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.
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