Backscattering of acoustic pulses from rough surfaces: Statistical properties of first arrivals

Abstract

In a number of applications, including echo sounding of the ocean bottom, nondestructive evaluation of materials, and satellite altimetry, measurements of travel time and/or shape of a backscattered pulse are employed to retrieve information about position and properties of scatterers. When the scatterer is an extensive rough surface with sufficiently large slopes, the backscattered wave consists of numerous pulses, of which the earliest arrivals are often of primary interest. In this paper, the geometrical acoustics approximation is applied to study signal intensities and the difference between the travel times of waves scattered by a random rough surface and those reflected from the mean, plane boundary. For a Gaussian statistical distribution of roughness, probability density functions (PDFs) of the travel-time differences are found for the first and second arrivals in terms of variances of the surface roughness elevation and slope. The joint PDFs of the travel times and intensities are derived. It allows one to obtain the travel-time PDF for signals exceeding a given intensity threshold. It is shown that the travel time and the intensity are strongly correlated; on average, the earlier a signal arrives, the smaller is its intensity.