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High-Frequency Forward Scattering from Gaussian Spectrum, Pressure Release, Corrugated Surface. I. Catastrophe Theory Modeling
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| Journal of the Acoustical Society of America |
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A high-frequency approximation is derived for forward scattering from Gaussian spectrum, pressure, release, corrugated surfaces. Their derivation uses ideas and results from catastrophe theory [M.V. Berry, Adv. Phys. 25, 1-26, (1976)] to include diffraction. The starting point is the Kirchhoff approximation for scattering from a rough surface. As a result of this analysis, the scattered pressure is written in terms of a finite set of diffraction catastrophes and stationary phase contributions. The high-frequency approximation is applied to forward scattering from a corrugated surface that is a single realization from a Gaussian spectrum population. The validity of the results is demonstrated in a comparison with numerical integration of the Helmholtz integral for this same surface. The physical insight that catastrophe theory supplies is demonstrated by dissecting the forward scattered pressure. This dissection separates the geometrical acoustics, diffractive, and interference contributions to the spatial structure of the scattered pressure. The high-frequency results are also used to calculate the pressure for short-tone bursts scattered from the surface. The scattered pressure consists of a series of pulse replicas, some of which are interfering. The region of the surface responsible for each pulse replica is determined, and the pulses classified, via the high-frequency approximation.
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