Finite difference analysis of Rayleigh wave transmission past an upward step change

Abstract

Abstract Transmission coefficients of the Rayleigh wave past an upward step change are obtained by the finite difference scheme. In the region of large height of a step relative to a wavelength h/λ, individual phases of the transmitted wave are investigated and the dominant wave in each phase is clarified. For smaller values of h/λ, we examine to what extent the contribution of the diffracted wave due to a step change accounts for the discrepancy between the finite difference results and the prediction of the theory of Mal and Knopoff. In order to explain the transmission coefficients with h/λ close to zero, a boundary-perturbation method is extended to the second order.