Rough sea surface scattering in the presence of an upward-refracting bubble layer

Abstract

Perturbation theory for scattering from rough surfaces is generalized to account for nonplanar insonifying waves. The generalized theory is applied to low-frequency (50–1500 Hz) sea surface scattering in the presence of an upward-refracting bubble layer. Using an exact numerical solution for the insonifying wave, it is shown that although the sea surface backscatter is enhanced by the upward-refracting bubble layer, the enhancement is not nearly enough to account for the experimentally observed backscatter. Several analytic approximations (plane wave, WKB, Snell’s law) are considered to gain some physical insight into the numerical calculation. At frequencies below a few hundred Hertz, the plane-wave approximation is adequate, that is, the bubble layer becomes acoustically transparent. At higher frequencies, the WKB approximation, which conserves energy, is surprisingly accurate. At low grazing angles and all frequencies, simply using the local wave number (i.e., Snell’s law) is a very poor approximation that does not conserve energy and grossly overestimates the effects of upward refraction. It is concluded that even with upward refraction present, scattering from the rough air–water interface is a minor contributor to the total acoustic backscatter. [Work supported by the Office of Naval Research.]