Acoustic scattering by benthic and planktonic shelled animals

Acoustic backscattering measurements and associated scattering modeling were recently conducted on a type of benthic shelled animal that has a spiral form of shell (Littorina littorea). Benthic and planktonic shelled animals with this shape occur on the seafloor and in the water column, respectively, and can be a significant source of acoustic scattering in the ocean. Modeling of the scattering properties allows reverberation predictions to be made for sonar performance predictions as well as for detection and classification of animals for biological and ecological applications. The studies involved measurements over the frequency range 24 kHz to 1 MHz and all angles of orientation in as small as 1 degree increments. This substantial data set is quite revealing of the physics of the acoustic scattering by these complex shelled bodies and served as a basis for the modeling. Specifically, the resonance structure of the scattering was strongly dependent upon angle of orientation and could be traced to various types of rays (e.g., subsonic Lamb waves and rays entering the opercular opening). The data are analyzed in both the frequency and time domain (compressed pulse processing) so that dominant scattering mechanisms could be identified. Given the complexity of the animal body (irregular elastic shell with discontinuities), approximate scattering models are used with only the dominant scattering properties retained. Two models are applied to the data, both approximating the body as a deformed sphere: (1) an averaged form of the exact modal-series-based solution for the spherical shell, which is used to estimate the backscattering by a deformed shell averaged over all angles of orientation, and produces reasonably accurate predictions over all k1a(esr) (k1 is the acoustic wave number of the surrounding water and a(esr) is the equivalent spherical radius of the body), and (2) a ray-based formula which is used to estimate the scattering at fixed angle of orientation, but only for high k1a(esr). The ray-based model is an extension of a model recently developed for the shelled zooplankton Limacina retroversa that has a shape similar to that of the Littorina littorea but swims through the water [Stanton et al., J. Acoust. Soc. Am. 103, 236-253 (1998b)]. Applications of remote detection and classification of the seafloor and water column in the presence of shelled animals are discussed.     

Backscattering of transients by tilted truncated cylindrical shells: time-frequency identification of ray contributions from measurements

Impulse backscattering measurements by a thick-walled finite cylindrical shell are examined in the time-frequency domain to identify and characterize individual ray contributions from generalized Lamb waves excited on the shell. Previous experiments and analysis in the frequency-aspect angle domain [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)] indicate that large backscattering enhancements occur in the midfrequency region for the shell tilted at large angles. Presently this experimental data is examined in the time-frequency domain for selected angles of incidence. Individual ray contributions are evident and their evolution over aspect angle is discussed. The most prominent contribution is due to the meridional ray of the a0 leaky Lamb wave. This feature distinctly highlights the truncation of the shell and is found over a range of aspect angles spanning 200 degrees for the frequencies examined. Also observed are periodic features corresponding to end-reflected helical waves of the a0-. These scattering features are significantly different from those reported for thin-walled finite cylinders at low frequencies. The present results may be useful for target identification and localization and as a comparison tool for high-frequency computational scattering models.     

Acoustically coupled gas bubbles in fluids: time-domain phenomena.

In previous work [C. Feuillade, J. Acoust. Soc. Am. 98, 1178-1190 (1995)] a coupled oscillator formalism was introduced for describing collective resonances, scattering, and superresonances, of multiple gas bubbles in a fluid. Subsequently, time-domain investigations of the impulse response of coupled systems have disclosed the exact conditions which determine whether the ensemble scattering behavior should be described using: either (a), a multiple scattering; or (b), a self-consistent methodology. The determining factor is the Q of the individual scatterers, and their typical spatial separations in the medium. For highly damped or sparse systems, e.g., scattering from loose schools of swimbladder fish, or from a gassy seabed containing entrained bubbles, the multiple scatter counting approach should be applicable. For more strongly coupled systems, e.g., a dense cloud of resonating bubbles in the water column, energy exchange may be due primarily to radiative cycling rather than scattering, in which case a self-consistent approach is indicated. The result has implications for both volume and bottom scattering applications.     

Acoustic radiation torque and the conservation of angular momentum (L)

This note concerns the evaluation of the static acoustic radiation torque exerted by an acoustic field on a scatterer immersed in a nonviscous fluid based on far-field scattering. The radiation torque is expressed as the integral of the time-averaged flux of angular momentum over a spherical surface far removed from the scattering object with its center at the centroid of the object. That result was given previously [G. Maidanik, J. Acoust. Soc. Am. 30, 620-623 (1956)]. Another expression given recently [Z. W. Fan et al., J. Acoust. Soc. Am. 124, 2727-2732 (2008)] is simplified to this formula. Comments are made on obtaining it directly from the general theorem of angular momentum conservation in the integral form.     

A time domain rough surface scattering model based on wedge diffraction: application to low-frequency backscattering from two-dimensional sea surfaces

A time domain method for calculating the acoustic impulse response of impenetrable, rough, two-dimensional (2D) surfaces is presented. The method is based on an extension of the wedge assemblage (WA) method to 2D surfaces and objects. Like the WA method for one-dimensional (1D) surfaces, the approach for 2D surfaces uses Biot's and Tolstoy's exact solution for the impulse response of an infinite impenetrable wedge [J. Acoust. Soc. Am. 29, 381-391 (1957)] as its fundamental building block. The validity of the WA method for backscattering from 2D sea surfaces is assessed through comparisons with calculations based on Milder's operator expansion (OE) method [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Average intensities for backscattering from 2D fully developed seas (20 m/s wind speed) were computed by the WA and OE methods using 50 surface realizations and compared at 11 frequencies between 100 and 200 Hz. A single, moderately low grazing angle of incidence (20 degrees) and several scattered grazing angles (90 degrees, 45 degrees, 20 degrees , and 10 ) were considered. Excellent overall agreement between the two models was obtained. The utility of the WA method as a tool to describe the physics of the scattering process is also discussed.     

A model for directional and distance hearing in swimbladder-bearing fish based on the displacement orbits of the hair cells

It is known that teleosts, without Weberian ossicles but with a swimbladder, can detect the direction of and, under appropriate conditions, the distance to a sound source [e.g., Schuijf and Hawkins, Nature 302, 143-144 (1983)]. It is hypothesized here that the underlying mechanism is the analysis of the parameters of the elliptical movement of the hair cells with respect to the otoliths. This movement results from the displacement wave impinging directly upon the labyrinth and the response displacement wave reradiated by the swimbladder. For a given swimbladder geometry, given the positions of the maculae of both labyrinths with respect to the swimbladder and the damping of the swimbladder, the displacement orbits of the maculae can be calculated [de Munck and Schellart, J. Acoust. Soc. Am. 81, 556-560 (1987)]. These calculations were made for the cod and the trout with the frequency, direction, and distance between the fish and the sound source as parameters with the source within the same horizontal plane as the fish. The orbit model predicts that the utriculus has the most strategic position to detect direction and distance of such a sound source. Moreover, the model predicts that this could basically be done monaurally. A hypothesis is proposed to describe how the utricular system analyzes the orbit parameters. The model is evaluated in relation to the results of behavioral experiments described in the literature.     

Negative group velocity Lamb waves on plates and applications to the scattering of sound by shells

Symmetric Lamb waves on plates exhibit anomalies for certain regions of frequency. The phase velocity appears to be double-valued [M. F. Werby and H. Uberall, J. Acoust. Soc. Am. 111, 2686-2691 (2002)] with one of the branches having a negative group velocity relative to the corresponding phase velocity. The classification of the symmetric plate modes for frequencies appearing to have a double-valued phase velocity is reviewed here. The complication of a double-valued velocity is avoided by examining mode orthogonality and the complex wave-number spectra. Various authors have noted an enhancement in the backscattering of sound by elastic shells in water that occurs for frequencies where symmetric leaky Lamb waves (generalized to case of a shell) have contra-directed group and phase velocities. The ray diagram for negative group velocity contributions to the scattering by shells [G. Kaduchak, D. H. Hughes, and P. L. Marston, J. Acoust. Soc. Am. 96, 3704-3714 (1994)] is unusual since for this type of mode the energy on the shell flows in the opposite direction of the wave vector. Circumnavigation of the shell is not required for the leaky ray to be backward directed.     

On acoustic scattering by a shell-covered seafloor

Acoustic scattering by the seafloor is sometimes influenced, if not dominated, by the presence of discrete volumetric objects such as shells. A series of measurements of target strength of a type of benthic shelled animal and associated scattering modeling have recently been completed (Stanton et al., "Acoustic scattering by benthic and planktonic shelled animals," J. Acoust. Soc. Am., this issue). The results of that study are used herein to estimate the scattering by the seafloor with a covering of shells at high acoustic frequencies. A simple formulation is derived that expresses the area scattering strength of the seafloor in terms of the average reduced target strength or material properties of the discrete scatterers and their packing factor (where the reduced target strength is the target strength normalized by the geometric cross section of the scatterers and the averaging is done over orientation and/or a narrow range of size or frequency). The formula shows that, to first order, the backscattering at high acoustic frequencies by a layer of shells (or other discrete bodies such as rocks) depends principally upon material properties of the objects and packing factor and is independent of size and acoustic frequency. Estimates of area scattering strength using this formula and measured values of the target strength of shelled bodies from Stanton et al. (this issue) are close to or consistent with observed area scattering strengths due to shell-covered seafloors published in other papers.     

Backscatter from a limestone seafloor at 2-3.5 kHz: measurements and modeling

Physics-based interface scattering models for the seafloor [H.-H. Essen, J. Acoust. Soc. Am. 95, 1299-1310 (1994); Gragg et al., ibid. 110, 2878-2901 (2001)] exhibit features in their predicted grazing angle dependence. These features have a strong dependence on the assumed composition and roughness of the bottom. Verifying such predictions requires data that cover a wide range of grazing angles and involve minimal sub-bottom penetration. Such measurements were performed in the frequency band 2-3.5 kHz over an exposed limestone bottom off the Carolina coast during the second Littoral Warfare Advanced Development Focused Technology Experiment of 1996 (LWAD FTE 96-2). Direct-path bottom scattering strengths were obtained in shallow water (198-310 m deep) for grazing angles from 8 degrees to 75 degrees using data fusion from multiple experimental geometries coupled with careful signal processing. The processing included corrections for the surface-reflected path, other multipaths, and characteristics of the reverberation decay observed over the pulse duration at higher grazing angles. The resulting frequency and grazing-angle dependences exhibit trends consistent with theoretical predictions, and geoacoustic parameters obtained by inversion are consistent with values expected for limestone.     

Effects of coupled vibrations on the parameters of tangentially polarized stripe-electroded piezoelectric cylinders (L)

The effects of coupled vibrations on the piezoelectric properties and electroacoustic transducer performance of radially polarized hollow cylindrical elements as a function of the choice of height-to-diameter ratio have been well documented [J. Acoust. Soc. Am. 120(3), 1374-1380 (2006); J. Acoust. Soc. Am. 122(6), 3419-3427 (2007)]. This letter presents experimental work on the effects of coupled (circumferential, axial, and flexural) vibrations on the resonance frequencies, effective electromechanical coupling coefficient, and acoustical performance of tangentially polarized piezoceramic cylindrical elements. Comparisons are made with analytical predictions of the properties of uniformly circumferentially polarized cylinders.     

Compilation of empirical ultrasonic properties of mammalian tissues. II

The compilation of the literature on ultrasonic propagation properties of mammalian tissues [J. Acoust. Soc. Am. 64, 423 (1978)] is continued with the addition of 45 papers yielding over 700 lines of parametric data.     

Models of auditory masking: a molecular psychophysical approach

Gilkey et al. [J. Acoust. Soc. Am. 78, 1207-1219 (1985)] measured hit proportions and false alarm proportions for detecting a 500-Hz tone at each of four starting phase angles in each of 25 reproducible noise samples. In the present paper, their results are modeled by fitting the general form of the electrical analog model of Jeffress [J. Acoust. Soc. Am. 48, 480-488 (1967)] to the diotic data. The best-fitting configurations of this model do not correspond to energy detectors or to envelope detectors. A detector composed of a 50-Hz-wide single-tuned filter, followed by a half-wave rectifier and an integrator with an integration time of 100 to 200 ms fits the data of all four subjects relatively well. Linear combinations of the outputs of several detectors that differ in center frequency or integration window provide even better fits to the data. These linear combinations assign negative weights to some frequencies or to some time intervals, suggesting that a subject's decision is based on a comparison of information in different spectral or temporal portions of the stimulus.     

Pitch and rhythm paradoxes: comments on "Auditory paradox based on fractal waveform"

Schroeder [J. Acoust. Soc. Am. 79, 186-189 (1986)] describes the paradox of acoustic waveforms that sound lower when reproduced at higher speeds. The author has also demonstrated this paradox [J.C. Risset, J. Acoust. Soc. Am. 46, 88 (A) (1969); see also Seventh ICA, Budapest, S10, 613-616 (1971)]; in addition he has recently synthesized a rhythmic analog of the paradox, namely rhythmical sequences that can sound slower when reproduced at higher speeds.     

Acoustic backscattering by Hawaiian lutjanid snappers. 1. Target strength and swimbladder characteristics

The target strengths and swimbladder morphology of six snapper species were investigated using broadband sonar, x rays, and swimbladder casts. Backscatter data were obtained using a frequency-modulated sweep (60-200 kHz) and a broadband, dolphinlike click (peak frequency 120 kHz) from live fish, mounted and rotated around each of their three axes. X rays revealed species-specific differences in the shape, size, and orientation of the swimbladders. The angle between the fish's dorsal aspect and the major axis of its swimbladder ranged from 3 degrees to 12 degrees and was consistent between individuals within a species. This angle had a one-to-one relationship with the angle at which the maximum dorsal aspect target strength was measured (r2 = 0.93), regardless of species. Maximum dorsal aspect target strength was correlated with length within species. However, the swimbladder modeled as an air-filled prolate spheroid with axes measured from the x rays of the swimbladder predicted maximum target strength significantly better than models based on fish length or swimbladder volume. For both the dorsal and lateral aspects, the prolate spheroid model's predictions were not significantly different from the measured target strengths (observed power >0.75) and were within 3 dB of the measured values. This model predicts the target strengths of all species equally well, unlike those based on length.     

Analyzing reverse middle-ear transmission: noninvasive Gedankenexperiments.

The phenomenological framework outlined in the companion paper [C. A. Shera and G. Zweig, J. Acoust. Soc. Am. 92, 1356-1370 (1992)] characterizes both forward and reverse transmission through the middle ear. This paper illustrates its use in the analysis of noninvasive measurements of middle-ear and cochlear mechanics. A cochlear scattering framework is developed for the analysis of combination-tone and other experiments in which acoustic distortion products are used to drive the middle ear "in reverse." The framework is illustrated with a simple psychophysical Gedankenexperiment analogous to the neurophysiological experiments of P. F. Fahey and J. B. Allen [J. Acoust. Soc. Am. 77, 599-612 (1985)].     

The differential and total bulk acoustic scattering cross sections of some human and animal tissues

This paper describes methods that have been developed for the accurate measurement of total and differential bulk acoustic scattering cross sections. Analysis is made of the sources of uncertainty entailed in measurements of this kind and a complete derivation is developed for the angular variation of the interrogated scattering volume. Experimentally determined values of differential scattering cross sections are reported for specimens of skeletal muscle, blood, liver, and secondary tumors arising in liver, obtained in the frequency range 4-7 MHz for scattering angles in the practically attainable range 60 degrees-150 degrees and also at 180 degrees (backscatter). A basis for extrapolating these results to other scattering angles can be derived from a combination of theoretical and experimental considerations, as presented in a companion paper [J. Acoust. Soc. Am. 79, 2048-2054 (1986)]. Based on such extrapolation, values for total scattering cross sections are estimated for the above tissues, the values are compared with determinations by different techniques as reported by other authors, and corresponding estimates are derived for the contribution of scattering processes to total attenuation in the tissues.     

Lateralization produced by interaural temporal and intensitive disparities of high-frequency, raised-sine stimuli: data and modeling

An acoustic pointing task was used to measure extents of laterality produced by combinations of ongoing envelope-based interaural temporal disparities (ITDs) and interaural intensitive disparities (IIDs) of 4-kHz-centered raised-sine stimuli [Bernstein and Trahiotis, J. Acoust. Soc. Am. 125, 3234-3242 (2009),] while varying, parametrically, their peakedness, depth of modulation, and frequency of modulation. The study was designed to assess whether IIDs act as "weights" within the putative "binaural display" at high spectral frequencies (where the envelopes convey ITD-information) as appears to be the case at low spectral frequencies (where the waveforms, i.e., fine-structure and envelopes, convey ITD-information). The data indicate that envelope-based IIDs do principally act as weights and that they appear to exert their influence on lateral position independently of the influence of ITDs. Quantitative analyses revealed that an augmented form of the cross-correlation-based "position-variable" model of Stern and Shear [J. Acoust. Soc. Am. 100, 2278-2288 (1996)] accounted for 94% of the variance in the data. This success notwithstanding, for a small subset of the data, predictions could be improved by assuming that the listeners utilized information within auditory filters having center frequencies above 4 kHz.     

鳀鱼(Engraulis japonicus)目标强度的模型法研究

采用声散射理论和目标强度近似模型评估法对黄海鲤鱼（Engraulis japonicus）的声散射特征和目标强度进行了数值计算与评估研究。散射模型由鱼鳔模型和鱼体模型两个部分构成，其中鱼鳔采用充满气体的椭球体模型，鳔除外的鱼体采用充满液体的椭球体模型。理论数值计算所需参数取自全长12．6cm的鲤鱼个体，其鱼鳔尺寸利用X光照片测得。平均目标强度利用模型算得的不同角度下的声散射强度与鲲鱼倾角分布函数的卷积计算，其中倾角（度）的分布函数设为N（-3．9，12．8^2）。结果显示，鲲鱼对声波的散射具有明显指向性；在38kHz和120kHz工作频率下，鲲鱼的最大背向目标强度分别为-41．2dB和-39．5dB，有效平均目标强度分别为-48．0dB和-51．5dB，与实测结果吻合较好。另外还对鲲鱼的反向散射指向性特征、目标强度的频率特征以及鱼鳔对鲲鱼整体目标强度的贡献等进行了分析与讨论。以上研究表明，模型法作为现场测定研究方法的重要补充和认知鱼类声学散射特性的有效途径，可在我国鱼类目标强度的研究中发挥重要作用。     

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).