The coherence length of a horizontal array is the maximum separation between two points where coherent processing gives useful gain when a distant source is at broadside. In shallow water, the coherence length is limited by the environmental variability caused by several relevant oceanographic processes. In the present study, a statistical model is developed that quantifies how one oceanographic process, linear internal waves, affects the coherence length. A key input to the ocean sub-model is the vertically integrated energy density of the internal wave field. The acoustic sub-model is based on the adiabatic normal mode approximation and so should be reasonable for frequencies under 1 kHz. Numerical calculations using environmental data from the Shallow Water 2006 Experiment (SW06) show how the coherence length of individual modes varies with consequent effects on array coherence. The coherence length is shown to be a strong function of where the source and array are positioned in the water column. For a bottom-mounted array above a moderately lossy seabed, the model predicts a coherence length that depends only weakly on range, an effect observed in field experiments.

Synthetic time reversal (STR) is a technique for blind deconvolution in an unknown multipath environment that relies on generic features (rays or modes) of multipath sound propagation. This paper describes how ray-based STR signal estimates may be improved and how ray-based STR sound-channel impulse-response estimates may be exploited for approximate source localization in underwater environments. Findings are based on simulations and underwater experiments involving source-array ranges from 100 m to 1 km in 60-m-deep water and chirp signals with a bandwidth of 1.5–4.0 kHz. Signal estimation performance is quantified by the correlation coefficient between the source-broadcast and the STR-estimated signals for a variable number N of array elements, 2 ≤ N ≤ 32, and a range of signal-to-noise ratio (SNR), ~5 dB ≤ SNR ≤ 30 dB. At high SNR, STR-estimated signals are found to have cross-correlation coefficients of ~90% with as few as four array elements, and similar performance may be achieved at a SNR of nearly 0 dB with 32 array elements. When the broadband STR-estimated impulse response is used for source localization via a simple ray-based backpropagation scheme, the results are less ambiguous than those obtained from conventional broadband matched field processing.

The waveguide invariant summarizes the pattern of constructive and destructive interference between acoustic modes propagating in the ocean waveguide. For many sonar signal-processing schemes, it is essential to know the correct numerical value for the waveguide invariant. While conventional beamforming can estimate the ratio between the waveguide invariant and the range to the source, it cannot unambiguously separate the two terms. In the present work, striation-based beamforming is developed. It is shown that the striation-based beamformer can be used to produce an estimate for the waveguide invariant that is independent of the range. Simulation results are presented.

Unlike in radio communications, there is no standard statistical model for the channel impulse response in underwater acoustic communications. To compare the performance of different communications strategies requires data collected under common environmental conditions. In the present paper, a data-driven simulator is developed for comparing single- and multicarrier communications algorithms. Models for the time-varying channel impulse response over a particular bandwidth are first constructed using archival experimental data. The models are then driven with novel communications sequences of lesser bandwidth. The output is synthetic received data that can then be demodulated to evaluate communications performance. By applying reciprocity to the single-input, multiple-output archival data, both multiple receive arrays and multiple transmit arrays can be simulated. Communications performance for the synthetic data is compared to actual experimental results.

Reflection off the rough sea surface typically introduces time spread in an acoustic signal. The details of channel response and hence the time spread will change as the sea surface evolves. Communications signals that are spread by the rough surface may still be recompressed and demodulated successfully by an equalizer providing that the channel response does not change too rapidly. To aid in designing an equalizer, it would be useful to know which acoustic paths should be treated as useful signal and which must be treated as noise because they change too rapidly. Viewed as a rough surface scattering problem, the classic Kirchhoff approximation should be appropriate for modeling reflected communications signals. Textbook descriptions of the Kirchhoff approximation are not promising, however, as they imply that the calculations depend on the details of the surface wave spectrum. In the present work, simplified expressions for the surface reflected communications signals are derived. The simplified results are tested in two ways: Predictions for the mutual coherence function are compared to numerically intense calculations, and predictions for communications performance are compared to experimental results.

Artificial time reversal (ATR) is a technique for blind deconvolution in an unknown multipath environment that relies on generic features of underwater sound propagation. Ray-based ATR uses a beam-former-determined reference-ray arrival direction to construct a frequency-dependent phase correction at the receiving array that allows the source-to-array impulse response of the sound channel and the original source waveform to be separately estimated. Although absolute timing and amplitude information is not recovered by ATR, the relative arrival timing of the various signal propagation paths can be determined from the temporal spacing of peaks in the ATR-determined impulse response. With this relative timing information, elementary source localization may be possible when some environmental information is available at the array, and ray-path arrivals can be separated by beamforming at the array. This presentation describes results from underwater experiments involving source-array ranges of 100-500 m in 60-m-deep water and 50-ms chirp signals with a bandwidth of 1.5 - 4.0 kHz. The ATR-based localization results are found to be comparable with those from coherent and incoherent Bartlett matched field processing.

The effect on the ambient noise level in shallow water of the ocean growing more acidic is modeled. Because most noise sources are near the surface, high-order acoustic modes are preferentially excited. Linear internal waves, however, can scatter the noise into the low-order, low-loss modes most affected by the changes in acidity. The model uses transport theory to couple the modes and assumes an isotropic distribution for the noise sources. For a scenario typical of the East China Sea, the noise at 3 kHz is predicted to increase by 30%, about one decibel, as the pH decreases from 8.0 to 7.4.

Nonlinear internal waves are a common event on the continental shelf. The waves depress the high-gradient region of the thermocline and thicken the surface mixed layer with consequent effect on acoustic propagation. After the waves have passed, it may take several hours for the thermocline to rise to its prewave level.

To examine the effect of the rising thermocline, oceanographic and acoustic data collected during the 2006 Shallow Water Experiment (SW06) are analyzed. Midfrequency acoustic data (1.5-10.5 kHz) taken for several hours at both fixed range (550 m) and along a tow track (0.1-8.1 km) are studied. At the fixed range, the rising thermocline is shown to increase acoustic intensity by approximately 5 dB. Along the tow track, the transmission loss changes 2 dB for a source-receiver pair that straddles the thermocline. Using oceanographic moorings up to 2.2 km away from the acoustic receiver, a model for the rising thermocline is developed. This ocean model is used as input to a broadband acoustic model. Results from the combined model are shown to be in good agreement with experimental observation. The effects on acoustic signals are shown to be observable, significant, and predictable.

Waveguide invariant theory is applied to horizontal line array (HLA) beamformer output to localize moving broadband noise sources from measured acoustic intensity striation patterns. Acoustic signals emitted by ships of opportunity (merchant ships) were simultaneously recorded on a HLA and three hydrophones separated by 10 km during the RAGS03 (relationship between array gain and shelf-break fluid processes) experiment. Hough transforms are used to estimate both the waveguide invariant parameter "beta" and the ratio of source range at the closest point of approach to source speed from the observed striation patterns. Broadband (50–150-Hz) acoustic data-sets are used to demonstrate source localization capability as well as inversion capability of waveguide invariant parameter beta. Special attention is paid to bathymetric variability since the acoustic intensity striation patterns seem to be influenced by range-dependent bathymetry of the experimental area. The Hough transform method is also applied to the HLA beam-time record data and to the acoustic intensity data from three distant receivers to validate the estimation results from HLA beamformer output. Good agreement of the results from all three approaches suggests the feasibility of locating broadband noise sources and estimating waveguide invariant parameter beta in shallow waters.

The performance of a communications equalizer is quantified in terms of the number of acoustic paths that are treated as usable signal. The analysis uses acoustical and oceanographic data collected off the Hawaiian Island of Kauai. Communication signals were measured on an eight-element vertical array at two different ranges, 1 and 2 km, and processed using an equalizer based on passive time-reversal signal processing. By estimating the Rayleigh parameter, it is shown that all paths reflected by the sea surface at both ranges undergo incoherent scattering. It is demonstrated that some of these incoherently scattered paths are still useful for coherent communications. At range of 1 km, optimal communications performance is achieved when six acoustic paths are retained and all paths with more than one reflection off the sea surface are rejected. Consistent with a model that ignores loss from near-surface bubbles, the performance improves by approximately 1.8 dB when increasing the number of retained paths from four to six. The four-path results though are more stable and require less frequent channel estimation. At range of 2 km, ray refraction is observed and communications performance is optimal when some paths with two sea-surface reflections are retained.

In "sound transmission through a fluctuating ocean," Flattxe et al. described saturation of a single acoustic path as that path becoming a number of interfering uncorrelated micropaths due to refraction by internal waves. The probability density function of intensity becomes exponential with a scintillation index of 1.0. In deep water, however, full saturation is not achieved due to weak scattering and absorption.

Mid-frequency (1–10 kHz) data from the Shallow Water 2006 Experiment are used to determine single-path intensity statistics. At a range of 1 km in water 80 m deep, an acoustic path is isolated that went through two upper turning points separated by a single bottom reflection. The data were collected during a period when large nonlinear internal waves were absent. The scintillation index calculated from the data increases with frequency until reaching a maximum of 1.2 around 6 kHz. It then decreases to 1.0, suggesting that single-path saturation can be achieved at mid-frequencies in shallow water. The probability density functions of intensity at various frequencies show a trend toward exponential. Because shallow water internal waves are dominated by the first mode, uncorrelated micropaths are an unlikely mechanism for producing the observed saturation.

The forward scattering of sound by a moving inhomogeneity can be observed when the inhomogeneity intersects a stationary path between an acoustic source and a receiving array. The scattered field is modeled as a weak perturbation of the direct signal when the inhomogeneity is near the direct path. Often the scattered field is masked by fluctuations in the direct signal. The task of a detection and parameter estimation of a moving inhomogeneity by the processing of acoustic signals as received on linear arrays is considered. After a review of methods, new experimental results are presented. The experiment was performed in the Bierke-Soond Strait of the Baltic in August 2006. The experiment geometry, propagation conditions, and spectra of direct signal fluctuations are discussed. Examples of experimental forward scattering observations obtained via various array-processing techniques are given. Good agreement between parameter estimates and true values is demonstrated for the intersection instant and the inhomgeneity's velocity, length and cross-sectional area. The minimum size of an inhomogeneity that can be observed is obtained.

The sonar simulation toolset (SST) is a ray-based propagation model capable of generating time series realizations with stochastic spreading of acoustic sequences. The model supports varying environments and geometries including moving sources and/or receivers. The simulated data were compared with experimental data collected at the Pacific Missile Range Facility, Kauai, Hawaii in 2003 (KauaiEx2003) and 2008 (KAM08). Models generated with appropriate sound speed profiles and wind speeds are shown to have similar channel impulse response functions to those observed during the experiments. The high-frequency communications sequences simulated from those models have been demodulated to demonstrate analogous results. These results suggest that underwater acoustic communications and networking can be effectively simulated with sonar simulation toolset to aid in experiment planning and data analysis.

A multistatic active sonar system with several widely distributed sensors must share information between the sensors. If acoustic communication is the means used to share information, it can consume a significant fraction of the system's total energy budget. In this communication, an energy consumption model is developed for a shallow-water acoustic communications network. The model includes the environmental factors like the sound-speed profile in the water column and the composition of the seabed. The model uses the waveguide invariant concept to incorporate efficiently the broadband nature of the communications signals. Numerical results demonstrate how relaying messages between intermediate sensors can save substantial energy compared to direct communications. The calculations also show that energy consumption can vary by more than an order of magnitude depending on the seabed composition.

The scintillation index and the intensity cumulative distribution function of mid-frequency (2–10 kHz) sound propagation are presented at ranges of 1–9 km in a shallow water channel. The fluctuations are due to water column sound speed variability. It is found that intensity is only correlated over a narrow frequency band (50–200 Hz) and the bandwidth is independent of center frequency and range. Furthermore, the intensity probability distribution peaks at zero for all frequencies, and follows an exponential distribution at small values.

Mid-frequency (1–10 kHz) sound propagation was measured at ranges 1–9 km in shallow water in order to investigate intensity statistics. Warm water near the bottom results in a sound speed minimum. Environmental measurements include sediment sound speed and water sound speed and density from a towed conductivity-temperature-depth chain. Ambient internal waves contribute to acoustic fluctuations. A simple model involving modes with random phases predicts the mean transmission loss to within a few dB. Quantitative ray theory fails due to near axial focusing. Fluctuations of the intensity field are dominated by water column variability.

Preliminary results are presented from an analysis of mid-frequency acoustic transmission data collected at range 550 m during the Shallow Water 2006 Experiment. The acoustic data were collected on a vertical array immediately before, during, and after the passage of a nonlinear internal wave on 18 August, 2006. Using oceanographic data collected at a nearby location, a plane-wave model for the nonlinear internal wave's position as a function of time is developed. Experimental results show a new acoustic path is generated as the internal wave passes above the acoustic source.

As part of the ONR-sponsored SW06 experiment, mid-frequency sound propagation was measured at ranges 1–10 km in the frequency band of 2–10 kHz in August, 2006. The water depth is 80 m and the source depth is 30 m, close to the minimum of a duct with a thermocline above and a warm salty water below. The receivers are clustered into two groups, one at 25 m depth, the other at 50 m. The region has active internal wave activity during this time. Because the source is near the axis of the sound channel, it is observed that propagation is dominated by trapped modes and behaves similar to sound propagation in a deep water duct. Amplitude fluctuations and cross-frequency correlations are estimated. The scintillation index as a function of frequency and bandwidth is calculated.

Active sonar systems can provide good target detection potential but are limited in shallow water environments by the high level of reverberation produced by the interaction between the acoustic signal and the ocean bottom. The nature of the reverberation is highly variable and depends critically on the ocean and seabed properties, which are typically poorly known. This has motivated interest in techniques that are invariant to the environment. In passive sonar, a scalar parameter termed the waveguide invariant, has been introduced to describe the slope of striations observed in lofargrams. In this work, an invariant for active sonar is introduced. This active invariant is shown to be present in the time–frequency structure observed in sonar data from the Malta Plateau, and the structure agrees with results produced from normal mode simulations. The application of this feature in active tracking algorithms is discussed.

A multistatic active sonar system with several widely distributed sensors must share information between the sensors. Acoustic communication is a viable method to share information and is particularly appropriate when the sensors are mobile. A potential drawback is that a significant fraction of the total energy budget for the system might be consumed just by sending information between the sensors. In the present work, an energy consumption model is developed that is appropriate for incoherent acoustic communication in shallow water. The model builds upon the foundation established by Sozer et al. [IEEE J. Oceanic Eng. 25, 72–83 (2000)], but uses an improved sub-model for acoustic propagation. The sub-model includes environmental factors like the sound speed profile in the water column and the composition of the seabed. By exploiting the waveguide invariant concept, the broadband nature of the communications signals can be included efficiently in the calculation. Numerical results demonstrate how relaying messages between intermediate sensors can save substantial energy compared to direct communications. The calculations also show that energy consumption can vary by more than an order of magnitude depending on the seabed composition.

In this paper, we address the problem of detecting an inhomogeneity in shallow water by observing changes in the acoustic field as the inhomogeneity passes between an acoustic source and vertical line array of receivers. A signal processing scheme is developed to detect the perturbed field in the presence of the much stronger primary source signal, and to estimate such parameters as the time when the inhomogeneity crosses the source-receiver path, its velocity, and its size. The effectiveness of incoherent, coherent, and partially coherent spatial processing of the array signals is evaluated using models and data obtained from experiments in a lake. The effect of different bottom types is also considered, and it is shown that partially coherent processing can have a significant advantage depending on the bottom type. Estimates of the minimum input signal-to-noise ratios (SNRs) for which the diffracted signal can be observed are presented.

Variability of physical ocean parameters can cause significant fluctuations of acoustic propagation in shallow water. In the Kauai experiment (KauaiEx) conducted during June-July 2003, extensive acoustic measurements along with various environmental measurements were made using a variety of vertical line arrays and a bottom mounted sound source in a 100-m shallow water region near the Kauai Island, Hawaii. In this paper, acoustic signals recorded on three autonomous receiving arrays are studied against the measured environmental parameters. It is shown that high frequency acoustic propagation is affected by the temporal and spatial changes in the water column and the sea surface. It is also shown that the ocean variability impacts different arrival rays depending on their travel paths.

The performance of a coherent acoustic communication algorithm is quantified using data collected off the Hawaiian island of Kauai. Performance is related to physics of acoustic propagation in shallow water. For data collected at range 1 km, performance is limited by the reflection of acoustic paths off of the sea surface. At range 2 km, the effects of acoustic ray refraction become apparent.

Data collected from the Kauai experiment (KauaiEx) shows that the fluctuations of the ocean environment can cause significant variations of the acoustic signals propagating in the shallow water regions. The power level of the arrivals that do not interact with the sea surface is mainly affected by the variability of the ocean water column. The power level of the arrivals that interact with the sea surface, especially those interacting with the sea surface multiple times, is mainly affected by the sea surface condition. Therefore, the signal to interference plus noise ratio (SINR) varies in a way related to the fluctuations of the physical ocean parameters, mainly the water temperature profile and the sea surface condition. Such SINR variations might be significant for certain source/receiver geometries. The ocean variability has impact on SINR and, therefore, on the performance of the coherent underwater acoustic communications (UAC) receiver, as demonstrated by the collected binary experiment.

Undersea noise was collected on a vertical array affected by ocean currents and internal waves. Such fluctuations are known to negatively affect the accuracy of the inferred bottom loss over grazing angles. However, bottom loss is just an intermediate parameter to sonar performance predictions. The bottom loss at the dominant incident angles on the ocean floor is of most importance to the prediction of sound transmission. Therefore, the focus of attention should be on the effect of waveguide dynamics on the predicted acoustic propagation using the estimated bottom loss. Simultaneous transmission loss measurements are compared against predictions from several snapshots of collected element-level wind-driven noise to determine the bias and statistical moments associated with the in situ sonar performance estimations across frequency and range. In addition, dominant mode rejection will be applied on a subset of the data that is influenced by nearby ship interference to examine its impact on the robustness of this approach to passive environmental assessment.

The vertical directivity pattern of the ambient noise field observed in shallow water is typically anisotropic with a trough in the horizontal. This trough, often called the ambient noise notch, develops because downward refraction steepens all rays emanating from near the sea surface. Variability in the environment has the potential to redistribute the noise into shallower angles and thereby fill the notch. In the present work, a model for the width and depth of the ambient noise notch is developed. Transport theory for acoustic propagation is combined with a shallow water internal wave model to predict the average output of a beamformer. Ambient noise data from the East China Sea are analyzed in the 1-to-5-kHz band. Good agreement between the model and the data for both the width and depth of the ambient noise notch is obtained at multiple frequencies, suggesting that internal wave effects are significant.

Time spread due to the multipaths in an underwater acoustic channel induces inter symbol interference (ISI) which increases the bit error rate (BER) in underwater acoustic communications. The time reversal or phase conjugation process has been adopted to reduce the ISI due to multipath time spread. However, a recent study on passive time reversal process (PTRP) underwater acoustic communication has shown that the BER depends on the relative drift rate between the transmitter and the receiver. In this study, the BER is qualified as a function of transmitter movement distance.

The extended Jones formulation is used to investigate propagation at nonnormal incidence through two- and three-layer systems of birefringent material in which the optic axes of the individual layers are in the plane of the layers. Such systems are equivalent to two optical elements in series--an equivalent retardation plate and a polarization rotator. Analytical solutions are obtained for the equivalent retardation and rotation. The major finding is that, in general, there are two nonnormal incidence directions for which the retardation vanishes; therefore these two directions are optic axes of the composite system. These simple layered systems therefore behave in a manner similar to biaxial crystals. Moreover, the results illustrate the fact that even if the optic axes of individual layers in composite systems are in the plane of the layers, the optic axes of the system are, in general, out of this plane.

Coherent underwater communication is hampered by the time spread inherent to acoustic propagation in the ocean. Because time-reversal signal processing produces pulse compression, communications has been suggested as a natural application of the technique. Passive versions of time-reversal processing use a receive-only array to do combined temporal and spatial matched filtering. It can be shown, however, that the pulse compression it achieves is not perfect and that an equalizer that relies solely on time-reversal processing will have an error floor caused by uncompensated intersymbol interference (ISI). In the present paper, a physics-based model is developed for the uncompensated ISI in a passive time-reversal equalizer. The model makes use of a normal-mode expansion for the acoustic field. The matched-filtering integral is approximated and the intermediate result interpreted using the waveguide invariant. After combining across the array and sampling, formal statistical averages of the soft demodulation output are calculated. The results show how performance scales with bandwidth, with the number and position of array elements, and with the length of the finite impulse response matched filters. Good agreement is obtained between the predicted scaling and that observed in field experiments.

Coherent underwater communication is hampered by the time spread inherent to acoustic propagation in the ocean. Because time-reversal signal processing produces pulse compression, communications has been suggested as a natural application of the technique. Passive versions of time-reversal processing use a receive-only array to do combined temporal and spatial matched filtering. It can be shown, however, that the pulse compression it achieves is not perfect and that an equalizer that relies solely on time-reversal processing will have an error floor caused by uncompensated intersymbol interference (ISI). In the present paper, a physics-based model is developed for the uncompensated ISI in a passive time-reversal equalizer. The model makes use of a normal-mode expansion for the acoustic field. The matched-filtering integral is approximated and the intermediate result interpreted using the waveguide invariant. After combining across the array and sampling, formal statistical averages of the soft demodulation output are calculated. The results show how performance scales with bandwidth, with the number and position of array elements, and with the length of the finite impulse response matched filters. Good agreement is obtained between the predicted scaling and that observed in field experiments.

An adaptive technique for underwater acoustic communication using passive phase conjugation (PPC) is developed. Multipath channel-parameter identification is accomplished by decision-directed model building and finite-window block-updated least squares computed by LSQR (an iterative linear systems solver). The resulting channel estimates are then used by the PPC processor to generate decisions for use in the next processing block. This architecture effectively accomplishes array equalization with low computation cost in shallow-water environments that exhibit rapidly fluctuating multipath scattering. The performance on shallow-water acoustic communications channels is demonstrated at ranges of 0.9–4.6 km under windy surface conditions and shipping noise, using measured wide-band telemetry data with binary phase-shift keying signaling. The algorithm is evaluated with sparse receiver apertures using subsets of a 14-element array.

The EU Framework 5 project CONVECTION aims to understand convection processes in the Greenland Sea. By studying water motion close to the surface we hope to determine how convection is linked to atmospheric conditions and local surface features.

The usual methods of studying such processes in the ocean are by taking multiple soundings of conductivity, temperature and pressure or towing a large chain measuring temperature and salinity through a cross-section of ocean. These have the disadvantage of yielding information only while the research vessel is in the area. We have employed an alternative acoustic method that can provide data for long periods using semi-permanent moorings.

The acoustic shadowgraph method relies on the fact that when an acoustic signal propagates through a region containing convective irregularities the temperature variations along the path cause the signal amplitude to fluctuate. Unlike tomography, the shadowgraph does not require travel times to be measured and so the equipment can be much cheaper.

This paper describes the experimental apparatus, its testing and deployment on Vesteris Bank in the Greenland Sea in October 2001 and its recovery in April 2002. It also gives an overview of some of the acoustic intensity results and shows how they can be interpreted to yield estimates of sub-surface convection velocities.

Passive Phase Conjugation is a method for coherent underwater acoustic communication that uses multiple receive-only hydrophones. The technique is essentially a space-time matched filter. Previous results from a field experiment demonstrating the method were reported by Rouseff et al. [IEEE J. Oceanic Eng. 26, pp. 821-831, 2001]. In this paper, performance results are presented for Decision-Directed Passive Phase Conjugation, an adaptive extension to the basic technique. Using decision directed estimates for the channel impulse response, the method requires training overhead of less than 2% for the 10000-symbol packets used in the experiment. Mean-Square-Error and Bit-Error-Rates are reported for various array configurations including a three-element horizontal array.

The 1995 Shallow Water Acoustics in a Random Medium (SWARM) experiment [Apel et al., IEEE J. Ocean. Eng. 22, 445-464 (1997)] was conducted off the New Jersey coast. The experiment featured two well-populated vertical receiving arrays, which permitted the measured acoustic field to be decomposed into its normal modes. The decomposition was repeated for successive transmissions allowing the amplitude of each mode to be tracked. The modal amplitudes were observed to decorrelate with time scales on the order of 100 s [Headrick et al., J. Acoust. Soc. Am. 107(1), 201-220 (2000)]. In the present work, a theoretical model is proposed to explain the observed decorrelation. Packets of intense internal waves are modeled as coherent structures moving along the acoustic propagation path without changing shape. The packets cause mode coupling and their motion results in a changing acoustic interference pattern. The model is consistent with the rapid decorrelation observed in SWARM. The model also predicts the observed partial recorrelation of the field at longer time scales. The model is first tested in simple continuous-wave simulations using canonical representations for the internal waves. More detailed time-domain simulations are presented mimicking the situation in SWARM. Modeling results are compared to experimental data.

The "invariant parameter" called "beta" is often useful for describing the acoustic interference pattern in a waveguide. For some shallow water waveguides, the measured acoustic intensity might contain contributions from several propagating acoustic modes. For each pair of these modes, a different value for the waveguide invariant might apply. If the acoustic intensity is measured over some distributed aperture and finite bandwidth, it may become difficult to assign a single value to beta. In the present work, the waveguide invariant is treated as a distribution. An algorithm for estimating this distribution for a general measurement geometry is developed. The algorithm is exercised for different classes of shallow water waveguides. When the propagation is dominated by modes interacting with the sea surface, the distribution can be sharply peaked. For cases where the sound speed profile creates a duct, the distribution is more diffuse. The effects of source/receiver depth, range, bandwidth and bottom attenuation are quantified.

A decision-directed extension to passive phase conjugation array demodulation is described. Initialisation by a training preamble is followed by block least-squares channel estimation via conjugate gradient and memoryless decisions, which are used by estimation in the next block. Excellent shallow-water performance is shown at ranges up to 46 km under windy conditions and shipping noise. The algorithm demonstrates low error rate and robust channel tracking.

A new method for underwater acoustic communication called passive phase conjugation is evaluated. The method begins with a source transmitting a single probe pulse. After waiting for the multipathed arrivals to clear, the source then transmits the data stream. At each element in the distant receiving array, the received probe is cross-correlated with the received data stream. This cross-correlation is done in parallel at each array element and the results are summed across the array to achieve the final communication signal suitable for demodulation. The parallel processing makes the method computationally efficient and allows near real-time communication.

We describe a novel decision-directed structure that extends the passive phase conjugation (PPC) array demodulation method of Rouseff et al.. The PPC transmission scheme is a single source and multiple receive sensors. Our algorithm uses an initial training period with known data, followed by block-update LS channel estimation via LSQR (Paige and Saunders, 1982) iterations, and subsequent memoryless decisions. Decisions are circulated back into the LS model for the next estimation block. Performance on a shallow-water acoustic channel is shown at ranges up to 4.6 km under windy surface conditions and shipping noise. The algorithm demonstrates good bit error rates, and robustly tracks time-varying channels. Its unquantized output can be further processed by conventional equalizers.

Active phase conjugation requires an array capable of both transmitting and receiving. A field incident on the array can be refocused both in space and time at the location of the original source. To do acoustic communication, an additional step in the processing is introduced; prior to backpropagation, the measured probe field is first convolved with a data stream. The direction of communication is from the active array to the location of the original point source. By contrast, in passive phase conjugation [D. R. Jackson et al., J. Acoust. Soc. Am. 108, 2607 (2000)] the direction of communication is from the point source to the passive array. Further results from an experiment conducted in Puget Sound are presented. The effects of array curvature and truncation are discussed.

A new method for coherent underwater acoustic communication called passive phase conjugation is evaluated. The method is so named because of conceptual similarities to active phase conjugation methods that have been demonstrated in the ocean. In contrast to active techniques, however, the array in passive phase conjugation needs only receive. The procedure begins with a source transmitting a single probe pulse. After waiting for the multipathed arrivals to clear, the source then transmits the data stream. At each element in the distant receiving array, the received probe is cross-correlated with the received data stream. This cross-correlation is done in parallel at each array element and the results are summed across the array to achieve the final communication signal suitable for demodulation. As the ocean changes, it becomes necessary to break up the data stream and insert new probe pulses. Results from an experiment conducted in Puget Sound near Seattle are reported. Measurements were made at multiple ranges and water depths in range-dependent environments.

Contour plots of underwater acoustic intensity, mapped in range and frequency, often exhibit striations. It has been claimed that a scalar parameter 'beta', defined in terms of the slope of the striations, is invariant to the details of the acoustic waveguide. In shallow water, the canonical value is β=1. In the present paper, the waveguide invariant is modelled as a distribution rather than a scalar. The effects of shallow water internal waves on the distribution are studied by numerical simulation. Realizations of time-evolving shallow water internal wave fields are synthesized and acoustic propagation simulated using the parabolic equation method. The waveguide invariant distribution is tracked as the internal wave field evolves in time. Both random background internal waves and more event-like solitary internal waves are considered.

An experiment was carried out over a nine day period from August 18 to 27, 1996 to examine acoustic wave propagation in random media at frequencies applicable to synthetic aperture sonar. The objective was to test experimentally the hypothesized imaging effects of variations in the sound speed along two different acoustic paths as put forth by F.S. Henyey et al. (1997). The focus of this paper is on describing the experiment and carrying out an initial analysis of the data in the context of the effect of ocean internal waves on imaging resolution. The oceanography is summarized to the extent needed to discuss important aspects relative to the acoustics experiment. In the acoustics experiment transmissions at 6, 20, 75, and 129 kHz between sources and receiver arrays were carried out. Source to receiver separation was about 815 m. All sources and receivers were mounted on bottom-deployed towers and were at least 9 m off the seafloor. The analysis concentrates on the 75-kHz data acquired during one day of the experiment. The time span examined Is sufficient to examine a diurnal tidal cycle of the oceanographic conditions. The results indicate the IW phase perturbations would have a significant effect on imaging for even the most benign conditions of the experiment if no autofocusing scheme is used. Also, though autofocusing should be useful in recovering the focus for these conditions, there are conditions (e.g., for the path that has a turning point at the thermocline and during times when solibores are present), where more sophisticated compensation schemes would be needed.

In March of 1997, a shallow water experiment was conducted near the Scripps Pier in La Jolla, CA, USA. The goal was to determine the dynamics, distribution, and acoustic effects of bubbles just offshore from active surf. A major component of the experiment was the "Delta Frame," an apparatus that supported two acoustic sources and eight receivers. Acoustic intensity was measured at frequencies between 39 and 244 kHz over the resulting 16 horizontal ray paths. Paths ranged in length from 2.5 to 8.6 m. In the present paper, a tomography algorithm is developed and implemented using Delta Frame data. Measurements are combined to produce quantitative cross-sectional images of the attenuation associated with the bubble cloud. Numerical simulations predict that the Frame ran resolve details of the field down to about 2 m. Images constructed at different acoustic frequencies are scaled and compared. A 5-min sequence of images is studied in detail. Swell waves are shown to cause rapid fluctuations in the images.

A new method for coherent underwater communication called passive phase conjugation is evaluated. The technique takes its name because of conceptual similarities to active phase conjugation methods that have been demonstrated in the ocean [Kuperman et al., J. Acoust. Soc. Am. 103, 25-40 (1998)]. In contrast to active techniques, however, the array in passive phase conjugation need only receive. This makes the method plausible for scenarios where spatially compact sources might be communicating to a distant receive-only array. Compared to other approaches for coherent communication, the computational burden is low allowing the method to be evaluated in the field in nearly real-time. Results from an experiment conducted in Puget Sound near Seattle in May 2000 are reported. Various modulation schemes and array geometries were employed. Measurements were made at several ranges and water depths in a range-dependent environment.

In the second edition of their book, Brekhovskikh and Lysanov [Fundamentals of Ocean Acoustics (Springer-Verlag, Berlin, 1991)] introduced the concept of intensity invariance to a larger audience. They showed how contour plots of acoustic intensity, mapped in range and frequency, would show definite striation patterns. A single scalar parameter called beta could characterize these patterns. Referencing a large body of Russian literature, they claimed that beta was invariant to the details of the environment, and that in shallow water it equaled one. The published Russian work was primarily analytical; consequently, it concentrated on relatively simple environments. In the present paper, the concept of intensity invariance is examined by numerical simulation for more complicated scenarios. Realizations of time-evolving shallow-water internal wave fields are generated. Acoustic propagation through the internal waves is simulated using the parabolic equation. Both random background internal waves and more eventlike solitary waves are considered. Beta is estimated from images of intensity using radon transforms and tracked as the internal wave field evolves. The effect of varying bottom attenuation is quantified. Receiver depths both above and below the thermocline are considered.