Sound Speed Field Research Articles

Phase stability of convergence zone propagation at mid-frequency.

Mid-frequency transmissions (1.5 to 7.5 kHz) from a towed source to a drifting array one convergence zone away demonstrate smoothly varying phase. Calculations of the strength and diffraction parameters Φ and Λ for a representative background environment predict partially saturated propagation. For a single convergence zone path, the evolving phase rate due to the changing internal wave field corresponds to a narrowband coherent integration time, defined by the length of a discrete Fourier transform that likely captures the signal, from ∼370 s at 10 kHz to ∼1370 s at 1 kHz in the absence of source motion. Simulated propagation with a split-step parabolic equation solver through a sound speed field with thermocline fine structure and a Garrett-Munk internal wave displacement field provides a full wave picture that is consistent with the statistical predictions. Experimental data from the Philippine Sea demonstrates signal phase that is highly correlated with source tow body vertical excursions, measured by a pressure sensor, that couple into horizontal motion. The received signal can be integrated for up to 128 s at 5.5 kHz, with the upper limit thought to be due to non-uniform source motion rather than ocean dynamics.

Acoustic wave propagation in depth-evolving sound-speed field using the lattice Boltzmann method

This study investigates the propagation of sound waves within deep-sea low-sound-speed channels using the lattice Boltzmann method, with a key focus on the influence of depth-dependent sound speed on wave propagation. The depth-variable sound speed condition is realized through the incorporation of an external force proportional to the density gradient. After the model verification, investigations into the two-dimensional spreading of sound sources reveal that the depth-dependent sound speed curves the wave propagation. When source depths differing from the low-sound-speed channel, wave paths deviate due to contrasting speeds above and below. When the sound source is situated within the low-sound-speed channel, waves exhibit converging patterns. The simulations also detail the total reflection behavior of sound waves. When the incident angle falls exceeds the critical angle, the waves remain intact within the low-sound-speed channel, thereby enabling the preservation of high amplitude acoustic signals even at remote locations. The subsequent simulations of sound wave propagation around obstacles demonstrate that the low-sound-speed channel also exhibits better signal transmission capabilities in the presence of obstacles. In a uniform sound speed environment, acoustic wave propagation around a submarine exhibits a symmetric pattern. By contrast, under depth-evolving speed conditions, submarines operating at various depths manifest distinct propagation characteristics, such as asymmetric wave propagation during shallow diving, as well as wave attenuation or even silencing when cruising within low-sound-speed channels. These findings underscore the profound implications of depth-evolving sound speed on underwater acoustic signal detection and transmission.

Classification of sound speed fields in the Western Pacific Ocean based on tensor decomposition

The three-dimensional (3-D) sound speed structure of the ocean is a fundamental environmental element in studying underwater sound propagation modeling and forecasting. The accurate classification of the sound speed fields (SSFs) provides a comprehensive understanding and analysis of the sound propagation pattern. To take advantage of the 3-D structure of the ocean SSFs, this paper presents a quick method based on tensor decomposition for classifying the ocean 3-D SSFs. Utilizing the WOA18 dataset, High Order Iterative Orthogonal (HOOI) decomposition of the 3-D SSFs is executed so as to accurately extract the characteristic information of the SSFs. The Fuzzy C-Means clustering (FCM) method is applied to classify the feature tensors, partitioning of regional categories in different seasons and revealing the typical SSFs structures. By combining the BELLHOP model with analysis of the characteristics of the first convergence zone of each category, it is concluded that there are six categories of SSFs in the Western Pacific Ocean. The SSFs across all categories are primarily latitudinally distributed, featuring distinct sound channel axes and surface sound speed variations.

Zero-shot reconstruction of ocean sound speed field tensors: A deep plug-and-play approach.

Reconstructing a three-dimensional ocean sound speed field (SSF) from limited and noisy measurements presents an ill-posed and challenging inverse problem. Existing methods used a number of pre-specified priors (e.g., low-rank tensor and tensor neural network structures) to address this issue. However, the SSFs are often too complex to be accurately described by these pre-defined priors. While utilizing neural network-based priors trained on historical SSF data may be a viable workaround, acquiring SSF data remains a nontrivial task. This work starts with a key observation: Although natural images and SSFs admit fairly different characteristics, their denoising processes appear to share similar traits-as both remove random components from more structured signals. This observation allows us to incorporate deep denoisers trained using extensive natural images to realize zero-shot SSF reconstruction, without any extra training or network modifications. To implement this idea, an alternating direction method of multipliers (ADMM) algorithm using such a deep denoiser is proposed, which is reminiscent of the plug-and-play scheme from medical imaging. Our plug-and-play framework is tailored for SSF recovery such that the learned denoiser can be simultaneously used with other handcrafted SSF priors. Extensive numerical studies show that the new framework largely outperforms state-of-the-art baselines, especially under widely recognized challenging scenarios, e.g., when the SSF samples are taken as tensor fibers. The code is available at https://github.com/OceanSTARLab/DeepPnP.

Learning data distribution of three-dimensional ocean sound speed fields via diffusion models.

The probability distribution of three-dimensional sound speed fields (3D SSFs) in an ocean region encapsulates vital information about their variations, serving as valuable data-driven priors for SSF inversion tasks. However, learning such a distribution is challenging due to the high dimensionality and complexity of 3D SSFs. To tackle this challenge, we propose employing the diffusion model, a cutting-edge deep generative model that has showcased remarkable performance in diverse domains, including image and audio processing. Nonetheless, applying this approach to 3D ocean SSFs encounters two primary hurdles. First, the lack of publicly available well-crafted 3D SSF datasets impedes training and evaluation. Second, 3D SSF data consist of multiple 2D layers with varying variances, which can lead to uneven denoising during the reverse process. To surmount these obstacles, we introduce a novel 3D SSF dataset called 3DSSF, specifically designed for training and evaluating deep generative models. In addition, we devise a high-capacity neural architecture for the diffusion model to effectively handle variations in 3D sound speeds. Furthermore, we employ state-of-the-art continuous-time-based optimization method and predictor-corrector scheme for high-performance training and sampling. Notably, this paper presents the first evaluation of the diffusion model's effectiveness in generating 3D SSF data. Numerical experiments validate the proposed method's strong ability to learn the underlying data distribution of 3D SSFs, and highlight its effectiveness in assisting SSF inversion tasks and subsequently characterizing the transmission loss of underwater acoustics.

Inversion of Sound Speed Field in Photoacoustic Imaging Based on Root Mean Square Propagation Algorithm

Inversion of Sound Speed Field in Photoacoustic Imaging Based on Root Mean Square Propagation Algorithm

Underwater Sound Speed Field Forecasting Based on the Least Square Support Vector Machine

Underwater sound speed is one of the most significant factors that affects high-accuracy underwater acoustic positioning and navigation. Due to its complex temporal variation, the forecasting of the underwater sound speed field (SSF) becomes a challenging task. Taking advantage of machine learning methods, we propose a new method for SSF forecasting based on the least square support vector machine (LSSVM) and a multi-parameter model, aiming to enhance the forecasting accuracy of underwater SSF with hourly resolution. We first use a matching extension method to standardize profile data and train the LSSVM with the parameters of observation time, temperature, salinity, and depth. We then employ radial basis function kernels to construct the forecasting model of SSF. We validate the feasibility and effectiveness of the LSSVM model by comparing it with the polynomial fitting (PF) and back propagation neural network (BPNN) methods, using hourly data obtained from the measured data and open data. The results show that the means of the root mean square for the LSSVM based on the observation time parameter and the LSSVM based on the multi-parameter model achieve 0.51 m/s and 0.45 m/s, respectively, presenting a significant improvement compared with the PF (0.82 m/s) and BPNN (0.76 m/s) methods.

Ocean sound speed field reconstruction with graph regularized deep matrix factorization

To reconstruct the ocean sound speed field (SSF), a matrix in horizontal could be formed by gridding the sea area, where some sparse entries were filled by the observation sound speed profiles (SSPs). The reconstruction of the SSF can be modeled as a matrix completion problem, using limited and noisy observation values to reconstruct the entire matrix. Furthermore, the spatial correlation of the SSF could be modeled by graph space model, utilizing with the low-rank property of the SSF matrix, the problem of graph regularization low-rank matrix completion was developed. The observed average SSPs in six cross section were estimated from the four underwater acoustic tomography moorings, and nine local SSPs were obtained from pressure inverted echo sounders (PIESs) inversion. By combining the method of deep matrix factorization and the graph regularization, the Graph Regularized Deep Matrix Factorization (GRDMF) method was proposed. The simulation results showed that the GRDMF performs better than the spatial interpolation algorithm in SSF reconstruction. Considering the application scenarios of deep-sea acoustic tomography, an average constraint (AC) item was designed additionally, and then a customized algorithm named GRDMF-AC is proposed. Finally, data of the experiment at the South China Sea in 2021 is processed to verify GRDMF-AC, the results showed that the reconstructed SSF captures mesoscale eddy in the experiment.

Ocean sound speed field reconstruction beyond tensor neural network

Obtaining accurate ocean sound speed fields (SSFs) across a three-dimensional (3D) geographic region is vital for various underwater acoustic tasks. However, the scarcity of measurements due to the high cost of underwater sensors, combined with the high dimensionality of complex 3D SSF, makes the reconstruction problem highly ill-conditioned, thus demanding advanced models and methods. Our recent work has analyzed the reconstruction error and identified one promising way: finding a representation model that is both concise and expressive. Following this path, we proposed a tensor neural network (TNN) model, which leverages the conciseness of tensor models and the expressive power of deep learning. However, existing TNN-based approaches have two limitations: (1) they are unable to capture long-range correlations within the SSF and (2) they can only handle discrete-indexed tensor data. To overcome these limitations and fully unleash the power of deep tensor learning, we seamlessly introduce attention schemes into the existing TNN framework without compromising its interpretability. Additionally, we employ Gaussian process models to evolve the original parameterized tensor model into a new functional tensor model, enabling reconstruction with a continuous grid. Numerical results obtained from real-life datasets demonstrate the superior performance of our approach compared to state-of-the-art methods.

Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part II: Applications.

The stochastic dynamically orthogonal (DO) narrow-angle parabolic equations (NAPEs) are exemplified and their properties and capabilities are described using three new two-dimensional stochastic range-independent and range-dependent test cases with uncertain sound speed field, bathymetry, and source location. We validate results against ground-truth deterministic analytical solutions and direct Monte Carlo (MC) predictions of acoustic pressure and transmission loss fields. We verify the stochastic convergence and computational advantages of the DO-NAPEs and discuss the differences with normal mode approaches. Results show that a single DO-NAPE simulation can accurately predict stochastic range-dependent acoustic fields and their non-Gaussian probability distributions, with computational savings of several orders of magnitude when compared to direct MC methods. With their coupling properties and their adaptation in range to the dominant uncertainties, the DO-NAPEs are shown to predict accurate statistics, from mean and variance to multiple modes and full probability distributions, and to provide excellent reconstructed realizations, from amplitudes and phases to other specific properties of complex realization fields.

Response of sound propagation characteristics to Luzon cold eddy coupled with tide in the Northern South China Sea

The northern part of the South China Sea is a complex ocean environment with a large range of tidal waves and the stable Luzon cold eddy, which significantly influence the sound propagation characteristics through their impact on sound speed. This study uses a 3D ocean-acoustic framework consisting of MITgcm and BELLHOP ray model to investigate the coupled effects of the Luzon cold eddy and tidal waves. Firstly, the model incorporates tidal assimilation to reconstruct the hydrographic field and compute the sound speed field. Subsequently, the sound propagation in a representative region in the northern South China Sea is simulated to compare the response of sound propagation characteristics to the Luzon cold eddy only, tide only, and the coupled effect of both. The results demonstrate that the cold eddy shifts the location of the convergence zone forward by over 5 km at most. Further, it also makes the acoustic energy focus on the first few arrivals and delays the arrival time of rays by about 0.1 s. The tidal waves intensify these effects, resulting in a further increase of the forward distance of the convergence zone by 2-5 km and a delay in arrival time by 0.02 s. Sound propagation in the coupled influence of these two dynamic processes is exposed to steady perturbations from the cold eddy and spatial-temporal perturbations from tidal waves. The model in this study provides valuable insight for underwater detection and positioning in the realistic ocean environment.

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.

Impact of internal waves on underwater acoustic propagation

The propagation of internal waves in the ocean can produce significant fluctuations in the local sound speed field. Understanding how these fluctuations affect acoustic propagation is an area of considerable interest in underwater acoustics. Previous studies have indicated that large fluctuations (of the order of 20 dB) in transmission loss (TL) of acoustic waves can occur due to focusing and defocusing effects as the acoustic waves propagate through an internal wave. This work looks to extend some of these studies by exploring the frequency and directional dependence of these fluctuations through the implementation of a 3D acoustic model (FOR3D) suitable for modelling low frequency (<1 kHz) acoustic propagation. The study utilises sound speed data produced using the non-hydrostatic model MITgcm, simulating a nonlinear three-dimensional internal wave field that was verified using in situ mooring observations. By also considering results from a study utilising an acoustic ray model (Bellhop3D) on the same data, this work gives a comprehensive picture of the internal wave induced TL fluctuations across a range of acoustic frequencies.

Reconstructions of time-evolving sound-speed fields perturbed by deformed and dispersive internal solitary waves in shallow water

The high-fidelity reconstruction of sound speeds is crucial for predicting acoustic propagation in shallow water where internal solitary waves (ISWs) are prevalent. Mapping temperatures from time series to spatial fields is an approach widely used to reproduce the sound speed perturbed by deformed internal waves. However, wave-shape distortions are inherent in the modeling results. This paper analyzes the formation mechanism and dynamic behavior of the distorted waveform that is shown to arise from the mismatch between the modeled and real propagation speeds of individual solitons within an ISW packet. To mitigate distortions, a reconstruction method incorporating the dispersion property of an ISW train is proposed here. The principle is to assign each soliton a real speed observed in the experiment. Then, the modeled solitons propagate at their intrinsic speeds, and the packet disperses naturally with time. The method is applied to reconstruct the sound speed perturbed by ISWs in the South China Sea. The mean and median of the root-mean-square error between the reconstructed and measured sound speeds are below 2 m/s. The modeled shape deformations and packet dispersion agree well with observations, and the waveform distortion is reduced compared with the original method. This work ensures the high fidelity of waveguide-environment reconstructions and facilitates the investigation of sound propagation in the future.

Striking the right balance: Three-dimensional ocean sound speed field reconstruction using tensor neural networks.

Accurately reconstructing a three-dimensional (3D) ocean sound speed field (SSF) is essential for various ocean acoustic applications, but the sparsity and uncertainty of sound speed samples across a vast ocean region make it a challenging task. To tackle this challenge, a large body of reconstruction methods has been developed, including spline interpolation, matrix/tensor-based completion, and deep neural networks (DNNs)-based reconstruction. However, a principled analysis of their effectiveness in 3D SSF reconstruction is still lacking. This paper performs a thorough analysis of the reconstruction error and highlights the need for a balanced representation model that integrates expressiveness and conciseness. To meet this requirement, a 3D SSF-tailored tensor DNN is proposed, which uses tensor computations and DNN architectures to achieve remarkable 3D SSF reconstruction. The proposed model not only includes the previous tensor-based SSF representation model as a special case but also has a natural ability to reject noise. The numerical results using the South China Sea 3D SSF data demonstrate that the proposed method outperforms state-of-the-art methods. The code is available at https://github.com/OceanSTARLab/Tensor-Neural-Network.

Analysis of the influence of the continental shelf slope in the South China Sea on sound propagation

Continental shelf slopes are widely found in transitional sea areas, which are the connecting part between shallow and deep seas. The sound propagation in this part has special effects. This paper takes the continental shelf slope sea area of the South China Sea (SCS) as the research object to analyze the influence of the shelf slope on sound propagation at different seasons. The seasonal difference in the three-dimensional sound ray trajectory and its corresponding transmission loss (TL) are mainly reflected in the case of a shallow sound source, which is caused by the difference in the sound speed field environment. Due to the presence of a strong surface sound channel in winter, the sound source at shallow depths can achieve long-distance propagation. As the strength of the surface sound channel becomes weaker, sound rays with large grazing angles can deflect across the surface sound channel towards the seabed, and sound energy leaks out of the surface sound channel. This part of the sound energy complements the area that the original sound energy can not reach, so the TL in this area is less than 90 dB. As for the slope enhancement effect, we verify it from the perspective of sound ray propagation, calculate the maximum distance between the sound ray and the shelf slope, and the mean absolute percentage error (MAPE) between the theoretical value and the actual value is 7.6%. The above results will have important implications for target detection and hydroacoustic communication in the sea area of continental shelf slopes.

Micro-multipath interference and its effect on sub-minute acoustic fluctuations: Observations of mid-frequency acoustic propagation in the upper ocean

An experiment was conducted to investigate how variability in the acoustic channel impulse response at signal processing timescales of seconds to minutes is related to internal-wave-driven changes in the ocean sound speed field on timescales of tens of minutes. We find that vertical fine-scale structures (≤10 m) embedded in the sound speed profile have strong second derivatives which allow for the formation of acoustic caustics as well as acoustic propagation pathways that interfere with each other (micro-multipaths). Both effects are sensitive to vertical displacement by internal waves, which can therefore produce sub-minute acoustic fluctuations from internal waves that have timescales longer than a minute.

Tomographic reconstruction of 3D sound speed fields to reveal internal tides on the continental slope of the South China Sea

Mirror-type coastal acoustic tomography (MCAT) is an advancement of coastal acoustic tomography (CAT) with a mirror function that enables the nearshore transmission of offshore observation data. Subsurface MCATs are used to monitor small-scale oceanographic phenomena over large areas on the continental slope of the South China Sea (300–1,000 m). This study investigated the performance of MCAT network observation for internal tide monitoring using 3D tomographic inversion. MCAT facilitates communication with each other and is networked. Results of 3D tomographic inversion were highly consistent with the Stanford unstructured nonhydrostatic terrain-following adaptive Navier–Stokes (SUNTANS) model data. The root-mean-square difference of the sound speed obtained by the inversion method was< 1.0 m/s. The high sound speeds induced by the internal tide were well captured by the results of 3D inversion. A high sound speed band of > 1,516 m/s was used as an index of internal tides, which propagated at a speed of 1.9 m/s. Sensitivity experiments demonstrated that a swing of the anchor tether of< 5 m had less impact on sound speed inversion, while distance drifts caused by human activities of > 50 m had a significant influence. The missing of one or several stations owing to natural factors did not generate significant variations in the results of network observation. This study demonstrated that the MCAT network observation strategy, equipped with numerous stations, is more effective in capturing the characteristics of internal tides.

Extreme Hydrometeorological Conditions of Sediment Waves’ Formation and Migration in Peter the Great Bay (The Sea of Japan)

New data were obtained on the formation mechanisms of relief sediment waves (SWs) in Peter the Great Bay of the Sea of Japan. From the studies, we can assume that the sediment waves in the bay originate from two types of turbidity (TB) currents: (1) fine-dispersed TB currents caused by disintegrating internal waves and entrained by the Primorsky current along the shelf through SWs troughs; (2) fine- and coarse-grained TB currents, formed and entrained by the Primorsky current, intensified by the typhoons. This work presents the geological structure of the shelf area containing SWs. We established that the area of SWs location is on the border of change in facies conditions of sediment bedding in the bay. The transition from the inner shelf facies to the outer shelf facies occurs at a depth of 50–60 m. We analyzed the space variability of temperature and sound speed fields peculiar to the region on the results of hydrological CTD measurements and long-term measurements with moored vertical thermostrings. In the course of measurements, seven typhoons during their passage off the Primorye coast of the Russian Federation were registered. We found a significant change in the hydrological situation in the bay under the influence of extreme external factors. Under calm meteorological conditions, up to three mild thermoclines were observed in the bay, located at depths of 8–15 m, 30–35 m, and 45–60 m. During the passage of typhoons, they combined into one powerful thermocline at a depth of approximately 50–60 m, and in some cases, a high-gradient thermocline formed at the depths of 30–40 m (about 12–15 °C per 10 m of depth). The high-gradient layer significantly increases the amplitude and strength of internal gravity waves, thereby increasing the speed of currents in the water media. We should note that this period of transformation of the hydrological profile on the shelf under the influence of typhoons covers the period from August to October-November. We established that in the SWs location area, firstly, the process of internal waves disintegration intensifies in the autumn season, resulting in the formation of the waves with lengths close to the SWs horizontal scales (SWs wavelengths); secondly, under the influence of the typhoons entering the Sea of Japan, the kinetic energy of the shelf branch of the Primorsky current increases. In this case, it acts as a source of TB currents, including medium- and coarse-grained sedimentary material that forms SWs.

Graph-guided Bayesian matrix completion for ocean sound speed field reconstruction.

Reconstructing ocean sound speed field (SSF) from limited and noisy measurements/estimates is crucial for many ocean acoustic applications, including underwater tomography, target localization/tracking, and communications. Classical reconstruction methods include deterministic approaches (e.g., spline interpolation) and geostatistical methods (e.g., kriging). They exhibit a strong link to linear regression and Gaussian process regression in machine learning (ML) literature, by uniformly viewing them as supervised regression models that learn the mapping from the geographical locations to the sound speed outputs. From a unified ML perspective, theoretical analysis indicates that classical reconstruction methods have several drawbacks, such as the sensitivity to noises and high computational cost. To overcome these drawbacks, inspired by the recent thriving development of graph machine learning, we introduce graph-guided Bayesian low-rank matrix completions (LRMCs) for fine-scale and accurate ocean SSF reconstruction. In particular, a more general graph-guided LRMC model is proposed that encompasses the state-of-the-art one as a special case. The proposed model and the associated inference algorithm simultaneously exploit the global (low-rankness) and local (graph structure) information of ocean sound speed data, thus striking an outstanding balance of reconstruction accuracy and computational complexity. Numerical results using real-life ocean SSF data have demonstrated the encouraging performances of the proposed approaches.