Abstract
The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also 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 applied.
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.
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Klimeš, L., Bulant, P. Errors due to the anisotropic-common-ray approximation of the coupling ray theory. Stud Geophys Geod 50, 463–477 (2006). https://doi.org/10.1007/s11200-006-0029-5
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DOI: https://doi.org/10.1007/s11200-006-0029-5