Time and Angle Spreading from Rough Sediments

Abstract

Employing the Fresnel and Kirchhoff approximations in the Helmholtz Integral equation and assuming a Gaussian correlation function, an equation can be derived that predicts the time and spatial distribution of the acoustic intensity from a pulse propagated over a rough bottom. Inputs to this equation include an “effective” slope of the acoustic basement obtained from echo half duration time estimates. [McCammon and Burns, JASA,90 No4, Pt2, 1991] Numerical evaluations of this expression have produced angle and time distributions whose statistical characteristics have been extracted. In this paper, the relationships between the statistical descriptors (variance, skew and kurtosis) of the time and angle distributions will be described. It will be shown that at low frequencies over rough thin sediment regions where significant reflection for the acoustic basement is encountered, there is a clear relationship between time and angle spreading.