Kenneth E. Gilbert Lucy J. Ameling
Appl. Res. Lab. and the Graduate Program in Acoust., Penn State Univ., P. O. Box 30, State College, PA 16804
A stochastic bubble-layer scattering model based on first-order perturbation theory (plane-wave Born approximation) has recently been developed [K. E. Gilbert, submitted to J. Acoust. Soc. Am. (1993)]. In the first-order model, the scattering is treated as a perturbation on the plane-wave solution for the bubble-free water and is written in terms of a ``geometric factor'' times the horizontal wave-number spectrum of the sound-speed fluctuations in the bubble layer. For low sea states and higher grazing angles, this approach is adequate. For high sea states and low grazing angles, first-order perturbation theory is less accurate and one needs to account for the average bubble density and compute backscatter due to fluctuations about the average. In this paper results are compared for scattering computed with the ordinary plane-wave Born approximation to that computed with the ``distorted-wave'' Born approximation (DWBA). It is shown that for high sea states and low grazing angles, distorted waves significantly enhance the backscatter at low frequencies and consequently give better agreement with experiment. The effect can be understood in terms of near-surface upward refraction that creates greater insonification and larger grazing angles near the surface than that obtained with plane waves. Finally, the effect of near-surface upward refraction on rough surface scattering is briefly discussed.