The propagation of Rayleigh waves over curved surfaces at high frequency

Abstract

AbstractA formal asymptotic theory, valid at high frequencies, is developed for the propagation of time harmonic Rayleigh surface waves over the general smooth free surface Σ of a homogeneous elastic solid. It is shown that on Σ these Rayleigh waves can be described by a system of surface rays, which are shown to be geodesics of Σ. The amplitude of the waves on Σ is shown to vary in such a way that the energy propagated along a strip of surface rays is constant. The waves are also shown to be dispersive and an explicit first-order dispersion formula is derived.