Omni-directional acoustic wave source interactions with a rough seabed with a continuously varying density and sound speed in a fluid-like sediment layer. The acoustic properties in the sediment layer possess an exponential type of variation in density and one of the three classes of sound speed profiles, which are constant,~$k^2$-linear, or inverse-square variations. Analytical solution of mean field. The mean field reflection coefficients corresponding to the aforementioned density and sound speed profiles for various frequencies, roughness parameters, are numberically generated and analyzed. Physical interpretations are provided for various results. This simple model characterizes two important features of sea floor, including seabed roughness, sediment inhomogenieties, therefore, provide a canonical analysis in seabed acoustics.

This paper studies is considered the problem of coherent re ection of an acoustic plane wave from a rough seabed with a randomly inhomogeneous sediment layer overlying a uniform elastic basement. The randomness of the sound eld is attributable to the rough- ness 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 uid and an elastic half space, respectively, is employed to obtain an analytic solution for the coherent eld in the sediment layer. Furthermore, a boundary perturbation the- ory developed by Kuperman and Schmidt [22] is applied to treat the problem of rough surface scattering. A linear system is then established to facilitate the computation of the coherent re ection eld. The coherent re ection coe cients 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 re ection. Physical interpretations of the various results are provided.