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.

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