A precise numerical method for Rayleigh waves in a stratified half space

This paper presents theory and results for Rayleigh waves propagating in a transversely isotropic stratified solid resting on an elastic semi-infinite space. It uses the precise integration method (PIM) and the extended Wittrick–Williams (W–W) algorithm. This problem can be reduced into the eigenvalue problem of ordinary differential equations (ODEs) in the frequency–wavenumber domain. The PIM used here is a precise method for solving the ODEs with two-point boundary conditions, and the eigenvalue counting method of the extended W–W algorithm is used to ensure that all eigenvalues are found without the possibility of any being missed. Hence the theory presented in this paper is exact, in the sense that its precision is limited only by the precision of the computer used