### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 3pUW4. Rough sea surface scattering in the presence of an upward-refracting
bubble layer.

**Kenneth E. Gilbert
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Kathy K. Bekker
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Lucy J. Kulbago
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*Appl. Res. Lab. and the Graduate Prog. in Acoust., Penn State Univ., P.O.
Box 30, State College, PA 16804
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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.]