Reflection and transmission by a random medium

Abstract

F rom ultrasonic inspections of heterogeneous materials the ultrasonic velocity in a test specimen and the ultrasonic reflection and transmission coefficients can be found over a certain range of frequencies. This paper presents a theoretical analysis of the frequency dependence of the reflection and transmission coefficients caused by random fluctuations of the material parameters. The procedure of using the effective frequency-dependent material parameters of an unbounded random medium to determine the wave propagation in a bounded random medium is not applicable at a distance of the boundary of the order of a correlation length. From this interface effect a contribution to the frequency dependence of the reflection and transmission coefficients arises. A previous consideration assuming the correlation length of the fluctuations to be small compared with the wavelength, is extended to shorter waves. Moreover, the wave propagation in a random half-space whose average material parameter differs from that of the exterior is considered. The consequences of the fluctuations of the elastic constants are of special interest, because they do not go with ω 2 in the governing wave equation as the density does. The interface effect is also discussed in the static limit of ‘homogeneous deformation’.