Approximation of a physics-based model of surface reflection loss

Abstract

A model of coherent acoustic reflection loss at the ocean surface had been prepared by the authors by combining a model of surface roughness loss with a description of surface incidence angle which accounted for the refractive effects of a uniformly stratified distribution of wind-driven bubbles. Here, surface roughness loss was based on a second-order small-slope approximation, and the surface incidence angle was obtained using a formulation for stratified media from Brekhovskikh applied to the sound speed variation resulting from the bubble distribution used by Ainslie [JASA 118, (2005)]. More recent work by the authors has shown that the analyses for each of surface roughness loss, and surface incidence angle, may be approximated adequately by relatively simple expressions, and that the complete model of surface reflection loss inclusive of the refractive effects of bubbles may be approximated in expressions suitable for hand calculations. Results from the use of this approximated model with a Gaussian-beam acoustic propagation code are compared with results obtained from the authors' more complete model for several surface ducted transmission scenarios. Both sets of results are also compared with predictions based on Monte Carlo parabolic equation (PE) transmission calculations.