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May 1984

Volume 75, Issue S1, pp. S1-S93

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back to top Session MM. Underwater Acoustics VI: Scattering
Contributed Papers
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Rough surface boundary wave attenuation due to incoherent scatter (A)

Ivan Tolstoy

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S73-S73 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The incremental energy loss ΔE/E per unit path length for a boundary mode traveling along a rough surface may be calculated from elementary low‐frequency scattering approximations, using previously published results [I. Tolstoy, J. Acoust. Soc. Am. 74, 1068–1070 (1983) and 72, 960–972 (1982)]. This allows one to calculate explicitly the attenuation factor exp( − δr), where r is the range, with δ  =  ½ΔE/E for rough two‐fluid interfaces with arbitrary impedances, constraints, and roughness shapes. It is shown that δ = Af6, where f is the frequency and A a parameter which depends upon the size, spacing, and form of the roughness (for close‐packed roughness elements A is proportional to the fifth power of the mean roughness height). Given a point source of sound and a receiver on the rough interface the boundary wave amplitude pB ∝ r−1/2 f3/2 exp( − δr) and exhibits, for fixed r, a well‐defined maximum in the frequency domain at fM = (4Ar) −1/6 and falls off rapidly for higher frequencies, i.e., it displays a bandpass behavior with slow roll‐off at low frequencies. The predictions of this theory agree with recently reported model work [G.L.D′Spain et al., J. Acoust. Soc. Am., in press]. [Work supported by ONR.]
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Low‐frequency, grazing propagation above randomly rough surfaces (A)

Gerald L. D'Spain, Emily H. Childs, and Herman Medwin

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S73-S73 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Previously we have summarized laboratory studies of the acoustic boundary wave due to coherent scattering at grazing propagation over surfaces with periodic roughness elements. Here we extend our study of low‐frequency propagation for surfaces with three‐dimensional, randomly rough elements [J. Acoust. Soc. Am. Suppl. 1 71, S24 (1982)]. The dependence of the boundary wave amplitude on scattering parameter, wavenumber, and range, ϵk3/2 r−1/2, predicted by Tolstoy for hemispheres, is found again for stochastic surfaces. However, the inferred scattering parameter can be an order of magnitude greater for sharp‐edged than for spherical protuberances of the same volume/area. The empirical dependence of ϵ on the volume/area, rms slope, and rms curvature of the surface is examined. The maximum boundary wave amplitude again suffers catastrophic attenuation at a range and frequency given approximately by kr = 2π/(kϵ)2 as in the case of rigid spherical protuberances. The dispersion approaches 1%–2% at high frequencies and follows an approximate k2 dependence. [Research supported by the Offce of Naval Research.]
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Double refraction near a rough bottom in isothermal waters (A)

Herman Medwin and Jorge C. Novarini

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S73-S73 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The occurence of a boundary wave during low‐frequency grazing scatter from rough rigid surfaces has been described by Tolstoy and experimentally verified by Medwin et al. [J. Acoust. Soc. Am. 66, 1131–1134 (1979)] for a homogeneous medium overlying the surface. Tolstoy [J. Acoust. Soc. Am. 69, 1290–1298 (1981)] has also shown that, when the velocity in the medium decreases away from the ocean bottom, tunneling into the shadow zone takes place, for source and receiver on the bottom. We re‐examine this case but for the source and receiver near the ocean surface and for bottoms of lesser roughness. It is predicted that, under certain conditions of velocity gradient, frequency, and bottom roughness, the boundary wave mode causes a splitting of the limiting ray above the rough bottom. As a result, two refracted rays would reach the ocean surface: a primary ray (classical limiting ray for smooth bottom), and a secondary ray with a significantly greater skip distance. This double refraction phenomenon should be detectable at sea, under suitable experimental conditions. [Research supported by ONR.]
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An assessment of second‐order perturbation theory as applied to the scattering of sound by statistically rough surfaces (A)

A. Tolstoy, D. Berman, O. Diachok, and I. Tolstoy

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S73-S73 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Second‐order perturbation theory is one of few theories presently capable of describing scattering of low‐frequency acoustic plane waves by statistically rough surfaces. In order to assess this theory we have compared its predictions of the magnitude of the reflection coefficient ∣R∣ with known near exact solutions, in particular, for surfaces which consist of identical, hard, ellipsoidal bosses sparsely and independently distributed on a hard plane by means of a uniform probability law. In order to apply perturbation theory to such a surface we needed to compute its correlation function, operate on that function, and compute an effective boundary admittance. Finally we compared that admittance with (farfield) near‐exact results for spherical and oblate ellipsoidal bosses with eccentricity e. Calculations of ∣R∣ are presented showing that discrepancies decrease as grazing angle increases and are less than 10% for e>0.99, and approximately 70% for e≈0. We conclude that perturbation theory is excellent in the case of oblate spheroids and not to be used for prolate spheroids. [This work was supported by ONR and NRL.]
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Perturbation theory for scattering from random rough surfaces using the extended boundary condition (A)

Dale Winebrenner and Akira Ishimaru

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S73-S73 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Scattering from surfaces with roughness small relative to the wavelength of the incident radiation has most often been calculated using the perturbation method developed by Rice. This method uses the Rayleigh hypothesis, i.e., the assumption that the scattered field on the surface can be represented as a sum of up‐going plane waves. This assumption is known to be invalid when slopes of the rough surface are sufficiently large. A way of treating scattering using a perturbation theory based on the extended boundary condition has been given by several authors. This method appears to avoid the Rayleigh hypothesis. We will compare the results of the two methods and discuss the connection between them. [Work supported by ONR.]
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The T‐matrix approach to scattering of waves by rough surfaces (A)

Akhlesh Lakhtakia, Vijay K. Varadan, and Vasundara V. Varadan

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S74 (1984); (1 page) | Cited 1 time

Online Publication Date: 12 Aug 2005

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In this paper, we use the extinction theorem to compute a T matrix which characterizes a given rough interface between two media. In particular, we concentrate on multiple‐layered geometries. Thus we consider an elastic rough infinite slab interfaced with different fluids on either side. This case serves as a model for studying water/ice plate/air systems. Numerical results illustrating the cases of longitudinal or shear wave incidence, as applicable, shall be presented.
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Acoustic intensity from manganese nodule deposits (A)

Y. Ma, V. K. Varadan, and V. V. Varadan

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S74 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Abundant information on manganese nodules in the deep ocean can be obtained from remote acoustic intensity measurements. The previously suggested low‐frequency reflectivity measurements, neglecting the incoherent part of the backscattered acoustic signals, are quite good in predicting the presence of these nodules. However, in order to judge the effect of the size distribution on the acoustic response and to get the mean nodule size information, a wider frequency range is required. The contribution of the incoherent part of the acoustic response to the backscattered intensity becomes increasingly important as the sounding frequency gets higher. One may actually under‐, or over‐, estimate the amount of, and the average size of, the manganese nodules by carelessly neglecting the incoherent acoustic intensity. The intensity calculation based on the energy principle for nonabsorbing scatterers will be discussed, and the results will be presented for different concentrations of nodules with uniform as well as Rayleigh size distributions. All results presented shall be for sparsely distributed nodules made using the single scattering theory. The future extension to highly concentrated nodule fields by using the multiple scattering theory will also be discussed.
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Backscattering from sub‐bottom microlayers (A)

Ronald J. Wyber and Thomas G. Muir

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S74 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Vertical profiling measurements of the bottom in the frequency band from 1–5 kHz showed the variance of the reflected signal to be proportional to the frequency and the horizontal correlation length to be in the order of 10 m. This indicated that the variance in the backscattered signal is a function of the sonar beam pattern and the pulse shape, frequency, and grazing angle of the incident wave. For a pulse length of 25 ms and a grazing angle of 10°, the predicted backscattering strength was found to be independent of frequency at a level of −40 dB. This behavior agreed with data measured at this angle. As the classical theory of backscattering assumes that the bottom reverberation is due to independent scatterers which add incoherently, this theory will become invalid if the dimensions of the area ensonified on the bottom are less than the correlation length. Thus, for sonars with a short pulse or a narrow beam, the backscattered power will no longer be proportional to the ensonified area. [Work supported by the Office of Naval Research.]
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Acoustic differential scattering cross section for internal waves (A)

Bruce J. Bates

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S74 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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The Garrett and Munk internal wave field is a second‐order process. It is also stationary, homogeneous, and anisotropic. Acoustic fields propagating through the internal waves are scattered by the internal wave sound speed fluctuations. The differential scattering cross section is derived employing the Born approximation and the “n frequency shell” condition. For comparison, the internal wave sound speed fluctuation is approximated by an anisotropic Gaussian correlation function and the resulting differential scattering cross section is evaluated for typical horizontal and vertical correlation lengths. Both differential scattering cross sections are compared as a function of scattering angle for selected angles of incidence and acoustic frequencies.
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Acoustic propagation with an oceanic sound‐speed model including a random field of internal waves (A)

Susan M. Bates

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S74 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Flatté and Tappert [J. Acoust. Soc. Am. 58, 1151–1159 (1975)] have shown that internal waves cause significant fluctuations in the transmission of acoustic energy through the ocean volume, comparable in size and frequency to the fluctuations observed in field experiments. They use the parabolic equation method to propagate acoustic signals. The random component of the sound‐speed field is modeled by a linear superposition of internal wave eigenmodes. Each eigenmode amplitude is selected independently from a complex Gaussian distribution. Using an improved version of their simulation, range versus loss data are generated for up to 100 h of simulated time at 0.5‐h intervals. The source of 100 Hz is located on the axis of the canonical profile. The ensemble average and variance of the acoustic signal, as a function of receiver location, are computed. [Work supported by NUSC.]
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Sound scattering in a turbulent medium (A)

Richard J. Lataitis, Greg Crawford, and Steven F. Clifford

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S74 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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Tatarski [V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw‐Hill, New York, 1960)] has derived an expression for the effective scattering cross section of an acoustic wave incident on a remote volume of atomospheric turbulence. His result is subject to the single scatter approximation and the restriction that both transmitter and receiver be in the farfield of the large scale inhomogeneities within the volume. We derive an expression for the effective scattering cross section valid in both the near and farfield and extend these results to include the scatter of acoustic waves from underwater turbulence.
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Near‐range scintillations in a nonisotropic scattering medium (A)

Shimshon Frankenthal

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S74-S75 (1984); (2 pages)

Online Publication Date: 12 Aug 2005

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Using the Rytov approximation, an expression is derived for the log‐amplitude correlation function of weak fluctuations induced in a plane wave propagating in a forward‐scattering medium. The expression is valid at any range where weak fluctuations exist, including those which are shorter than the correlation length. The behavior of the scintillation index at very short ranges in isotropic media characterized by one or two scales is examined, and its dependence on frequency (k) and range (z) is listed for several regimes. Propagation is also studied in a nonisotropic medium, where the refractivity fluctuations are governed by the Garrett‐Munk internal‐wave spectrum. Here, the frequency‐range dependence of the scintillation index changes from k3/2 z5/2 at very near ranges to kz2 at more distant ones.
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Calculated and measured fish‐school echoes (A)

Paul D. Ingalls

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S75-S75 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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A simulation model that generates the waveform of a high‐frequency acoustic echo from a model fish school has been developed. The echo model generates the waveform by coherent addition of echoes from a collection of model point scatterers that have position, scattering amplitude, and velocity parameters chosen to reproduce some of the observable properties of echoes from real fish schools. Sample echo waveforms, spectra, and split‐beam phase difference will be presented. This model has been used to show the effects of partial ensonification on apparent size and scattering parameters of fish schools. [Work supported by U.S. Navy.]
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Determination of the ocean wave directional spectrum from acoustic backscatter (A)

Steven F. Clifford and Richard J. Lataitis

J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S75-S75 (1984); (1 page)

Online Publication Date: 12 Aug 2005

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We describe a technique for extracting the ocean wave height directional spectrum (OWHDS) from underwater acoustic backscatter measurements. Our technique requires a bottom‐mounted acoustic transceiver consisting of a quasi‐isotropic source of sound and a receiver array designed to measure the mutual coherence function (MCF) of the surface scattered and reflected fields. The MCF is shown to be directly related to the OWHDS which can then be extracted using a simple inversion scheme. Our results are applicable for all relative values of the rms surface wave height to acoustic wavelength provided the rms surface wave slope s < 1.
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