Sound Speed Profile Research Articles

Theoretical investigation of sound propagation from a moving directional source in a shallow-water waveguide

Doppler phenomena resulting from a moving directional source can be complicated in shallow water environments. This study presents a semi-analytical method to calculate the Doppler-shifted field (DSF) caused by a directional source moving horizontally in a shallow-water waveguide. First, an improved normal-mode (NM) model is developed to comprehensively account for the Doppler-induced changing modal shapes, eigenvalue shifts, and the contribution of the branch cut integral. Next, an analytical, modal expression for the DSF is derived based on the principles of Huygens and Taylor series expansion. The solution is expressed as a sum over propagating eigenmodes, with the modal excitation determined by the source directivity depending upon the grazing angle of each pair of modal plane waves. This modal expression is applicable to any type of radiators moving in a shallow-water environment with an arbitrary sound speed profile. By employing the proposed theoretical model, we analyze the beam Doppler shift produced by a piston-like radiator moving in a two-layer waveguide. The simulation indicates that an apparent asymmetry arises in the DSF when the beam grazing angle sweeps over the critical angle of the seafloor. This finding confirms that the beam Doppler shift acts as the third mechanism causing significant differences between the field generated by a directional moving source and that by the same source at rest, which may have practical applications in underwater acoustic detection for moving sources.

Observations and simulations of caustic formation due to oceanographic fine structure.

An at-sea experiment in deep water was conducted to explore the impact of small-scale sound-speed variability on mid-frequency (1-10 kHz) acoustic propagation. Short-range (1-5 km) acoustic transmissions were sent through the upper ocean (0-200 m) while oceanographic instruments simultaneously measured the ocean environment within 2 km of the single upper turning points of the acoustic transmissions. During these transmissions, acoustic receptions over a 7.875 m vertical line array show closely spaced, sometimes interfering arrivals. Ray and full-wave simulations of the transmissions using nearby sound-speed profiles are compared deterministically to the received acoustic signals. The sensitivity of the acoustic arrivals to the vertical scales of ocean sound speed is tested by comparing the observed and simulated arrival intensity where the sound-speed profile used by the simulation is smoothed to varying scales. Observations and modeling both suggest that vertical fine-scale structures (1-10 m) embedded in the sound-speed profile have strong second derivatives which allow for the formation of acoustic caustics as well as potentially interfering acoustic propagation multipaths.

Investigating the reliable acoustic path properties in a global scale

Leveraging the benefits of low transmission loss and high signal-to-noise ratio, the reliable acoustic path (RAP) has been extensively employed in various underwater applications. In this study, we investigate RAP properties on a global scale. Acoustic simulations were conducted using global grids with a 0.25° × 0.25° spatial resolution, revealing that RAP range is positively correlated with ocean depth. Contrary to the prevailing belief that RAP properties are relatively unaffected by sound speed variations, our findings indicate that sound speed profiles (SSPs) play a crucial role in determining RAP properties by altering the RAP from 15 km to 50 km at a constant ocean depth of 4000 m. Additionally, the receiver angle can vary by nearly 5 km at the same source location due to SSP variations. Consequently, utilizing highly accurate SSPs can enhance the performance of underwater localization or communication systems that rely on RAP.

A meta-deep-learning framework for spatio-temporal underwater SSP inversion

Sound speed distribution, represented by a sound speed profile (SSP), is of great significance because the nonuniform distribution of sound speed will cause signal propagation path bending with Snell effect, which brings difficulties in precise underwater localization such as emergency rescue. Compared with conventional SSP measurement methods via the conductivity-temperature-depth (CTD) or sound-velocity profiler (SVP), SSP inversion methods leveraging measured sound field information have better real-time performance, such as matched field process (MFP), compressed sensing (CS) and artificial neural networks (ANN). Due to the difficulty in measuring empirical SSP data, these methods face with over-fitting problem in few-shot learning that decreases the inversion accuracy. To rapidly obtain accurate SSP, we propose a task-driven meta-deep-learning (TDML) framework for spatio-temporal SSP inversion. The common features of SSPs are learned through multiple base learners to accelerate the convergence of the model on new tasks, and the model’s sensitivity to the change of sound field data is enhanced via meta training, so as to weaken the over-fitting effect and improve the inversion accuracy. Experiment results show that fast and accurate SSP inversion can be achieved by the proposed TDML method.

An inter-model comparison of parabolic equation methods for sound propagation from wind turbines.

The modeling of sound propagation for land-based wind turbines is a complex task that takes various parameters into account. Not only do the wind speed and wind direction affect the noise received at a certain position by changing the refraction of the sound, but also the terrain complexity, ground impedance, and receiver position relative to the source and ground all affect propagation. These effects are seen by the reflections of the sound at the ground surface causing interference of sound waves, or by the receiver being positioned in and out of noise shadow zones in the upwind far field position, or in steep terrain irregularities. Several sound propagation models with different levels of fidelity have been developed through time to account for these effects. This paper will focus on two different parabolic equation models, the Beilis-Tappert Parabolic Equation and the Generalized Terrain Parabolic Equation, through theoretical studies of varying terrain complexity, ground impedance, and sound speed profiles (upwind, downwind, and no wind). In addition, the propagation models are validated through spectral comparisons to noise measurements from two different campaigns considering loudspeaker noise and wind turbine noise, respectively.

Broad-Learning-Based Localization for Underwater Sensor Networks With Stratification Compensation

Localization is an indispensable service for underwater sensor networks (USNs). Generally, the convex optimization method is adopted to solve the localization problem. However, the acoustic ray in water medium does not propagate along a straight line, which makes it difficult or impossible to transform the non-convex optimization problem into a convex optimization problem. This paper develops a broad learning (BL) based localization solution for USNs with isogradient sound speed profile. We first employ the ray tracing model to compensate the range bias caused by straight-line propagation. On the basis of collected range information from anchor nodes, the localization optimization problem is transformed into supervised, unsupervised and semisupervised learning frameworks. Correspondingly, three BL-based location estimators are developed to seek the position information of sensor nodes, where the incremental learning schemes are conducted for fast parameter tuning and remodeling. In addition, the Cramer-Rao Lower Bound (CRLB) of positioning error and the convergence to global optimality are both analysed. Finally, simulation and experiment results are presented to show the effectiveness of our approach. It is demonstrated that the proposed solution in this paper has the following nice features: 1) relax the dependence of convex relaxation over convex optimization-based location estimators; 2) reduce the training time and improve the localization efficiency over deep learning-based location estimators.

A feature-compressed multi-task learning U-Net for shallow-water source localization in the presence of internal waves

The spatiotemporal variation of sound speed profile caused by internal waves usually causes the mismatch in the Matched-Field Processing (MFP) source localization. A feature-compressed multi-task learning U-Net with Convolutional Block Attention Module (MTL-UNET-CBAM) is proposed to estimate the range and depth of underwater sources in the South China Sea environment with the presence of internal waves. To handle the mismatch caused by internal waves, the temperature sensor chain data are used to reconstruct the two-dimensional sound speed profiles (2D-SSPs) based on the 2D advection model. Then, 2D-SSPs are used to generate the training set with the parabolic equation method. Sensitivity analysis is investigated to examine the effects of sound speed profile mismatch on the source localization performance. The simulation result shows the higher robustness of MTL-UNET-CBAM to the sound speed profile mismatch compared with the conventional Matched-Field Processing (CMFP) method. Experiment data in the South China Sea also used to validate the source localization performance of MTL-UNET-CBAM.

Acoustic error approximation due to Gouy phase in the sea

In order to estimate the statistical phase of underwater propagation for coherent acoustic systems, a calculation of background structure functions, based on wavespeeds, provides a wavefront distortion metric that excludes the phase due to focusing. In 1890, Gouy measured a phase change through the focus that differs for spherical vs cylindrical convergence by a factor of 2 from π/2. Statistics for the locations of the probable focus waist can use structure functions based on the measured sound speed profiles. Phase estimates are susceptible to errors in phase estimation unless results consider the Gouy phase while passing through focus waists. These foci may counteract or average with other errors of estimation, including scattering, type of spreading (cylindrical vs spherical foci), and reflections from the surface and bottom. Oceans have a sufficient range for the spatial derivatives of sound speed profiles to contribute persistently to foci that we show have coherence time and cross-sectional spatial (imaging) coherence. As an alternative, specular point theory can estimate deterministic pressure solutions. Convergence of these ray models that violate the stationary phase requires methods such as catastrophe theory to estimate the focal effects. Sommerfeld had an early comprehensive ray theory description that includes the Gouy phase. Using Flatté’s data, the foci are clearly time and length coherent. Statistically, the mutual coherence function for the Atlantic, Caribbean, and Gulf of Mexico regions shows that even distorted and out-of-phase convergence has full spatial coherence.

Observed transmissions and ocean-ice-acoustic coupled modelling in the Beaufort Sea

An ocean-ice-acoustic coupled model is configured for the Beaufort Sea. The model uses outputs from a data assimilating global scale ice-ocean-atmosphere forecast to drive a bimodal roughness algorithm for generating a realistic ice canopy. The resulting range-dependent ice cover obeys observed roughness, keel number density, depth, and slope, and floe size statistics. The ice is inserted into a parabolic equation acoustic propagation model as a near-zero impedance fluid layer along with a model defined range-dependent sound speed profile. Year-long observations of transmissions at 35 Hz from the Coordinated Arctic Acoustic Thermometry Experiment and 925 Hz from the Arctic Mobile Observing System source were recorded over the winter of 2019–2020 on a free-drifting, eight-element vertical line array designed to vertically span the Beaufort duct. The ocean-ice-acoustic coupled model predicts receive levels that reasonably agree with the measurements over propagation ranges of 30–800 km. At 925 Hz, seasonal and sub-seasonal ocean and ice driven variations of propagation loss are captured in the data and reproduced in the model.

Quantification of spatial and seasonal trends in the atmosphere and construction of statistical models for infrasonic propagation

SUMMARY Infrasonic waves are influenced by variations in the density, pressure and temperature as well as the ambient winds. Modelling infrasonic propagation can be challenging due to the dynamic nature of the atmosphere as well as the sparseness of measurements which result in variability and notable uncertainty. A framework is presented to quantify spatial and seasonal trends in atmospheric structure via analysis of the effective sound speed profile and identification of temporal trends in the middle atmospheric waveguide produced by the circumpolar vortex winds. Seasonal definitions identifying typical atmospheric structures during the summer, winter and spring/fall transition periods are identified using atmospheric data from 2010 through 2020. Seasonal trend analysis is conducted for a number of locations across the contiguous United States to quantify spatial variations in atmospheric structure that impact infrasonic propagation. For each season and location, empirical orthogonal function analysis is used to reduce the historical archive of atmospheric data into a smaller representative set that can be analysed using numerical tools more efficiently. Infrasonic ray tracing and finite-frequency modal propagation analyses are applied to construct propagation path geometry and transmission loss statistics which are useful in localization and yield estimation for infrasonic sources, respectively. An example application is detailed in which transmission loss statistics are combined with an explosive source model and noise statistics to quantify the capability of a network to detect nearby sources.

Time series prediction of shallow water sound speed profile in the presence of internal solitary wave trains

The internal waves, especially the internal solitary wave (ISW) trains, cause violent perturbations of sound speed. Sound speed profile (SSPs) facilitates the pre-understanding of the sound field distribution in the experimental sea, therefore, the real-time prediction of SSPs in the presence of ISW trains are of great significance. In this paper, an orthogonal representation of SSPs that considers the background field (background SSP) variation is proposed. Based on the statistical characteristics of time-series SSPs, high-precision SSP prediction is realized by the long short-term memory recurrent neural network (LSTM). The prediction accuracy is demonstrated with the SSP data from an experiment in the South China Sea, and the mean RMSE of SSP prediction is reduced to about 1 m/s.

Joint trans-dimensional inversion for water-column sound speed and seabed geoacoustic models.

This letter considers joint estimation of the water-column sound-speed profile (SSP) and seabed geoacoustic model through Bayesian inversion of ocean-acoustic data. The inversion is formulated in terms of separate trans-dimensional models for the water column (as an unknown number of nodes of a piecewise-continuous SSP) and seabed (as an unknown number of uniform layers) to intrinsically parameterize each according to the information content of the data. The inversion estimates marginal posterior probability profiles, quantifying the resolution of water-column and seabed structure. To validate the proposed method, modal-dispersion data from the New England Mud Patch, collected using hand-deployable systems, are considered.

Geoacoustic Inversion with a Single Vector Sensor and Multichannel Dispersion Curves

This paper discusses the value added by using a single vector sensor over a conventional pressure-only hydrophone for geoacoustic inversions. Inversion methods based on genetic algorithms are used to estimate the seabed properties. Synthetic signals of impulsive arrivals first are modeled using KRAKEN and RAM propagation models, each being modified to predict components of the vector field. While KRAKEN is utilized to directly compute dispersion curves, RAM provides full-field results that require the application of time warping to separate the modal arrivals. Combinations of dispersion curves utilizing all vector sensor channels are compared to curves estimated with the pressure-only channel. Within the time warping analysis, both binary masking and band-pass filter masking methods are applied to compare stability of results. The environment modeled for the synthetic analysis and inversion method utilize sound speed profiles measured during the Monterey Bay 2019 at-sea experiment and assume a sediment layer of constant thickness overlying a deeper sub-bottom type. White noise is added to the synthetic data at different signal-to-noise ratios to evaluate the impact of signal excess on the results. A hybrid optimization approach is used to improve the results of the genetic algorithm method. The analysis with synthetic data is consistent with the analysis of broadband, impulsive data collected from the experiment, indicating that the additional information from the vertical velocity channel further improves the geoacoustic parameter estimates.

Performance of single empirical orthogonal function regression method in global sound speed profile inversion and sound field prediction

The sound speed profile (SSP) reflects the change in sound speed from the surface to the bottom of the seawater, which will have an important influence on underwater acoustic detection and communication. Depending on the inversion of sea surface data sets measured by satellite to obtain near-real-time and high-precision SSPs has become a research hotspot. In this paper, based on the Argo data and the sea surface data sets, we use the single empirical orthogonal function regression (sEOF-r) method to inverse the global SSPs and evaluate the performance of this method. There are also differences in the performance of inversed results at different sites and in different months at the global scale of the ocean. The eddy kinetic energy (EKE) affects the accuracy of inversion, we propose to add the EKE into the inversion formula at the same time to further optimize the inversed results and improve the accuracy, the global average inversion error after optimization reduces by 20%. Finally, we verify the effectiveness of the optimized method from the perspective of sound field prediction. In most cases, the correlation coefficient of the transmission loss (TL) calculated through the inversion SSP and Argo-SSP exceeds 0.7 and the error is controlled below 6 dB, which will have important implications for the actual sound field prediction and hydroacoustic communication.

Inversion of Full-depth Temperature Profiles Based on Surface Temperature and AUV Measured Data

The sound speed profile has an important impact on sound propagation and underwater acoustic detection, and the water temperature has the most significant impact on the sound speed, so it is critical to obtain high-precision full-depth temperature profiles. With the rapid development of marine mobile platforms, it is possible to obtain depth-fixed temperature data using surface velocimeter or autonomous underwater vehicles (AUVs). This paper uses the measured thermistor chain data to carry out numerical simulation, and discusses the feasibility of reconstructed full-depth temperature profiles using measured temperature of few discrete depths. The back propagation (BP) neural network is used to generate the nonlinear mapping relationship between the temperature in a few discrete depths and the first two empirical orthogonal function (EOF) coefficients. The experimental results show that the temperature at two specially selected depths can reflect the full-depth temperature profiles to a certain extent. However, the information about the water temperature at different depths is diverse and the thermocline contains the most information. As the depth-fixed data measured by the AUV increases, the inversion accuracy of the full-depth temperature profiles increases accordingly. Results shows that, even in ocean regions that have solitary internal waves, when the depth of the depth-fixed data is selected the same as the depth of the surface layer and the two extreme points of the second EOF, the root mean square error (RMSE) of almost all reconstructed temperature profiles in the test set is less than 0.2°C, and the mean RMSE is about 0.12°C.

Experimental demonstration of low signal-to-noise ratio matched field processing with a geoacoustic model extracted from noise.

Passive localization of a low signal-to-noise ratio (SNR) source in a shallow water waveguide without prior geoacoustic information is accomplished by combining the mode-extraction method modal-MUSIC (multiple signal classification) with range-coherent matched field processing (MFP). Range-coherent MFP coherently combines snapshots from different resolution cells to obtain gain over noise. Modal-MUSIC uses knowledge of the water column sound speed profile (no bottom information) to extract noisy estimates of modal wavenumbers from ship noise recorded on a partially spanning vertical line array (VLA). A geoacoustic model is then fit to the wavenumber estimates extracted from noise with modal-MUSIC and used to compute replicas for range-coherent MFP. The combination of these two methods applied to a 21-element VLA achieves successful source localization at SNR levels as low as -20 dB using ten tonals transmitted during the SWellEx96 experiment.

An efficient 3D localization algorithm for compensating stratification effect in underwater acoustic sensor network

AbstractCommunication and networking plays a crucial role in data transmission in UASN. The sensor nodes in UASN are intermittently deployed randomly in the three‐dimension scenario. As a consequence, the three‐dimension based localization algorithm is the need for an hour. To fulfill the objective, we have proposed a localization algorithm I‐LASP (Improvement of localization algorithm for compensating stratification effect based on extended improved particle swarm optimization technique) in three‐dimensional UASN, based on compensation of stratification effect for the improvement of the performance parameters such as localization accuracy, ranging accuracy, convergence rate and execution time. To compute the accurate position of target nodes, EIPSO (Extended improved PSO) technique is applied, and the degree of coplanarity is checked before the calculation of distance among nodes in order to get the accurate location of target nodes. The Centroid method is used to initialize the position of sensor nodes, and the ray theory method is used to compensate the stratification effect on the layered ocean water. The proposed algorithm is compared to the existing LASP, Std PSO, and GNA‐ESSP (Gauss‐newton algorithm‐extended sound speed profile) localization algorithm. The proposed algorithm provides 34.50%, 38.87%, and 42.66% of high accuracy in terms of localization with low density of target sensor nodes and 37.96%, 29.58%, and 50.77% high accuracy in terms of localization with a high density of target sensor nodes respectively. The proposed algorithm is compared with LASP, GNA‐ESSP, and TDOA to obtain 66.84%, 71.14%, and 86.13% of high accuracy in terms of ranging with low density of target sensor nodes and 42.34%, 89.00%, and 95.08% high accuracy in terms of ranging with a high density of target sensor nodes respectively. Experimental results represents that the proposed algorithm obtains better performance in terms of localization accuracy, ranging accuracy, root mean square error, normalized localization error, execution time and convergence rate.

Reconstruction of the Sound Speed Profile in Typical Sea Areas Based on the Single Empirical Orthogonal Function Regression Method

The sound speed profile (SSP) is a necessary prerequisite for acoustic field computation and underwater target localization and monitoring. Due to the dynamic nature of the ocean, the reconstruction of SSPs with surface characteristics is a big challenge. In this study, the Single Empirical Orthogonal Function Regression (sEOF-R) method is employed to establish the regression relationship between the surface parameters and the sound speed anomaly profile (SSAP) in three typical sea areas, namely the equator, Kuroshio Extension (KE), and Northeast Pacific. Based on the established regression relationship and the surface parameters, the underwater SSP is reconstructed. Results show that the reconstruction effects in the three areas show the best performance in the Northeast Pacific, followed by the equator and finally the KE. The quantitative analysis suggests that the local sea level anomaly (SLA) plays the dominant role in influencing the reconstruction effect, followed by the sea surface temperature anomaly (SSTA). Further analysis demonstrates that the sEOF-R method is limited in time-varying and space-varying areas. The SSP reconstructed from the sea surface information in this study is useful for the inversion of the underwater structures.

Improvement of Seafloor Positioning Through Correction of Sound Speed Profile Temporal Variation

Dear Editor, This letter proposes a high-precision seafloor transponder positioning method based on the correction of sound speed profile (SSP) temporal variation. In the proposed method, the ocean sound speed error is modeled as the temporal variation of a background SSP, and the linearized expression of the acoustic travel time with respect to the sound speed coefficient is derived based on the ray acoustic model. Moreover, the proposed method introduces the constraint of acoustic ranging observations between seafloor transponders and determines the weights of travel time and ranging observations using Akaike's Bayesian information criterion (ABIC) to reduce the positioning error caused by the correlation between sound speed and position parameters. The experimental results in the South China Sea show that the proposed method performs better than the global navigation satellite system-acoustic ranging combined positioning solver (GARPOS) [1], in terms of rigid distance errors and long baseline positioning accuracy.

Estimating Arctic Ocean Acoustic Travel Times Using an Earth System Model

AbstractThe hydroacoustic environment of a rapidly warming Arctic Ocean will be impacted by interconnected changes in the physical environment and increased human activity. Previous acoustic calculations will need to be updated to reflect current and future conditions. Earth System Models are important tools for making projections of changes in a wide range of physical processes under future climates. We present a comparison of Arctic acoustic travel times based on output from the Department of Energy's Energy Exascale Earth System Model with measured travel times from the 2016–2017 Canada Basin Acoustic Propagation Experiment and with travel times predicted by empirical temperature and salinity observations. This comparison allows us to test the impact of changes in Arctic sound speed profiles on acoustic travel times and connects Arctic hydroacoustics with the changing Arctic environment as described by a climate model.