## 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

The coupling ray theory bridges the gap between the isotropic
and anisotropic ray theories,
and is considerably more accurate than the anisotropic ray theory.
The coupling ray theory is often approximated by various
quasi-isotropic approximations.

Commonly used quasi-isotropic approximations of the coupling ray theory
are discussed.
The exact analytical solution for the plane S wave,
propagating along the axis of spirality
in the 1-D anisotropic "oblique twisted crystal" model,
is then numerically compared with
the coupling ray theory and its three quasi-isotropic approximations.
The three quasi-isotropic approximations of the coupling ray theory are
(a) the quasi-isotropic projection of the Green tensor,
(b) the quasi-isotropic approximation of the Christoffel matrix,
(c) the quasi-isotropic perturbation of travel times.
The comparison is carried out numerically in the frequency domain,
comparing the exact analytical solution with the results of the 3-D
ray tracing and coupling ray theory software.
In the oblique twisted crystal model,
the three studied quasi-isotropic approximations considerably increase
the error of the coupling ray theory.
Since these three quasi-isotropic approximations do not
noticeably simplify the numerical implementation of the coupling ray theory,
they should definitely be avoided.
The common ray approximations of the coupling ray theory do not
affect the plane wave, propagating along the axis of spirality
in the 1-D oblique twisted crystal model, and should be studied
in more complex models.

### Keywords

Coupling ray theory, quasi-isotropic approximation,
seismic anisotropy, travel time, amplitude, Green tensor.

### Whole paper

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*Studia Geophysica et Geodaetica*, **48** (2004), 97-116.

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