Acoustic scattering by smooth elastic cylinders insonified by directional transceivers: Monostatic theory and experiments.

A theoretical model for predicting the acoustic field scattered by an elastic cylinder that is partially insonified by a directional transceiver is proposed in the form of a simple approximate one-dimensional integral. This model accounts for spherical spreading and directivity of the incident waves and extends the formulation used in a preceding article [Gurley and Stanton, J. Acoust. Soc. Am. 94, 2746-2755 (1993)] by including effects due to oblique insonification of a long cylinder assuming negligible end-contributions. The scattered field of an infinitely long cylinder for obliquely incident plane waves and point receivers is used to approximate the apparent volume flow of cylinders partially insonified by directional transceivers. The scattered pressure that is derived using the apparent volume flow, in contrast to the previous formulation, is capable of predicting axially propagating guided wave resonances; these natural modes are excited, in addition to circumferential ones, at off-normal incident angles. The model is compared with exact numerical simulations and with previously published as well as new laboratory data. The analysis illustrates the different realistic effects associated with scattering from elastic cylinders insonified by a directional transceiver both theoretically and experimentally.

Frequency- and depth-dependent target strength measurements of individual mesopelagic scatterers.

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.

Macroscopic observations of diel fish movements around a shallow water artificial reef using a mid-frequency horizontal-looking sonar.

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.

Echo statistics associated with discrete scatterers: A tutorial on physics-based methods.

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.

Broadband classification and statistics of echoes from aggregations of fish measured by long-range, mid-frequency sonar.

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.

Comparisons among ten models of acoustic backscattering used in aquatic ecosystem research.

Analytical and numerical scattering models 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 m(2)) 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.

Echo statistics of individual and aggregations of scatterers in the water column of a random, oceanic waveguide.

The relative contributions of various physical factors to producing non-Rayleigh distributions of echo magnitudes in a waveguide are examined. Factors that are considered include (1) a stochastic, range-dependent sound-speed profile, (2) a directional acoustic source, (3) a variable scattering response, and (4) an extended scattering volume. A two-way parabolic equation model, coupled with a stochastic internal wave model, produces realistic simulations of acoustic propagation through a complex oceanic sound speed field. Simulations are conducted for a single frequency (3 kHz), monostatic sonar with a narrow beam (5° -3 dB beam width). The randomization of the waveguide, range of propagation, directionality of the sonar, and spatial extent of the scatterers each contribute to the degree to which the echo statistics are non-Rayleigh. Of critical importance are the deterministic and stochastic processes that induce multipath and drive the one-way acoustic pressure field to saturation (i.e., complex-Gaussian statistics). In this limit predictable statistics of echo envelopes are obtained at all ranges. A computationally low-budget phasor summation can successfully predict the probability density functions when the beam pattern and number of scatterers ensonified are known quantities.

Orientation dependence of broadband acoustic backscattering from live squid.

A controlled laboratory experiment of broadband acoustic backscattering from live squid (Loligo pealeii) was conducted using linear chirp signals (60-103 kHz) with data collected over the full 360° of orientation in the lateral plane, in <1° increments. The acoustic measurements were compared with an analytical prolate spheroid model and a three-dimensional numerical model with randomized squid shape, both based on the distorted-wave Born approximation formulation. The data were consistent with the hypothesized fluid-like scattering properties of squid. The contributions from the front and back interfaces of the squid were found to dominate the scattering at normal incidence, while the arms had a significant effect at other angles. The three-dimensional numerical model predictions out-performed the prolate spheroid model over a wide range of orientations. The predictions were found to be sensitive to the shape parameters, including the arms and the fins. Accurate predictions require setting these shape parameters to best describe the most probable squid shape for different applications. The understanding developed here serves as a basis for the accurate interpretation of in situ acoustic scattering measurements of squid.

Use of the distorted wave born approximation to predict scattering by inhomogeneous objects: application to squid.

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.

Calibration of broadband active acoustic systems using a single standard spherical target.

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).

Classification of broadband echoes from prey of a foraging Blainville's beaked whale.

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.

Acoustic diffraction by deformed edges of finite length: theory and experiment.

The acoustic diffraction by deformed edges of finite length is described analytically and in the frequency domain through use of an approximate line-integral formulation. The formulation is based on the diffraction per unit length of an infinitely long straight edge, which inherently limits the accuracy of the approach. The line integral is written in terms of the diffraction by a generalized edge, in that the "edge" can be a single edge or multiple closely spaced edges. Predictions based on an exact solution to the impenetrable infinite knife edge are used to estimate diffraction by the edge of a thin disk and compared with calculations based on the T-matrix approach. Predictions are then made for the more complex geometry involving an impenetrable thick disk. These latter predictions are based on an approximate formula for double-edge diffraction [Chu et al., J. Acoust. Soc. Am. 122, 3177 (2007)] and are compared with laboratory data involving individual elastic (aluminum) disks spanning a range of diameters and submerged in water. The results of this study show this approximate line-integral approach to be versatile and applicable over a range of conditions.

Higher-order acoustic diffraction by edges of finite thickness.

A cw solution of acoustic diffraction by a three-sided semi-infinite barrier or a double edge, where the width of the midplanar segment is finite and cannot be ignored, involving all orders of diffraction is presented. The solution is an extension of the asymptotic formulas for the double-edge second-order diffraction via amplitude and phase matching given by Pierce [A. D. Pierce, J. Acoust. Soc. Am. 55, 943-955 (1974)]. The model accounts for all orders of diffraction and is valid for all kw, where k is the acoustic wave number and w is the width of the midplanar segment and reduces to the solution of diffraction by a single knife edge as w-->0. The theory is incorporated into the deformed edge solution [Stanton et al., J. Acoust. Soc. Am. 122, 3167 (2007)] to model the diffraction by a disk of finite thickness, and is compared with laboratory experiments of backscattering by elastic disks of various thicknesses and by a hard strip. It is shown that the model describes the edge diffraction reasonably well in predicting the diffraction as a function of scattering angle, edge thickness, and frequency.

Determining dominant scatterers of sound in mixed zooplankton populations.

High-frequency acoustic scattering techniques have been used to investigate dominant scatterers in mixed zooplankton populations. Volume backscattering was measured in the Gulf of Maine at 43, 120, 200, and 420 kHz. Zooplankton composition and size were determined using net and video sampling techniques, and water properties were determined using conductivity, temperature, and depth sensors. Dominant scatterers have been identified using recently developed scattering models for zooplankton and microstructure. Microstructure generally did not contribute to the scattering. At certain locations, gas-bearing zooplankton, that account for a small fraction of the total abundance and biomass, dominated the scattering at all frequencies. At these locations, acoustically inferred size agreed well with size determined from the net samples. Significant differences between the acoustic, net, and video estimates of abundance for these zooplankton are most likely due to limitations of the net and video techniques. No other type of biological scatterer ever dominated the scattering at all frequencies. Copepods, fluid-like zooplankton that account for most of the abundance and biomass, dominated at select locations only at the highest frequencies. At these locations, acoustically inferred abundance agreed well with net and video estimates. A general approach for the difficult problem of interpreting high-frequency acoustic scattering in mixed zooplankton populations is described.

Improved parameterization of Antarctic krill target strength models.

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.

Broadband acoustic backscatter and high-resolution morphology of fish: measurement and modeling.

Broadband acoustic backscattering measurements, advanced high-resolution imaging of fish morphology using CT scans and phase-contrast x rays (in addition to traditional x rays), and associated scattering modeling using the images have been conducted involving alewife (Alosa pseudoharengus), a swimbladder-bearing fish. A greater-than-octave bandwidth (40-95 kHz) signal was used to insonify live, individual, adult alewife that were tethered while being rotated in 1-deg increments over all angles in two planes of rotation (lateral and dorsal/ventral). These data, in addition to providing the orientation dependence of the scattering over a continuous band of frequencies, were also used (after pulse compression) to identify dominant scattering features of the fish (including the skull and swimbladder). The x-ray and CT scan images of the swimbladder were digitized and incorporated into two scattering models: (1) Kirchhoff-ray mode (KRM) model [Clay and Horne, J. Acoust. Soc. Am. 96, 1661-1668 (1994)] and (2) conformal-mapping-based Fourier matching method (FMM), which has recently been extended to finite-length bodies [Reeder and Stanton, J. Acoust. Soc. Am. 116. 729-746 (2004)]. Comparisons between the scattering predictions and data demonstrate the utility of the CT scan imagery for use in scattering models, as it provided a means for rapidly and noninvasively measuring the fish morphology in three dimensions and at high resolution. In addition to further validation of the KRM model, the potential of the new FMM formulation was demonstrated, which is a versatile approach, valid over a wide range of shapes, all frequencies and all angles of orientation.

On the acoustic diffraction by the edges of benthic shells.

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.

High-frequency acoustic scattering from turbulent oceanic microstructure: the importance of density fluctuations.

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, sigma(v), 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, sigma(v) 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 sigma(v). 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.

Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton.

Scattering models that correctly incorporate organism size and shape are a critical component for the remote detection and classification of many marine organisms. In this work, an acoustic scattering model has been developed for fluid-like zooplankton that is based on the distorted wave Born approximation (DWBA) and that makes use of high-resolution three-dimensional measurements of the animal's outer boundary shape. High-resolution computerized tomography (CT) was used to determine the three-dimensional digitizations of animal shape. This study focuses on developing the methodology for incorporating high-resolution CT scans into a scattering model that is generally valid for any body with fluid-like material properties. The model predictions are compared to controlled laboratory measurements of the acoustic backscattering from live individual decapod shrimp. The frequency range used was 50 kHz to 1 MHz and the angular characteristics of the backscattering were investigated with up to a 1 degree angular resolution. The practical conditions under which it is necessary to make use of high-resolution digitizations of shape are assessed.