Reverberation and backscatter at very small grazing angles.

Abstract

Reverberation in shallow waters can be generally considered as a combination of two‐way forward scatter and a single backscatter. With increasing range, reverberation consists of backscattered signals at ever smaller grazing angles. First‐order perturbation theory is a suitable choice to model boundary roughness scatter if the rms roughness height is small compared to the acoustic wavelength. With decreasing grazing angle, the first‐order theory works even better. To apply the first‐order approximation, a zeroth‐order problem is assumed known, which is often conveniently chosen to be the case where the boundary is flat. However, if the boundary has a low‐wavenumber component, the flat boundary assumption for the zeroth‐order field can result in modeling error. To quantitatively assess such error, perturbation results are compared to exact numerical solutions using COMSOL. It is found that such errors are found when grazing angles are on the order of a few degrees, because at such small grazing angles the true local grazing angle is sensitive to variations of the local boundary slopes.