Reflection of waves from the boundary of a random elastic semi-infinite medium

In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. II has been shown that an incident SH or SV type of wave gives rise to reflected SH, P and SV waves, the main components being SH and P, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity epsilon, where epsilon measures the deviation of the medium from homogeneity. An incident P-type wave produces mainly a P component and also a weak SH component to the order of epsilon(2). The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.