Ocean Acoustic Tomography Research Articles

Performance study of ray-based ocean acoustic tomography methods for estimating submesoscale variability in the upper ocean.

Ocean acoustic tomography (OAT) methods aim at estimating variations of sound speed profiles (SSP) based on acoustic measurements between multiple source-receiver pairs (e.g., eigenray travel times). This study investigates the estimation of range-dependent SSPs in the upper ocean over short ranges (<5 km) using the classical ray-based OAT formulation as well as iterative or adaptive OAT formulations (i.e., when the sources and receivers configuration can evolve across successive iterations of this inverse problem). A regional ocean circulation model for the DeSoto Canyon in the Gulf of Mexico is used to simulate three-dimensional sound speed variations spanning a month-long period, which exhibits significant submesoscale variability of variable intensity. OAT performance is investigated in this simulated environment in terms of (1) the selected source-receivers configuration and effective ray coverage, (2) the selected OAT estimator formulations, linearized forward model accuracy, and the parameterization of the expected SSP variability in terms of empirical orthogonal functions, and (3) the duration over which the OAT inversion is performed. Practical implications for the design of future OAT experiments for monitoring submesoscale variability in the upper ocean with moving autonomous platforms are discussed.

Enhancing ocean environment prediction in Yellow Sea through targeted observation using ocean acoustic tomography

Ocean Acoustic Tomography (OAT) is an efficient and economical marine acoustic observation technique. Targeted observation is an appealing procedure to reduce the uncertainty of ocean environment prediction through additional observation. This study aimed to assess the validity of OAT as an observation method for targeted observation. OAT based on Niche Genetic Algorithm was employed to extract sound speed and temperature profiles from acoustic transmission time, utilizing data from the 2019 Yellow Sea experiment. The inversion results were compared with measurement data, which are found to be accurate and reliable. To further evaluate OAT as targeted observation method, the vertical bias structure of OAT was added on synchronous measurement data in the sensitive area of targeted observation to simulate OAT observation in sensitive area. This simulated data was then incorporated into a 3D-Var assimilation system to improve the short-term prediction of the target region. Comparing the predictions derived with the measurement data at the verification time, it shows that the simulated OAT observation improved the quality of target region prediction, indicating that OAT can be an effective observation method for targeted observation. An Observing System Simulation Experiment was conducted to assess the impact of OAT characteristics on prediction improvement. The results show that both adding observation nodes and extending the observation duration have positive effects, while extending the observation duration performs better.

Sensitivity of phase difference between short-range acoustic multipaths to changes in sound speed and source depth

Ocean acoustic tomography often relies on precise clocks and knowledge of the range between acoustic instruments to estimate ocean-driven sound speed changes. In this study, we explore an alternative method utilizing the difference in the carrier phase between two broadband pulse arrivals to estimate small-scale changes in source depth and sound speed. By leveraging acoustic multipathing, this phase difference approach obviates the need to know the acoustic propagation's precise range and absolute travel time. Observations from a mid-frequency (1–10 kHz) acoustic experiment at short ranges (2–3 km) demonstrate the sensitivity of the difference in the 4 kHz carrier phase between two arrivals to changes in both source depth and sound speed. The difference in the arrival phase is modeled using measurements of the time-varying source depth and sound speed. The comparison between the modeled and observed arrival phase differences reveals a significant agreement, supporting the potential of using phase difference as a reliable estimator for perturbations in either source depth or sound speed for short-range acoustic propagation.

Design of performance-weighted blended mode filters for underwater experiments

Normal mode signals are valuable in ocean acoustic tomography and source localization, assuming that they can be separated using spatial or temporal filtering. Common spatial mode filters include the matched filter (MF) [Ferris, JASA, 1972] and the pseudo-inverse (PI) filter [Tindle et al., JASA, 1978]. Choosing a filter and its parameters, e.g., the PI filter rank, requires knowledge that is not readily available. For instance, it is unlikely that the levels of ambient noise or interference from other modes is known a priori. To address this problem, Chakrabarti and Wage [IEEE Oceans, 2021, 2022] developed a Performance-Weighted Blended mode filtering algorithm that adapts quickly to changing conditions and achieves better performance than a single fixed mode filter. The PWB filter blends a set of PI filters of varying ranks, including a rank-1 PI filter (MF). A PI filter can suppress interference from neighboring modes but is more vulnerable to noise than the MF, which has the maximum white noise gain. This talk explores practical aspects of the PWB implementation, including how to select the set of filters to blend given realistic underwater noise conditions. We will show experimental and simulated data to illustrate performance in different environments. [Work supported by ONR.]

Acoustic transmission loss observed on a tomographic array in the Beaufort Gyre during 2016–2017

The Arctic Ocean is undergoing dramatic changes. The 2016–2017 Canada Basin Acoustic Propagation Experiment (CANAPE) 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 transceivers and a long vertical receiving array measured the impulse responses of the ocean every four hours using broadband signals with center frequencies that ranged from 172.5 to 275 Hz. Ice-profiling sonar data showed a gradual increase in ice draft over the winter with daily median ice drafts reaching maxima of about 1.5 m, suggesting that the ice was first-year ice. The transmission loss of early, resolved ray arrivals from steep ray paths with lower turning depths below 500 m was lowest when open water was present and increased as the ice draft increased. The transmission loss per surface reflection increased with center frequency and surface grazing angle. The values are greater than observed during the 1988–1989 Greenland Sea Tomography experiment, but the ice conditions likely differed significantly.

Estimation of surface layer and Pacific summer water properties from acoustic transmissions in the Beaufort duct using a tomographic array during 2016–2017

The 2016–2017 Canada Basin Acoustic Propagation Experiment (CANAPE) was conducted to assess the effects of the changing Beaufort Gyre on low-frequency underwater acoustic propagation and ambient sound. A 150-km radius ocean acoustic tomography array was deployed with six transceivers and a distributed vertical line array (DVLA) measuring the impulse responses every four hours with broadband signals centered from 172.5 to 275 Hz. The nominal transceiver source depth was 175-m, placing them near the Beaufort duct axis, and the 60 hydrophone DVLA spanned 50 to 600 m. The Beaufort duct (approximately 90-m to 240-m depth) and the surface layer (approximately 0 to 90-m depth) form a coupled double-duct system. Observed arrivals in this system show reverse dispersion with the lowest Beaufort duct modes arriving first and higher double duct modes making up a transmission finale. In this talk, we investigate the oceanographic information content contained in the first and last arrivals which are the easiest to detect and track. The first arrival shows fluctuations from eddies, tides/inertial oscillations, and small seasonal heating/cooling. The last arrival shows a strong seasonal heating/cooling signal but is un-trackable during periods of significant ice cover due to enhanced transmission loss.

Using long-range transmissions in the Beaufort Gyre to test the sound-speed equation at high pressure and low temperature.

An ocean acoustic tomography array with a radius of 150 km was deployed in the central Beaufort Gyre during 2016-2017 for the Canada Basin Acoustic Propagation Experiment. Five 250-Hz transceivers were deployed in a pentagon, with a sixth transceiver at the center. A long vertical receiving array was located northwest of the central mooring. Travel-time anomalies for refracted-surface-reflected acoustic ray paths were calculated relative to travel times computed for a range-dependent sound-speed field from in situ temperature and salinity observations. Travel-time inversions for the three-dimensional sound-speed field consistent with the uncertainties in travel time [∼2 ms root mean square (rms)], receiver and source positions (∼ 3 m rms), and sound speed calculated from conductivity-temperature-depth casts could not be obtained without introducing a deep sound-speed bias (below 1000 m). Because of the precise nature of the travel-time observations with low mesoscale and internal wave variability, the conclusion is that the internationally accepted sound-speed equation (TEOS-10) gives values at high pressure (greater than 1000 m) and low temperature (less than 0 °C) that are too high by 0.14-0.16 m s-1.

Acoustic travel-time variability observed on a 150-km radius tomographic array in the Canada Basin during 2016-2017.

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 Comparative Study of the Temperature Change in a Warm Eddy Using Multisource Data

An ocean acoustic tomography (OAT) experiment conducted in the northern South China Sea in 2021 measured a month-long record of acoustic travel times along paths of over one hundred kilometers in range. A mesoscale eddy passed through the experimental region during the deployment of four acoustic moorings, providing unique OAT data for examining the deep temperature change in the eddy and for comparison with the Hybrid Coordinate Ocean Model (HYCOM) data. The existence of the eddy is first confirmed by the merged sea level anomaly (MSLA) image and HYCOM data and it can exceed the depth of the sound channel axis. The temperature changes measured by temperature and depth (TD)/conductivity–temperature–depth (CTD) loggers and by the OAT sound speed are in accordance with those reflected on the MSLA image during the movement of the eddy. However, the eddy movement prompted by temperature changes in the HYCOM data is different from that measured by TD/CTD. The modeled eddy intensity is at least two times less than the measured eddy intensity. At the sound channel axis depth, a factor of approximately 4.17 ms−1 °C−1 can be used to scale between sound speed and temperature. The transmission/reception path-averaged temperature of the eddy derived from the OAT-computed sound speed at the depth of the sound channel axis is five times greater than those in the HYCOM data. OAT is feasible as a tool to study mesoscale eddy properties in the deep ocean, while HYCOM data are not accurate enough for this mesoscale eddy at the sound channel axis depth. It is suggested that the model be refined by the OAT path-averaged temperature as constraints when the HYCOM data capture the mesoscale eddies.

Performance study of ocean acoustic tomography methods in the upper-ocean environment using autonomous platforms

Accurate knowledge of the spatial and temporal evolution of the three-dimensional ocean sound speed profile (SSP) is crucial for underwater source localization. Ocean acoustic tomography (OAT) methods aim at reconstructing SSPs variations based on acoustic measurements between multiple source-receiver pairs (e.g., eigenrays arrival times). This study investigates the estimation of range-dependent SSPs using a classical model-based OAT method (i.e., ray-based ocean acoustic tomography), for various configurations of source and receiver configurations using autonomous platforms in a highly-dynamic upper ocean environment. A regional oceanographic simulation of the De Soto Canyon circulation in the Gulf of Mexico is used to construct 3D sound speed variations spanning a month long which exhibits significant sub-mesoscale variability. Two main aspects affecting OAT performance in the presence of high 3D SSPs variability are investigated: (1) The influence of the input acoustic data (i.e., source-receivers configuration and platform motion, arrival-times accuracy...) and (2) the actual implementation of the OAT scheme (i.e., selection of complexity reduction basis, linearized forward model assumptions as well as the use of iterative solvers) on SSPs estimations errors. Practical implications for the design of OAT experiments in the dynamic upper ocean will be discussed. [Work supported by the Office of Naval Research.]

Machine learning approaches for ray-based ocean acoustic tomography.

Underwater sound propagation is primarily driven by a nonlinear forward model relating variability of the ocean sound speed profile (SSP) to the acoustic observations (e.g., eigenray arrival times). Ocean acoustic tomography (OAT) methods aim at reconstructing SSP variations (with respect to a reference environment) from changes of the acoustic measurements between multiple source-receiver pairs. This article investigates the performance of three different OAT methods: (1) model-based methods (i.e., classical ray-based OAT using a linearized forward model), (2) data-driven methods (such as deep learning) to directly learn the inverse model, and (3) a hybrid solution [i.e., the neural adjoint (NA) method], which combines deep learning of the forward model with a standard recursive optimization to estimate SSPs. Additionally, synthetic SSPs were generated to augment the variability of the training set. These methods were tested with modeled ray arrivals calculated for a downward refracting environment with mild fluctuations of the thermocline. Idealized towed and fixed source configurations are considered. Results indicate that merging data-driven and model-based methods can benefit OAT predictions depending on the selected sensing configurations and actual ray coverage of the water column. But ultimately, the robustness of OAT predictions depends on the dynamics of the SSP variations.

Statistical Characterization of Seismic Signals

This paper presents a study on the applicability of a method for the statistical characterization of seismic signals which is based on the statistics of their wavelet sub-band coefficients using [Formula: see text] stable distributions. The method was originally applied to underwater acoustic signals of the type used in ocean acoustic tomography and seabed classification applications. The same protocol was applied to seismic signals representing the vertical displacement, measured on a traditional seismograph. The study showed that this process can indeed provide a means of characterizing a seismic signal and be used to estimate similarities between seismic signals, which is an important factor in studying seismic activity in an area.

Physics-Guided Reduced-Order Representation of Three-Dimensional Sound Speed Fields with Ocean Mesoscale Eddies

Ocean mesoscale eddies have an important role in the ocean and affect the underwater sound speed field (SSF). Many physical models have been proposed for mesoscale eddy three-dimensional (3D) structure analysis and construction. Here, we propose a model for the reduced-order representation of 3D SSF with ocean mesoscale eddies. Particularly, the radial basis functions (RBFs), which are guided by the universal physics model of mesoscale eddy in horizontal dimensions, are employed. RBF and empirical orthogonal function (EOF) are used as basis functions for 3D representation. The proposed method is an approximation of the classical Gaussian eddy model in the first-order form. Simulation results confirm the reduced-order representation performance and effectiveness in reconstruction using 136 days of HYCOM data in the northwestward of the South China Sea with a warm eddy and a cold eddy. The proposed RBF + EOF method roughly halves the number of coefficients for mesoscale eddy representation, compared with classical methods. The reduced-order representation method can be utilized in ocean acoustic tomography and acoustic remote sensing in a mesoscale area.

On the use of machine learning for ray-based ocean acoustic tomography

Underwater sound propagation is primarily driven by a non-linear forward model relating variability of the ocean sound speed profile (SSP) to the acoustic observations (e.g., eigenray arrival times). Ocean acoustic tomography (OAT) methods aim at reconstructing SSPs variations (with respect to a reference environment) from changes of the acoustic measurements between multiple source-receiver pairs. We investigated the performance of three different OAT methods: (1) model-based methods (i.e., classical ray-based OAT using a linearized forward model), (2) data-driven methods (such as deep learning) to directly learn the inverse model, and (3) a hybrid solution (i.e., the Neural Adjoint-NA- method) which combines deep learning of the forward model followed by a standard recursive optimization to estimate SSPs. Additionally, synthetic SSPs were generated to augment the variability of the training set. We tested these methods with modeled ray arrivals calculated for a downward refracting environment with mild fluctuations of the thermocline using idealized towed and fixed source configurations. Results indicate that merging data-driven and model-based methods can benefit OAT predictions depending on the selected sensing configurations and actual ray coverage of the water column. But ultimately, the robustness of the OAT predictions depends on the actual dynamics of the SSP variations.

Ocean acoustic tomography in the Beaufort Gyre

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.

Travel-time variability during the 2016–2017 deep-water Canada Basin Acoustic Propagation Experiment

The Arctic Ocean is undergoing dramatic changes in response to increasing atmospheric concentrations of greenhouse gases. The decreases in ice extent, the near disappearance of multiyear ice, and changes in the stratification of the ocean all have important implications for underwater acoustic propagation. During the 2016–2017 Canada Basin Acoustic Propagation Experiment (CANAPE), a long vertical receiving array was embedded within an ocean acoustic tomography array of six acoustic transceivers with a radius of 150 km. The impulse response of the ocean was measured every four hours using broadband signals centered at about 250 Hz. The observed travel-time variability was extraordinarily low, reflecting both the low internal-wave energy level and sparseness of mesoscale eddies in the Canada Basin. The peak-to-peak travel time variability of the early, resolved ray arrivals was only a few tens of milliseconds, and the standard deviations over the entire year were only a few milliseconds. 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. The travel-time fluctuations are roughly an order of magnitude smaller than is typical in midlatitudes at similar ranges.

Surprises in Physical Oceanography: Contributions from Ocean Acoustic Tomography

The author has employed ocean acoustic tomography over the past 30 years to examine problems in physical oceanography, often with surprising results. Tomography offers an accurate measurement of current or sound speed (temperature) averaged over 100s to 1000s of kilometers. It has been used to test the fundamental equation for the speed of sound in seawater and to show that the normal state of the ocean has smooth, stable, well-behaved characteristics of acoustic propagation. This latter property has been challenging for ocean models to reproduce. Tomography measures barotropic tidal currents with remarkable accuracy, and it was used to discover that low-mode internal tides radiate far into the ocean’s interior, while retaining a surprising coherence. Tomographic measurements of large-scale temperature are complementary to point measurements by hydrography; the present observing system, relying principally on altimetry and Argo floats, has little skill in predicting the available tomographic data. The addition of tomographic data to the system would substantially reduce the uncertainty of ocean state estimates. The information content of integral acoustic observations is best exploited as a constraint on ocean models by data assimilation. The applications of tomography for measuring large-scale barotropic current, relative vorticity, and temperature have been under-exploited. Dedicated research programs, supporting novel acoustical oceanography, associated instrumentation development, and multidisciplinary research would further the applications of this observational approach.

Moving source ocean acoustic tomography with uncertainty quantification using controlled source-tow observations.

Ocean sound speed and its uncertainty are estimated using travel-time tomography at ranges up to 2 km using a moving source in ∼600 m water depth. The experiment included two 32-element vertical line arrays deployed about 1 km apart and a towed source at ∼10 m depth transmitting a linear frequency modulated waveform. The inversion accounts for uncertainties in the positions and velocities of the source and receivers in addition to the background sound speed state. At these short ranges, the sound speed effects are small and the representational error of the candidate forward models must be carefully evaluated and minimized. This is tested stringently by a separate position parameter inversion and by cross-validating the estimates of sound speed and arrival time, including uncertainties. In addition, simulations are used to explore the effects of adding additional constraints to the inversion and to compare the performance of moving to fixed source tomography. The results suggest that the ray diversity available from the moving source reduces the posterior sound speed uncertainty compared to the fixed source case.

Tensor-based basis function learning for three-dimensional sound speed fields.

Basis function learning is the stepping stone towards effective three-dimensional (3D) sound speed field (SSF) inversion for various acoustic signal processing tasks, including ocean acoustic tomography, underwater target localization/tracking, and underwater communications. Classical basis functions include the empirical orthogonal functions (EOFs), Fourier basis functions, and their combinations. The unsupervised machine learning method, e.g., the K-singular value decomposition (K-SVD) algorithm, has recently tapped into the basis function design, showing better representation performance than the EOFs. However, existing methods do not consider basis function learning approaches that treat 3D SSF data as a third-order tensor, and, thus, cannot fully utilize the 3D interactions/correlations therein. To circumvent such a drawback, basis function learning is linked to tensor decomposition in this paper, which is the primary drive for recent multi-dimensional data mining. In particular, a tensor-based basis function learning framework is proposed, which can include the classical basis functions (using EOFs and/or Fourier basis functions) as its special cases. This provides a unified tensor perspective for understanding and representing 3D SSFs. Numerical results using the South China Sea 3D SSF data have demonstrated the excellent performance of the tensor-based basis functions.

State Estimates and Forecasts of the Northern Philippine Sea Circulation including Ocean Acoustic Travel Times

AbstractThe 2010–11 North Pacific Acoustic Laboratory (NPAL) Philippine Sea experiment measured travel times between six acoustic transceiver moorings in a 660-km diameter ocean acoustic tomography array in the northern Philippine Sea (NPS). The travel-time series compare favorably with travel times computed for a yearlong series of state estimates produced for this region using the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational (MITgcm-ECCO 4DVAR) assimilation system constrained by satellite sea surface height and sea surface temperature observations and by Argo temperature and salinity profiles. Fluctuations in the computed travel times largely match the fluctuations in the measurements caused by the intense mesoscale eddy field in the NPS, providing a powerful test of the observations and state estimates. The computed travel times tend to be shorter than the measured travel times, however, reflecting a warm bias in the state estimates. After processing the travel times to remove tidal signals and extract the low-frequency variability, the differences between the measured and computed travel times were used in addition to SSH, SST, and Argo temperature and salinity observations to further constrain the model and generate improved state estimates. The assimilation of the travel times reduced the misfit between the measured and computed travel times, while not increasing the misfits with the other assimilated observations. The state estimates that used the travel times are more consistent with temperature measurements from an independent oceanographic mooring than the state estimates that did not incorporate the travel times.