The coupling ray theory S-wave tensor Green function is frequency dependent. Its prevailing-frequency approximation removes this frequency dependence and allows us to introduce the coupling-ray-theory travel times and the coupling-ray-theory amplitudes, and to process the coupling-ray-theory wave field in the same way as the anisotropic-ray-theory wave field. This simplification may be decisive when storing the tensor Green function at the nodes of dense grids.
The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. In a generally anisotropic medium, the actual wave paths may be approximated by the anisotropic-ray-theory rays if these rays behave reasonably. In an approximately transversely isotropic medium, we can define and trace the SH and SV reference rays, and use them as reference rays for the prevailing-frequency approximation of the coupling ray theory.
We test the accuracy of the proposed prevailing-frequency approximation of the coupling ray theory numerically. The additional inaccuracy introduced by the prevailing-frequency approximation is smaller than the inaccuracy of the standard frequency-domain coupling ray theory.
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