Rayleigh waves on a viscoelastic solid half-space

Abstract

It is shown that the secular equation for Rayleigh waves propagating on a viscoelastic half-space always admits only one complex root corresponding to a surface wave. This result is proved in those cases in which the displacement field can be obtained analytically, including the isotropic case. The root is obtained in terms of complex integrals extending to the viscoelastic case, a result by Nkemzi [Wave Motion 26, 199–205 (1997)]. The wave solution is shown to represent an admissible surface wave for any viscoelastic relaxation kernel compatible with thermodynamics. A correspondence is then established between elastic and viscoelastic Rayleigh waves and their propagation properties are pointed out by an approximated analysis of the solution. Illustrative results are given by a numerical evaluation of the complex root for anisotropic viscoelastic half-spaces.