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An underwater navigation algorithm that provides a “cold start” (CSA) geographic position, geo-position, underwater while submerged using travel times measured from a constellation of acoustic sources is described in Mikhalevsky, Sperry, Woolfe, Dzieciuch, and Worcester [J. Acoust. Soc. Am. 147(4), 2365 – 2382 (2020)]. The CSA geo-position is used as the receive position in the ocean for acoustic modeling runs using an ocean general circulation model (GCM). A different geo-position is calculated using adjusted ranges from the travel time offsets between the data and modeled arrival times for each source. Because the CSA geo-position is close to the true position, the source to CSA position propagation model path and the source to true vehicle position data path of the acoustic arrivals are nearly coincident, enabling accurate measurement of travel time offsets. The cold start with model (CSAM) processing reduced the CSA geo-position errors from a mean of 58 to 25 m. A simulation is developed to estimate CSA and CSAM performances as a function of group speed variability between the source paths. The CSAM geolocation accuracy can be calculated from and is controlled by the accuracy of the GCM.

The Arctic Ocean is undergoing dramatic changes in response to increasing atmospheric concentrations of greenhouse gases. The 2016–2017 Canada Basin Acoustic Propagation Experiment was conducted to assess the effects of the changes in the sea ice and ocean structure in the Beaufort Gyre on low-frequency underwater acoustic propagation and ambient sound. An ocean acoustic tomography array with a radius of 150 km that consisted of six acoustic transceivers and a long vertical receiving array measured the impulse responses of the ocean at a variety of ranges every four hours using broadband signals centered at about 250 Hz. The peak-to-peak low-frequency travel-time variability of the early, resolved ray arrivals that turn deep in the ocean was only a few tens of milliseconds, roughly an order of magnitude smaller than observed in previous tomographic experiments at similar ranges, reflecting the small spatial scale and relative sparseness of mesoscale eddies in the Canada Basin. The high-frequency travel-time fluctuations were approximately 2 ms root-mean-square, roughly comparable to the expected measurement uncertainty, reflecting the low internal-wave energy level. The travel-time spectra show increasing energy at lower frequencies and enhanced semidiurnal variability, presumably due to some combination of the semidiurnal tides and inertial variability.

A regional ocean model for Fram Strait provides a framework for interpretation of the variability and structure of acoustic tomography arrivals. The eddy-permitting model (52 vertical levels and 4.5 km horizontal resolution) was evaluated using long-term moored hydrography data and time series of depth-range averaged temperature obtained from the inversion of acoustic tomography measurements. Geometric ray modeling using the ocean model fields reproduces the measured arrival structure of the acoustic tomography experiment. The combination of ocean and acoustic models gives insights into acoustic propagation during winter and spring. Moreover, overlapping arrivals coming from different vertical angles can be resolved and explained. The overlapping arrival of purely refracted rays and surface-reflected/bottom-reflected (SRBR) rays has implications for the inversion of tomography data in Fram Strait. The increased knowledge about the ray-length variations of SRBR rays is valuable for choosing appropriate observation kernels for the data assimilation of acoustic tomography data in Fram Strait.

The cross correlation of the underwater noise field recorded at two receivers conveys information about the time-domain Green's function between the two locations, provided that sufficient energy is channeled into the acoustic paths connecting these. The efficiency of this procedure depends on the locations and characteristics of the receivers and noise sources, as well as on the refraction properties of the ocean sound channel. The sensitivity of the finite-frequency noise cross-correlation function with respect to the location and amplitude of the noise sources is studied here, taking into account the refractive features of the ocean environment. The sensitivity kernel describing changes in the cross-correlation envelope due to changes in the noise source distribution is used to highlight noise-source locations with maximum potential impact on the cross-correlation output.

An ocean acoustic tomography array with a radius of 150 km was installed in the central Beaufort Gyre during 2016–2017 for the Canada Basin Acoustic Propagation Experiment (CANAPE). Five transceivers were deployed in a pentagon shape with a sixth transceiver at the center and a long vertical receiving array northwest of the central mooring. At least 12 refracted-surface-reflected (RSR) ray arrivals with lower turning points at depths between 500 and 3500 m were resolved in the acoustic receptions at all receivers. Travel-time anomalies were computed relative to a range-dependent sound-speed reference made by objectively interpolating annual-average sound-speed profiles constructed from the temperature data at each mooring. The travel time anomalies were inverted to estimate the 3-D sound-speed anomaly, including corrections to the positions of sources and receivers consistent with the uncertainty from long-baseline acoustic navigation systems at each mooring. Although the deep water in the Canada Basin is nearly homogeneous in temperature and salinity and highly stable (slowly warming in response to geothermal heating), it proved necessary to allow for a sound-speed change in the deep ocean to obtain consistent inversions, suggesting that the sound-speed equation at high pressure and low temperature is in error by about 0.1–0.2 ms−1.

The spatial correlation of a diffuse isotropic noise field generated from a uniform distribution of uncorrelated noise sources contains information about the time-domain Green's function (TDGF) corresponding to propagation between the correlated locations. The distribution of noise in the ocean due to shipping—the prevailing origin of continuous low-frequency noise—is far from uniform. Besides the location of noise sources, the propagation conditions and the hydrophone locations have a significant influence on whether the TDGF can be reliably reconstructed through the cross-correlation procedure. A wave-theoretic scheme is implemented to simulate the cross-correlation function of a noise field in the time domain for arbitrary distributions of deterministic or random noise sources in refractive environments, and it is used to study the influence of propagation conditions and receiver motion on the efficiency of the cross-correlation procedure to obtain the TDGF from shipping noise.The spatial correlation of a diffuse isotropic noise field generated from a uniform distribution of uncorrelated noise sources contains information about the time-domain Green's function (TDGF) corresponding to propagation between the correlated locations. The distribution of noise in the ocean due to shipping—the prevailing origin of continuous low-frequency noise—is far from uniform. Besides the location of noise sources, the propagation conditions and the hydrophone locations have a significant influence on whether the TDGF can be reliably reconstructed through the cross-correlation procedure. A wave-theoretic scheme is implemented to simulate the cross-correlation function of a noise field in the time domain for arbitrary distributions of deterministic or random noise sources in refractive environments, and it is used to study the influence of propagation conditions and receiver motion on the efficiency of the cross-correlation procedure to obtain the TDGF from shipping noise.

The 2010i–2012 ACOBAR acoustic thermometry experiment in Fram Strait resulted in 2-year-long timeseries of sound speed and temperature. These timeseries are section- and depth-average along 4 sections covering the deep part of Fram Strait (77.9°–78.9°N, 4.2°W–8.7°E). They were obtained by inversion from the acoustic travel times measured in the thermometry experiment. Such large-scale average measurements in a highly turbulent environment at one of the important sites for ocean circulation in the Arctic are unique and will hopefully increase our understanding of volume and heat exchanges between the Arctic and Atlantic. A regional ocean model of Fram Strait was set up for the assimilation of the ACOBAR measurements using the 4-DVAR data assimilation technique. The forward model part was evaluated using both oceanographic and acoustic measurements (Geyer et al., 2019). First assimilation results show a cost reduction of 85% after 10 iterations. The resulting ocean state estimate will be evaluated using the long-term oceanographic mooring section in Fram Strait at 78°50’N. The aim of this study is to use the ocean state estimate to facilitate the interpretation of the acoustic thermometry results and to investigate how the circulation dynamics in Fram Strait are influencing the volume and heat exchanges through the strait.

A moving source tomography experiment was conducted in 2016 off the coast of Southern California. From the travel time data extracted from the experiment, ocean sound speed and its uncertainty were estimated. The moving source poses extra complexity and adds components that need to be accounted for in a successful inversion. The sound speed estimation with uncertainties was validated against in situ observations to quantify the efficacy and accuracy of the method. Experimental results and additional simulations suggest that the ray diversity available in the moving source case reduces the posterior sound speed uncertainty compared to the fixed source case. [Work sponsored by the Office of Naval Research.]

Sensitivity kernels for travel-time observables defined on the noise cross-correlation pattern – the envelope of the cross-correlation function of the underwater noise field between two locations – with respect to changes in the sound-speed field in refractive underwater environments will be addressed. A wave-theoretic scheme allowing for finite-frequency calculations in 2 and 3 dimensions combined with the Born approximation for perturbations of the Green’s function and the peak-arrival approach is used to obtain peak-time sensitivity kernels (PTSKs) with respect to environmental (sound-speed) changes. PTSK results for different propagation conditions and noise-source distributions, ranging from spatial distributions of uncorrelated noise sources to point sources such as individual ships, will be presented. The PTSKs can be a useful tool for obtaining environmental information from noise measurements. [Work supported by the Office of Naval Research.]

An ocean acoustic tomography system consisting of three moorings with low frequency, broadband transceivers and a moored receiver located approximately in the center of the triangle formed by the transceivers was installed in the central, deep-water part of Fram Strait during 2010-2012. Comparisons of the acoustic receptions with predictions based on hydrographic sections show that the oceanographic conditions in Fram Strait result in complex arrival patterns in which it is difficult to resolve and identify individual arrivals. In addition, the early arrivals are unstable, with the arrival structures changing significantly over time. The stability parameter α suggests that the instability is likely not due to small-scale variability, but rather points toward strong mesoscale variability in the presence of a relatively weak sound channel as being largely responsible. The estimator-correlator [Dzieciuch, J. Acoust. Soc. Am. 136, 2512-2522 (2014)] is shown to provide an objective formalism for generating travel-time series given the complex propagation conditions. Because travel times obtained from the estimator-correlator are not associated with resolved, identified ray arrivals, inverse methods are needed that do not use sampling kernels constructed from geometric ray paths. One possible approach would be to use travel-time sensitivity kernels constructed for the estimator-correlator outputs.

In the Philippine Sea, from April 2010 to March 2011, a 330-km radius pentagonal acoustic transceiver array with a sixth transceiver in the center transmitted broadband signals with center frequencies between 172 and 275 Hz and 100 Hz bandwidth eight times a day every other day. The signals were recorded on a large-aperture vertical-line array located near the center of the pentagon at ranges of 129, 210, 224, 379, 396, and 450 km. The acoustic arrival structures are interpretable in terms of ray paths. Depth and time variability of the acoustic observations are analyzed for six ray paths (one from each transceiver) with similar vertical sampling properties in the main thermocline. Acoustic-field statistics treated include: (1) variances of phase and intensity, (2) vertical coherence and intensity covariance, (3) glinting and fadeout rates, and (4) intensity probability density functions. Several observed statistics are compared to predictions using Feynman path-integral theory assuming the Garrett-Munk internal-wave spectrum. In situ oceanographic observations support this assumption and are used to estimate spectral parameters. Data and theory differ at most by a factor of two and reveal the wave propagation regimes of unsaturated, partially saturated, and fully saturated. Improvements to the evaluation of path-integral quantities are discussed.

The uncertainty of estimating relative channel impulse responses (CIRs) obtained using the radiated signature from a ship of opportunity is investigated. The ship observations were taken during a 1.4 km (11 min) transect in a shallow water environment during the Noise Correlation 2009 (NC09) experiment. Beamforming on the angle associated with the direct ray-path yields an estimate of the ship signature, subsequently used in a matched filter. Relative CIRs are estimated every 2.5 s independently at three vertical line arrays (VLAs). The relative arrival-time uncertainty is inversely proportional to source bandwidth and CIR signal-to-noise ratio, and reached a minimum standard deviation of 5 μs (equivalent to approximately 1 cm spatial displacement). Time-series of direct-path relative arrival-times are constructed for each VLA element across the 11 min observation interval. The overall structure of these time-series compares favorably with that predicted from an array element localization model. The short-term standard deviations calculated on the direct-path (7 μs) and bottom-reflected-path (17 μs) time-series are in agreement with the predicted arrival-time accuracies. The implications of these observed arrival-time accuracies in the context of estimating sound speed perturbations and bottom-depth are discussed.

The waveguide invariant (WGI) is a property that can be used to localize acoustic radiators and extract information about the environment. Here the WGI is determined using ships as sources of opportunity, tracked using the Automatic Identification System (AIS). The relationship between range, acoustic intensity, and frequency for a ship in a known position is used to determine the WGI parameter β. These β values are interpolated and a map of β is generated. The method is demonstrated using data collected in a field experiment on a single hydrophone in a shallow water environment off the coast of Southern California.

From April 2010 to March 2011, low frequency acoustic transmissions were carried out on a 330-km radius pentagonal acoustic array with a sixth transceiver in the middle in the Philippine Sea. Herein, we describe the fluctuation statistics of the signals originating on the six transceivers and recorded on a water column spanning receiver array located slightly off center of the pentagon. The signals analyzed here are interpretable in terms of specific acoustic ray paths clearly separable in time. Acoustic field statistics treated include (1) variances of phase and intensity, (2) vertical coherence and intensity covariance, (3) glinting and fade out rates, and (4) intensity probability density functions. Several of these observables are compared to predictions from Feynman path integral theory assuming the Garrett-Munk internal wave model suitably modified using Philippine Sea oceanographic observations. Data and theory differ by at most a factor of 2 and reveal the wave propagation regimes of unsaturated, and partially saturated.

Seismic surveys using arrays of airguns are a ubiquitous feature of the ocean ambient sound environment. An approach is presented to use airguns as a sound source to study how physical oceanographic variability shapes long range acoustic propagation. Signal processing and data analysis tools are presented to allow opportunistic use of commercial seismic surveys in the Gulf of Mexico (GOM) for environmental characterization. Airgun propagation data are analyzed and compared to models generated from conventional physical oceanographic data collection for large scale features such as the Loop Current.Seismic surveys using arrays of airguns are a ubiquitous feature of the ocean ambient sound environment. An approach is presented to use airguns as a sound source to study how physical oceanographic variability shapes long range acoustic propagation. Signal processing and data analysis tools are presented to allow opportunistic use of commercial seismic surveys in the Gulf of Mexico (GOM) for environmental characterization. Airgun propagation data are analyzed and compared to models generated from conventional physical oceanographic data collection for large scale features such as the Loop Current.

A wave-theoretic tool, the source kernel, is introduced to describe the sensitivity of the finite-frequency underwater noise cross-correlation function to the location of the noise sources taking into account the refractive features of the ocean environment. The cross correlation of the noise field at two receivers conveys information about the corresponding time-domain Green’s function (TDGF), provided that sufficient energy is channeled into the acoustic paths connecting the two locations. The efficiency of the TDGF recovery is determined by the receiver and noise source locations and characteristics, as well as by the refraction properties of the ocean sound channel. The source kernel takes these characteristics into account and highlights the locations where noise sources can have maximum impact on the cross-correlation output. The distribution and coherence of the noise sources can be specified in a variety of ways to investigate a wide range of scenarios, from random noise-source distributions to coherent radiators. [Work supported by the Office of Naval Research.]

Ocean acoustic travel-time-tomography attempts to map heterogeneities such as ocean temperature with mesoscale resolution. The Santa Barbara Channel Experiment in 2016 (SBCEx16) contained both controlled and uncontrolled (i.e., ships of opportunity) sources, in addition to environmental data collected by a variety of sensors. The path to developing a methodology for utilizing noise from ships of opportunity for oceanographic imaging involves benchmarking our processing with a controlled source-tow. This latter moving source tomography, itself, is a procedure that still remains to be quantitatively validated and documented. We present results from the source-tow tomographic component of SBCEx16 with the added objective of understanding the requirements for minimizing the uncertainties associated with uncontrolled, random sources of opportunity.

Measurements of acoustic ray travel-times in the ocean provide synoptic integrals of the ocean state between source and receiver. It is known that the ray travel-time is sensitive to variations in the ocean at the transmission time, but the sensitivity of the travel-time to spatial variations in the ocean prior to the acoustic transmission have not been quantified. This study examines the sensitivity of ray travel-time to the temporally and spatially evolving ocean state in the Philippine Sea using the adjoint of a numerical model. A one year series of five day backward integrations of the adjoint model quantify the sensitivity of travel-times to varying dynamics that can alter the travel-time of a 611 km ray by 200 ms. The early evolution of the sensitivities reveals high-mode internal waves that dissipate quickly, leaving the lowest three modes, providing a connection to variations in the internal tide generation prior to the sample time. They are also strongly sensitive to advective effects that alter density along the ray path. These sensitivities reveal how travel-time measurements are affected by both nearby and distant waters. Temporal nonlinearity of the sensitivities suggests that prior knowledge of the ocean state is necessary to exploit the travel-time observations.

The article of record as published may be found at https://doi.org/10.1121/1.3666014 Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the −1.81 power, whereas the spice spectrum shows a −1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three. This work was supported by the Office of Naval Research, and Professor Colosi gratefully acknowledges his additional support from the Naval Postgraduate School’s Undersea Warfare Chair that he holds.

A regional ocean model for Fram Strait allows to understand the variability and structure of acoustic tomography arrivals. The eddy-permitting model (52 vertical layers and 4.5 km horizontal resolution) was evaluated using long-term moored hydrography data and time series of depth-range averaged temperature obtained from the inversion of acoustic tomography measurements. Geometric ray modelling on the ocean model fields reproduces the measured arrival structure of the acoustic tomography experiment. The combination of ocean and acoustic model gives insights into acoustic propagation during winter and spring. Overlapping arrivals coming from different vertical angles can be resolved and explained. The overlapping arrival of sound channel rays and bottom-reflected rays has implications for the inversion of tomography data in Fram Strait. The increased knowledge about the ray-length variations of bottom-reflected rays is valuable information for choosing appropriate observation kernels for the data assimilation of acoustic tomography data in Fram Strait.A regional ocean model for Fram Strait allows to understand the variability and structure of acoustic tomography arrivals. The eddy-permitting model (52 vertical layers and 4.5 km horizontal resolution) was evaluated using long-term moored hydrography data and time series of depth-range averaged temperature obtained from the inversion of acoustic tomography measurements. Geometric ray modelling on the ocean model fields reproduces the measured arrival structure of the acoustic tomography experiment. The combination of ocean and acoustic model gives insights into acoustic propagation during winter and spring. Overlapping arrivals coming from different vertical angles can be resolved and explained. The overlapping arrival of sound channel rays and bottom-reflected rays has implications for the inversion of tomography data in Fram Strait. The increased knowledge about the ray-length variations of bottom-reflected rays is valuable information for choosing appropriate observation kernels for the data assimilat...

The uncertainty of estimating relative channel impulse responses (CIRs) obtained using the radiated signature from a ship of opportunity is investigated. The ship observations were taken during a 1.4 km (11 min) transect during the Noise Correlation 2009 (NC09) experiment. Beamforming on the angle associated with the direct ray-path yields an estimate of the ship signature, subsequently used as a matched filter. Relative CIRs are estimated every 2.5 s independently at three vertical line arrays (VLAs) for a total of 270 observations per VLA. The estimated relative arrival-time uncertainty is inversely proportional to source bandwidth and CIR signal-to-noise ratio, and reached a minimum standard deviation of 5 μs (approximately 1 cm). The direct-path relative arrival-times are used to construct time series for each VLA element across the 11 min observation interval. The overall structure of these time series compares favorably with that predicted from an array element localization (AEL) model that exhibits sensitivity on the order of centimeters. The short-term standard deviations calculated on direct-path (7 μs) and bottom-reflected-path (17 μs) time series are in agreement with the estimated arrival-time accuracies. The implication of these observed arrival-time accuracies in the context of making sound speed perturbation and bottom-depth estimates is discussed.The uncertainty of estimating relative channel impulse responses (CIRs) obtained using the radiated signature from a ship of opportunity is investigated. The ship observations were taken during a 1.4 km (11 min) transect during the Noise Correlation 2009 (NC09) experiment. Beamforming on the angle associated with the direct ray-path yields an estimate of the ship signature, subsequently used as a matched filter. Relative CIRs are estimated every 2.5 s independently at three vertical line arrays (VLAs) for a total of 270 observations per VLA. The estimated relative arrival-time uncertainty is inversely proportional to source bandwidth and CIR signal-to-noise ratio, and reached a minimum standard deviation of 5 μs (approximately 1 cm). The direct-path relative arrival-times are used to construct time series for each VLA element across the 11 min observation interval. The overall structure of these time series compares favorably with that predicted from an array element localization (AEL) model that exhibits...

We examine statistical and directional properties of the ambient noise in the 10-100 Hz frequency band from the NPAL array. Marginal probability densities are estimated as well as mean square levels, skewness and kurtoses in third octave bands. The kurotoses are markedly different from Gaussian except when only distant shipping is present. Extremal levels reached approximately 150 dB re 1 micro Pa, suggesting levels 60dB greater than the mean ambient were common in the NPAL data sets. Generally, these were passing ships. We select four examples: i) quiescent noise, ii) nearby shipping, iii) whale vocalizations and iv) a micro earthquake for the vertical directional properties of the NPAL noise since they are representative of the phenomena encountered. We find there is modest broadband coherence for most of these cases in their occupancy band across the NPAL aperture. Narrowband coherence analysis from VLA to VLA was not successful due to ambiguities. Examples of localizing sources based upon this coherence are included. kw diagrams allow us to use data above the vertical aliasing frequency. Ducted propagation for both the quiescent and micro earthquake (T phase) are identified and the arrival angles of nearby shipping and whale vocalizations. MFP localizations were modestly successful for nearby sources, but long range ones could not be identified, most likely because of signal mismatch in the MFP replica.

Wave-theoretic ocean acoustic propagation modeling is combined with the peak arrival approach for tomographic travel-time observables to derive the sensitivity kernel of travel times with respect to sound-speed variations. This is the Born–Frechet kernel relating the three-dimensional spatial distribution of sound-speed variations with the induced travel-time variations. The derivation is based on the first Born approximation of the Green’s function. The application of the travel-time sensitivity kernel to an ocean acoustic waveguide gives a picture close to the ray-theoretic one in the case of high frequencies. However, in the low-frequency case, of interest in ocean acoustic tomography, for example, there are significant deviations. Low-frequency travel times are sensitive to sound-speed changes in Fresnel-zone-scale areas surrounding the eigenrays, but not on the eigenrays themselves, where the sensitivity is zero. Further, there are areas of positive sensitivity, where, e.g., a sound-speed increase re...

The final cutoff of a deep-water ocean acoustic tomography reception is often interpreted through a modal analysis. An alternative approach is presented here. First, a stable travel-time is generated by using an estimator-correlator to account for the statistical variability of the final low-angle arrival with the assumption of an appropriate coherent bandwidth and depth coherence. A time-series of these travel-times can then be tracked using the Viterbi algorithm. Then, the resolvable, trackable peaks are interpreted using the travel-time sensitivity kernel (TSK). The TSK has been previously used to account for the full-wave effects of ray-like arrivals. But the TSK machinery can be adapted to any processing strategy with the application of the chain-rule. The question of how to interpret an arrival produced by an Estimator-Correlator vs. an arrival produced by standard processing is examined. The feasibility of this approach is first analytically determined with the Pekeris waveguide and then an example...

Previously, we demonstrated using the Noise-09 data set that it is possible to estimate the relative channel impulse responses (CIR) over a 1.5 km transect independently at 3 vertical line arrays (VLAs). This vessel provided sufficient SNR and bandwidth for the uncertainty of the direct arrival time to reach 5 microseconds. The time evolution of the CIRs as the ship passed by was subsequently used to determine VLA hydrophone positions relative to a reference hydrophone with accuracy on the order of centimeters. An experiment was performed in the Santa Barbara Channel using four VLAs placed between the sea lanes of in- and outgoing shipping traffic. Ship tracks were obtained from the Automatic Identification System (AIS). We extend the previous processing to this data set and discuss the uncertainties of relative multi-path arrival-times and differential travel times between VLAs.

The slopes of undersea canyon regions impart complexity to underwater acoustic fields for two reasons: intricate patterns of reflection from the seabed, and sound-speed anomalies from internal tides generated at the slopes. Both may spread the horizontal directional spectrum of sound from “line of sight” to a source. The directional spectrum is tied to the covariance matrix of the field, a fundamental quantity that can be measured or modeled. Here, sound-field horizontal-lag spatial covariance matrices and other derived quantities are generated from time-stepped 3D parabolic equation acoustic simulations made using sound-speed fields from ocean models. The covariance matrices are then inserted into the direction-of-arrival (DOA) estimation problem. Analysis of DOA estimates and error bounds is done for a conventional beamformer and for a Gauss-Markov inverse-based beamformer for a variety of signal-to-noise ratios. The method treats non-line of sight acoustic energy as a form of noise. At low signal-to-no...

An experiment was performed in the Santa Barbara Channel (SBCEx16) using four vertical line arrays (VLAs) of hydrophones placed midway between the in- and out-going shipping lanes of a maritime highway. The goal of this experiment was to study whether these sources of opportunity can be used for passive tomographic purposes. In addition to the continuous passive observations, active acoustic source-tows were conducted. The environment was monitored continuously throughout the course of the experiment using thermistor strings, and ship tracks were obtained from the Automatic Identification System (AIS). The results from both types of tomography are presented and compared.

An experiment was performed in the Santa Barbara Channel using four vertical acoustic receive arrays placed between the sea lanes of in- and outgoing shipping traffic. The purpose of the experiment was to determine whether these sources of opportunity can be utilized for tomographic inversion of water column properties. The environment was continuously monitored throughout the duration of the experiment. Ship tracks were obtained from the Automatic Identification System (AIS). Processing was developed to extract relative time delays between the arrays from the ships’ random radiation fields. This information, together with AIS constraints were used for inversion. Initial results are presented that also include an error analysis of the inversion.

Passive acoustic tomography exploits the acoustic energy generated by sources with unknown spectral content such as sources of opportunity (e.g., cargo ships) to study the ocean. The recording at each sensor within a vertical line array (VLA) is the channel impulse response (CIR) convolved with the noise generated by the moving random radiator. Using an incremental approach, we estimate the source signal locally at three VLAs by beamforming on the direct ray-path to deconvolve each CIR. CIR arrival uncertainty is inversely proportional to the bandwidth of the source and SNR, the latter estimated from the deconvolved time domain waveform. Over the 10 min source track, we present the time evolution of CIR arrival uncertainty computed at three VLAs horizontally separated by 1.5 km and discuss constraints on integration time. Data are presented using the Noise Correlation 2009 Experiment and application to the Santa Barbara Channel Experiment 2016 is discussed.

High-frequency underwater acoustic transmissions across the Strait of Gibraltar are used to examine the feasibility of acoustically measuring several physical processes in the Strait, a difficult area to sample with conventional instruments. Internal undular bores propagate along the interface between an upper layer of Atlantic water and a lower layer of Mediterranean water. As they cross the acoustic path they are recognized by their scattering effects in the acoustic record. The time between internal bore crossings is influenced more by the tidal phase of the bore release at the Camarinal Sill than by variability in the bore’s propagation time to the acoustic path. When internal bores were present, the acoustic arrival patterns could be classified as one of three types with different internal bore and internal tide amplitudes. The arrival types alternate during spring to neap tide transitions, suggesting that internal bore amplitude is not linearly related to tidal height. The sensitivity of acoustic observables to several physical parameters is investigated using a forward model, and a demonstration of inverse techniques provides estimates of several physical parameters from spring tidal cycles.

High-frequency underwater acoustic transmissions across the Strait of Gibraltar were used to examine acoustic scattering caused by the unique internal wave field in the Strait. Internal solitary waves of 100 m in amplitude propagate along the interface between an upper layer of Atlantic water and a lower layer of Mediterranean water. The interface is also strongly modulated by internal tides of comparable amplitude. As internal solitary waves cross the acoustic path, they cause sharp soundspeed gradients which intermittently refract acoustic rays away from normal sound channels. Internal tides vertically shift soundspeed profiles for additional travel time variability. Although the acoustic scattering is quite complicated, it is also surprisingly robust, making it a good candidate for modeling. Key features of the acoustic arrival pattern can be accounted for in some detail by a model description of the complex hydraulics in the Strait.

During the Acoustic Engineering Test (AET) of the Acoustic Thermometry of Ocean Climate (ATOC) program, acoustic signals were transmitted from a broadband source with 75-Hz center frequency to a 700-m-long vertical array of 20 hydrophones at a distance of 3252 km; receptions occurred over a period of six days. Each received pulse showed early identifiable timefronts, followed by about 2 s of highly variable energy. For the identifiable timefronts, observations of travel-time variance, average pulse shape, and the probability density function (PDF) of intensity are presented, and calculations of internal-wave contributions to those fluctuations are compared to the observations. Individual timefronts have rms travel time fluctuations of 11 to 19 ms, with time scales of less than 2 h. The pulse time spreads are between 0 and 5.3 ms rms, which suggest that internal-wave-induced travel-time biases are of the same magnitude. The PDFs of intensity for individual ray arrivals are compared to log-normal and exponential distributions. The observed PDFs are closer to the log-normal distribution, and variances of log intensity are between (3.1 dB)2 (with a scintillation index of 0.74) for late-arriving timefronts and (2.0 dB)2 (with a scintillation index of 0.2) for the earliest timefronts. Fluctuations of the pulse termination time of the transmissions are observed to be 22 ms rms. The intensity PDF of nonidentified peaks in the pulse crescendo are closer to a log-normal distribution than an exponential distribution, but a Kolmogorov–Smirnov test rejects both distributions. The variance of the nonidentified peaks is (3.5 dB)2 and the scintillation index is 0.92. As a group, the observations suggest that the propagation is on the border of the unsaturated and partially saturated regimes. After improving the specification of the ray weighting function, predictions of travel-time variance using the Garrett–Munk (GM) internal-wave spectrum at one-half the reference energy are in good agreement with the observations, and the one-half GM energy level compares well with XBT data taken along the transmission path. Predictions of pulse spread and wave propagation regime are in strong disagreement with the observations. Pulse time spread estimates are nearly two orders of magnitude too large, and Λ–Φ methods for predicting the wave propagation regime predict full saturation.

Broadband acoustic signals were transmitted during November 1994 from a 75-Hz source suspended near the depth of the sound-channel axis to a 700-m long vertical receiving array approximately 3250 km distant in the eastern North Pacific Ocean. The early part of the arrival pattern consists of raylike wave fronts that are resolvable, identifiable, and stable. The later part of the arrival pattern does not contain identifiable raylike arrivals, due to scattering from internal-wave-induced sound-speed fluctuations. The observed ray travel times differ from ray predictions based on the sound-speed field constructed using nearly concurrent temperature and salinity measurements by more than a priori variability estimates, suggesting that the equation used to compute sound speed requires refinement. The range-averaged ocean sound speed can be determined with an uncertainty of about 0.05 m/s from the observed ray travel times together with the time at which the near-axial acoustic reception ends, used as a surroga...

The article of record as published may be found at http://dx.doi.org/10.1121/1.4818784 As an aid to understanding long-range acoustic propagation in the Philippine Sea, statistical and phenomenological descriptions of sound-speed variations were developed. Two moorings of oceanographic sensors located in the western Philippine Sea in the spring of 2009 were used to track constant potential-density surfaces (isopycnals) and constant potential-temperature surfaces (isotherms) in the depth range 120–2000 m. The vertical displacements of these surfaces are used to estimate sound-speed fluctuations from internal waves, while temperature/salinity variability along isopycnals are used to estimate sound-speed fluctuations from intrusive structure often termed spice. Frequency spectra and vertical covariance functions are used to describe the space-time scales of the displacements and spiciness. Internal-wave contributions from diurnal and semi-diurnal internal tides and the diffuse internal-wave field [related to the Garrett–Munk (GM) spectrum] are found to dominate the sound-speed variability. Spice fluctuations are weak in comparison. The internal wave and spice frequency spectra have similar form in the upper ocean but are markedly different below 170-m depth. Diffuse internal-wave mode spectra show a form similar to the GM model, while internal-tide mode spectra scale as mode number to the minus two power. Spice decorrelates rapidly with depth, with a typical correlation scale of tens of meters. Office of Naval Research

International audience; Data collected over more than eight consecutive hours between two source-receiver arrays in a shallow water environment are analyzed through the physics of the waveguide invariant. In particular, the use of vertical arrays on both the source and receiver sides provides source and receiver angles in addition to travel-times associated with a set of eigenray paths in the waveguide. From the travel-times and the source-receiver angles, the eigenrays are projected into a group-velocity versus phase-velocity (Vg-Vp) plot for each acquisition. The time evolution of the Vg-Vp representation over the 8.5-h long experiment is discussed. Group speed fluctuations observed for a set of eigenrays with turning points at different depths in the water column are compared to the Brunt-Väisälä frequency.

Numerically simulated acoustic transmission from a single source of known position (for example, suspended from a ship) to receivers of partially known position (for example, sonobuoys dropped from the air) are used for tomographic mapping of ocean sound speed. The maps are evaluated for accuracy and utility. Grids of 16 receivers are employed, with sizes of 150, 300, and 700 km square. Ordinary statistical measures are used to evaluate the pattern similarity and thus the mapping capability of the system. For an array of 300 km square, quantitative error in the maps grows with receiver position uncertainty. The large and small arrays show lesser mapping capability than the mid‐size array. Mapping errors increase with receiver position uncertainty for uncertainties less than 1000‐m rms, but uncertainties exceeding that have less systematic effect on the maps. Maps of rms error of the field do not provide a complete view of the utility of the acoustic network. Features of maps are surprisingly reproducible ...

Active ocean acoustic tomography transmits known source signals and often includes precise source and receiver positioning. Passive estimation of channel Greens functions has been widely demonstrated using both diffuse and concentrated noise sources, including the estimation of ocean sound speeds and currents. The uncertainty of surface ship positions determined by the Automatic Identification System (AIS) translates to travel time variability that is larger than expected from ocean structure at ranges of a few kilometers, but listening to the same source from spatially-distributed receivers adds more data while maintaining the same source position unknowns and may allow useful estimates of bottom depths from bottom-interacting rays and perhaps ocean structure. A fall 2016 experiment will test these ideas in the Santa Barbara Basin using 4 vertical line receiver arrays recording ship-radiated sound for 10 days. Estimates of the expected performance of the estimates of bottom depth and ocean sound speed have been a part of the design process. A general circulation model will be used to increase the efficiency of information use by parameterizing the four-dimensional ocean sound speed structure in terms of initial conditions, boundary conditions, and surface forcing. We present the design process and some proof-of-concept calculations from experimental observations.

The North Pacific Acoustic Laboratory (NPAL) Philippine Sea experiment deployed a variety of instruments in the northern Philippine Sea during April 2010 through April 2011, including six acoustic transceivers for reciprocal measurements of travel times between instruments. Five transceivers were moored in a pentagon approximately 660 km in diameter with the sixth transceiver moored in the center. Observed travel-time time series were compared with travel times computed from ocean state estimates made using an eddy-active regional implementation of the MITgcm that were constrained by satellite sea surface height and sea surface temperature observations and by temperature and salinity profiles from Argo, CTDs, and XBTs but not by the acoustic data. The similarities cross-validate the state estimates, while the differences provide a simple estimate of the novel information present in the travel times. Smoothness in the modeled sound speed field had a large effect on the ability to find eigenrays. The ocean ...

Using the Born approximation, a linearized sensitivity kernel is derived to describe the relationship between a local change at the free surface and its effect on the acoustic propagation in the water column. The structure of the surface scattering kernel is investigated numerically and experimentally for the case of a waveguide at the ultrasonic scale. To better demonstrate the sensitivity of the multipath propagation to the introduction of a localized perturbation at the air-water interface, the kernel is formulated both in terms of point-to-point and beam-to-beam representations. Agreement between theory and experiment suggests applications to sensitivity analysis of the wavefield for sea surface perturbations.

Broadband acoustic signals were transmitted from a moored 250‐Hz source to a 3‐km‐long vertical line array of hydrophones 1000 km distant in the eastern North Pacific Ocean during July 1989. The sound‐speed field along the great circle path connecting the source and receiver was measured directly by nearly 300 expendable bathythermograph (XBT), conductivity‐temperature‐depth (CTD), and air‐launched expendable bathythermograph (AXBT) casts while the transmissions were in progress. This experiment is unique in combining a vertical receiving array that extends over much of the water column, extensive concurrent environmental measurements, and broadband signals designed to measure acoustic travel times with 1‐ms precision. The time‐mean travel times of the early raylike arrivals, which are evident as wave fronts sweeping across the receiving array, and the time‐mean of the times at which the acoustic reception ends (the final cutoffs) for hydrophones near the sound channel axis, are consistent with ray predictions based on the direct measurements of temperature and salinity, within measurement uncertainty. The comparisons show that subinertial oceanic variability with horizontal wavelengths shorter than 50 km, which is not resolved by the direct measurements, significantly (25 ms peak‐to‐peak) affects the time‐mean ray travel times. The final cutoffs occur significantly later than predicted using ray theory for hydrophones more than 100–200 m off the sound channel axis. Nongeometric effects, such as diffraction at caustics, partially account for this observation.

Wave-theoretic ocean acoustic propagation modeling is used to derive the sensitivity of pressure, and complex demodulated amplitude and phase, at a receiver to the sound speed of the medium using the Born–Frechet derivative. Although the procedure can be applied for pressure as a function of frequency instead of time, the time domain has advantages in practical problems, as linearity and signal-to-noise are more easily assigned in the time domain. The linearity and information content of these sensitivity kernels is explored for an example of a 3–4 kHz broadband pulse transmission in a 1 km shallow water Pekeris waveguide. Full-wave observations (pressure as a function of time) are seen to be too nonlinear for use in most practical cases, whereas envelope and phase data have a wider range of validity and provide complementary information. These results are used in simulated inversions with a more realistic sound speed profile, comparing the performance of amplitude and phase observations.

A 1000‐km acoustical transmission experiment has been carried out in the North Pacific, with pulses broadcast between a moored broadband source (250‐Hz center frequency) and a moored sparse vertical line of receivers. Two data records are reported: a period of 9 days at a pulse rate of one per hour, and a 21‐h period on the seventh day at six per hour. Many wave‐front segments were observed at each hydrophone depth, and arrival times were tracked and studied as functions of time and depth. Arrivals within the final section of the pulse are not trackable in time or space at the chosen sampling rates, however. Broadband fluctuations, which are uncorrelated over 10‐min sampling and 60‐m vertical spacing, are observed with about 40 (ms)2 variance. The variance of all other fluctuations (denoted as low‐frequency) is comparable or smaller than the broadband value; this low‐frequency variance can be separated into two parts: a wave‐front segment displacement (with vertical correlation length greater than 1 km) that varies substantially between rays with different ray identifiers, and a distortion (with vertical correlation length between 60 m and 1 km) of about 2 (ms)2 variance. The low‐frequency variance may be explained as the effect of internal waves, including internal tides. The variance of the broadband fluctuations is reduced somewhat but not eliminated if only high‐intensity peaks are selected; this selection does not affect the statistics of the low‐frequency fluctuations.

Wave-theoretic travel-time sensitivity kernels (TSKs) are calculated in two-dimensional (2D) and three-dimensional (3D) environments and their behavior with increasing propagation range is studied and compared to that of ray-theoretic TSKs and corresponding Fresnel-volumes. The differences between the 2D and 3D TSKs average out when horizontal or cross-range marginals are considered, which indicates that they are not important in the case of range-independent sound-speed perturbations or perturbations of large scale compared to the lateral TSK extent. With increasing range, the wave-theoretic TSKs expand in the horizontal cross-range direction, their cross-range extent being comparable to that of the corresponding free-space Fresnel zone, whereas they remain bounded in the vertical. Vertical travel-time sensitivity kernels (VTSKs)—one-dimensional kernels describing the effect of horizontally uniform sound-speed changes on travel-times—are calculated analytically using a perturbation approach, and also numerically, as horizontal marginals of the corresponding TSKs. Good agreement between analytical and numerical VTSKs, as well as between 2D and 3D VTSKs, is found. As an alternative method to obtain wave-theoretic sensitivity kernels, the parabolic approximation is used; the resulting TSKs and VTSKs are in good agreement with normal-mode results. With increasing range, the wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels.

Sensitivity kernels for receptions of broadband sound transmissions are used to study the effect of the transmitted signal on the sensitivity of the reception to environmental perturbations. A first-order Born approximation is used to obtain the pressure sensitivity of the received signal to small changes in medium sound speed. The pressure perturbation to the received signal caused by medium sound speed changes is expressed as a linear combination of single-frequency sensitivity kernels weighted by the signal in the frequency domain. This formulation can be used to predict the response of a source transmission to sound speed perturbations. The stability of time-reversal is studied and compared to that of a one-way transmission using sensitivity kernels. In the absence of multipath, a reduction in pressure sensitivity using time reversal is only obtained with multiple sources. This can be attributed both to the presence of independent paths and to cancellations that occur due to the overlap of sensitivity kernels for different source-receiver paths. The sensitivity kernel is then optimized to give a new source transmission scheme that takes into account knowledge of the medium statistics and is related to the regularized inverse filter.

International audience; Acoustic remote sensing of the oceans requires a detailed understanding of the acoustic forward problem. The results of a shallow-water transmission experiment between a vertical array of sources and a vertical array of receivers are reported. The source array is used to provide additional degrees of freedom to isolate and track raylike arrivals by beamforming over both source and receiver arrays. The coordinated source-receiver array processing procedure is presented and its effectiveness in an example of tracking raylike arrivals in a fluctuating ocean environment is shown. Many of these arrivals can be tracked over an hour or more and show slowly varying amplitude and phase. The use of a double-beamforming algorithm lays the foundation for shallow-water acoustic remote sensing using travel time and source and receive angles of selected eigenrays.

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used.

Complementing a forward model with its adjoint has some nice features that can be helpful in inverse problems. We will review our previous work on constructing an adjoint for forward propagaton using an implicit finite‐differences parabolic equation model and some simulated results in inverting for the sound speed in the water column. We will also review how an adjoint can aid in model identification, or the question of how the inverse problem should be modeled (e.g., in inverting for the properties of the bottom, how many layers should be used to parametrize the bottom). We will demonstrate this for a range‐dependent inversion, in which in one case there is a bottom inclusion (bottom properties are abruptly different over some range interval between the source and receiver), and another case where there is an internal wave. After reviewing these examples, we will discuss some practical issues in applying adjoint models to real data.

Measurements of acoustic ray travel-times in the ocean provide synoptic integrals of the ocean state between source and receiver. It is known that the ray travel-time is sensitive to variations in the ocean at the transmission time, but the sensitivity of the travel-time to spatial variations in the ocean prior to the acoustic transmission have not been quantified. Using an advanced numerical model, we can identify both the ocean dynamics that control the ocean state along a ray path and quantify the informational content of the ray travel-time observation. This study examines the sensitivity of ray travel-time to the temporally and spatially evolving ocean state in the Philippine Sea over a one year experiment. The travel-times are found to be sensitive to the internal tide generation prior to the sample time and to advective effects that alter density along the ray path. Temporal nonlinearity of these sensitivities suggest that prior knowledge of the ocean state is necessary to exploit the travel-time observations. After assimilating the travel-time observations, the contribution of the travel-time information to our estimation of the ocean state is quantified and evaluated to further identify what the travel-time observation reveals about the ocean.

Six transceivers and one distributed vertical line array (DVLA) receiver were moored in the northern Philippine Sea from April 2010 to May 2011 for low-frequency (325 Hz and below), deep water propagation experiments. The shortest range was about 130 km and the longest about 640 km. A 2009 equipment test yielded travel times between a moored source and a more limited DVLA at about 185 km range along one of the 2010–2011 paths. Experimental goals included understanding the impacts of fronts, eddies, and internal tides on acoustic propagation and determining the utility of acoustic measurements for ocean state estimation. This presentation will report on comparisons between ray travel times computed in a state estimate for the Northern Philippine Sea excluding the ray data, and observations from the 2009 and 2010–2011 experiments. The state estimate uses satellite sea surface height and sea surface temperature observations as well as Argo and XBT profiles. Ray arrival times calculated from the state estimate will be compared to observations as a simple estimate of the novel information present in the data.

Ocean flows impart a time dependence to interference patterns of sound reflecting at low horizontal angle from sloping bathymetry. This is a higher level of complexity than interference patterns within vertical slices in spherically symmetric environments. The time-space statistics may be co-dependent and non-normal, making conventional methods inapplicable. Here, patterns that occur when 100-1000 Hz sound reflects at slopes are simulated with three-dimensional methods. Multiple statistics of sound at virtual arrays are computed over the domain, including incoherent power, beam power, spatial correlation length, and array gain assuming idealized noise conditions. These depend on source and receiver locations with respect to bathymetric features, and can be computed for instantaneously sampled ocean conditions to study their evolution within the time frame of the dominant flow, or computed via averaging over a few periods of the dominant flow features (tides, for example). Here, the spatial complexity of p...