The standard anisotropic ray theory does not work properly or even fails when applied to S-wave propagation in inhomogeneous weakly anisotropic media or in the vicinity of shear-wave singularities, where the two shear waves propagate with similar phase velocities. The coupling ray theory was proposed to avoid this problem. In it, amplitudes of the two S waves are computed by solving two coupled, frequency-dependent differential equations along a common S-wave reference ray. In this paper, we test two recently developed algorithms of the coupling ray theory. As a reference, we use the Fourier pseudo-spectral method, which does not suffer from limitations of the ray method and yields very accurate results. We study the behavior of shear waves in weakly anisotropic media as well as in the vicinity of intersection or conical singularity. By comparing the coupling ray theory results with results of the Fourier pseudo-spectral method, we illustrate clearly applicability of the coupling ray theory in the mentioned regions.
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