Coherent reflection of acoustic plane wave from a rough seabed, with a random sediment layer overlying an elastic basement

The problem of coherent reflection of an acoustic plane wave from a rough seabed with a randomly inhomogeneous sediment layer overlying a uniform elastic basement is considered in this analysis. The randomness of the sound field is attributable to the roughness of the seabed and the sound-speed perturbation in the sediment layer, resulting in a joint rough surface and volume scattering problem. An approach based upon perturbation theory, combined with a derived Green's function for a slab bounded above and below by a fluid and an elastic half-space, respectively, is employed to obtain an analytic solution for the coherent field in the sediment layer. Furthermore, a boundary perturbation theory developed by Kuperman and Schmidt (1989) is applied to treat the problem of rough surface scattering. A linear system is then established to facilitate the computation of the coherent reflection field. The coherent reflection coefficients for various surface roughness, sediment randomness, frequency, sediment thickness, and basement elasticity have been generated numerically and analyzed. It was found that the higher/larger size of surface and/or medium randomness, frequency, thickness, and shear-wave speed, the lower the coherent reflection. Physical interpretations of the various results are provided.