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A Physical Model for the Distribution of Sonar Clutter from a Rough Interface

A physical model for clutter from rough interface scatter in low frequency active sonar systems is developed. Perturbation theory relates the mean scattering strength from a rough surface to the mean rough surface wavenumber spectrum at the Bragg wavenumber. Perturbation scattering theory is generalized to relate the clutter statistics to statistics of the interface surface roughness spectrum evaluated at Bragg wavenumbers. Focusing on application to ocean bottom reverberation, an examination of high resolution bathymetry data reveals that bathymetry spectra obey power laws. The power laws apply not only to the mean spectra, but also to higher order statistics. Therefore, these power laws can be used to extrapolate lower resolution bathymetry data to the required Bragg wavenumbers. The non-Gaussian distributions of clutter are then directly related to the non-Gaussian distributions of these rough interface wavenumber spectra