SCATTERING OF RAYLEIGH WAVES IN AN ELASTIC THREE-QUARTER SPACE

Abstract

This study investigates the generation of waves, due to the incidence of Rayleigh waves upon the corner of an elastic three-quarter space. Incident Rayleigh waves travel along one surface of the elastic three-quarter space. Integral equations are derived by use of the Fourier transform technique, and are solved by deforming the integration paths into paths along which the integrands vary smoothly in magnitude. Expressions for the energy flux of Rayleigh waves along two free surfaces and for scattered body waves, were obtained. Partition of energy flux and directivity of the scattered P and S waves are discussed. The agreement between our theory and the experiment made by another investigator is considerably good. Substantial amounts of energy of incident Rayleigh waves are scattered away in the form of S waves, in the same direction as incident Rayleigh waves. Another interesting and important feature is the fact that, just around the corner of the elastic medium, the dilatational and distortional parts of waves are very large in magnitude. In other words, a kind of trapping of these waves occurs around the corner. These two kinds of waves are out of phase and the resultant waves are small in magnitude, due to the result of cancelling.