Scattering from a corrugated surface: Comparison between experiment, Helmholtz–Kirchhoff theory, and the facet-ensemble method

Abstract

The facet-ensemble method is used to compute the complex field scattered by a corrugated surface with large roughness. The method employs in part the frequency transform of an asymptotic approximation to the exact impulse solution for diffraction from a rigid (or pressure release, if desired) ridge or trough [M. A. Biot and I. Tolstoy, J. Acoust. Soc. Am. 29, 381–391 (1957); A. D. Pierce, Acoustics (McGraw–Hill, New York, 1981), pp. 489–490.] In the method, the scattering surface is approximated by joining edge to edge long plane strips (facets). Each adjacent pair of facets makes up a ridge or trough. Theoretical scattered acoustic pressure amplitude values are then obtained by superposing the diffracted and reflected contributions from individual ridges and troughs. A similar method was introduced by Novarini and Medwin [J. C. Novarini and H. Medwin, J. Acosut. Soc. Am. 64, 260–268 (1978); H. Medwin and J. C. Novarini, J. Acoust. Soc. Am. 69, 108–111 (1981)]. A comparison is provided here between amplitude values measured in a water-tank, scattering experiment [G. A. Sandness, Ph.D. thesis, Univ. of Wisconsin, Madison (1971)] and values predicted using the facet-ensemble method. Agreement is good in general and remains so when the number of approximating facets per spatial wavelength of the surface is changed. Also provided is a comparison (for the experimental geometry) between the facet-ensemble method and numerical evaluation of the Helmholtz–Kirchhoff integral. Most of the scattering occurred near the normal direction, and the Helmholtz–Kirchhoff integral is accurate for that direction. Agreement in this case between the integral solution and the facet-ensemble method, therefore, is good. The facet-ensemble method shows promise for estimating accurately the complex field scattered from a rough rigid (or pressure release) surface for any number of receivers at any number of locations.

The diffracted field and its gradient near the edge of a thin screen

“…10,11 Obviously, the secondary edge source line integral formulation must possess the same characteristics around shadow zone boundaries, and this has been verified in Ref. 12.…”

Diffraction by a Hard Half-Plane: Useful Approximations to an Exact Formulation

“…To circumvent this problem, it is informative to note from equation (6) that most of the signal information, i.e., its energy content, lies in proximity of the least time . Thus, Medwin proposed to decompose the time signal into two parts, one having a simple form with a known exact Fourier transform, and the other component being just the left part of the di!racted "eld, and the Fourier transform of which is to be made digitally [12,13]. This latter has, of course, to be truncated somewhere in the time domain depending on the working frequency range, but mostly on the behaviour of the di!racted "eld, hence depending on the geometry of the problem.…”

Exact solution for a density contrast shallow-water wedge using normal coordinates

“…This result agrees exactly with that predicted using ray theory. The expression for diffracted waves is identical to that given by Kinney et al (1983) except that now we replace the wedge angle 0w by 0 •o, and the source and observation angles 0o, 0 by 0 • and 0 ', respectively. Similar results can be obtained without difficulty for the case ofp' -• 0 andp finite.…”