## Errors due to the common ray approximations of the coupling ray theory.

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

The "coupling ray theory" is applicable at all degrees of anisotropy,
from isotropic models to considerably anisotropic ones.
There are many commonly used "quasi-isotropic approximations"
of the coupling ray theory, which deteriorate the accuracy of
the coupling ray theory both with increasing frequency and increasing
degree of anisotropy. Most of these quasi-isotropic approximations
can be avoided with minimal effort, except for the "common ray
approximation" for S waves. In the common ray approximation,
only one reference ray is traced for both S-wave polarizations,
and both S-wave travel times are approximated by the perturbation
from the common reference ray. The common ray approximation thus
considerably simplifies the coding of the coupling ray theory and
numerical calculations, but may introduce errors in travel times due
to the perturbation. These travel-time errors can deteriorate
the coupling ray theory solution at high frequencies. It is thus
of principal importance for numerical applications to estimate
the error due to the common ray approximation.

In the common ray approximation, the S-wave travel times are usually
approximated by the linear perturbation from the common reference ray.
The errors of S-wave travel times may then be approximated by the
second-order perturbations. The calculation of these estimates of
travel-time errors due to the "isotropic common ray approximation"
and the "anisotropic common ray approximation" is proposed and
numerically demonstrated.

### Whole expanded abstract

The expanded abstract is available in
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*8th SAGA Biennial Technical Meeting and Exhibition (CD-ROM)*,
South African Geophysical Association, Blairgowrie, 2003, 7 pp.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.