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

Surface waves dispersion is studied in 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 a displacement potential for the liquid. the frequency equation and velocity dispersion curves are developed. several solid materials are considered for the bed, and both phase and group velocity curves are calculated. higher modes are also discussed and the respective curves are plotted. various special cases are considered by letting the liquid layer depth take zero value, to form a solid half-space, or very large values to form a full-space bi-material. moreover, an isotropic bed material can be obtained as a special case by appropriately setting the respective elastic constants. reduced frequency equations and numerical results are derived for each case to confirm the results with existing ones.