the
reference ray and onto the line tangent to the reference ray, travel
times corresponding to the anisotropic ray theory may be approximated
in several ways, e.g., by linear quasi-isotropic perturbation with
respect to the density-normalized elastic moduli, etc.

Commonly used quasi-isotropic approximations of the coupling ray theory
are discussed. The coupling ray theory and its quasi-isotropic
approximations are then numerically compared with the exact analytical
solution for the plane S wave, propagating along the axis of spirality
in the 1-D anisotropic "oblique twisted crystal" model.

### Whole expanded abstract

The expanded abstract is available in
PostScript (277 kB)
and GZIPped PostScript (87 kB).

*8th SAGA Biennial Technical Meeting and Exhibition (CD-ROM)*,
South African Geophysical Association, Blairgowrie, 2003, 9 pp.

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