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Approximate reflection and transmission coefficients at an interface between two contrasting viscoelastic anisotropic halfspaces


 We present and compare two new methods to calculate the reflection and transmission coefficients of qP-, qSV- and qSH-waves at a flat interface between two contrasting viscoelastic anisotropic halfspaces. The first method is a new version of the real ray-tracing method that extends the traditional real ray-tracing method to tackle the triplications of the qSV-wave. This new version is valid for computing the reflection and transmission coefficients of the qP- and qSV-waves for all pre- and post-critical angles of incidence, which cannot be handled by the previous approach. The second method employs the real slowness direction and Snell's law to provide approximate reflection and transmission coefficients for such wave modes. This approximate method has attractive advantages which are not only the avoidance of the searching process inherent in the real ray-tracing method but also offers competitive economical solutions to the first method. Many viscoelastic VTI models are utilized to validate the two methods. The numerical results show that (1) the ray angles, ray velocities, ray Q-factors, and the magnitudes of the reflection and transmission coefficients obtained by the two methods closely agree with each other, except in the vicinity of the critical angles, and (2) the phase angles of the reflected and transmitted waves exhibit complexities due to the existence of some reverse phenomena between the approximate and the real ray-tracing solutions. However, such phase discrepancies do not affect the magnitudes of the reflection and transmission coefficients. Moreover, the energy ratios of the different wave modes satisfy the energy conservation criterion at the interface.