Index of content:
Volume 87, Issue 1, January 1990

Acoustical measurement of fish abundance
View Description Hide DescriptionThe theory of echo formation provides formulas relating echo energy to physical characteristics of the target. Single‐target theory (applicable to counting isolated fish) is extended to the multiple‐target case relevant to schooling fish. An echo‐integrator equation relates fish density to echo energy integrated over a time gate corresponding to the depth channel of interest. Parameters include the equivalent beam angle, the expected backscattering cross section per fish, equipment sensitivity, and a time‐varied‐gain correction factor. Variation of environmental factors (sound speed and absorption) affects the parameter values. More important is the variation of biological factors (fish behavior and physiology) which affects backscattering cross section and target strength. Verification of the echo‐integrator equation, depending upon the linearity principle concerning the addition of signals from randomly distributed multiple targets, is discussed in the fisheries context. The swimbladder is the dominant sound reflector in fish having one. Accordingly, fish targets may be classified as (a) bladder closed, (b) bladder open, or (c) no bladder. Within each category, fish of the same size have similar target strengths. Target strength variation with fish size, water depth, and time is discussed. Experimental target strengths are well scattered even for nominally similar fish. Nevertheless, useful information about fish stocks can be obtained through careful application of acoustical techniques.

Target strengths of Antarctic krill (E u p h a u s i a s u p e r b a) at 38 and 120 kHz
View Description Hide DescriptionEncaged aggregations of live krill in good to pristine condition have been ensonified at 38 and 120 kHz. Concurrent underwater television observations of behavior resemble those made by underwater divers in naturally occurring swarms, with comparably high densities of the order of 10^{4} animals/m^{3} . Mean, single‐animal target strengths have been inferred from measurements of echo energy. For aggregations with mean lengths in the range [30,39] mm, the mean single‐krill target strengths are in the range [−88,−83] dB at 38 kHz and [−81,−74] dB at 120 kHz. Collateral measurements on some of the same encaged specimens determined a density contrast of 1.0357±0.0067 and sound‐speed contrast of 1.0279±0.0024, relative to seawater. These numbers have been used with the fluid‐sphere model as stated by Greenlaw [Limnol. Oceanogr. 2 4, 226–242 (1979)] . Computed backscattering cross sections have been averaged over the length distributions of each measuredaggregation, resulting in target strength predictions in the range [−86,−80] dB at 38 kHz and [−79,−76] dB at 120 kHz.

Multiple scattering by finite regular arrays of resonators
View Description Hide DescriptionEarlier results for multiple scattering by arbitrary configurations of N obstacles are applied to seven regular arrays of two to six monopole resonators (with radius a, maximum scattering cross section σ_{ c }, and normalized resonance frequency x _{ c }=k _{ c } a). The arrays involve m=1, 2, or 3 different values of the separations of monopole centers, with d as the smallest. For each array, the corresponding scattering amplitude reduces to a sum of m+1 collective oscillator modes F _{ n } (orthogonal in the same sense as the spherical harmonics). The doublet, triangular, and tetrahedral arrays are specified by two modes, F _{0} and F _{1}; the square, pentagonal, and octahedral arrays require a third, F _{2}; and the hexagonal array also requires a fourth, F _{3}. The scattering cross section S of each array is less than 2Nσ_{ c }, with maximum at a frequency k a=x near x _{ c } for relatively large k d=y=x/p≫x. If y>2x is small, the F _{ n } reduce to simple multipoles in terms of spherical harmonics and elementary functions of x, p, and x _{ c }. Then S has narrow resonance peaks S _{ n }=O(σ_{ c }) at frequencies x _{ n } relatively far from x _{ c } (with x _{0}<x _{ c }, and the other x _{ n }>x _{ c }); the averages over orientation S̄_{ n } add up to Nσ_{ c } (an average oscillator‐strengthsum rule). The separations of the resonance frequencies x _{ n } and the fineness of the peaks S _{ n } (nonoverlapping at half‐power) provide distinctive signatures for diagnostic and related applications.

Observables due to beam‐to‐mode conversion of a high‐frequency Gaussian P‐wave input in an aluminum plate in vacuum
View Description Hide DescriptionObliquely incident Gaussian P‐wave inputs furnish important test signals for ultrasonic detection of flaws in layered elastic media. Unlike vertically impinging beams, multiply reflected oblique beams eventually are converted into guided modes. The horizontal ranges over which the field is beamlike or modelike must be well understood for selection of a diagnostic scheme with ‘‘good’’ features for detection and identification. An analytical study is conducted here to detail the beam‐to‐mode conversion and P–S V coupling processes in an aluminum plate. The rigorously based approach utilizes the complex source point (CSP) method for generation of the input beam, and offers ray, mode, and hybrid ray–mode alternatives for best characterization of the wave phenomena. Numerical reference results over a representative range of parameters, which furnish potentials and displacements in various cross sections and on the plate boundaries, are interpreted in terms of beam or mode observables and related to the spectral wavenumber content of the incident signal. These considerations lead to the formulation of certain rules that categorize the detected signal in a manner which may be helpful in the construction of inversion algorithms for flaw detection.

Effects of fiber motion on the acoustic behavior of an anisotropic, flexible fibrous material
View Description Hide DescriptionThe acoustic behavior of a flexible fibrous material was studied experimentally. The material consisted of cylindrically shaped fibers arranged in a batting with the fibers primarily aligned parallel to the face of the batting. This type of material was considered anisotropic, with the acoustic propagation constant depending on whether the direction of sound propagation was parallel or normal to the fiber arrangement. Normal‐incidence sound‐absorptionmeasurements were taken for both fiber orientations over the frequency range 140–1500 Hz and with bulk densities ranging from 4.6–66.7 kg/m^{3}. When the sound propagated in a direction normal to the fiber alignment, the measuredsound absorption showed the occurrence of a resonance, which modified the absorption that was primarily attributed to viscous and thermal effects. When the sound propagated in a direction parallel to the fiber alignment, indications of resonances in the data were not present. From comparing these two sets of data and from considering the material structure, the resonance in the data for fibers normal to the direction of sound propagation was attributed to fiber motion. An analytical model for the acoustical behavior of the material displayed the same fiber‐motion characteristics shown in the measurements.

Determination of blocking locations and cross‐sectional area in a duct by eigenfrequency shifts
View Description Hide DescriptionA theoretical determination of the location and size of blockages in the one‐dimensional duct has been carried out. It is found that the blockage cross‐section area function can be calculated from the measured eigenfrequencies obtained using two boundary conditions, i.e., closed–closed (or open–open) and closed–open ends. When the blockages are small, the area function of the blocked duct can be expressed as a one‐dimensional spatial Fourier transform, whose spatial frequencies are related to the eigenfrequency shifts caused by the blockages in the duct. The method developed can be applied to the detection of the multiple blockages. The experimental results show that the accuracy of the calculated blockage area function is dependent on the number of the eigenfrequencies used. The agreements between the calculated blockage area and the actual blockage are excellent when the half‐wavelength of the eigenfrequency used is greater than the length of the blockage.

The transient field of a planar ultrasonic transducer coupled to a lens: Experiments and simulations
View Description Hide DescriptionIn this paper a study of the transient ultrasonic field radiated, in a fluid, by a planar transducer coupled to a lens is proposed. The transient pressure is measured using two small probes of different radii. Experimental waveforms are compared to waveforms that have been calculated using the impulse response method, extended in order to take account of the finite size of the receivers. The transient pressure field is interpreted by the concept of geometrical wave and edge waves. The averaging effect due to the finite size of the receivers, which acts differently on the ultrasonic field components, is put in evidence.

Oscillational instabilities in single‐mode acoustic levitators
View Description Hide DescriptionAn extension of standard results for the acoustic force on an object in a single‐mode resonant chamber yields predictions for the onset of oscillational instabilities when objects are levitated or positioned in these chambers. The results are consistent with experimental investigations. The present approach accounts for the effect of time delays on the response of a cavity to the motion of an object inside it. Quantitative features of the instabilities are investigated. The experimental conditions required for sample stability, saturation of sample oscillations, hysteretic effects, and the loss of the ability to levitate are discussed.

Acoustic pulse propagation above grassland and snow: Comparison of theoretical and experimental waveforms
View Description Hide DescriptionTheoretical predictions are made of the effect of an absorbing ground surface on acoustic impulsive waveforms propagating in a homogeneous atmosphere for frequencies below 500 Hz. The lower frequencies of the pulse are enhanced as the effective flow resistivity of the ground surface decreases and as the propagation distance increases. The pulse waveforms and peak amplitude decay observed for propagation distances of 40 to 274 m over grassland were satisfactorily matched by calculations using an assumed effective flow resistivity of 200 kN s m^{−4}. Measurements over snow gave much greater amplitude decay rates, and the waveforms were radically changed in appearance, being dominated by the lower frequencies. These waveforms were satisfactorily matched only when a layered ground was incorporated into the calculations; then, an assumed surface effective flow resistivity of 20 kN s m^{−4} gave good agreement with the observed waveforms and peak amplitude decay.

Experimental measurements of three‐dimensional propagation in a wedge‐shaped ocean with pressure‐release boundary conditions
View Description Hide DescriptionThe theoretical solution for three‐dimensional acoustic propagation in a wedge‐shaped ocean with ideal pressure‐release boundaries predicts a well‐defined beam in the down‐slope direction that diverges as the energy propagates out towards deep water. Outside of the beam, shadow zones are formed, and its spatial extent is determined by the lowest mode of propagation. The purpose of the experimental results presented here is to check the theoretical analyses, as part of an ongoing investigation into three‐dimensional propagation in the ocean environment. The wedge model in this experiment has a pressure‐release bottom and a slope that is around 20 deg. For convenience of analysis, only the lowest mode is excited by locating a source near the cutoff range. It has been found that for down‐slope propagation, the spatial characteristics of the field in a direction parallel to the shore line are in good agreement with the theoretical solution, and the azimuthal extent of the beam depends on the wedge angle. In addition to the evaluation of the exact theory, measurements have been made of acoustic pulse propagation and distortion in the wedge.

Resonances and surface waves in the scattering of an obliquely incident acoustic field by an infinite elastic cylinder
View Description Hide DescriptionThe relationship between resonances and surface waves in the scattering of an obliquely incident acoustic wave from an infinite elastic cylinder is discussed. From the three‐dimensional normal‐mode solutions for a free cylinder, the resonance frequencies of the cylinder and, correspondingly, the phase velocities of helical surface waves and their relation to the helical angles are obtained. Furthermore, as the cylinder is excited by sound waves incident through ambient water, the dispersion of phase velocity for helical surface waves as a function of the angle of incidence has also been derived. Comparing the results of the present work with the results given by Flax e t a l. [J. Acoust. Soc. Am. 6 8, 1832 (1980)], it was found that, for the case of oblique incidence, the resonance frequencies are basically in agreement with the frequencies of the minimum values of the form function, analogous to the case of perpendicular incidence.

A simple low‐frequency acoustic technique for remote measurement of the temporal ocean wave spectrum
View Description Hide DescriptionA theory is presented that describes a method for using low‐frequency sound (≲150 Hz) to measure the waveheight variance and the nondirectional temporal waveheight spectrum of a random rough surface such as the sea surface. The technique requires a vertically pointing broadbeam acoustic source and a colocated broadbeam receiver which records the amplitude and phase fluctuations of the backscattered field. When the rms surface waveheight is much smaller than the acoustic wavelength, the temporal spectrum of the amplitude and phase fluctuations can be directly related to the nondirectional temporal surface waveheight spectrum. The theory predicts that the temporal waveheight spectrum out to frequencies of roughly 0.5 Hz can be retrieved.

Analysis of backscattering data in the Tyrrhenian Sea
View Description Hide DescriptionResearch has been conducted in the Tyrrhenian Sea basin to measure low‐frequency basin reverberation and relate the measurements to backscattered strength. The receivers were a towed horizontal array and a suspended vertical array. Standard Italian Navy depth (74 kg) and SUS (0.818 kg) charges were used as sources. The unique factor in this broadband basin reverberation experiment was that data were collected simultaneously from the horizontal and vertical array. Towed‐array data were taken on multiple headings; combining different headings permitted removal of the ambiguous directionality information from the towed array. Frequency‐domain beamformed data are presented and reveal that, in the area examined, basin features are the strongest backscatterers. Receiver beam level data are presented primarily for 300 Hz, but some data are given for 100, 450, and 730 Hz as well. Estimates of backscattering strengths of different features are provided and are in the range quoted in other publications. A comparison of the horizontal and vertical array scattering strengths estimated for some selected basin features is also included. Statistics for the dominant backscatterers are given, and the results from one basin feature are presented showing detailed backscatter structure.

Attenuation in a saddle‐point analysis of the reflected acoustic field
View Description Hide DescriptionBottom attenuation is included in a saddle‐point analysis of the acoustic field formed by reflection of sound at the interface between two fluids. The loci of the saddle points as a function of range are substantially changed when attenuation is included, but previous approximate analytic expressions in terms of the saddle points can still be used and give a good approximation to the field. The suggestion made elsewhere that the inclusion of attenuation simplifies a beam displacement analysis of bottom reflection is shown to lead to poor results.

Free oscillations of near‐surface bubbles as a source of the underwater noise of rain
View Description Hide DescriptionA bubble that is oscillating with a small amplitude may be thought of as a damped, undriven harmonic oscillator. If the bubble is near a free surface, it may be considered as a simple acoustic source close to a pressure release boundary and will therefore radiate as a dipole. It has been shown in a previous paper [Pumphrey e t a l., J. Acoust. Soc. Am. 8 5, 1518–1526 (1989)] that this mechanism is the major cause of the sound produced by rain and probably makes a contribution to the Knudsen spectrum of ambient noise in the ocean. Experimental results are presented for such freely oscillatingbubbles, mostly entrained by drop impacts, which show that they have the resonance frequencies and damping constants predicted by theory. The presence of the free surface affects these values to a certain extent. The radiation pattern was measured and was shown to be a dipole, as predicted. Calculations of the amplitude of the bubbleoscillation indicate that it is small, confirming that the linear approximation is valid. The spectrum level caused by a rain shower was calculated and compared with field measurements.

Seabed generation of ambient noise
View Description Hide DescriptionAlthough the seabed has not generally been noted as an active originator of underwater sound, it can in some circumstances behave as an acoustic source, and contribute to marine ambient noise conditions. This arises when near‐bed current flow, induced by tides and waves, exerts sufficient shear stress at the bottom boundary to cause the bedload transport of sediments. Interparticle collisions of this mobile material occur and sound is generated by particle impacts. To understand this addition to ambient noise, an examination of this source of sound generation has been conducted in the laboratory and at sea. The laboratory observations were taken using colliding sediments covering size fractions from medium sand to large cobbles. The marine records of ambient noise conditions were obtained over a mobile shingle bed. Comparison of predictions based on rigid body radiation theory with the data has been carried out and similar results obtained.

Acoustic navigation of a large‐aperture array
View Description Hide DescriptionAcoustic travel time measurements were used to navigate the elements of a large‐aperture (900 m) acoustic array. Array navigation system performance was evaluated during a vertical deployment in the northeast Pacific from the Research Platform FLIP. A network of bottom‐moored acoustic transponders were interrogated from FLIP and their 12‐kHz replies were detected by receivers at 75‐m intervals along the array. A nonlinear least‐squares algorithm was used to estimate FLIP and array element positions from the travel time measurements. The FLIP positions derived from this procedure agreed with positions obtained from global positioning system(GPS) satellite navigation to within a 10‐m rms error. Navigated positions for FLIP were internally consistent with a 0.5‐m mean rms error and standard deviation of 1.1 m, and, for an array element, were consistent with a 2.8‐m mean rms error and standard deviation of 0.8 m. The resulting time series of array and FLIP motions were analyzed with respect to wind, tidal, and internal wave forcing functions. Wind and tidal forcing had the greatest influence on FLIP motion, whereas array motion was governed by FLIP movement, tides, and higher frequency sources. Low‐frequency array motion, with periods on the order of hours, was a result of FLIP towing the array over a horizontal range of 300 m in response to the wind and the semidiurnal tidal oscillations; the array remained within a 30‐m horizontal range of FLIP’s position. Higher frequency array motion had apparent internal wave and surface‐coupled components. The array shape was primarily straight and nearly vertical, to within approximately a 2° tilt, responding as a simple pendulum with small displacements.

A subarray approach to matched‐field processing
View Description Hide DescriptionA simplified approach is presented for matched‐field processing of large vertical arrays in typical ocean environments. The large array is divided into subarrays such that a plane‐wave decomposition of the signal field is a good approximation over each subarray. A simple rule, based on the sound‐speed profile, is presented for subarray sizing. Plane‐wave beamforming is then performed to provide multiple beams from each subarray. For long‐range situations, only those beams need to be formed that are steered to receive rays that are not strongly bottom interacting. When elements are spaced at one‐half wavelength, the typical result of considering only these beams is a significant reduction in the size of the problem with far fewer beams required than elements. This first step is very robust and does not require a detailed knowledge of the signal field, or an assumption of signal coherence across the full array aperture. Beam outputs can then be combined to achieve full matched‐field processing. The relative performance of suboptimal approaches such as incoherent combination of beam outputs or simply choosing the best beam is also examined. It is shown that full optimum coherent matched‐field processing in spatially white noise yields an output signal‐to‐noise ratio that depends only on the total signal power intercepted by the aperture, and not on the details of the signal field. For an array that spans the full water column, this can be estimated simply on the basis of cylindrical power flow and falls off as the reciprocal of range. Detailed results are presented for a Pacific winter profile at three widely separated ranges. A small percentage of the beams is found to contain almost all of the signal power. The ray angle diagram (RAD) is used to relate rays, normal modes, and subarray beams, providing insight into the underlying principles. It is shown that the signal field has a fixed number of degrees of freedom and can be represented by that number of beams or normal modes.

Describing small‐scale structure in random media using pulse‐echo ultrasound
View Description Hide DescriptionA method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J. J. Faran, J. Acoust. Soc. Am. 2 3, 405–418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere‐in‐agar and polystyrene sphere‐in‐agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.

Theory of symmetric multilayer structures as layer replacements for Chebyshev acoustic antireflection coatings
View Description Hide DescriptionChebyshev filter theory can be applied to the design of wideband acoustic multilayer antireflection (ar) coatings. However, in many cases the acoustic impedance required for a particular layer is not readily available among common materials. In such cases, this study shows that the Chebyshev layer can be replaced by an acoustic symmetric multilayer (ASM) with the prescribed impedance. On the other hand, ASMs are dispersive, i.e., their reflection properties are a function of frequency. Consequently, the ASM replacement will somewhat degrade the performance of the resulting Chebyshev ar coating. In this study, theoretical results are obtained for a number of ASM replacement designs. For each design, normal‐incidence reflection coefficient versus frequency is calculated. It is concluded that the performance of a Chebyshev ar coating is only slightly degraded by the use of ASM replacements, provided that the ASM dispersion is kept as small as possible. Accordingly, the ASM technique offers a useful means for the practical design of acoustic Chebyshev ar coatings.