Volume 103, Issue 1, January 1998
 UNDERWATER SOUND [30]


A note on differential equations of coupledmode propagation in fluids
View Description Hide DescriptionThere is a significant discrepancy between bathymetric contributions to ocean acoustic mode coupling matrix elements derived by various authors. In this paper, the discrepancy is shown to be due to incorrectness of the traditional approach to mode coupling theory, originated by A. D. Pierce [J. Acoust. Soc. Am. 37, 19–27 (1965)] and D. M. Milder [J. Acoust. Soc. Am. 46, 1259–1263 (1969)], in the presence of a sloping interface or a rangedependent rigid boundary. Physically, their approach is consistent with neither energy conservation nor reciprocity. Mathematically, the problem with the traditional approach consists of formal, unjustified, termbyterm differentiation of a series representing the acoustic pressure in terms of local normal modes. The series is poorly convergent when a nonhorizontal interface of fluids with distinct densities is present. A rigorous derivation of the acoustic mode coupling equations in media with piecewise continuous density and sound speed is given here on the basis of the reciprocity principle. Necessary corrections to the results presented recently by B. E. McDonald [J. Acoust. Soc. Am. 100, 219–224 (1996)] are discussed.

Bistatic bottom scattering: Model, experiments, and model/ data comparison
View Description Hide DescriptionA model is presented for bistatic scattering from ocean sediments. It treats scattering due to both roughness of the seabed and volume inhomogeneities within the sediment. Accordingly, the scattered intensity is assumed to be a sum of two terms, one proportional to the roughnessscattering cross section and the other proportional to the volumescattering cross section. The model is tested against data acquired as part of the Coastal Benthic Boundary Layer (CBBL) research program. As part of that program, an autonomous, circularly scanning sonar system was deployed in wellcharacterized regions. This sonar operated at 40 kHz, had a 5° horizontal beam, and acquired backscattering data over a 50m radius. During part of the deployment, it operated in conjunction with a mobile receiving array so as to acquire bistatic data. The experimental apparatus and procedures are presented, and results are compared with model predictions.

Comparison of basinscale acoustic transmissions with rays and further evidence for a structured thermal field in the northeast Pacific
View Description Hide DescriptionFrom May to September of 1987, 250Hz, 16ms resolution acoustic signals were transmitted between four sources and nine receivers in the northeast Pacific. This paper examines the acoustic transmissions across nine of the sections within this group, with path lengths ranging from approximately 1700 to 3300 km. Acoustic multipaths are tracked in the data, and ray theory is successfully used to identify the multipaths, where the spring and summer Levitus’ climatological databases are used to determine the sound speeds. The observed multipaths arrive on the order of 1 s later than the predicted rays. Travel time differences greater than 0.15 s are due to temperature errors in Levitus’ climatology within the ocean’s upper 1 km. The resulting corrections to Levitus’ spring and summer oceans are and respectively. The upper turning depths for all rays are found to vary by less than 50 m from spring to summer. Variations in the measured travel times over the four month period are about 0.5 s. Some sections warm between the spring and summer seasons, while other sections cool. This variability is inconsistent with a temperature field dominated by seasonal effects. The spatial and temporal scales of the heat content are qualitatively similar to those found from other basinscale acoustic sections in the northeast Pacific [J. L. Spiesberger et al., J. Acoust. Soc. Am. 92, 384–396 (1992)].

Single mode excitation, attenuation, and backscatter in shallow water
View Description Hide DescriptionIn shallow water, bottom interaction may have a negative effect on the performance of active sonars. In this paper it is shown that a vertical array of weighted sources driven in an appropriate frequency band can be used to minimize the deleterious effects of bottom interaction, i.e., attenuation and backscatter. Simulation results (based on twodimensional cw field calculations) are presented for three canonical geoacoustic models using both a winter and summer sound speed profile. It is shown through selective excitation of only mode one there exists a favorable frequency band providing both minimum attenuation and bottom generated backscatter.

The effect of temperature, pressure, and salinity on sound attenuation in turbid seawater
View Description Hide DescriptionThe acoustic attenuation coefficient in shallow coastal waters is of interest to designers and operators of devices such as naval minehunting sonars, sidescan surveying sonars, and acoustic Dopplercurrent profilers, typically employing frequencies ranging from tens of kHz to several hundred kHz, possibly up to 1 MHz. At these frequencies attenuation due to suspended particulate matter which characterizes turbid coastal waters is an important contribution to the total attenuation coefficient. In this paper the effect of temperature, pressure, and salinity on the total attenuation coefficient for seawater containing a suspension of solid particles is investigated by employing suitable expressions for the sound speed, density, and viscosity of seawater as functions of temperature, salinity, and pressure. Results presented demonstrate that while there is little variation in the attenuation with pressure in up to a few hundred meters of water, there is significant variation with temperature and salinity over the ranges found globally in the sea.

Pilot experiment for the acquisition of marine sediment properties via small scale tomography system
View Description Hide DescriptionA 3D high resolution crosswell acoustic tomography system was designed and tested in a shallow water environment. This system makes use of a damped leastsquared inversion technique and is used to construct compressional wavevelocity images from measured travel time data. Use of singular value decomposition allowed checks of the linear inversion confirming the validity of the modeled environment. It is shown that when the ratio of width to depth of the cross section is about unity or smaller and the domain has not been overparametrized the inverted image model has sufficiently good figures of merit in resolution and variance to visualize small variations in the magnitude compressional velocity field.

Sound scattering by several zooplankton groups. I. Experimental determination of dominant scattering mechanisms
View Description Hide DescriptionThe acoustic scatteringproperties of live individual zooplankton from several gross anatomical groups have been investigated. The groups involve (1) euphausiids (Meganyctiphanes norvegica) whose bodies behave acoustically as a fluid material, (2) gastropods (Limacina retroversa) whose bodies include a hard elastic shell, and (3) siphonophores (Agalma okeni or elegans and Nanomia cara) whose bodies contain a gas inclusion (pneumatophore). The animals were collected from ocean waters off New England (Slope Water, Georges Bank, and the Gulf of Maine). The scatteringproperties were measured over parts or all of the frequency range 50 kHz to 1 MHz in a laboratorystyle pulseecho setup in a large tank at sea using live fresh specimens. Individual echoes as well as averages and pingtoping fluctuations of repeated echoes were studied. The material type of each group is shown to strongly affect both the overall echo level and pattern of the target strength versus frequency plots. In this first article of a twopart series, the dominant scattering mechanisms of the three animal types are determined principally by examining the structure of both the frequency spectra of individual broadband echoes and the compressed pulse (time series) output. Other information is also used involving the effect on overall levels due to (1) animal orientation and (2) tissue in animals having a gas inclusion (siphonophores). The results of this first paper show that (1) the euphausiids behave as weakly scattering fluid bodies and there are major contributions from at least two parts of the body to the echo (the number of contributions depends upon angle of orientation and shape), (2) the gastropods produce echoes from the front interface and possibly from a slowtraveling circumferential (Lamb) wave, and (3) the gas inclusion of the siphonophore dominates the echoes, but the tissue plays a role in the scattering and is especially important when analyzing echoes from individual animals on a pingbyping basis. The results of this paper serve as the basis for the development of acoustic scatteringmodels in the companion paper [Stanton et al., J. Acoust. Soc. Am. 103, 236–253 (1998)].

Sound scattering by several zooplankton groups. II. Scattering models
View Description Hide DescriptionMathematical 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, modalseries 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 DWBAbased formulation which could predict echo levels over all angles of incidence (including the difficult region of endon 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 gasbearing animals (siphonophores) is a hybrid model which is composed of the summation of the exact solution to the gas sphere and the approximate DWBAbased formulation for arbitrarily shaped fluidlike bodies. There is also a simplified raybased model for the siphonophore. The models are applied to data involving single pings, pingtoping 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.

Differences between sound scattering by weakly scattering spheres and finitelength cylinders with applications to sound scattering by zooplankton
View Description Hide DescriptionA modeling study was conducted to determine the conditions under which fluidlike zooplankton of the same volume but different shapes (spherical/cylindrical) have similar or dramatically different scatteringproperties.Models of sound scattering by weakly scattering spheres and cylinders of finite length used in this analysis were either taken from other papers or derived and herein adapted for direct comparison over a range of conditions. The models were examined in the very low ( ), moderately low ( ), and highfrequency regions ( ), where is the acoustic wave number, is the radius (spherical or cylindrical) of the body, and is the length of the cylinders (for an elongated body with “moderately low” corresponds to the range ). Straight and bent cylinder models were evaluated for broadside incidence, endon incidence, and averages over various distributions of angle of orientation. The results show that for very low frequencies and for certain distributions of orientation angles at high frequencies, the averaged scattering by cylinders will be similar, if not identical, to the scattering by spheres of the same volume. Other orientation distributions of the cylinders at high frequencies produce markedly different results. Furthermore, over a wide range of orientation distributions the scattering by spheres is dramatically different from that of the cylinders in the moderately lowfrequency region and in the Rayleigh/geometric transition region: (1) the Rayleigh to geometric scattering turning point occurs at different points for the two cases when the bodies are constrained to have the same volume and (2) the functional dependence of the scattering levels upon the volume of the bodies in the moderately lowfrequency region is quite often different between the spheres and cylinders because of the fact that the scattering by the cylinders is still directional in this region. The study demonstrates that there are indeed conditions under which different shaped zooplankton of the same volume will yield similar (ensemble average) scattering levels, but generally the shape and orientation distribution of the elongated bodies must be taken into account for accurate predictions.

Double monopole resonance of a gasfilled, spherical cavity in a sediment
View Description Hide DescriptionThe monopole response of a gasfilled, spherical cavity in a sediment is investigated. The sediment is either a fluid, elasticsolid, or saturated poroelastic medium. The present method entails the scattering of an incident displacement field that preferentially excites the monopole resonance of the cavity. The main result demonstrates that a gasfilled, spherical cavity in a saturated poroelastic medium can exhibit two distinct monopole resonances. These resonances arise from the two distinct longitudinal modes of propagation in saturated poroelastic medium as described by Biot’s theory.

Nearfield scattering through and from a twodimensional fluid–fluid rough interface
View Description Hide DescriptionA general analytical expression for the timedependent meansquare incoherent field scattered from or through (penetrating) a 2D fluid–fluid rough interface for a narrowband incident planewave source is derived and expressed in terms of the second moment of the rough interfacematrix. This analytical expression is independent of the scattering solution technique, and for distances greater than only a few wavelengths from the interface, is equivalently expressed in terms of the bistatic scattering cross section per unit area per unit solid angle (differential cross section) of the rough interface. Using this rigorously derived result, the scattered field for a narrowband point source is heuristically derived. This derivation leads to the usual sonar equation in the limit as the narrowband signal approaches the cw (continuous wave) case. Firstorder perturbation calculations for the case of a baseband Gaussian shaped source pulse illustrate narrowband pulse dispersion effects of the incoherent field for forward scattering into a lossy sediment. For the case of incidence below the critical grazing angle, firstorder perturbation computations also show that the incoherent field scattered through a rough interface can be much greater than the zerothorder field (coherent) transmitted below the corresponding flatsurface depending on loss and receiver depth. These computations for the firstorder mean square incoherent field penetrating the rough interface are compared to the results for the flatsurface case, for both planewave and point sources.

Theory of compressional and shear waves in fluidlike marine sediments
View Description Hide DescriptionAn unconsolidated, saturated marine sediment consists of a more or less loose assemblage of mineral grains in contact, with seawater in the interstices. It is postulated that the twophase medium possesses no skeletal frame, implying that the elastic rigidity modulus of the material is zero. A theory of wave propagation in such a sediment is developed, in which the medium is treated as a fluid that supports a specific form of intergranular dissipation. Two important equations emerge from the analysis, one for compressional wave propagation and the second describing transverse disturbances. For the type of dissipation considered, which exhibits hysteresis or memory, the shear equation admits a wavelike solution, and is thus a genuine wave equation, even though the sediment shows no elastic rigidity. In effect, the medium possesses a “dissipative” rigidity, which is capable of supporting shear. This behavior is distinct from that of a viscous fluid, for which the shear equation is diffusionlike in character, giving rise to critically damped disturbances rather than propagating waves. The new theory predicts an attenuation coefficient for both compressional and shear waves that scales with the first power of frequency, in accord with published data. The wavetheory is combined with a model of the mechanical properties of marine sediments to yield expressions relating the compressional and shear wave speeds to the grain size, the porosity, and the density of the medium. These expressions show compelling agreement with a number of measurements from the literature, representing a variety of sediment types ranging from clay to coarse sand.

Sound radiation by various types of laboratory breaking waves in fresh and salt water
View Description Hide DescriptionA recent article [A. R. Kolaini and L. A. Crum, J. Acoust. Soc. Am. 96, 1755–1765 (1994)] reported the measurements of the ambient sound generated by laboratory breaking waves over the range 100–20 000 Hz in fresh water. Those observations from both spilling and plungingtype breakers have been repeated in the same manner and wavemaker/anechoic tank with water that had 25‰ salt in its content. The observations in salt water, just like those in fresh water, reveal that the sources of sound in laboratory spilling breakers are due primarily to single bubble oscillations that can have frequencies lower than a few hundred Hertz. In the case of weak spilling breakers, the sound spectra level in fresh water was due primarily to single bubble oscillation, while the same breakers in salt water have introduced smaller size bubbles with large density. The relatively highdensity populated bubble cloud generated by weak breakers shows the evidence of the onset of collective oscillation that was absent for the same breakers in the fresh water. In the case of moderate spilling and plunging breakers, it appears that both individual bubbles and bubble clouds can contribute to the acoustic emissions in fresh and salt water. The average sound spectra reveal that the peak frequencies of the spectra shift from a few kHz (weak, spilling breaker) to few hundred Hz (plunging breaker), and the highfrequency portions have slopes approximately 5–6 dB/oct, which are the slopes observed from the noise spectra of the ocean. Besides the high bubble density and smaller bubble sizes in salt water, all breakers experienced a significant increase in soundpressure level in all observed frequency range. The ionic structure of the medium alters the sound radiation from bubbles. In this paper some of the observed acoustic signatures from breaking waves are discussed and a plausible explanation of how salt can effect the sound radiation from bubbles is given.

From geology to geoacoustics—Evaluation of Biot–Stoll sound speed and attenuation for shallow water acoustics
View Description Hide DescriptionA procedure for estimating acoustic wave velocity and attenuation in ocean sediment using a minimum amount of geological and geotechnical data is demonstrated. First, the Biot–Stoll theory is presented. Next, various asymptotic formulae for the attenuation coefficient are derived for high, low, and intermediate frequencies. These expressions clearly isolate the effects of intergranular Coulomb friction and fluid viscous dissipation on the attenuation of shear and compressional waves. Under the constraint of a minimum amount of geological and geotechnical information, a sequence of empirical equations is compiled to convert basic data, such as blow count number from a Standard Penetration Test or shipboard density, into sediment geoacoustic properties. As a demonstration, two wellknown field cases, the Atlantic Generating Station (AGS) site and the Atlantic Margin Coring (AMCOR 6010) site, are examined. By incorporating the uncertainty involved in the data collection, the estimated geoacoustical parameters are provided with a standard deviation.

Separation of current and sound speed in the effective refractive index for a turbulent environment using reciprocal acoustic transmission
View Description Hide DescriptionHere a highfrequency acoustic experiment through a turbulent flow in Cordova Channel is described which is specifically designed to measure the contribution of scalar and vector fluctuations to the total scattered signal over a 48h period. The effective refractive indexfluctuations are determined by both the random changes in sound speed (scalars) and the random motion of the medium (vectors), and so in this paper it is demonstrated that reciprocal acoustic transmission is a technique which unambiguously separates their effects. The effective refractive index structure parameter, is defined as the sum of scalar and vector contributions through the equation The effective refractive index structure parameter is also measured from the forward propagation acoustical scintillation variances, thus providing an independent check on the interpretation.

Predicted scattering of sound by diffuse hydrothermal vent plumes at midocean ridges
View Description Hide DescriptionAmplitude and phase fluctuations of monochromatic acoustic signals traveling through diffuse midocean ridge hydrothermal vent plumes are modeled using existing theory in an attempt to find suitable frequencies and path lengths for plume monitoring. Weakscattering solutions are evaluated numerically, with model parameters adjusted to match observed plume characteristics. Constraints required for weakscattering solutions to be valid can be met for transmission ranges of 500–2000 m and frequencies of 20–80 kHz. Therefore, because fluid structure and scattering strength are more closely linked for weak scattering than for stronger scattering, inversion for fluid statistical properties may be possible, enabling diffuse vent monitoring. Such monitoring would be subject to geometric assumptions such as transmission entirely within a statistically homogeneous plume. Performancelimiting phase fluctuations have also been computed for a 13–17 kHz geodetic survey system.

Scattering from elastic sea beds: Firstorder theory
View Description Hide DescriptionA perturbation model for highfrequency sound scattering from an irregular elastic sea bed is considered. The sea bed is assumed homogeneous on the average and two kinds of irregularities are assumed to cause scattering: roughness of the water–sea bed interface and volume inhomogeneities of the sediment mass density and the speeds of compressional and shear waves. The firstorder small perturbation approximation is used to obtain expressions for the scattering amplitude and bistatic scattering strength. The angular dependence of the scattering strength is calculated for sedimentary rock and the influence of shear elasticity is examined by comparison with the case of a fluid bottom. Shear effects are shown to be strong and complicated.

Effects of shear elasticity on sea bed scattering: Numerical examples
View Description Hide DescriptionIt is known that marine sediments can support both compressional and shear waves. However, published work on scattering from irregular elastic media has not examined the influence of shear on sea bed scattering in detail. A perturbation model previously developed by the authors for joint roughnessvolume scattering is used to study the effects of elasticity for three sea bed types: sedimentary rock, sand with high shear speed, and sand with “normal” shear wave speed. Both bistatic and monostatic cases are considered. For sedimentary rock it is found that shear elasticity tends to increase the importance of volume scattering and decrease the importance of roughness scattering relative to the fluid case. Shear effects are shown to be small for sands.

Wideband optimal a posteriori probability source localization in an uncertain shallow ocean environment
View Description Hide DescriptionA wideband extension of the Optimum Uncertain Field Processor (OUFP) is presented. Combined with Monte Carlo estimation methods, this processor provides a fast, efficient, and robust technique for MatchedField Processing (MFP). Under a simulated Hudson Canyon environment, a quantitative, probabilistic analysis of the sensitivity of the Optimum MatchedField Processor (OMFP) to various kinds of environmental mismatch is shown. Similarly, the performance of the OUFP is calculated. Finally, the optimum wideband OUFP is applied to a data set collected from the Hudson Canyon, the results tabulated, and then compared to a standard Bartlett processor. The performance of the optimum wideband OUFP and the suboptimum Bartlett processor are in very good agreement with the performance predicted from simulation results.

Tracking and localizing a moving source in an uncertain shallow water environment
View Description Hide DescriptionAn optimal approach to tracking a moving source in the presence of environmental variability is presented. This tracking algorithm, called the optimum uncertain field tracking algorithm (OUFTA), incorporates a model for the source motion as well as the uncertain ocean environment. The performance of the OUFTA is evaluated over a range of signaltonoise ratios (SNRs) as a function of the number of observations by examining its ability to correctly estimate both the current source position and the entire source track. The improvement in performance provided by the OUFTA is illustrated by comparison to two suboptimal tracking algorithms. Results show that incorporating a priori knowledge of both the source dynamics and the oceanmodel provides the most accurate estimates of the source track.
