Reflection and Refraction of plane SH Waves at Irregular Interfaces. I.

Abstract

An approximate solution of the problem of reflection and refraction of plane harmonic SH waves at irregular interfaces is obtained using a perturbation method of approximation on the assumption that the magnitude of the irregularities is small compared with the incident wavelength and that the slope of the interface is everywhere small. In the case of a periodic interface it is found that the reflected and refracted waves are composed of specularly reflected waves and scattered waves travelling in various directions. If the wavelength of the shear waves in the media are long compared with that of the interface, the amplitudes of some of the scattered waves decrease exponentially with distance from the interface. In general the phase angles of the scattered waves are functions of the wavelength of the interface and the angle of incidence of the primary wave. It is verified, in the case of zero angle of incidence, that the energy going into the scattered radiation is obtained at the expense of the energy in the specularly reflected and refracted waves.