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The reflection and transmission of Rayleigh waves Clement, Maurice James Young

Abstract

The techniques of two-dimensional model seismology were employed to investigate the problem of Rayleigh waves incident upon the boundary between two solid elastic media. The object of the investigation was the determination of the reflection and transmission coefficients. As a preliminary, the special case of a quarter space was examined to test the hypothesis that the reflection coefficient could be successfully approximated by selecting the amplitude of the reflected Rayleigh wave so that the normal and tangential stresses imposed on the free surface are minimized in the least square sense. Analogously for the half space, it was proposed that the reflection and transmission coefficients should be such as to minimize the differences (or residuals) between the respective stresses and displacements on either side of the discontinuity. This is a reasonable assumption since the boundary conditions require continuity in this case. It was found that the agreement between the measured and calculated values of the coefficients was only qualitative and it had to be concluded that the proposed hypotheses were not sufficient to explain the reflection and transmission of Rayleigh waves. For a half space consisting of an aluminium alloy and plexiglass, the reflection and transmission coefficients were measured as a function of the angle with which the plane interface between the two media meets the free surface. The angle was varied in steps of 10° from 0° to 180° and the observed coefficients are presented with no attempt at a theoretical derivation.

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