### ASA 126th Meeting Denver 1993 October 4-8

## 5pUW5. High-frequency forward scattering from Gaussian spectrum, pressure
release, corrugated surfaces: Catastrophe theory modeling.

**K. L. Williams
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*Appl. Phys. Lab., Univ. of Washington, 1013 NE 40th St., Seattle, WA
98105
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**J. S. Stroud
P. L. Marston
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*Washington State Univ., Pullman, WA
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Exact integral equations for the acoustical pressure scattered from a
rough pressure release surface can be written down and solved numerically.
However, analytical head way into the problem, gained at the expense of various
approximations, can lend physical insight not easily obtained numerically.
This, in part, motivated the work to be discussed. In particular, a
high-frequency approximation will be presented for forward scattering from
Gaussian spectrum, pressure release, corrugated surfaces. The analysis is most
directly applicable to forward scattering from an ocean surface dominated by
swell. The presentation uses ideas and results from catastrophe theory [M. V.
Berry, ``Waves and Thom's Theorem,'' Advan. Phys. 25, 1--26 (1976); P. L.
Marston, Physical Acoustics (Academic, New York, 1992), Vol. 21, pp. 1--234] to
include diffraction. Catastrophe theory allows one to write down the scattered
pressure in terms of a finite set of diffraction catastrophes and stationary
phase contributions. The catastrophe theory results will be compared to
numerical integration results for an individual rough surface to demonstrate
their validity and the insight they supply. Both steady state and pulse
comparisons will be made. Evidence will be presented that this
``high-frequency'' approximation is usable down to frequencies where the
wavelength is twice the rms roughness of the surface. [Work supported by Office
of Naval Research.]