## Errors due to the anisotropic-common-ray
approximation of the coupling ray theory

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

The common-ray approximation considerably simplifies
the numerical algorithm of the coupling ray theory for S waves,
but may introduce errors in travel times due to the perturbation
from the common reference ray.
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 errors due to the common-ray approximation.

The anisotropic-common-ray approximation of the coupling ray theory
is more accurate than the isotropic-common-ray approximation.
We derive the equations
for estimating the travel-time errors due to
the anisotropic-common-ray (and also isotropic-common-ray)
approximation of the coupling ray theory.
The errors of the common-ray approximations
are calculated along the *anisotropic common rays*
in smooth velocity models without interfaces.
The derivation is based on the general equations for
the second-order perturbations of travel time.

The derived equations are numerically tested in three
smooth 1-D velocity models of differing degree of anisotropy.
The first-order and second-order perturbation expansions of travel time
from the anisotropic common rays to anisotropic-ray-theory rays
are compared with the anisotropic-ray-theory travel times.
In the numerical example,
the errors of the anisotropic-common-ray approximation
are considerably smaller than
the errors of the isotropic-common-ray approximation.
### Keywords

Coupling ray theory, common-ray approximation, travel time,
perturbation theory, seismic anisotropy, inhomogeneous media.

### Whole paper

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In: Seismic Waves in Complex 3-D Structures, Report 15,
pp. 267-287, Dep. Geophys., Charles Univ., Prague, 2005.

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