Seismic Wave Propagation in a Self-Gravitating Anisotropic Earth
The mathematical theory is discussed of the propagation of acceleration waves in a spherical, elastic Earth, which has spherical symmetry and the material of which is transversely isotropic at each point with respect to the radial direction, both as a result of its intrinsic nature and as a result of the effect of self-gravitation. An arbitrary variation of density with radial distance from the Earth’s centre is assumed. The differential equation for the ray path is obtained and solved in the case of an SH-wave. It is seen that the usual Herglotz-Wiechert method for the determination of the dependence of wave speed on radial position breaks down.
KeywordsTransverse Wave Radial Direction Wave Front Seismic Wave Wave Speed
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