On acoustic reflection from a seabed exhibiting a non-uniform sound speed profile, with relevance to fine-grained sediments.

An analysis of the plane wave reflection coefficient of the seabed, R, is developed for two upward-refracting sediment sound speed profiles: the two-parameter linear and the three-parameter inverse-square, both extending to infinite depth. For the linear profile, it turns out that |R| = 1, representing total reflection for all grazing angles and all frequencies, signifying that in this special case, |R| is insensitive to the gradient. The implication is that if |R| is to return information about the shape of a profile, the gradient must change with depth, either smoothly through the presence of second- and/or higher-order depth derivatives or discontinuously at, say, an interface between sediment layers. The inverse-square is an example of a profile with a smoothly varying gradient, for which a general, closed-form expression for R is derived, valid for all grazing angles and all frequencies. When the sound speed ratio is less than unity, representative of a fine-grained sediment (mud), |R| exhibits two frequency regimes, designated high and low, separated by a transition frequency, f. In each of these regimes, |R| exhibits a frequency-dependent angle of intromission, which exhibits high- and low-frequency limiting values, differing by approximately 3.5°, depending on the geo-acoustic parameters of the sediment.