Echo fluctuations from the rough seafloor: Predictions based on acoustically measured microrelief properties

Description of echo fluctuations due to a rough seafloor requires knowledge of the product σ2IC, where σ is the rms roughness and IC is the integral of the two-dimensional correlation function C(ξ,η) of the floor [IC≡∫∫C(ξ,η)dξ dη; ξ and η are the x and y correlation parameters]. Under small roughness conditions (4k2σ2≪1, where k is the acoustic wavenumber) we recently derived a simple formula relating the PDF of the echo amplitude to the product σ2IC [T. K. Stanton, J. Acoust. Soc. Am. 75, 809–818 (1984)]. The calculations involved normal incidence sonar pings. In this paper, we do similar calculations by performing both inverse and forward calculations involving the echo PDF. We first do the inverse problem by extracting σ2IC from coherence function data published by Dunsiger et al. [A. D. Dunsiger, N. A. Cochrane, and W. J. Vetter, IEEE J. Ocean. Eng. OE-6 (3), 94–106 (1981)]. Their data were from a downward-looking towed boomer source. We then use that information as input into our theory to predict the echo amplitude PDF from several downward looking sonars for a range of frequencies and beamwidths. Dunsiger et al.’s data were specific to their boomer source. However, once we carefully extract σ2IC from their data, the product may be used for any sonar as shown in our examples.