Sound Speed Profile Research Articles

Automatically Differentiable Higher-Order Parabolic Equation for Real-Time Underwater Sound Speed Profile Sensing

This paper is dedicated to the acoustic inversion of the vertical sound speed profiles (SSPs) in the underwater marine environment. The method of automatic differentiation is applied for the first time in this context. Representing the finite-difference Padé approximation of the propagation operator as a computational graph allows for the analytical computation of the gradient with respect to the SSP directly within the numerical scheme. The availability of the gradient, along with the high computational efficiency of the numerical method used, enables rapid inversion of the SSP based on acoustic measurements from a hydrophone array. It is demonstrated that local optimization methods can be effectively used for real-time sound speed inversion. Comparative analysis with existing methods shows the significant superiority of the proposed method in terms of computation speed.

The Parameterized Oceanic Front-Guided PIX2PIX Model: A Limited Data-Driven Approach to Oceanic Front Sound Speed Reconstruction

In response to the demand for high-precision acoustic support under the condition of limited data, this study utilized high-resolution reanalysis data and in situ observation data to extract the Kuroshio Extension Front (KEF) section through front-line identification methods. By combining the parameterized oceanic front model and the statistical features of big data, the parameterized oceanic front was reconstructed. A proxy dataset was generated using the Latin hypercube sampling method, and the sound speed reconstruction model based on the PIX2PIX model was trained and validated using single sound speed profiles at different positions of the oceanic front, combined with the parameterized oceanic front model. The experimental results show that the proposed sound speed reconstruction model can significantly improve the reconstruction accuracy by introducing the parameterized front model as an additional input, especially in the shallow-water area. The mean absolute error (MAE) of the full-depth sound speed reconstruction for this model is 0.63~0.95 m·s−1, and the structural similarity index (SSIM) is 0.76~0.78. The MAE of the sound speed section within a 1000 m depth is reduced by 6.50~37.62%, reaching 1.95~3.31 m·s−1. In addition, the acoustic support capabilities and generalization of the model were verified through ray tracing models and in situ data. This study contributes to advancing high-precision acoustic support in data-limited oceanic environments, laying a solid groundwork for future innovations in marine acoustics.

Cross-Layer Routing Protocol Based on Channel Quality for Underwater Acoustic Communication Networks

Due to the physical characteristics of acoustic channels, the performance of underwater acoustic communication networks (UACNs) is more susceptible to the impacts of multipath and Doppler effects. Channel quality can serve as a measure of the reliability of underwater communication links. A cross-layer routing protocol based on channel quality (CLCQ) is proposed to improve the overall network performance and resource utilization. First, the BELLHOP ray model is used to calculate the channel impulse response combined with the winter sound speed profile data of a specific sea area. Then, the channel impulse response is integrated into the communication system to evaluate the channel quality between nodes based on the bit error rate (BER). Finally, during the selection of the next hop node, a reinforcement learning algorithm is employed to facilitate cross-layer interaction within the protocol stack. The optimal relay node is determined by the channel quality index (BER) from the physical layer, the buffer state from the data link layer, and the node residual energy. To enhance the algorithm’s convergence speed, a forwarding candidate set selection method is proposed which takes into account node depth, residual energy, and buffer state. Simulation results show that the packet delivery rate (PDR) of the CLCQ is significantly higher than that of Q-Learning-Based Energy-Efficient and Lifetime-Extended Adaptive Routing (QELAR) and Geographic and Opportunistic Routing (GEDAR).

Advancing glider-based acoustic measurements of underwater-radiated ship noise.

Ocean gliders are versatile and efficient passive acoustic monitoring platforms in remote marine environments, but few studies have examined their potential to monitor ship underwater noise. This study investigates a Slocum glider's capability to assess ship noise compared to the ability of fixed observers. Trials were conducted in shallow coastal inlets and deep bays in Newfoundland, Canada, using a glider, hydrophone array, and single-moored system. The study focused on (1) the glider's self-noise signature, (2) range-depth-dependent propagation loss (PL) models, and (3) identifying the location of the vessel to the glider using glider acoustic measurements. The primary contributors to the glider's self-noise were the buoyancy pump and rudder. The pitch-motor noise coincided with the buoyancy pump activation and did not contribute to the glider self-noise in our experiments. PL models showed that seafloor bathymetry and sound speed profiles significantly impacted estimates compared to models assuming flat and range-independent profiles. The glider's performance in recording ship noise was superior to that of other platforms. Using its hydrophones, the glider could identify the bearing from the vessel, although a third hydrophone would improve reliability and provide range. The findings demonstrate that gliders can characterize noise and enhance our understanding of ocean sound sources.

High-resolution acoustically informed maps of sound speed.

As oceanographic models advance in complexity, accuracy, and resolution, in situ measurements must provide spatiotemporal information with sufficient resolution to inform and validate those models. In this study, water masses at the New England shelf break were mapped using scientific echosounders combined with water column property measurements from a single conductivity, temperature, and depth (CTD) profile. The acoustically-inferred map of sound speed was compared with a sound speed cross section based on two-dimensional interpolation of multiple CTD profiles. Long-range acoustic propagation models were then parameterized by the sound speed profiles estimated by the two methods and differences were compared.

Localisation for underwater acoustic networks with a piece-wise linear sound speed profile

ABSTRACT Underwater agent localisation is a precondition for plenty of ocean applications. The variation of the underwater sound speed (USS) is one of the main factors that constrain the performance of underwater localisation. In this paper, a scheme is designed to reduce the agent localisation error arising from the USS variation in deep water and an agent localisation algorithm named ‘localisation with a piecewise linear USS' (LPL) is proposed. According to the characteristics of a real USS in deep water, a piecewise linear USS model is introduced to approximate the real USS. The agent above under the ‘sound fixing and ranging’ (SOFAR) channel are both considered. The LPL algorithm consists of three parts: initial value estimation, horizontal distance estimation and localisation. Considering the piecewise linear USS profile, the proposed LPL algorithm improves the performance for localisation with 60% more precision than the state-of-the-art methods.

Inferring the Speed of Sound and Wind in the Nighttime Martian Boundary Layer From Impact‐Generated Infrasound

AbstractThe properties of the first kilometers of the Martian atmospheric Planetary Boundary Layer have until now been measured by only a few instruments and probes. InSight offers an opportunity to investigate this region through seismoacoustics. On six occasions, its seismometers recorded short low‐frequency waveforms, with clear dispersion between 0.4 and 4 Hz. These signals are the air‐to‐ground coupling of impact‐generated infrasound, which propagated in an low‐altitude atmospheric waveguide. Their group velocity depends on the structure of effective sound speed in the boundary layer. Here, we conduct a Bayesian inversion of effective sound speed up to 2,000 m altitude using the group velocity measured for events S0981c, S0986c and S1034a. The inverted effective sound speed profiles are in good agreement with estimates provided by the Mars Climate Database. Differences between inverted and modeled profiles can be attributed to a local wind variation in the impact→station direction, of amplitude smaller than 2 m/s.

Improvement of a Green's Function Estimation for a Moving Source Using the Waveguide Invariant Theory.

Understanding the characteristics of underwater sound channels is essential for various remote sensing applications. Typically, the time-domain Green's function or channel impulse response (CIR) is obtained using computationally intensive acoustic propagation models that rely on accurate environmental data, such as sound speed profiles and bathymetry. Ray-based blind deconvolution (RBD) offers a less computationally demanding alternative using plane-wave beamforming to estimate the Green's function. However, the presence of noise can obscure low coherence ray arrivals, making accurate estimation challenging. This paper introduces a method using the waveguide invariant to improve the signal-to-noise ratio (SNR) of broadband Green's functions for a moving source without prior knowledge of range. By utilizing RBD and the frequency shifts from the striation slope, we coherently combine individual Green's functions at adjacent ranges, significantly improving the SNR. In this study, we demonstrated the proposed method via simulation and broadband noise data (200-900 Hz) collected from a moving ship in 100 m deep shallow water.

Plane-wave and cylindrical-wave acoustic reflection from a marine sediment with layering representative of the New England Mud Patch.

An analysis is presented of reflection from a marine sediment consisting of a homogeneous mud layer overlying a sand-mud basement, the latter with an upward-refracting, inverse-square sound speed profile. Such layering is representative of the sediment at the New England Mud Patch (NEMP). By applying appropriate integral transforms and their inverses to the Helmholtz equations for the ocean and the two sediment layers, along with the boundary conditions, a Sommerfeld-Weyl type of wavenumber integral is obtained for the cylindrical-wave reflection coefficient of the sediment, R. A stationary phase evaluation of this integral yields a closed-form expression for the plane-wave reflection coefficient, R0. In the absence of attenuation, the plane-wave solution exhibits total reflection up to a critical grazing angle, ac, but when attenuation in the sediment is introduced, the region of total reflection in |R0| is replaced by a sequence of contiguous peaks. With realistic levels of sediment attenuation, the cylindrical-wave solution, |R|, exhibits a quasi-critical grazing angle, less than ac, which is strongly dependent on the source-plus-receiver height above the seabed, which is mildly dependent on the depth of the mud layer but is essentially independent of frequency. Such behavior is consistent with independent experimental observations at the NEMP.

Comment on: "Anomalous reflection from a two-layered marine sediment" [J. Acoust. Soc. Am. 155, 1285-1296 (2024)] (L).

Buckingham [(2024). J. Acoust. Soc. Am. 155, 1285-1296] analyzed the dependence of the reflection coefficient on the grazing angle in two-layer marine sediment model. The upper layer in his model consists of a fine-grained material (mud), while seawater and the basement below the mud layer are treated as homogeneous halfspaces. Buckingham's analyses revealed several narrow spikes in this dependence that appeared only in the presence of a sound velocity gradient in the mud layer, a phenomenon he called acoustic glint. His derivation was accomplished for certain specific dependencies of the sound velocity on the depth. Surprisingly, the authors appear to reach the conclusion that for a slightly different vertical sound speed profile in the mud layer the spikes are no longer present in the dependence of the reflection coefficient on the grazing angle. More precisely, the same problem is examined in this letter for the case of an n2-linear layer (often called Airy medium). Acoustic glint effect is therefore very sensitive to the exact parametrization of the mud layer.

Response to "Comment on 'Anomalous reflection from a two-layered marine sediment' " [J. Acoust. Soc. Am. 156, 1524-1527 (2024)

In their Comment, the authors conclude that acoustic glint is not present in the reflection coefficient of a two-layer sediment in which the top layer is an Airy medium. They conclude, not that the original, inverse-square analysis of the glint is incorrect, but rather that the presence of glint is very sensitive to the detailed shape of the sound speed profile in the top layer.

Experimental characterization of littoral atmospheric acoustics: Concurrent meteorological and acoustic observations.

The aim of this work is to describe a rich set of acoustic transmission loss observations that were completed in a coastal environment. The data library, enumerated in detail and publicly posted, is comprised of pitch-catch acoustic transmission loss measurements along with concurrent high spatial resolution meteorological observations. The meteorological parameters include near-surface temperature profiles, vertical wind speed profiles in the acoustic propagation direction, and significant wave height estimates. The acoustic source is positioned on an anchored vessel such that the first several hundred meters of the acoustic range is over open water with one microphone array positioned at the shore. A second microphone array is placed several hundred meters inland along the same source-to-receiver heading. The path between the two acoustic arrays is uniform salt marsh vegetation. Observations were made during seven sessions, which represent a variety of atmospheric conditions. That variety of conditions allows for some experimental generalizations about transmission loss as a function of meteorological observations. These include (1) the relationship between vertical effective sound speed profile and transmission loss, and (2) the variability of acoustic pressure with turbulence over time and elevation.

Extending gravitational potentials from the surface boundaries of compact objects

The solutions of the Einstein field equations of general relativity (GR) are prone to rendering systems which are physically non-viable as shown by Delgaty and Lake (1998). This does not detract from the success of general relativity but rather suggests the possibility for implementing new solution methods while being cautious that the resulting systems are indeed physically viable. This emphasizes the importance of applying appropriate criteria in closing the system of non-linear, coupled differential equations of GR. In the case of static systems describing massive compact bodies, an intrinsic property is the vanishing of the radial pressure at the surface boundary of the object which is embedded in an empty Schwarzschild exterior spacetime. In attempting to complete the gravitational description, we first assume a standard, physically plausible metric potential such as that of Finch and Skea. We then attempt to solve for the other metric component by imposing an ansatz which assists in extrapolating from the vanishing pressure boundary condition. Our model is guided by the physicality of the sound speed profiles and associated stability conditions.

Testing a non-local 1-equation turbulent convection model: A solar model

Turbulent convection models treat stellar convection more physically than standard mixing-length theory by including non-local effects. We recently successfully applied the Kuhfuss version to convective cores in main sequence stars. Its usefulness for convective envelopes remains to be tested. The solar convective envelope constitutes a viable test bed for investigating the usefulness of the 1-equation Kuhfuss turbulent convection model. We used the one-dimensional stellar evolution code GARSTEC to calculate a standard solar model with the 1-equation Kuhfuss turbulent convection model, and compared it to helioseismic measurements and a solar model using standard mixing-length theory. Additionally, we investigated the influence of the additional free parameters of the convection model on the solar structure. The 1-equation Kuhfuss model reproduces the sound-speed profile and the lower boundary of the convective region less well than the mixing-length model, because the inherent non-local effects overestimate the amount of convective penetration below the Schwarzschild boundary. We trace this back to the coupling of the temperature gradient to the convective flux in the 1-equation version of the Kuhfuss theory. The temperature stratification of the solar convective envelope is not well modelled by the 1-equation Kuhfuss turbulent convection model, and the more complex 3-equation version is needed to improve the modelling of convection in the envelopes of 1D stellar evolution models.

Eigenvalues of the noise covariance matrix in ocean waveguides.

The eigenvalue (EV) spectra of the theoretical noise covariance matrix (CM) and observed sample CM provide information about the environment, source, and noise generation. This paper investigates these spectra for vertical line arrays (VLAs) and horizontal line arrays (HLAs) in deep and shallow water numerically. Empirically, the spectra are related to the width of the conventional beamforming output in angle space. In deep water, the HLA noise CM tends to be isotropic regardless of the sound speed profile. Thus, the EV spectrum approaches a step function. In contrast, the VLA noise CM is non-isotropic, and the EVs of the CM jump in two steps. The EVs before the first jump are due to sea surface noise, while those between the first and second jump are due to bottom-reflected noise. In shallow water, the VLA noise CM is affected by the environment (sound speed profile and seabed density, sound speed, attenuation, and layers) and array depth, the EVs have a more complicated structure. For Noise09 VLA experimental data, the noise sample CM EVs match the waveguide noise model better than the three-dimensional isotropic noise model.

Solar Models and Astrophysical S-factors Constrained by Helioseismic Results and Updated Neutrino Fluxes

The ratio of metal abundance to hydrogen abundance of the solar photosphere, (Z/X) s , has been revised several times. Standard solar models, based on these revised solar abundances, are in disagreement with seismically inferred results. Recently, Magg et al. introduced a new value for (Z/X) s , which is still under debate in the community. The solar abundance problem or solar modeling problem remains a topic of ongoing debate. We constructed rotating solar models in accordance with various abundance scales where the effects of convection overshoot and enhanced diffusion were included. Among these models, those utilizing Magg’s abundance scale exhibit superior sound speed and density profiles compared to models using other abundance scales. Additionally, they reproduce the observed frequency separation ratios r 02 and r 13. These models also match the seismically inferred surface helium abundance and convection zone depth within the 1σ level. Furthermore, the calculated neutrino fluxes from these models agree with detected ones at the level of 1σ. We found that neutrino fluxes and density profile are influenced by nuclear reactions, allowing us to use the combination of detected neutrino fluxes and seismically inferred density for diagnosing astrophysical S-factors. This diagnostic approach shows that S 11 may be underestimated by 2%, while S 33 may be overestimated by about 3% in previous determinations. The S-factors favored by updated neutrino fluxes and helioseismic results can lead to significant improvements in solar models.

Research on reconstruction of the global sound speed profile combining partial underwater prior information

The sound speed profile (SSP) is an important factor affecting the acoustic propagation characteristics of the ocean, making the accurate acquisition of SSP a crucial step in the interdisciplinary research of oceanography and underwater acoustics. Limited by the cost of in-situ measurement and the performance of the instrument itself, direct measurement of SSP inevitably leads to insufficient depth or even missing information. In this paper, we propose using partial underwater prior information (UWPI) only including underwater sound speed to obtain preliminary reconstruction results of global SSP for the first time. The empirical orthogonal function (EOF) reconstruction algorithm is optimized by employing assimilated SSP as the background SSP to further reduce reconstruction errors. The maximum global average reconstruction error and root mean square error (RMSE) after optimization decrease by >51% and 71%, respectively, which indicates that the performance of the optimized algorithm combined with partial UWPI is further improved. Finally, the performance of the optimized algorithm is discussed from the perspective of acoustic propagation. This research provides a reliable technical approach for SSP reconstruction under incomplete depth conditions, which can be applied in underwater sound field prediction and acoustic detection in the future.

Real-time estimation of underwater sound speed profiles with a data fusion convolutional neural network model

Sound speed profiles (SSPs) characterize the spatial distribution of sound velocity, significantly impacting the trajectory of acoustic signals. Consequently, they play a crucial role in determining the efficiency and precision of communication, localization, and other practical applications. Recently, SSP inversion methods significantly improve real-time performance compared to the direct measurement method, but it is highly dependent on sonar observation data so that the application scope is limited. To obtain real-time sound speed distribution in larger scale areas, we proposes a data-fusion-driven multi-input multi-output convolutional regression neural network (DF-MIMO-RCNN) , which combines satellite-based real-time remote sensing sea surface temperature (SST), historical SSP feature vector, historical mean temperature below the sea surface with corresponding spatial coordinate information. The model gets rid of the dependence on sonar observation data and can be applied to a wider spatial region. Then two sets of experiments were conducted based on the Argo database and marine experimental data respectively. Experimental results based on Argo data show that the proposed method is not only suitable for deep-sea environments at the same depth, but even for shallow water of different depths. At the same time, compared with other algorithms, the root mean square error (RMSE) and RMSE distributions are smaller and more robust. Finally, we conducted deep-sea experiments in the South China Sea. The results show that even in non-strictly gridded sea areas, our proposed model still has lower RMSE and higher robustness, which demonstrates the superiority of our proposed algorithm.

Predictive Modeling of Future Full-Ocean Depth SSPs Utilizing Hierarchical Long Short-Term Memory Neural Networks

The spatial-temporal distribution of underwater sound speed plays a critical role in determining the propagation mode of underwater acoustic signals. Therefore, rapid estimation and prediction of sound speed distribution are imperative for facilitating underwater positioning, navigation, and timing (PNT) services. While sound speed profile (SSP) inversion methods offer quicker response times compared to direct measurement methods, these methods often focus on constructing spatial sound velocity fields and heavily rely on sonar observation data, thus imposing stringent requirements on data sources. To delve into the temporal distribution pattern of sound speed and achieve SSP prediction without relying on sonar observation data, we introduce the hierarchical long short-term memory (H-LSTM) neural network for SSP prediction. Our method enables the estimation of sound speed distribution without the need for on-site data measurement, significantly enhancing time efficiency. Compared to other state-of-the-art approaches, the H-LSTM model achieves a root mean square error (RMSE) of less than 1 m/s in predicting monthly average sound speed distribution. Its prediction accuracy has improved several-fold over alternative methods, which validates the robust capability of our proposed model in predicting SSP.

Phase space representation of sound field excited by a noise source in underwater acoustic waveguide.

The analysis of the field excited in a waveguide by a point noise source is performed using the phase space representation of this field given by the distribution of its amplitude in the depth-angle-time space. The transition from the traditional description of the field amplitude as a function of depth and time to phase space representation is performed using the coherent state expansion developed in quantum mechanics. In this paper, the correlation function of noise signals arriving at different points of the phase plane depth-angle is investigated. Numerical simulation data show that measurements of signal correlations in phase space, performed with the help of a receiving vertical antenna, can be used as input data in solving the problem of source localization and reconstruction of unknown parameters of the sound speed profile. It is shown that in phase space there is an analog of the classical interference pattern observed in the distribution of sound intensity in the distance-frequency plane. The slopes of striations in this interference pattern, as in the conventional one, are given by the Chuprov waveguide invariant.