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.
In two series of helicopter noise experiments, sound-pressure-level recordings were made on the ground while a helicopter flew over (i) an array of microphones placed in an open field, and (ii) a similar array placed in the center of a city street surrounded by tall buildings. For given helicopter altitude and airspeed, it was found that the flyover noise recorded in the street, although initially lower, built up rapidly as the aircraft approached such that the peak recorded noise was actually more intense than that recorded in the open field. This result is in qualitative accord with the results of previous laboratory scale-model experiments performed by Lyon and Pande. The differences between the two sets of field data are attributed in major part to the fact that a reverberant sound field builds up in the street during flyover. This enhancement is less pronounced for higher flight altitudes. A simple theory based on geometrical acoustics and statistical concepts is described that quantitatively explains the sound enhancement found for a helicopter flying over a city street.
Numerical computations of time-domain impulsive functions require a low-pass-filter operation to satisfy the Nyquist sampling rule. For example, the exact impulsive solutions for diffraction and reflection from a rigid wedge [M. A. Biot and I. Tolstoy, J. Acoust. Soc. Am. 29, 381–391 (1957)] both have singularities at their initial arrival times. These particular solutions can be approximated and low-pass filtered to satisfy the sampling rule in numerical computations. In evaluating specular reflection from a finite plane facet, a reinterpretation of the physical meanings of the terms resulting from the impulsive solution of the Fresnel–Kirchhoff integral is introduced [M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), Sec. A.9, and A. W. Trorey, Geophysics 35, 762–784 (1970)]. It is believed that the solution contains terms associated only with reflection, and that the interpretation of the Rubinowicz representation of the boundary terms as boundary diffraction waves is physically incorrect. As a consequence, for amplitude calculations of a specular facet reflection, a working hypothesis is proposed, namely that the reflected amplitude is proportional to the incident signal where the constant of proportionality is a function of the geometry, facet width, and the signal waveform. By numerical studies, the constant of proportionality g(v) can be expressed as a polynomial in v, where v=w(λAr)1/2, w is the facet width, λA is the wavelength corresponding to the peak frequency of the signal, and r is the distance from a colocated source and receiver to the facet. The function g(v) depends on the waveform of the signal (i.e., a boxcar, single cycle of a sinewave, etc.). As v tends to zero, the facet reflection tends to zero. For large v (>2 or 3), g(v) tends to one and the facet reflection is effectively that from a full plane.
The results of a shallow-water localization experiment, performed 19 miles south of Panama City, Florida in October 1985, are presented. The experiment involved a 450-Hz source placed 2.2 km from a vertical array of 16 hydrophones in ∼33 m of water. The experimental site was essentially range independent with a flat, hard, sandy bottom. Successful passive localization of the source was obtained using a maximum-likelihood matched-field processor. Studies were undertaken to determine the robustness of the localization to variation of the following parameters: water depth, sediment sound-speed profile, sediment density and attenuation, and array tilt. It was found that, in order to ensure localization accuracy and robustness, the environmental parameters important to know well are the water depth, sediment sound speed, and array tilt. However, the matched-field processor is much more tolerant to inaccuracies in estimates of the sediment density and attenuation. This corresponds clearly with the results of two simulation studies by DelBalzo et al. [J. Acoust. Soc. Am. 83, 2180–2185 (1988)] and Feuillade et al. [J. Acoust. Soc. Am. 85, 2354–2364 (1989)]. A further conclusion drawn from the experiment is that localization in a shallow-water waveguide using maximum-likelihood processing is complicated by the repetitive sidelobe structure of the acoustic field. This suggests that time-domain and other broadband localization techniques may achieve better localization performance because of their additional frequency-averaging capability.
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