Scattering of Rayleigh wave at a vertical boundary.

Abstract

In this work the author studies scattering of Rayleigh wave at a vertical interface, which is the boundary between two quarter spaces with different densities and elastic constants welded together to form a half-space. The incident wave is a two-dimensional periodic Rayleigh wave. The method of approach is such that integral equations are derived by use of the Fourier transform technique and that they are solved by deforming their integration path along which the integrals vary smoothly in magnitude. Energy fluxes of the transmitted and reflected Rayleigh waves, the scattered body waves and Stoneley wave (if exists) are numerically computed. The accuracy of computed results is sufficiently high for the purpose.The models treated are then sorted out into four cases, i.e., cases of the discontinuity of density (i), P velocity (ii), and S velocity (iii)-in these three cases, no Stoneley waves exist-, and further a case for which Stoneley wave is present (iv). Through all the above four cases, the following common features are found: (a) the energy flux of the transmitted Rayleigh waves is the most remarkable among all the partitioned waves, (b) the forward and backward transmissions of Rayleigh waves for a model are almost the same in energy and (c) the scattered P waves are propagated along the boundaries as if they are trapped there. Meanwhile, the effect of the existence of Stoneley wave upon partitioned energies are discussed by comparing them with those in the case without Stoneley wave. In order to explain the features thus brought out, the author directed his attention to the difference in the energy profiles between the Rayleigh waves in the respective two media; the difference is believed to reflect the converging and diverging processes of waves transmitted through the vertical interface.For the case without Stoneley wave, the author introduced an approximate expression which enables us to evaluate the energy flux of the transmitted Rayleigh waves with an error of 10% or so.