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

Ludek Klimes & Petr Bulant


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.


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

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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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