Stanton Timothy K.

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Stanton

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Timothy K.

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Improved parametrization of Antarctic krill target strength models

(Acoustical Society of America, 2006-01) Lawson, Gareth L. ; Wiebe, Peter H. ; Ashjian, Carin J. ; Chu, Dezhang ; Stanton, Timothy K.

There are historical discrepancies between empirical observations of Antarctic krill target strength and predictions using theoretical scattering models. These differences are addressed through improved understanding of key model parameters. The scattering process was modeled using the distorted-wave Born approximation, representing the shape of the animal as a bent and tapered cylinder. Recently published length-based regressions were used to constrain the sound speed and density contrasts between the animal and the surrounding seawater, rather than the earlier approach of using single values for all lengths. To constrain the parameter governing the orientation of the animal relative to the incident acoustic wave, direct measurements of the orientation of krill in situ were made with a video plankton recorder. In contrast to previous indirect and aquarium-based observations, krill were observed to orient themselves mostly horizontally. Averaging predicted scattering over the measured distribution of orientations resulted in predictions of target strength consistent with in situ measurements of target strength of large krill (mean length 40–43 mm) at four frequencies (43–420 kHz), but smaller than expected under the semi-empirical model traditionally used to estimate krill target strength.
Ray representation of sound scattering by weakly scattering deformed fluid cylinders : simple physics and application to zooplankton

(Acoustical Society of America, 1993-12) Stanton, Timothy K. ; Clay, Clarence S. ; Chu, Dezhang

Data indicate that certain important types of marine organisms behave acoustically like weakly scattering fluid bodies (i.e., their material properties appear fluidlike and similar to those of the surrounding fluid medium). Use of this boundary condition, along with certain assumptions, allows reduction of what is a very complex scattering problem to a relatively simple, approximate ray-based solution. Because of the diversity of this problem, the formulation is presented in two articles: this first one in which the basic physics of the scattering process is described where the incident sound wave is nearly normally incident upon a single target (i.e., the region in which the scattering amplitude is typically at or near a maximum value for the individual) and the second one [Stanton et al., J. Acoust. Soc. Am. 94, 3463–3472 (1993)] where the formulation is heuristically extended to all angles of incidence and then statistically averaged over a range of angles and target sizes to produce a collective echo involving an aggregation of randomly oriented different sized scatterers. In this article, a simple ray model is employed in the deformed cylinder formulation [Stanton, J. Acoust. Soc. Am. 86, 691–705 (1989)] to describe the scattering by finite length deformed fluid bodies in the general shape of elongated organisms. The work involves single realizations of the length and angle of orientation. Straight and bent finite cylinders and prolate spheroids are treated in separate examples. There is reasonable qualitative comparison between the structure of the data collected by Chu et al. [ICES J. Mar. Sci. 49, 97–106 (1992)] involving two decapod shrimp and this single-target normal-incidence theory. This analysis forms the basis for successful comparison (presented in the companion article) between the extended formulation that is averaged over an ensemble of realizations of length and angle of orientation and scattering data involving aggregations of up to 100's of animals.
Broadband classification and statistics of echoes from aggregations of fish measured by long-range, mid-frequency sonar

(Acoustical Society of America, 2017-06-13) Jones, Benjamin A. ; Stanton, Timothy K. ; Colosi, John A. ; Gauss, Roger C. ; Fialkowski, Joseph M. ; Jech, J. Michael

For horizontal-looking sonar systems operating at mid-frequencies (1–10 kHz), scattering by fish with resonant gas-filled swimbladders can dominate seafloor and surface reverberation at long-ranges (i.e., distances much greater than the water depth). This source of scattering, which can be difficult to distinguish from other sources of scattering in the water column or at the boundaries, can add spatio-temporal variability to an already complex acoustic record. Sparsely distributed, spatially compact fish aggregations were measured in the Gulf of Maine using a long-range broadband sonar with continuous spectral coverage from 1.5 to 5 kHz. Observed echoes, that are at least 15 decibels above background levels in the horizontal-looking sonar data, are classified spectrally by the resonance features as due to swimbladder-bearing fish. Contemporaneous multi-frequency echosounder measurements (18, 38, and 120 kHz) and net samples are used in conjunction with physics-based acoustic models to validate this approach. Furthermore, the fish aggregations are statistically characterized in the long-range data by highly non-Rayleigh distributions of the echo magnitudes. These distributions are accurately predicted by a computationally efficient, physics-based model. The model accounts for beam-pattern and waveguide effects as well as the scattering response of aggregations of fish.
Calibration of broadband active acoustic systems using a single standard spherical target

(Acoustical Society of America, 2008-07) Stanton, Timothy K. ; Chu, Dezhang

When calibrating a broadband active acoustic system with a single standard target such as a sphere, the inherent resonances associated with the scattering by the sphere pose a significant challenge. In this paper, a method is developed which completely eliminates the source of resonances through isolating and exploiting the echo from the front interface of a sphere. This echo is relatively insensitive to frequency over a wide range of frequencies, lacking resonances, and is relatively insensitive to small changes in material properties and, in the case of spherical shells, shell thickness. The research builds upon the concept of using this echo for calibration in the work of Dragonette et al. [J. Acoust. Soc. Am. 69, 1186–1189 (1981)]. This current work generalizes that of Dragonette by (1) incorporating a pulse compression technique to significantly improve the ability to resolve the echo, and (2) rigorously accounting for the scattering physics of the echo so that the technique is applicable over a wide range of frequencies and material properties of the sphere. The utility of the new approach is illustrated through application to data collected at sea with an air-filled aluminum spherical shell and long broadband chirp signals (30–105 kHz).
Sound scattering by live zooplankton and micronekton : empirical studies with a dual-beam acoustical system

(Acoustical Society of America, 1990-11) Wiebe, Peter H. ; Greene, Charles H. ; Stanton, Timothy K. ; Burczynski, Janusz

Measurements and analyses are presented of the backscattering of 420-kHz sound by 43 individual animals of representative zooplanktonic and micronektonic taxa. Direct measurements of an individual's target strength were made with a commercial dual-beam sonar system in an enclosure filled with filtered seawater deployed off a dock at Friday Harbor, Washington. The dependence of target stengths upon individual length, wet weight, and dry weight was investigated. In addition, the ``target strength'' and statistical variations of echo amplitude due to variations in shape and orientation of the organism were compared with acoustic scattering models involving different shapes (the general shapes of the sphere, and straight and uniformly bent finite cylinders were used along with attempts to take into account roughness). It was found that: (1) backscattering cross sections are proportional to volume of the organisms rather than area as would be predicted by a sphere scattering model, (2) mean target strength based on average backscattering crossection is best described by the bent cylinder model whose modal series solution is truncated, and (3) the fluctuations of the echo amplitudes are well described by the Rice probability density function whose shape parameter is related to the randomly rough straight cylinder model. These extensive studies showed conclusively that the elongated animals scattered sound more like elongated targets than spherical ones, thus demonstrating the need for models more sophisticated than the spherical ones routinely used to date. The data and model analyses provide a basis for devising future acoustical data acquisition and processing techniques for bioacoustical field studies.
New broadband methods for resonance classification and high-resolution imagery of fish with swimbladders using a modified commercial broadband echosounder

(Oxford University Press, 2010-01-05) Stanton, Timothy K. ; Chu, Dezhang ; Jech, J. Michael ; Irish, James D.

A commercial acoustic system, originally designed for seafloor applications, has been adapted for studying fish with swimbladders. The towed system contains broadband acoustic channels collectively spanning the frequency range 1.7–100 kHz, with some gaps. Using a pulse-compression technique, the range resolution of the echoes is ~20 and 3 cm in the lower and upper ranges of the frequencies, respectively, allowing high-resolution imaging of patches and resolving fish near the seafloor. Measuring the swimbladder resonance at the lower frequencies eliminates major ambiguities normally associated with the interpretation of fish echo data: (i) the resonance frequency can be used to estimate the volume of the swimbladder (inferring the size of fish), and (ii) signals at the lower frequencies do not depend strongly on the orientation of the fish. At-sea studies of Atlantic herring demonstrate the potential for routine measurements of fish size and density, with significant improvements in accuracy over traditional high-frequency narrowband echosounders. The system also detected patches of scatterers, presumably zooplankton, at the higher frequencies. New techniques for quantitative use of broadband systems are presented, including broadband calibration and relating target strength and volume-scattering strength to quantities associated with broadband signal processing.
Further analysis of target strength measurements of Antarctic krill at 38 and 120 kHz : comparison with deformed cylinder model and inference of orientation distribution

(Acoustical Society of America, 1993-05) Chu, Dezhang ; Foote, Kenneth G. ; Stanton, Timothy K.

Data collected during the krill target strength experiment [J. Acoust. Soc. Am. 87, 16–24 (1990)] are examined in the light of a recent zooplankton scattering model where the elongated animals are modeled as deformed finite cylinders [J. Acoust. Soc. Am. 86, 691–705 (1989)]. Exercise of the model under assumption of an orientation distribution allows absolute predictions of target strength to be made at each frequency. By requiring that the difference between predicted and measured target strengths be a minimum in a least-squares sense, it is possible to infer the orientation distribution. This useful biological quantity was not obtainable in the previous analysis which involved the sphere scattering model.
Macroscopic observations of diel fish movements around a shallow water artificial reef using a mid-frequency horizontal-looking sonar

(Acoustical Society of America, 2018-09-18) Lee, Wu-Jung ; Tang, Dajun ; Stanton, Timothy K. ; Thorsos, Eric I.

The twilight feeding migration of fish around a shallow water artificial reef (a shipwreck) was observed by a horizontal-looking, mid-frequency sonar. The sonar operated at frequencies between 1.8 and 3.6 kHz and consisted of a co-located source and horizontal line array deployed at 4 km from the reef. The experiment was conducted in a well-mixed shallow water waveguide which is conducive to characterizing fish aggregations at these distances. Large aggregations of fish were repeatedly seen to emerge rapidly from the shipwreck at dusk, disperse into the surrounding area during the night, and quickly converge back to the shipwreck at dawn. This is a rare, macroscopic observation of an ecologically-important reef fish behavior, delivered at the level of aggregations, instead of individual fish tracks that have been documented previously. The significance of this observation on sonar performance associated with target detection in the presence of fish clutter is discussed based on analyses of echo intensity and statistics. Building on previous studies of long-range fish echoes, this study further substantiates the unique utility of such sonar systems as an ecosystem monitoring tool, and illustrates the importance of considering the impact of the presence of fish on sonar applications.
Frequency- and depth-dependent target strength measurements of individual mesopelagic scatterers

(Acoustical Society of America, 2020-08-18) Bassett, Christopher ; Lavery, Andone C. ; Stanton, Timothy K. ; DeWitt Cotter, Emma

Recent estimates based on shipboard echosounders suggest that 50% or more of global fish biomass may reside in the mesopelagic zone (depths of ∼200–1000 m). Nonetheless, little is known about the acoustic target strengths (TS) of mesopelagic animals because ship-based measurements cannot resolve individual targets. As a result, biomass estimates of mesopelagic organisms are poorly constrained. Using an instrumented tow-body, broadband (18–90 kHz) TS measurements were obtained at depths from 70 to 850 m. A comparison between TS measurements at-depth and values used in a recent global estimate of mesopelagic biomass suggests lower target densities at most depths.
Sound scattering by spherical and elongated shelled bodies

(Acoustical Society of America, 1990-09) Stanton, Timothy K.

Describing the scattering of sound by elongated objects with high aspect ratios (ratio of length to diameter) usually involves great numerical difficulties. The recently developed deformed cylinder solution was shown to be increasingly accurate in the limit of very high aspect ratios (≥5:1) while requiring relatively low computation times and was applied to objects of constant composition [T. K. Stanton, ``Sound scattering by cylinders of finite length. III. Deformed cylinders,'' J. Acoust. Soc. Am. 86, 691–705 (1989)]. In this article, the approximate formulation is used to describe scattering by prolate spheroids, straight finite cylinders, and uniformly bent cylinders where the objects are composed of an elastic shell surrounded by fluid and filled with either a fluid or gas. The calculations are compared with those involving spherical shells based on the formulation derived in Goodman and Stern [J. Acoust. Soc. Am. 34, 338–344 (1962)]. The calculations are made over a wide range of frequencies and shell thicknesses (ranging from solid elastic objects to thin-shelled objects). Since the deformed cylinder formulation is most accurate for angles of incidence normal or near normal to the lengthwise axis, the calculations are limited to broadside incidence. The simulations show significant variations in the modal interference structure as the shell thickness and shape are varied. Comparisons are also made between predictions and laboratory data involving straight and bent finite-length cylindrical shells (stainless steel) with 3:1 aspect ratios and 52% shell thicknesses. The study not only shows reasonable agreement between the predictions and data, but also illustrates the dramatic change in scattering cross section due to the bend of the object (12 dB in this case).
Resonance classification of mixed assemblages of fish with swimbladders using a modified commercial broadband acoustic echosounder at 1–6 kHz

(NRC Research Press, 2012-04-19) Stanton, Timothy K. ; Sellers, Cynthia J. ; Jech, J. Michael

Recently developed broadband acoustic methods were used to study mixed assemblages of fish spanning a wide range of lengths and species. Through a combination of resonance classification and pulse-compression signal processing, which provides for high-range resolution, a modified commercial broadband echosounder was demonstrated to provide quantitative information on the spatial distribution of the individual size classes within an assemblage. In essence, this system spectrally resolves the different size classes of fish that are otherwise not resolved spatially. This method reveals new insights into biological processes, such as predator–prey interactions, that are not obtainable through the use of a conventional narrowband high-frequency echosounder or previous broadband systems. A recent study at sea with this system revealed aggregations containing bladdered fish 15–30 cm in length (Atlantic herring (Clupea harengus) and silver hake (Merluccius bilinearis)) and a variety of species of smaller fish 2–5 cm in length. These observations infer that the smaller 2–5 cm fish can be colocated in the same aggregations as their predator, the larger silver hake, as well as pre-spawning herring. While this technological advancement provides more information, there remain challenges in interpreting the echo spectra in terms of meaningful biological quantities such as size distribution and species composition.
Echo statistics associated with discrete scatterers: A tutorial on physics-based methods

(Acoustical Society of America, 2018-12-06) Stanton, Timothy K. ; Lee, Wu-Jung ; Baik, Kyungmin

When a beam emitted from an active monostatic sensor system sweeps across a volume, the echoes from scatterers present will fluctuate from ping to ping due to various interference phenomena and statistical processes. Observations of these fluctuations can be used, in combination with models, to infer properties of the scatterers such as numerical density. Modeling the fluctuations can also help predict system performance and associated uncertainties in expected echoes. This tutorial focuses on “physics-based statistics,” which is a predictive form of modeling the fluctuations. The modeling is based principally on the physics of the scattering by individual scatterers, addition of echoes from randomized multiple scatterers, system effects involving the beampattern and signal type, and signal theory including matched filter processing. Some consideration is also given to environment-specific effects such as the presence of boundaries and heterogeneities in the medium. Although the modeling was inspired by applications of sonar in the field of underwater acoustics, the material is presented in a general form, and involving only scalar fields. Therefore, it is broadly applicable to other areas such as medical ultrasound, non-destructive acoustic testing, in-air acoustics, as well as radar and lasers.
Comparisons among ten models of acoustic backscattering used in aquatic ecosystem research

(Acoustical Society of America, 2015-12-21) Jech, J. Michael ; Horne, John K. ; Chu, Dezhang ; Demer, David A. ; Francis, David T. I. ; Gorska, Natalia ; Jones, Benjamin A. ; Lavery, Andone C. ; Stanton, Timothy K. ; Macaulay, Gavin J. ; Reeder, D. Benjamin ; Sawada, Kouichi

Analytical and numerical scatteringmodels with accompanying digital representations are used increasingly to predict acoustic backscatter by fish and zooplankton in research and ecosystem monitoring applications. Ten such models were applied to targets with simple geometric shapes and parameterized (e.g., size and material properties) to represent biological organisms such as zooplankton and fish, and their predictions of acoustic backscatter were compared to those from exact or approximate analytical models, i.e., benchmarks. These comparisons were made for a sphere, spherical shell, prolate spheroid, and finite cylinder, each with homogeneous composition. For each shape, four target boundary conditions were considered: rigid-fixed, pressure-release, gas-filled, and weakly scattering. Target strength (dB re 1 m2) was calculated as a function of insonifying frequency (f = 12 to 400 kHz) and angle of incidence (θ = 0° to 90°). In general, the numerical models (i.e., boundary- and finite-element) matched the benchmarks over the full range of simulation parameters. While inherent errors associated with the approximate analytical models were illustrated, so were the advantages as they are computationally efficient and in certain cases, outperformed the numerical models under conditions where the numerical models did not converge
Non-Rayleigh acoustic scattering characteristics of individual fish and zooplankton

(IEEE, 2004-04) Stanton, Timothy K. ; Chu, Dezhang ; Reeder, D. Benjamin

It has long been known that the statistical properties of acoustic echoes from individual fish can have non-Rayleigh characteristics. The statistical properties of echoes from zooplankton are generally less understood. In this study, echoes from individual fish and zooplankton from a series of laboratory measurements from the past decade are investigated. In the experiments, acoustic echoes from various individual organisms were measured over a wide range of frequencies and orientations, typically in 1/spl deg/-3/spl deg/ increments. In the analysis in this paper, the echoes from most of those measurements are grouped according to ranges of orientation, which correspond to typical orientation distributions of these organisms in the natural ocean environment. This grouping provides a distribution of echo values for each range of orientation. This approach, in essence, emulates a field experiment whereby distributions of echoes would be recorded for different distributions of orientations of the organisms. For both the fish and zooplankton data, there are conditions under which the echoes are strongly non-Rayleigh distributed. In some cases, the distribution is quantitatively connected to the physics of the scattering process while, in other cases, the connection is described qualitatively. Exploitation of the animal-specific statistics for classification purposes is suggested.
High-frequency acoustic scattering from turbulent oceanic microstructure : the importance of density fluctuations

(Acoustical Society of America, 2003-11) Lavery, Andone C. ; Schmitt, Raymond W. ; Stanton, Timothy K.

Acoustic scattering techniques provide a unique and powerful tool to remotely investigate the physical properties of the ocean interior over large spatial and temporal scales. With high-frequency acoustic scattering it is possible to probe physical processes that occur at the microstructure scale, spanning submillimeter to centimeter scale processes. An acoustic scattering model for turbulent oceanic microstructure is presented in which the current theory, which only accounts for fluctuations in the sound speed, has been extended to include fluctuations in the density as well. The inclusion of density fluctuations results in an expression for the scattering cross section per unit volume, σv, that is explicitly dependent on the scattering angle. By relating the variability in the density and sound speed to random fluctuations in oceanic temperature and salinity, σv has been expressed in terms of the temperature and salinity wave number spectra, and the temperature-salinity co-spectrum. A Batchelor spectrum for temperature and salinity, which depends on parameters such as the dissipation rates of turbulent kinetic energy and temperature variance, has been used to evaluate σv. Two models for the temperature-salinity co-spectrum have also been used. The predictions indicate that fluctuations in the density could be as important in determining backscattering as fluctuations in the sound speed. Using data obtained in the ocean with a high resolution vertical microstructure profiler, it is predicted that scattering from oceanic microstructure can be as strong as scattering from zooplankton.
Use of the distorted wave Born approximation to predict scattering by inhomogeneous objects : application to squid

(Acoustical Society of America, 2009-01) Jones, Benjamin A. ; Lavery, Andone C. ; Stanton, Timothy K.

A new method has been developed to predict acoustic scattering by weakly scattering objects with three-dimensional variability in sound speed and density. This variability can take the form of inhomogeneities within the body of the scatterer and/or geometries where the acoustic wave passes through part of the scattering body, into the surrounding medium, and back into the body. This method applies the distorted wave Born approximation (DWBA) using a numerical approach that rigorously accounts for the phase changes within a scattering volume. Ranges of validity with respect to material properties and numerical considerations are first explored through comparisons with modal-series-based predictions of scattering by fluid-filled spherical and cylindrical fluid shells. The method is then applied to squid and incorporates high resolution spiral computerized tomography (SCT) scans of the complex morphology of the organism. Target strength predictions based on the SCT scans are compared with published backscattering data from live, freely swimming and tethered squid. The new method shows significant improvement for both single-orientation and orientation-averaged scattering predictions over the DWBA-homogeneous-prolate-spheroid model.
Classification of broadband echoes from prey of a foraging Blainville's beaked whale

(Acoustical Society of America, 2008-03) Jones, Benjamin A. ; Stanton, Timothy K. ; Lavery, Andone C. ; Johnson, Mark P. ; Madsen, Peter T. ; Tyack, Peter L.

Blainville's beaked whales (Mesoplodon densirostris) use broadband, ultrasonic echolocation signals with a −10 dB bandwidth from 26 to 51 kHz to search for, localize, and approach prey that generally consist of mid-water and deep-water fishes and squid. Although it is well known that the spectral characteristics of broadband echoes from marine organisms vary as a function of size, shape, orientation, and anatomical group, there is little evidence as to whether or not free-ranging toothed whales use spectral cues in discriminating between prey and nonprey. In order to study the prey-classification process, a stereo acoustic tag was deployed on a Blainville's beaked whale so that emitted clicks and the corresponding echoes from targets in the water could be recorded. A comparison of echoes from targets apparently selected by the whale and those from a sample of scatterers that were not selected suggests that spectral features of the echoes, target strengths, or both may have been used by the whale to discriminate between echoes. Specifically, the whale appears to favor targets with one or more nulls in the echo spectra and to seek prey with higher target strengths at deeper depths.
On the acoustic diffraction by the edges of benthic shells

(Acoustical Society of America, 2004-07) Stanton, Timothy K. ; Chu, Dezhang

Recent laboratory measurements of acoustic backscattering by individual benthic shells have isolated the edge-diffracted echo from echoes due to the surface of the main body of the shell. The data indicate that the echo near broadside incidence is generally the strongest for all orientations and is due principally to the surface of the main body. At angles well away from broadside, the echo levels are lower and are due primarily to the diffraction from the edge of the shell. The decrease in echo levels from broadside incidence to well off broadside is shown to be reasonably consistent with the decrease in acoustic backscattering from normal incidence to well off normal incidence by a shell-covered seafloor. The results suggest the importance of the edge of the shell in off-normal-incidence backscattering by a shell-covered seafloor. Furthermore, when considering bistatic diffraction by edges, there are implications that the edge of the shell (lying on the seafloor) can cause significant scattering in many directions, including at subcritical angles.
Sound scattering by several zooplankton groups. II. Scattering models

(Acoustical Society of America, 1998-01) Stanton, Timothy K. ; Chu, Dezhang ; Wiebe, Peter H.

Mathematical scattering models are derived and compared with data from zooplankton from several gross anatomical groups—fluidlike, elastic shelled, and gas bearing. The models are based upon the acoustically inferred boundary conditions determined from laboratory backscattering data presented in part I of this series [Stanton et al., J. Acoust. Soc. Am. 103, 225–235 (1998)]. The models use a combination of ray theory, modal-series solution, and distorted wave Born approximation (DWBA). The formulations, which are inherently approximate, are designed to include only the dominant scattering mechanisms as determined from the experiments. The models for the fluidlike animals (euphausiids in this case) ranged from the simplest case involving two rays, which could qualitatively describe the structure of target strength versus frequency for single pings, to the most complex case involving a rough inhomogeneous asymmetrically tapered bent cylinder using the DWBA-based formulation which could predict echo levels over all angles of incidence (including the difficult region of end-on incidence). The model for the elastic shelled body (gastropods in this case) involved development of an analytical model which takes into account irregularities and discontinuities of the shell. The model for gas-bearing animals (siphonophores) is a hybrid model which is composed of the summation of the exact solution to the gas sphere and the approximate DWBA-based formulation for arbitrarily shaped fluidlike bodies. There is also a simplified ray-based model for the siphonophore. The models are applied to data involving single pings, ping-to-ping variability, and echoes averaged over many pings. There is reasonable qualitative agreement between the predictions and single ping data, and reasonable quantitative agreement between the predictions and variability and averages of echo data.
Sound scattering by rough elongated elastic objects. II: Fluctuations of scattered field

(Acoustical Society of America, 1992-09) Stanton, Timothy K. ; Chu, Dezhang

Sonar echoes from unresolved features of rough objects tend to interfere with each other. Because of these interferences, properties of the echoes, such as its envelope level, will vary from realization to realization of stochastically rough objects. In this article, the nature of the fluctuations of the backscattered echo envelope of rough solid elastic elongated objects is investigated. A general formulation is initially presented after which specific formulas are derived and numerically evaluated for straight finite-length cylinders. The study uses both the approximate modal-series- and Sommerfeld–Watson-transformation-based deformed cylinder solutions presented in the first part of this series [T. K. Stanton, J. Acoust. Soc. Am. 92, XXX (1992)]. The fluctuations of the backscattered echo envelope are related to the Rice probability density function (PDF) and shown to depend upon δ/a and [script L]/L in the Rayleigh scattering region (ka≪1) and kδ and [script L]/L in the geometric region (ka≫1), where δ is the rms roughness, a is the radius of the cylinder, [script L] is the correlation length of the roughness, L is the length of the cylinder, and k is the acoustic wave number in the surrounding fluid. There are similarities shown between these fluctuations in the geometric region and those from rough planar interfaces. In addition, analytical expressions and numerical examples show that the fluctuation or ``incoherent'' component of the scattered field is random only in amplitude—its phase approaches a constant value, in phase with the mean scattered field, which needed to be taken into account in the formulation. Finally, applications of the theory developed in this article to backscatter data involving live marine shrimp-like organisms are discussed.

Stanton Timothy K.

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