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The reflection and transmission coefficients for Rayleigh waves propagating from one type of wave guide to another can be computed by an approximate variational method. The method can be applied to Rayleigh waves that are normally incident on vertical discontinuities in any plane layered structure. The coefficients are computed for two-dimensional monochromatic Rayleigh waves. The method has been used to compute reflection and transmission coefficients for two simple cases—a step discontinuity of the free surface of an otherwise homogeneous half-space and 2 quarter-spaces with different densities and elastic constants welded together to form a half-space. Two-dimensional model experiments of these cases have been performed to verify the theory. The experimental data show good agreement with the computed results as long as the structural changes at the discontinuities are not extreme.
McGarr et al. (Sat,) studied this question.