qP-wave at a corrugated interface between two dissimilar pre-stressed elastic half-spaces

A plane qP-wave (quasi-P-wave) is assumed to be incident at a corrugated interface between two dissimilar pre-stressed elastic solid half-spaces. Using Rayleigh's method of approximation, the reflection and transmission coefficients have been presented for the first-order approximation of the corrugation. These coefficients are obtained in closed form for a corrugated interface of periodic shape. We found that these coefficients depend on the angle of incidence, frequency of the incident wave, initial stresses and incremental elastic properties of the half-spaces. The coefficients corresponding to irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are also influenced significantly by the initial stresses of the half-spaces. Some more results including the results of Sidhu and Singh [Reflection of P and SV-waves at the free surface of a prestressed elastic half-space, Journal of the Acoustical Society of America 76(2) (1984) 594–598] have been deduced as particular cases from the present problem.