The small-slope approximation has found application to unlayered seabeds and is generally regarded as an improvement over methods that employ either small-roughness perturbation theory or the Kirchhoff approximation. Unfortunately, the usual small-slope ansatz fails when applied to layered seabeds, as it is inconsistent with perturbation theory. This ansatz is replaced by an alternative which is found to satisfy the criteria of reciprocity and consistency with the perturbation and Kirchhoff approximations. This approach will be illustrated by computation of the coherent reflection coefficient and scattering strength for a seabed consisting of a single rough fluid layer over a semi-infinite, elastic basement with flat upper boundary. Computation time is significantly longer than for the unlayered case, increasing as the desired accuracy increases. The results will be contrasted with those obtained using a variety of existing approximations.

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