A complete solution based on wavenumber-frequency (ω-k) method for a buried point source in a homogeneous transversely isotropic elastic or anelastic half-space is presented. By means of the method of steepest descent, a high frequency approximation to the nongeometrical S* wave in a weakly anisotropic elastic half-space is also developed. Full-wave synthetic seismograms with a buried vertical point force and an explosive point source show the existence of the S* arrival in the anisotropic Austin Chalk (weakly anisotropic) and Gypsum Soil (strongly anisotropic). However, the nongeometrical S* arrival is much more prominent in the weakly anisotropic solid than in the strongly anisotropic solid.
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