Gravitationally perturbed elastic waves

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Abstract
In Lamb's problem there are two interface pulses. When the half-space is incompressible the locked Rayleigh (S) pulse travels with a speed γ = 0.9553β where β is the shear pulse speed, and the leaking Rayleigh (P) pulse travels with a speed δ = 1.966β. In the absence of gravity the S pulse is the more dominant pulse. The effect of gravity is to enhance the importance of the P pulse. In the presence of gravity, as β decreases, the S pulse becomes insignificant, and the P pulse becomes dispersive and approaches the behavior of the classical gravity wave. Several theoretical seismograms and hodographs, for the buried line source problem, are presented to illustrate the effect of gravity. The effect of gravity on dispersion curves, for a layer with a rigid bottom, is to distort them in such a way that one should observe wave groups similar to the classical gravity waves in a fluid layer when the shear speed is small. In addition one should observe very slow wave groups with wavelengths shortened by gravity. Several dispersion curves are presented to illustrate these features. The propagator coefficient matrix is given for a transversely isotropic material including gravity.

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