Purnima Ratilal

Critical population density triggers rapid formation of vast oceanic fish shoals.

Similarities in the behavior of diverse animal species that form large groups have motivated attempts to establish general principles governing animal group behavior. It has been difficult, however, to make quantitative measurements of the temporal and spatial behavior of extensive animal groups in the wild, such as bird flocks, fish shoals, and locust swarms. By quantifying the formation processes of vast oceanic fish shoals during spawning, we show that (i) a rapid transition from disordered to highly synchronized behavior occurs as population density reaches a critical value; (ii) organized group migration occurs after this transition; and (iii) small sets of leaders significantly influence the actions of much larger groups. Each of these findings confirms general theoretical predictions believed to apply in nature irrespective of animal species.

Long range acoustic imaging of the continental shelf environment: The Acoustic Clutter Reconnaissance Experiment 2001

An active sonar system is used to image wide areas of the continental shelf environment by long-range echo sounding at low frequency. The bistatic system, deployed in the STRATAFORM area south of Long Island in April-May of 2001, imaged a large number of prominent clutter events over ranges spanning tens of kilometers in near real time. Roughly 3000 waveforms were transmitted into the water column. Wide-area acoustic images of the ocean environment were generated in near real time for each transmission. Between roughly 10 to more than 100 discrete and localized scatterers were registered for each image. This amounts to a total of at least 30000 scattering events that could be confused with those from submerged vehicles over the period of the experiment. Bathymetric relief in the STRATAFORM area is extremely benign, with slopes typically less than 0.5 degrees according to high resolution (30 m sampled) bathymetric data. Most of the clutter occurs in regions where the bathymetry is locally level and does not coregister with seafloor features. No statistically significant difference is found in the frequency of occurrence per unit area of repeatable clutter inside versus outside of areas occupied by subsurface river channels.

A unified model for reverberation and submerged object scattering in a stratified ocean waveguide

A unified model for reverberation and submerged target scattering in a stratified medium is developed from wave theory. The advantage of the unified approach is that it enables quantitative predictions to be made of the target-echo-to-reverberation ratio in an ocean waveguide. Analytic expressions are derived for both deterministic and stochastic scattering from the seafloor and subseafloor. Asymptotic techniques are used to derive expressions for the scattering of broadband waveforms from distant objects or surfaces. Expressions are then obtained for the scattered field after beamforming with a horizontal line array. The model is applied to problems of active detection in shallow water. Sample calculations for narrow-band signals indicate that the detection of submerged target echoes above diffuse seafloor reverberation is highly dependent upon water column and sediment stratification as well as array aperture, source, receiver, and target locations, in addition to the scattering properties of the target and seafloor. The model is also applied to determine the conditions necessary for echo returns from discrete geomorphologic features of the seafloor and subseafloor to stand prominently above diffuse seafloor reverberation. This has great relevance to the geologic clutter problem encountered by active sonar systems operating in shallow water, as well as to the remote sensing of underwater geomorphology.

Low-frequency target strength and abundance of shoaling Atlantic herring (Clupea harengus) in the Gulf of Maine during the Ocean Acoustic Waveguide Remote Sensing 2006 Experiment.

The low-frequency target strength of shoaling Atlantic herring (Clupea harengus) in the Gulf of Maine during Autumn 2006 spawning season is estimated from experimental data acquired simultaneously at multiple frequencies in the 300-1200 Hz range using (1) a low-frequency ocean acoustic waveguide remote sensing (OAWRS) system, (2) areal population density calibration with several conventional fish finding sonar (CFFS) systems, and (3) low-frequency transmission loss measurements. The OAWRS systems instantaneous imaging diameter of 100 km and regular updating enabled unaliased monitoring of fish populations over ecosystem scales including shoals of Atlantic herring containing hundreds of millions of individuals, as confirmed by concurrent trawl and CFFS sampling. High spatial-temporal coregistration was found between herring shoals imaged by OAWRS and concurrent CFFS line-transects, which also provided fish depth distributions. The mean scattering cross-section of an individual shoaling herring is found to consistently exhibit a strong, roughly 20 dB/octave roll-off with decreasing frequency in the range of the OAWRS survey over all days of the roughly 2-week experiment, consistent with the steep roll-offs expected for sub-resonance scattering from fish with air-filled swimbladders.

Mean and variance of the forward field propagated through three-dimensional random internal waves in a continental-shelf waveguide

The mean and variance of the acoustic field forward propagated through a stratified ocean waveguide containing three-dimensional (3-D) random internal waves is modeled using an analytic normal mode formulation. The formulation accounts for the accumulated effects of multiple forward scattering. These lead to redistribution of both coherent and incoherent modal energies, including attenuation and dispersion. The inhomogeneous medium’s scatter function density is modeled using the Rayleigh-Born approximation to Green’s theorem to account for random fluctuations in both density and compressibility caused by internal waves. The generalized waveguide extinction theorem is applied to determine attenuation due to scattering from internal wave inhomogeneities. Simulations for typical continental-shelf environments show that when internal wave height exceeds the acoustic wavelength, the acoustic field becomes so randomized that the expected total intensity is dominated by the field variance beyond moderate ranges....

Mean and covariance of the forward field propagated through a stratified ocean waveguide with three-dimensional random inhomogeneities

Compact analytic expressions are derived for the mean, mutual intensity, and spatial covariance of the acoustic field forward propagated though a stratified ocean waveguide containing three-dimensional random surface and volume inhomogeneities. The inhomogeneities need not obey a stationary random process in space, can be of arbitrary composition and size relative to the wavelength, or can have large surface roughness and slope. The form of the mean forward field after multiple scattering through the random waveguide is similar to that of the incident field, except for a complex change in the horizontal wave number of each mode. This change describes attenuation and dispersion induced by the medium’s inhomogeneities, including potential mode coupling along the propagation path. The spatial covariance of the forward field between two receivers includes the accumulated effects of both coherent and incoherent multiple forward scattering through the random waveguide. It is expressed as a sum of modal covariance terms. Each term depends on the medium’s expected modal extinction densities as well as the covariance of its scattering properties, which potentially couple each mode to every other mode. Three-dimensional scattering effects can become important at ranges where the Fresnel width exceeds the cross-range coherence scale of the medium’s inhomogeneities.

Empirical dependence of acoustic transmission scintillation statistics on bandwidth, frequency, and range in New Jersey continental shelf

The scintillation statistics of broadband acoustic transmissions are determined as a function of signal bandwidth B, center frequency f(c), and range with experimental data in the New Jersey continental shelf. The received signal intensity is shown to follow the Gamma distribution implying that the central limit theorem has led to a fully saturated field from independent multimodal propagation contributions. The Gamma distribution depends on the mean intensity and the number of independent statistical fluctuations or coherent cells micro of the received signal. The latter is calculated for the matched filter, the Parseval sum, and the bandpassed center frequency, all of which are standard ocean acoustic receivers. The number of fluctuations mu of the received signal is found to be an order of magnitude smaller than the time-bandwidth product TB of the transmitted signal, and to increase monotonically with relative bandwidth Bfc. A computationally efficient numerical approach is developed to predict the mean intensity and the corresponding broadband transmission loss of a fluctuating, range-dependent ocean waveguide by range and depth averaging the output of a time-harmonic stochastic propagation model. This model enables efficient and accurate estimation of transmission loss over wide areas, which has become essential in wide-area sonar imaging applications.

Effects of multiple scattering, attenuation and dispersion in waveguide sensing of fish

An ocean acoustic waveguide remote sensing system can instantaneously image and continuously monitor fish populations distributed over continental shelf-scale regions. Here it is shown theoretically that the areal population density of fish groups can be estimated from their incoherently averaged broadband matched filtered scattered intensities measured using a waveguide remote sensing system with less than 10% error. A numerical Monte-Carlo model is developed to determine the statistical moments of the scattered returns from a fish group. It uses the parabolic equation to simulate acoustic field propagation in a random range-dependent ocean waveguide. The effects of (1) multiple scattering, (2) attenuation due to scattering, and (3) modal dispersion on fish population density imaging are examined. The model is applied to investigate population density imaging of shoaling Atlantic herring during the 2006 Gulf of Maine Experiment. Multiple scattering, attenuation and dispersion are found to be negligible at the imaging frequencies employed and for the herring densities observed. Coherent multiple scattering effects, such as resonance shifts, which can be significant for small highly dense fish groups on the order of the acoustic wavelength, are found to be negligible for the much larger groups typically imaged with a waveguide remote sensing system.

Validity of the sonar equation and Babinet’s principle for scattering in a stratified medium

The sonar equation rests on the assumption that received sound pressure level after scattering can be written in decibels as a sum of four terms: source level, transmission loss from the source to the target, target strength, and transmission loss from the target to the receiver. This assumption is generally not valid for scattering in a shallow water waveguide and can lead to large errors and inconsistencies in estimating a targets scattering properties as well as its limiting range of detection. By application of coherent waveguide scattering theory, the sonar equation is found to become approximately valid in a shallow water waveguide when the objects complex scatter function is roughly constant over the equivalent horizontal grazing angles +/- delta psi spanned by the dominant waveguide modes. This is approximately true (1) for all objects of spatial extent L and wavelength lambda when 2delta psi<lambda/2L and (2) for spheres and certain other rounded objects in nonforward scatter azimuths, even when (1) does not hold. The sonar equation may be made valid by lowering the active frequency of operation in a waveguide. This is often desirable because it greatly simplifies the analysis necessary for target classification and localization. Similarly, conditions are given for when Babinets principle becomes approximately valid in a shallow water waveguide.

Extinction theorem for object scattering in a stratified medium

A simple relation for the rate at which energy is extinguished from the incident wave of a far field point source by an obstacle of arbitrary size and shape in a stratified medium is derived from wave theory. This relation generalizes the classical extinction theorem, or optical theorem, that was originally derived for plane wave scattering in free space and greatly facilitates extinction calculations by eliminating the need to integrate energy flux about the obstacle. The total extinction is shown to be a linear sum of the extinction of each wave guide mode. Each modal extinction involves a sum over all incident modes that are scattered into the extinguished mode and is expressed in terms of the object’s plane wave scatter function in the forward azimuth and equivalent plane wave amplitudes of the modes. The only assumptions are that multiple scattering between the object and wave guide boundaries is negligible, and the object lies within a constant sound speed layer. Modal extinction cross sections of a...