Dispersion of surface waves in a transversely isotropic half-space underlying a liquid layer

Surface waves dispersion is studiedin a two-layer half-space consisting of a finite liquid layer overlying a transversely isotropic solid half-space. A couple of complete potential functions are utilized to uncouple the equation of motion of the transversely isotropic solid along with the displacement potential for the liquid. The frequency equationand the dispersion curves are developed. Several solid materials are considered for the bed and phase and group velocity curves are presented. Higher modes of dispersion are also discussed and the respective graphs are plotted. Various special cases are considered by letting the liquid layer depth take zero value to form a solid half-space as well as very large values to form a full-space bi-material. Moreover, an isotropic bed material can be obtained as a reducedcase, setting the respective elastic constants.Reduced frequency equations and numerical results are derived for each case to confirm the results with existing ones.