Sound Speed Profile Research Articles

A CNN for Range and Seabed Estimation on Normalized and Extracted Time-Series Impulses

Deep learning techniques have the potential to address real-time source localization and seabed characterization from passive ocean acoustic signals. The challenge grows when considering single-sensor cases that lack absolute travel time with no known source or environmental parameters. To address this, convolutional neural networks (CNNs) are trained to predict the source–receiver range and the seabed type on extracted and normalized 1-s pressure time series from explosive charges measured during the 2017 Seabed Characterization Experiment. To investigate the impact of ocean variability, two training data sets containing different sets of water sound-speed profiles (SSPs) are used. CNNs trained on the first synthetic data set, which contains a static ocean depth but significant variability in water SSPs, predict seabed class more accurately than the second data set from the measured data. Conversely, CNNs trained on the second synthetic data set, which contains fewer SSPs (similar to those measured during the experiment) and multiple ocean depths, predict the source–receiver range more accurately than the first data set from the measured data. The CNNs, with a degree of uncertainty, predict the seabed type and the source range when trained on synthetic data that have been stripped of source–receiver information, such as arrival time and amplitude. The CNNs trained to only predict the seabed type also make more accurate predictions on the seabed type when compared to those for multiple prediction types. This study highlights the importance of accounting for ocean variability and prediction uncertainties in training deep learning algorithms for marine applications.

Hybrid Seabed Parameterization to Investigate Geoacoustic Gradients at the New England Mud Patch

This article applies Bayesian geoacoustic inversion with a hybrid seabed-model parameterization to modal-dispersion data from the New England Mud Patch to estimate gradient structure in the upper mud layer. The hybrid parameterization comprises an upper layer with general smooth (continuous) gradients represented by Bernstein polynomials (BPs) for the mud, above an unknown number of discrete (uniform) layers. The Bayesian information criterion is applied to estimate BP orders for sound-speed and density profiles in the mud, and trans-dimensional (trans-D) inversion is applied for the underlying layered structure. The data, collected during the 2017 Seabed Characterization Experiment, include high-order modes (up to mode 21) extracted via warping time-frequency analysis from recordings of a combustive sound source at a vertical hydrophone array. Inversion results for the hybrid parameterization are compared to those from trans-D inversion with no gradient layer. Hybrid-inversion results indicate a nearly iso-speed mud layer with a rapidly increasing gradient near its base, consistent with increasing sand content in the mud above a sand interface, as indicated by cores. The sound-speed ratio of surficial sediments to bottom seawater is found to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt;$</tex-math></inline-formula> 1 with high probability, which differs from trans-D inversion results, indicating the significance of the choice of parameterization in interpreting structure.

Rapid environmental assessment in the South China Sea: Improved inversion of sound speed profile using remote sensing data

Rapid environmental assessment in the South China Sea: Improved inversion of sound speed profile using remote sensing data

Modal-MUSIC: A passive mode estimation algorithm for partially spanning arrays.

State-of-the-art mode estimation methods either utilize active source transmissions or rely on a full-spanning array to extract normal modes from noise radiated by a ship-of-opportunity. Modal-MUSIC, an adaptation of the MUSIC algorithm (best known for direction-of-arrival estimation), extracts normal modes from a moving source of unknown range recorded on a partially spanning vertical line array, given knowledge of the water column sound speed profile. The method is demonstrated on simulations, as well as on data from the SWellEx-96 experiment. Extracted normal modes from ship noise during the experiment are used to successfully localize a multitone source without any geoacoustic information.

On acoustic reflection from a seabed exhibiting a non-uniform sound speed profile, with relevance to fine-grained sediments.

An analysis of the plane wave reflection coefficient of the seabed, R, is developed for two upward-refracting sediment sound speed profiles: the two-parameter linear and the three-parameter inverse-square, both extending to infinite depth. For the linear profile, it turns out that |R| = 1, representing total reflection for all grazing angles and all frequencies, signifying that in this special case, |R| is insensitive to the gradient. The implication is that if |R| is to return information about the shape of a profile, the gradient must change with depth, either smoothly through the presence of second- and/or higher-order depth derivatives or discontinuously at, say, an interface between sediment layers. The inverse-square is an example of a profile with a smoothly varying gradient, for which a general, closed-form expression for R is derived, valid for all grazing angles and all frequencies. When the sound speed ratio is less than unity, representative of a fine-grained sediment (mud), |R| exhibits two frequency regimes, designated high and low, separated by a transition frequency, fT. In each of these regimes, |R| exhibits a frequency-dependent angle of intromission, which exhibits high- and low-frequency limiting values, differing by approximately 3.5°, depending on the geo-acoustic parameters of the sediment.

Numerical modeling and observations of seismo-acoustic waves propagating as modes in a fluid-solid waveguide.

This paper discusses the nature of the low-frequency seismo-acoustic waves generated by submarine earthquakes in the ocean. In a finite-depth homogeneous ocean over a semi-infinite solid crust, the derivation of the acoustic equations shows that waves propagate as modes. The waves propagating with the speed of sound in water (T waves) are preceded by waves with frequencies below the Airy phase. Furthermore, the group speeds of these modes are sensitive to the environmental setting. As a test, we applied the spectral finite-element code SPECFEM2D in a simplified configuration with an ocean layer overlaying a solid crust, and a seismic source below a Gaussian seamount surrounded by a flat seafloor. The simulations confirm that the generated T waves and their precursors follow the theoretical dispersion curves. A more realistic environment with a seismically-layered crust and a sound-speed profile in the ocean is then used to predict the expected acoustic modes. Although noisy, recordings by ocean bottom seismometers from the southwest Indian Ocean show T waves preceded by ultra-low frequency waves, which display two modes comparable to the theoretical ones. They are in good agreement for mode 1, whereas, for mode 0, a slight offset in frequency has yet to be explained.

Improved techniques to resolve the water column sound speed structure for multibeam ray-tracing

Multibeam bathymetry surveys conducted in highly stratified environments are routinely affected by sound speed errors. The approach proposed here aims to combine measured with synthetic sound speed profiles in order to minimize sound speed errors. The adequacy of synthetic profiles derived from a regional hydrodynamic model and spatiotemporal interpolation is therefore investigated. Ray-tracing comparisons at the 65° launch angle between measured and synthetic profiles demonstrates that the expected depth bias for modeled profiles will be in excess of 1% of water depth. Spatiotemporally interpolating hourly sampled profiles decreases the depth bias up to a factor of three for higher beam angles. Residual sounding depth biases are observed and ascribed to a residual surface sound speed error.

A Novel Sound Speed Profile Prediction Method Based on the Convolutional Long-Short Term Memory Network

As an important marine environmental parameter, sound velocity greatly affects the sound propagation characteristics in the ocean. In marine surveying work, prompt and low-cost acquisition of accurate sound speed profiles (SSP) is of immense significance for improving the measurement and positioning accuracy of marine acoustic equipment and ensuring underwater wireless communication. To address the problem of not being able to glean the accurate SSP in real time, we propose a convolution long short-term memory neural network (Conv-LSTM) which combines the long short-term memory (LSTM) neural network and convolution operation to predict the complete sound speed profile based on historical data. Considering SSP is a typical time series and has strong spatial correlation, Conv-LSTM can grasp not only the temporal relevance of time series, but also the spatial characteristics. The Argo temperature and salinity grid data of the North Pacific from 2004 to 2019 is imported to establish the model’s SSP dataset, and the convolution of input data is performed before going through the neurons in this recurrent neural network to extract the spatial relevance of the data itself. In the meantime, in order to prove the advanced nature of this model, we compare it with the LSTM network under the same parameter settings. The experimental results show that predicting the SSP time series at a single coordinate position under the same parameter conditions, it is best to predict the future SSP next month through the historical data of 24 months, and the prediction effect of Conv-LSTM is much better than that of the LSTM network, and the relative error (RE) is 0.872 m/s, which is 1.817 m/s less than that of LSTM. Predictions in the selected area are also exceedingly accurate relative to the actual data; the prediction error of deep water is less than 0.3 m/s, while RE on the surface layer is larger, exceeding 1.6 m/s.

Wave mode computing method using the step-split Padé parabolic equation

Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.

Machine learning approach to prediction of real-time ocean sound speed profile

Sound speed profile (SSP) determines sound propagation in the ocean. Variation of sound speed profiles with time and location heavily impacts underwater sonar systems used in ocean science and engineering. However, mapping sound speed profile over a vast area of the oceans in real-time is impossible by the traditional way, where sound speed is calculated from insitu profiling measurements of temperature, salinity, and pressure, which is expensive and, therefore, limited in sparse locations and time. Here, we aim to develop a machine learning model to predict real-time sound speed profiles anywhere in the global oceans. Our model takes advantage of the big data of long-term global temperature, salinity, and pressure measurements and further accounts for the variability of the surface ocean by inputting sea surface temperature and sea surface salinity data, which can be updated by satellite remote sensing in real-time. Here, SSPs are predicted for Pacific, Atlantic, and Indian ocean regions. The results show that the estimated SSPs had a root-mean-square error of 0.26 m/s and a coefficient of determination of 0.99. About 99% of the estimates lie within ±0.4 m/s of the SSPs obtained from in situ temperature and salinity profiles.

Coupled modeling of the seasonal transmission loss in the Beaufort Sea

An eight-element drifting vertical line array was deployed overwinter 2019–20 in the Beaufort Sea to record transmissions from two moored 35 Hz sources deployed as part of the Coordinated Arctic Acoustic Thermometry Experiment (CAATEX), and seven 925 Hz sources deployed by the Arctic Mobile Observing Systems (AMOS) experiment. Transmissions were received every day on the array at ranges of 10 to 850 km. A probabilistic rough-ice canopy was integrated to a Parabolic Equation code to predict the propagation loss. Sound speed profiles and percent ice cover along the propagation paths were obtained at daily resolution from data-assimilative Global Ice Ocean Prediction System (GIOPS, 20 km spatial resolution). Sea ice roughness and keel properties are empirically determined from the GIOPS ice thickness. The ice roughness is generated using a random pulse-train model with a characteristic wavenumber spectrum slope determined by ice age. Empirical probability distributions of ice keel depth, slope, and spatial densities are used to randomly add keels. Spatial averaging is used to account for signal bandwidth and uncertainty in receiver positions. The environment files and modeling are performed in piece-wise steps to manage memory footprints over long ranges. Modeled propagation losses compare well with the data and reproduce the seasonal variability observed in the measured results.

Sound field variability and mode coupling in the presence of internal Kelvin waves in Lake Kinneret, Israel

Spatiotemporal variability of the low- and mid-frequency sound field in the presence of internal Kelvin waves (IKWs) was studied theoretically and in experiment in Lake Kinneret, Israel. The experiments were done in 2021, where sound field was being recorded during two days (two periods of IKW) using two synchronized vertical line arrays (VLAs) of ten hydrophones each and 10 m between them, deployed in the center of the lake (depth ∼41 m). Wideband linearly frequency modulated sound signals (300Hz–7 kHz) were transmitted from the source deployed near the shore (depth ∼11 m, distance 5.5 km from VLA). IKWs were registered with thermistor strings together with CTD. Sound speed profile is characterized by the thermocline located between 15 and 20 m of the depth with sound speeds 1510 and 1480 m/s above and below the thermocline, respectively. The sound propagation modeling was done using a Parabolic Equation and Normal Modes approaches, considering the real parameters of the gas-saturated bottom and the bathymetry. Results show strong mode coupling along the acoustic track, initiating ∼12 dB variability of the sound intensity. Results of modeling are verified in the experiment. [This work was supported by RFBR, grant 20-55-S52005.]

Normal incidence reflection coefficient measurements of layered sand-mud sediment and comparison to models

Depth-dependent variability in seabed acoustic and geophysical properties can be introduced by both physical and biogenic processes. An experiment was conducted near the mouth of Mobile Bay, Alabama to investigate spatial variability over a mud-sand gradient, where sediment properties showed lateral changes on the scales of tens of meters. Additionally, sediment layering on the scale of centimeters was evident in the top 20 cm of the seabed. Normal-incidence seabed reflection coefficient measurements (20–60 kHz) were acquired using a ship-mounted system to survey a 1.9 km2 area of the seabed, and diver cores were collected for direct analysis of near-surface seabed properties. The cores were acoustically logged to obtain vertical profiles of sound speed and attenuation (10–1000 kHz) and then analyzed for vertical profiles of sediment physical properties (porosity, grain size, organic matter content), infauna community composition, and tensile strength. Physical and acoustic profiles obtained from the cores were then used as inputs to model the n-layer reflection coefficient. Comparison of the modeled and measured reflection coefficients will be discussed. [Work supported by ONR.]

Normal mode acoustic modeling using measurements of ocean sound speed from the Beaufort Sea

Over the last few decades, environmental changes in the Arctic have resulted in a subsurface acoustic duct located between 100- and 300-m depth, known as the Beaufort Duct. This subsurface duct allows for long-range acoustic transmission with little to no interaction with the sea surface or seafloor. In a 2017 long-range acoustic tomography experiment, two Seagliders traversed between five active sources moored within the duct which transmitted linear frequency modulated (LFM) sweeps centered around 250 Hz. These Seagliders were equipped with conductivity, temperature, depth (CTD) sensors as well as passive acoustic receivers. The environmental measurements were used to create sound speed profiles for input into broadband parabolic equation and normal mode acoustic propagation models. The normal mode models provide physical insight into the relationship between the peak arrival and the final cutoff of the ducted acoustic receptions. Modal group speeds from the predictions are used to interpret the acoustic arrival patterns measured on the Seagliders.

Model-data comparison of sound propagation in a glacierized fjord with a simulated brash ice surface.

Glacier ice loss impacts sound propagation within Arctic fjords. Regular calving events contribute to a collection of floating ice fragments, known as brash ice, at the ocean surface that obstruct the natural and anthropogenic acoustic signals, yet are difficult to characterize. Transmission loss measurements using a maximum length sequence (m-sequence) signal were conducted in September 2017 near Hansbreen glacier in Hornsund Fjord, Svalbard with dense brash ice present at the water surface. An acoustic model of the brash ice surface was inferred through consideration of the experimental geometry, arrival amplitude, and travel time difference between the direct and surface reflected arrivals from the source to two receivers. The inferred surface was then incorporated into a forward simulation of the environment using sound speed profiles measured during the experiment. BELLHOP ([Porter and Bucker (1987). J. Acoust. Soc. Am. 82(4), 1349-1359],), a ray tracing code available in the Acoustics Toolbox (HLS Inc., San Diego, CA), was used to track the time difference of arrivals and amplitudes of the modeled direct and surface reflected rays. Comparisons between the measured and simulated results provide insight into the geometric shape and reflection characteristics of the brash ice surface within this and similar environments.

Modeling the effects of internal waves on synthetic aperture sonar resolution

Synthetic aperture sonar (SAS) beamforming is performed under the assumption of a constant sound speed within the water column or by utilizing a measured sound speed profile. Water column features, such as internal waves or internal wave boluses that cause a sound speed structure different than that assumed, can break the constant sound speed assumption resulting in image defocusing and loss of resolution. The resultant loss of resolution can be quantified using the point spread function (PSF). An ellipse fitting technique was applied to SAS images collected by the Norwegian Defence Research Establishment (FFI) using the HISAS system. In conjunction with the analysis conducted on real data, a ray tracing method was applied to model the broadening effects on the PSF for sound speed differences caused by internal wave boluses. A wavenumber beamforming algorithm was also applied to artificial echo data, in which sound speed errors were introduced. It is hoped that the two models can be used in conjunction with SAS data to determine the sound speed within an internal wave feature from the observed loss in resolution.

Under-ice acoustic navigation using real-time model-aided range estimation.

The long baseline (LBL) underwater navigation paradigm relies on the conversion of travel times into pseudoranges to trilaterate position. For real-time autonomous underwater vehicle (AUV) operations, this conversion assumes an isovelocity sound speed. For re-navigation, computationally and/or labor-intensive acoustic modeling may be employed to reduce uncertainty. This work demonstrates a real-time ray-based prediction of the effective sound speed along a path from source to receiver. This method was implemented for an AUV-LBL system in the Beaufort Sea in an ice-covered and a double-ducted propagation environment. Given the lack of Global Navigation Satellite Systems (GNSS) data throughout the vehicle's mission, the pseudorange performance is first evaluated on acoustic transmissions between GNSS-linked beacons. The mean real-time absolute range error between beacons is roughly 11 m at distances up to 3 km. A consistent overestimation in the real-time method provides insights for improved eigenray filtering by the number of bounces. An operationally equivalent pipeline is used to reposition the LBL beacons and re-navigate the AUV, using modeled, historical, and locally observed sound speed profiles. The best re-navigation error is 1.84 ± 2.19 m root mean square. The improved performance suggests that this approach extends the single meter accuracy of the deployed GNSS units into the water column.

Modal dispersion curve extraction from shipping noise at two synchronized vertical arrays

The results of modal dispersion analysis, using low-frequency (20 to 250 Hz) shipping noise in shallow water with a soft bottom is presented. Experiments were carried out in the Sea of Galilee (Lake Kinneret, Israel) having a maximum depth of ∼40 m and a gassy upper sedimentary layer. A receiving system combined two synchronized, 10-hydrophone vertical line arrays (VLAs) located at the center of the lake with distance Dr = 40 m between them. The noise source, R/V “Hermona,” was moving along the straight line joining VLAs, up to 1 km from VLAs. A method of obtaining modal dispersion curves from shipping noise is proposed. For each frequency ω and variable horizontal wavenumber q = ω/cph the noise is spatially filtered at each VLA using calculated solution of the wave equation with the measured sound speed profile in water and the pressure-release condition imposed at the water surface. Then, the ratio of complex modal amplitudes at VLAs is calculated and multiplied by a factor of . The real part of the resulting 2-D structure exhibits the modal dispersion curves, which are used for acoustic characterization of the seabed. [Work supported by ISF, grant 946/20, and RFBR, grant 20-05-00119.]

Layered and gradient model parameterizations in geoacoustic inversion

This paper considers the importance of model parameterization in geoacoustic inversion and uncertainty estimation, including quantitative approaches to model selection as well as potential limitations of the information content of acoustic data to determine the form of geoacoustic profiles, e.g., differentiating between layered and gradient structures. In particular, general parameterizations are considered based on trans-dimensional (trans-D) inversion, which represents profiles as an unknown number of uniform layers, and Bernstein polynomial (BP) inversion, which represents smooth gradients as polynomials of unknown order. These approaches are illustrated and compared for the inversion of high-order modal-dispersion data collected at the New England Mud Patch. It is shown that while the data constrain the sound-speed profile in the mud layer to reasonably high precision, the data cannot differentiate between trans-D layered or BP gradient representations. However, simpler (fixed) parameterizations, such as a homogeneous layer or linear gradient, can be ruled out based on the Bayesian information criterion. Furthermore, the prior choice of parameterization (layers or gradient) has implications on whether the sound-speed ratio at the water–sediment interface is estimated to be less or greater than one with high probability (an issue other acoustic datasets may share). [Work supported by the Office of Naval Research]

Target depth estimation by deep neural network based on acoustic interference structure in deep water

Automatic and robust target depth estimation is an important issue of an active detection system working in the reliable acoustic path (RAP) environment. In this paper, the target depth-sensitive acoustic interference structure is used as input, and a deep neural network (DNN) method is proposed to realize automatic depth estimation. Furthermore, to improve the robustness of the network, both the sound speed profile (SSP) uncertainty and the target trajectory uncertainty are considered in the training dataset. The former is modelled as a random weighted sum of the empirical orthogonal function (EOF), and the latter is modelled by the partial-data-lacking of the network input. The method was evaluated through simulated data and compared with the conventional method of matching the measured interference structure with the replicas. The presented method exhibits a higher accuracy of depth estimate in uncertain environments when the signal-to-noise ratio (SNR) is higher than −6 dB, but its performance deteriorates rapidly as the SNR decreases further. The method is also verified by semi-simulation with experimental data in deep water.