Reflection and Refraction of Plane SH Waves at Irregular Interfaces. II.

Abstract

The effect of an irregular interface with an isolated irregularity like a trough or a depression on the reflection and refraction of plane harmonic SH waves is investigated on the assumption that the maximum depth of the depression is small compared with the wave-lenghth of the incident wave and that the slope of the surface is everywhere small. It is found that besides the specularly reflected and refracted SH waves there exists various scattered SH waves. In particular the scattered field contains the following secondary wave types whose amplitudes are proportional to the depth of the depression: (i) Direct reflected and refracted SH waves which appear to come from the point of intersection of the axis of symmetry of the depression and the horizontal plane asymptotic to the interface. They have cylindrical divergence. (ii) A diffracted wave which travelled along the interface with the higher of the two shear wave velocities for the media and is finally refracted into the medium with the slower velocity at the critical angle. (iii) An interface wave travelling with the slower of the two velocities in the media. Its energy is confined to the neighbourhood of the interface in the higher velocity halfspace.