On the Causality of the Rayleigh Wave

Abstract

An explicit hyperbolic-elliptic formulation for surface Rayleigh waves is analysed with an emphasis on the causality of obtained results. As an example, a 3D moving load problem for a distributed vertical load is considered. A simple approximate solution is derived for a near-resonant regime, and the related point load solution is recast as a limiting case. It is shown that causality is characteristic only for the longitudinal wave potential along the surface, where it is governed by a hyperbolic equation modelling the small dilatation disturbances propagating at the Rayleigh wave speed.