The coupling ray theory provides a continuous transition between the isotropic and anisotropic ray theories, and is particularly important at degrees of anisotropy and frequencies typical in seismic exploration and structural seismology on all scales. In the common ray approximation of the coupling ray theory, only one reference ray is traced for both anisotropic-ray-theory S waves, and both S-wave anisotropic-ray-theory travel times are approximated by the first-order perturbation expansion 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 first-order perturbation. Fortunately, the accuracy of the common ray approximations can be estimated by quadratures along the reference rays. The accuracy of the common ray approximation depends considerably on the selection of the reference rays, and it is much worse for the isotropic common rays calculated in the isotropic reference model, than for the anisotropic common rays, traced in the anisotropic model using the averaged Hamiltonian of both anisotropic-ray-theory S waves.
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