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 anisotropic-common-ray approximation of the coupling ray theory, the coupling equation is solved along a single common reference ray, which is traced using the average Hamiltonian of both anisotropic-ray-theory S waves.
In this paper, isotropic-ray-theory, coupling-ray-theory, and anisotropic-ray-theory seismograms in a realistic weakly anisotropic model are compared. The most pronounced differences can be observed in polarization. Then, the coupling-ray-theory seismograms in four models of differing anisotropy are compared. For weaker anisotropy, just the polarization changes with increasing anisotropy. If anisotropy is increased further, the clear development of S-wave splitting can be observed.
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