Wave Theory for Surface and Bottom Acoustic Reverberation

Abstract

The scattering of sound by the ocean surface or bottom is generally assumed to be proportional to sinnφ, where φ is the grazing angle at incidence and n may have a value from zero to two, with the latter corresponding to Lambert's law. Wave theory indicates that the scattering form is not as simple, and requires a space-directivity factor to account for the scattering from an insonified strip on a surface. For short pulses and at small grazing angles for long pulses, plane-wave theory is satisfactory. With other situations, the space-directivity factors are similar, but require different arguments. At intermediate angles, the curvature of the wavefront for long pulses and the scattering due to random specular reflections dominate the form of the directivity space factors. Consequently, if an emperical formulation must be retained to define a scattering coefficient, and if the equivalent width of the strip is that on the wavefront, then: n=0 is satisfactory at small grazing angles; n=2 is possibly satisfactory at some intermediate angles with long pulses; while, at the other extreme, n=−4 is applicable to intermediate angles with very short pulses or to small grazing angles with long pulses.