It has become necessary in seismology to consider more complicated models of the Earth's structure in order to obtain synthetic seismograms that are more consistent with actual field data. Gassmann (1964) and Postma (1955) have presented results dealing with travel-time methods in anisotropic media—in particular, transversely isotropic media. Kinematic properties alone, however, are not enough to conclusively interpret seismic records. Consequently, dynamic properties must be considered producing a need for synthetic seismograms.

One of the most efficient methods for obtaining synthetic seismograms is through the use of asymptotic ray theory (Hron and Kanasewich, 1971; Hron, 1973; Hron, Kanasewich and Alpaslan, 1974). A necessary step in the implementation for layered media displaying transverse isotropy is the computation of reflection and transmission coefficients at the interface between two such layers. Reflection coefficients for a free interface and the corresponding surface conversion coefficients must be computed, as well.

Theoretical formulas for reflection, transmission, and surface conversion coefficients corresponding to the zero-order approximation of asymptotic theory are presented for the above-mentioned media.

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