Abstract
Integral solutions for wave scattering over slightly rough surfaces generally include the source and receiver directivity. In this paper, it is shown that integrating the point source, point receiver solution over the source and receiver apertures leads to solutions with a clear physical interpretation. The scintillation, time-of-arrival, and direction-of-arrival spatial covariances of the specular echo are derived for a multibeam-subbottom-profiler configuration and result in surface integrals that can be evaluated numerically. In addition, algebraic expressions are obtained for the variances when the roughness has a Gaussian autocorrelation function and the source and receiver arrays have Gaussian apodization functions. Variances obtained from a numerical evaluation of the surface integrals compare well with estimates from a realistic three-dimensional numerical experiment. A simple inversion scheme is used to extract the roughness parameters from the numerical experiment signals.
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