Dispersion of Rayleigh, Scholte, Stoneley and Love waves in a model consisting of a liquid layer overlying a two-layer transversely isotropic solid medium

Abstract

The dispersion of interface waves is studied theoretically in a model consisting of a liquid layer of finite thickness overlying a transversely isotropic solid layer which is itself underlain by a transversely isotropic solid of dissimilar elastic properties. The method of potential functions and Hankel transformation was utilized to solve the equations of motion. Two frequency equations were developed: one for Love waves and the other for the remaining surface and interface waves. Numerical group and phase velocity dispersion curves were computed for four different classes of model, in which the substratum is stiffer or weaker than the overlying layer, and for various thickness combinations of the layers. Dispersion curves are presented for generalized Rayleigh, Scholte, Stoneley and Love waves, each of which are possible in all proposed models. They show the dependence of the velocity on layer thicknesses and material properties (elastic constants). Special cases involving zero thickness for the water layer or the solid layer, and/or isotropic material properties for the solid exhibit interesting features and agree favourably with previously published results for these simpler cases, thus validating the new formulation.