Ocean sound speed field reconstruction with graph regularized deep matrix factorization

Wavefront distortion can affect the performance of underwater acoustic communication (a-comms) and imaging systems. A measure of wavefront distortion, the background structure functions (BSFs) are functions of sound speed profiles (SSPs) that are functions of depth. Long term, BSFs can use established commercial software to reduce wavefront distortion and forecast phase statistics for coherent systems. Historically, a suite of path-integral, ray tracing, and modal methods replaced the initial methods for statistical acoustics developed in the latter half of the last century. Underwater (UW) acoustics methods provide the amalgamation of deterministic and statistical expressions to help estimate Doppler and delay for UW acoustics by integrating the classical structure functions from the source to the receiver. In the interim years, non-acoustic communications industries used the older methods with algorithms and hardware that alleviated some of the old shortcomings in order to forecast communication performance. For acoustics, the use of databases of BSFs and SSPs recently helped simulate proof-of-concept forecasting of a-comms operating envelopes. These purely statistical BSFs have less than a quarter of the degrees of freedom (DOFs) in classical UW structure functions. Symmetries also drastically reduce the required background DOFs. For decades industry used these purely statistical structure functions to estimate wavefront wander, lensing (ducting), and fade. Commercial methods to estimate comms fade assume the medium has BSFs that are sufficiently symmetric in order to simplify the calculations. While these metrics can require re-calculation at different stations along the propagation path, extra phase screens are compatible with the evolution of computer technology during the past half century. Conditions of acoustical symmetry and invariance allow simplification of the acoustical calculations in most of the deep-water ocean and in littorals under iso-speed conditions. Results from shallow-sea measurements show that background BSFs in the littorals validate the simplified calculations for sufficiently symmetric sound speed fields. However, the complex calculations that arise from removing the simplifications are tractable with recent algorithms. Adaptive wavefront methods can use BSFs with arrays to guide the wavefront through less lossy paths. Nevertheless, even the value of the ability to forecast phase and throughput statistics in locations where measurements or estimates of sound speed fields exist is of adequate value to provide this foundation for the future use of these purely statistical methods.

Matrix completion by deep matrix factorization

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

Estimating the sound speed profile by matching the acoustic intensity striation using a mounted horizontal line array is investigated. Due to constructive and destructive interference between normal modes, the acoustic intensity manifests range-frequency striation structure in shallow water. Using the environment and acoustic data measured during a tomography experiment conducted in the South China Sea in June, 2010, the possibility and validity of inverting for the water column sound speed profile by matching the acoustic intensity striations are studied. The results show that the fluctuation of the sound speed profile has obvious influence on the acoustic intensity striations. The acoustic data recorded in an experiment conducted in the South China Sea in June 2010 are analyzed to invert for the sound speed profiles. The sound speed profile is represented by Empirical Orthogonal Functions (EOFs) to reduce the unknown parameters. The estimates agree well with the measured sound speed profiles and most of the standard deviations are less than 1 m/s.

Environment-aware underwater acoustic detection and communications demand precise forecasting of the sound speed field (SSF) both temporally and spatially. Toward this goal, recent machine learning models, such as recurrent neural networks and Gaussian process regressions, have outperformed classical autoregressive models. However, from the unified theoretical perspective of conditional distribution learning, there is still significant room for improvement, as existing works have not fully learned the conditional distribution of future SSFs given past SSFs. To address these limitations, in this paper, we leverage the use of diffusion models, the foundation of recent successful deep generative models, such as DALL-E 2 and SORA, to learn the conditional distribution even under limited training data, through careful neural architecture and training strategy design. Our experiments, conducted on real-life South China Sea datasets, confirm that our proposed model outperforms the state-of-the-art baselines in forecasting range-dependent SSFs and the associated underwater transmission losses. Additionally, our model provides reliable confidence intervals that quantify the uncertainties of predictions.

Underwater sound speed exerts a significant influence on underwater acoustic communication by altering the propagation path of sound waves. Existing sound speed inversions rely on remote sensing data. These methods predominantly reflect variations of the ocean surface, resulting in low accuracy in the main thermocline layer. To address this issue, a spatio-temporal imputation and forecast (STIF) method is proposed, which conceptualizes the inversion of sound speed fields (SSFs) as a sequence forecast problem independent of remote sensing data. First, to overcome the obstacle in three-dimensional data forecast posed by the sparsity of SSFs, the spatio-temporal imputation is applied to reconstruct complete SSFs. It employs the alternating direction method of multipliers (ADMM) to break the reconstruction problem down into a series of denoising sub-problems. Secondly, the convolutional long short-term network (ConvLSTM) is utilized for future SSFs forecast to capture the dynamic features of temporal and spatial variations. Numerical experimental results demonstrate that the proposed STIF method effectively addresses the constraint of inversion imposed by remote sensing data. Meanwhile, STIF exhibits lower inversion errors under conditions of sparse spatial.

Time-varying range-dependent sound speed profiles (SSPs) computed from high-resolution submesoscale-permitting ocean models can exhibit strong lateral and vertical gradients which are numerically challenging for standard ray-tracing methods, especially in complex environments with abrupt topography. These strong SSPs gradients affect the stability of the predicted eigenrays, e.g., yielding spurious ray arrivals intermittently. Here an anisotropic smoothing kernel, with tailored kernel sizes in the vertical and horizontal dimensions, is applied to the simulated SSPs to enhance the stability of predicted eigenray from standard ray-tracing while retaining the underlying dynamics of the original SSPs. The arrival-times predicted from these smoothed ray tracing simulations—for frequency <1 kHz—match those obtained from parabolic equation (PE) simulations used as benchmark. Furthermore, the predicted arrival-times from PE simulations are found to remain unaffected whether the anisotropic smoothing procedure is applied to the input high-resolution SSPs, as expected since frequency-dependent diffraction effects captured by PE inherently apply a smoothing effect to the SSP gradients. Hence using this smoothing procedure allows to retain the computational efficiency of ray tracing in complex environments while ensuring accurate arrival-time predictions comparable to results from more stable but significantly more computationally intensive PE simulations, [Work supported by ONR.]

The estimation of sound speed fields using ocean acoustic tomography (OAT) in operational systems is limited because user intensive post processing and manual association of arrivals with ray paths are required. Furthermore, inversion techniques typically rely on CTD casts or historical data to create reference sound speed profiles and Gaussian statistical characterizations for the inversion, which may be either unavailable, out of date, or too approximate due to the intermittent ocean dynamics. A method is presented for real-time implementation of OAT, including the tracking of acoustic arrivals, model-data association of ray paths to arrivals (ray identification), and tomographic inversions. One- and two-dimensional tomographic inversions for sound speed fields are performed using stochastic ensemble forecasts of the sound speed field generated via the Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) Primitive-Equation probabilistic ocean modeling system. The method is demonstrated on simulated and real data obtained from moored tomographic sources and receivers, deployed in deep water 100 km South of Nantucket, MA. [This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). ]

IntroductionIn underwater acoustic applications, the three-dimensional sound speed distribution has a significant impact on signal propagation. However, the traditional sound speed profile (SSP) measurement method requires a lot of manpower and time, and it is difficult to popularize. Satellite remote sensing can collect information on a large ocean surface area, from which the underwater information can be derived.MethodIn this paper, we propose a method for reconstructing the SSP based on an extensible end-to-end tree boosting (XGBoost) model. Combined with satellite remote sensing data and Argo profile data, it extracts the characteristic matrix of the SSP and analyzes the contribution rate of each order matrix to reduce the introduction of noise. The model inverts the SSP above 1000 m in the South China Sea by using the root mean square error (RMSE) as the precision evaluation index.ResultThe results showed that the XGBoost model could better reconstruct the SSP above 1000 m, with a RMSE of 1.75 m/s. Compared with the single empirical orthogonal function regression (sEOF-r) model of the linear regression method, the RMSE of the XGBoost model was reduced by 0.59 m/s.DiscussionFor this model, the RMSE of the inversion results was smaller, the robustness was better, and the regression performance was superior to that of the sEOF-r model at different depths. This study provided an efficient tree boosting model for SSP reconstruction, which could reliably and instantaneously monitor the 3D sound speed distribution.

Localizing a cloud of points from noisy measurements of a subset of pairwise distances has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. In [1], Drineas et al. proposed a natural two-stage approach, named SVD-MDS, for this purpose. This approach consists of a low-rank matrix completion algorithm, named SVD-Reconstruct, to estimate random missing distances, and the classic multidimensional scaling (MDS) method to estimate the positions of nodes. In this paper, we present a detailed analysis for this method. More specifically, we first establish error bounds for Euclidean distance matrix (EDM) completion in both expectation and tail forms. Utilizing these results, we then derive the error bound for the recovered positions of nodes. In order to assess the performance of SVD-Reconstruct, we present the minimax lower bound of the zero-diagonal, symmetric, low-rank matrix completion problem by Fano's method. This result reveals that when the noise level is low, the SVD-Reconstruct approach for Euclidean distance matrix completion is suboptimal in the minimax sense; when the noise level is high, SVD-Reconstruct can achieve the optimal rate up to a constant factor.

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Horizontal deflection often occurs when a ray propagates in shallow water with an irregular sea bottom, which makes it difficult to determine eigen-ray trajectory and transmission time. A new method for seeking eigen-ray in three dimensions was proposed and sound speed profile (SSP) was inverted in three-dimensional shallow water using the fastest eigen-ray transmission times to form the cost function. In order to satisfy long-time monitoring of SSP, a kind of sonobuoy was developed with the function of DGPS, short wave radio controlling and dada transmission and experiment was implemented in the South China Sea. It is indicated that the sonobuoy has high reliability and stability in rough sea condition. The precision of SSP inversion can be enhanced dramatically by considering horizontal deflections of eigen-ray. In addition, the influence of small mismatch of seabed depth on precision of inversion can be neglected.

This work is devoted to the statistical approach to ocean acoustic tomography. Maximum-likelihood (ML) estimate of sound speed field is considered. Deterministic, quasi-deterministic and gaussian signals in the presence of gaussian background noise are examined. A rigorous expression for the functional derivative of the Green function with respect to the sound speed field is applied to find the ML estimate. Fisher information matrices (FIM) giving the Cramer-Rao bounds are obtained for various signal models. The modal, ray and interference tomography methods for global, large scale and small scale inhomogeneities are derived using the statistical approach. FIM of estimate of mode or ray delay are obtained. Some numerical evaluations of potential accuracy of sound-speed field reconstruction in typical propagation conditions are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Most acoustic tomography methods neglect density variations in order to obtain speed of sound and attenuation profiles. However, density may provide additional sources of image contrast. In this work, two approaches for density imaging using inverse scattering were explored through simulations in order to evaluate the feasibility of density imaging. The first method consisted of inverting the wave equation by solving for a single functional that depended on both speed of sound and density variations. Density profiles were separated by combining reconstructions at two frequencies (DF-DBIM approach). The second method consisted of solving for two functionals simultaneously: one that depended only on compressibility and one that depended only on density variations. A T-matrix approach was used to relate these functionals to the scattered data. The DF-DBIM approach allowed separation of density and speed of sound profiles at low termination tolerance values and less than an order of magnitude between the largest and smallest frequencies used. However, the convergence of DF-DBIM was compromised even when moderate (around 2%) termination tolerances were used. The T-matrix approach converged when multiple frequency data was used, but required a ka product smaller than one at the lowest frequency. The DF-DBIM requires a very high SNR to obtain reliable quantitative density reconstructions, while the T-matrix approach requires excessively large bandwidths when imaging large targets. These limitations will serve as reference points for further algorithmic improvements required for practical implementation of density imaging on ultrasound tomographic systems.

The ocean acoustic tomographic (OAT) approach to sound speed field estimation is generalized to include a variety of sources of information of interest such as an oceanographic model of the sound speed field, direct local sound speed measurements, and a full field acoustic propagation model as well as measurements. The inverse problem is presented as a four-dimensional field estimation problem using a variational approach commonly used in oceanographic data assimilation. The current OAT approach is shown to be a special case of the general framework. The matched-field tomography (MFT) approach is also discussed within this context. A simple implementation of this novel approach is then investigated in the absence of a suitable oceanographic model, and acoustic propagation is accounted for using a standard parabolic equation model. The inverse equations derived are validated numerically through a simple inversion example, and some issues on environmental mismatch and computations are discussed. The developments then provide a basic framework for ongoing data-model melding in acoustically focused oceanographic sampling (AFOS) network.