Exact solutions ofSH wave equation in transversely isotropic inhomogeneous elastic media

Summary TheSH wave equation in a transversely isotropic inhomogeneous elastic medium, where the elastic parameters and density are functions of vertical coordinate, is considered. A general procedure is given for finding the inhomogeneities for which the equation can be solved in terms of hypergeometric, Whittaker, Bessel and exponential functions. A few simple inhomogeneities and the corresponding solutions in terms of these transcendental functions are presented.