Time spreads incurred by multipath reflections from a random surface

Abstract

The complexity of formalisms that deal with broadband acoustic channel distortions suggests temporary retrenchment to a “zeroth-order” model that can be easily compared with experimental data. Such a model is provided by the present work, which characterizes—via a ray-acoustic approach similar to that of J. J. Martin. [J. Acoust. Soc. Am. 47, 1303–1309 (1970)]—distortions of broadband acoustic signals reflecting from a planar surface with random roughness. The essence of the approach is to require that a ray-path reflect specularly from each surface element. A ray arrives at a receiver if and only if the position and slope of a surface element provides the requisite specular path given the incident beam angle. In this way, the probability of reception of a ray with a given incident angle is tied to the distributions of slope and height at the reflecting surface. Whereas Martin has characterized the reflected beam's angle spread, we will assess the arrival-time spread of a pulse due to pathlength differences between the rays arriving at the receiver.