Abstract: The canonical problem in theoretical work on rough surface scattering concerns monochromatic plane waves incident on a single infinite irregular interface in a constant sound speed environment. Scattering amplitudes are calculated, and it is hoped that the differential cross-section per unit area (i.e., the scattering strength) formed from the square of the magnitude of the scattering amplitude will be adequate to describe experiments which use point sources in variable sound speed settings where there are multiple boundaries, e.g., reverberation in the ocean. Ray based reverberation models which allow computation of a local angle of incidence do use the differential cross-section. However, there are many workable wave propagation models for which the scattering strength can only be introduced in an ad hoc manner. In the present paper some variational principles will be examined as starting points for describing rough surface scattering by point sources. Dashen's exact, manifestly reciprocal formula for scattering amplitudes follows from a variational calculation and can be somewhat generalized to a point-source, variable sound-speed setting. In the special case of reverberation with a constant sound-speed with a pulsed source, the small-slope approximation, which follows simply from Dashen's formula, will be shown to have a simple form in both the near and far field.!12
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