Sound Speed Profile Research Articles

Effect of oceanographic fluctuations on geo-acoustic inversions and source localization using ships of opportunity

Several merchant ship-radiated noise events were recorded in two separate seabed characterization experiments in the New England Mudpatch region in 2017 (SBCEX17) and 2022 (SBCEX22). These shallow water acoustic experiments were conducted under different oceanographic conditions, resulting in fluctuations in sound propagation. Several statistical inference approaches are used to invert geo-acoustic parameters such as sound speed and density in a mud over sand sediment (See https://doi.org/10.1121/10.0008419). In this work, we explore the effect of sound speed profile fluctuations in the water column on geo-acoustic inversions in the 360–1100 Hz frequency band. Inversions based on measured and simulated data using acoustic models are provided to support our findings. The results demonstrate that sediment parameters become more sensitive to oceanographic variations as the frequency increases and, therefore, sound speed profile fluctuations in the water column need to be taken into close consideration for more accurate geo-acoustic inversions. [Work supported by ONR].

A modular neural network to quickly approximate the modal dispersion in coastal waters

Low-frequency acoustic propagation modeling in coastal waters usually relies on numerical models based on modal theory such as Kraken and Orca. These models compute the modal parameters (e.g., modal wavenumbers and depth functions) that can be used in the calculation of the acoustic field. Their repeated use in broadband applications, or for inversion purposes, comes with a notable computational cost. To mitigate this, a modular neural network (NN) was trained to approximate modal parameters for varying modes and frequencies, across diverse environments, with variable water sound speed profile and variable seabed geoacoustic parameters. The training dataset is generated using Kraken and the NN is evaluated on many environments not seen during training. Once trained, the NN can make broadband predictions without prior knowledge on the number of modes, even when the number of modes changes over the frequency-band of interest. This approach reduces computation time compared to the original forward propagation model, while maintaining high precision. The effectiveness of our method is demonstrated through transmission loss calculations and a simulated geoacoustic inversion scenario.

Robustness of vortex wave based communications to operational variables

Orbital angular momentum (OAM) based acoustic communications are a promising method of increasing bandwidth in underwater acoustic communications networks as their unique phase patterns form an orthogonal basis set on which communications protocols may be based. The underwater acoustic environment, however, is highly complex and dynamic. These complexities make developing systems capable of long-range communications challenging. Methods for using BELLHOP’s ray tracing software to simulate the time series of vortex-wave based communications signals are presented. Additionally, this study explores the robustness of the inner product deconvolution method of decoding OAM-based communications against various operating conditions, considering both environmental and platform variations. The effects on channel cross-talk are assessed against sound speed profile uncertainty, position errors, Doppler Effect, and turbulence in the water column. These analyses shed light on the operational implementation of OAM-based communications systems.

Deep-water ambient sound on near-bottom receivers in the New England Seamount Chain

Ambient sound was recorded for about two months by three synchronized, single-hydrophone receivers that were moored at depths of 2573, 2994, and 4443 m on seamount flanks. Hydrophones were located within 5 m from the seafloor. The data reveal the power spectra and intermittency of the ambient sound intensity in a 13-octave frequency band from 0.5 to 4000 Hz. Statistical distribution of pressure amplitude exhibits much heavier tails than the expected Rayleigh distribution throughout the frequency band of observations. Spatial variability of the observed ambient sound is controlled by the seafloor properties, bathymetric shadowing, and nonuniform distribution of the noise sources on the sea surface due to the Gulf Stream and its meanders. Interferometry of the ambient sound recorded by the receivers with the horizontal separations of 7.0 km shows strong variations of the acoustic travel time between the receivers along a surface-reflected path due to the evolution of the Gulf Stream position. The magnitude of the variations of the passively measured acoustic travel time is consistent with the available contact measurements of the sound speed profiles. Environmental inferences derived from the ambient, shipping, and flow noise data will be discussed. [Work supported by the ONR TFO DRI.]

Subsurface acoustic ducts in the Northern California current system.

This study investigates the subsurface sound channel or acoustic duct that appears seasonally along the U.S. Pacific Northwest coast below the surface mixed layer. The duct has a significant impact on sound propagation at mid-frequencies by trapping sound energy and reducing transmission loss within the channel. A survey of the sound-speed profiles obtained from archived mooring and glider observations reveals that the duct is more prevalent in summer to fall than in winter to spring and offshore of the shelf break than over the shelf. The occurrence of the subsurface duct is typically associated with the presence of a strong halocline and a reduced thermocline or temperature inversion. Furthermore, the duct observed over the shelf slope corresponds to a vertically sheared along-slope velocity profile, characterized by equatorward near-surface flow overlaying poleward subsurface flow. Two potential duct formation mechanisms are examined in this study, which are seasonal surface heat exchange and baroclinic advection of distinct water masses. The former mechanism regulates the formation of a downward-refracting sound-speed gradient that caps the duct near the sea surface, while the latter contributes to the formation of an upward-refracting sound-speed gradient that defines the duct's lower boundary.

The Acoustic Laboratory for Marine Applications (ALMA) applied to fluctuating environment analysis

The Acoustic Laboratory for Marine Applications (ALMA) has been used to address problems in underwater acoustics, such as sound propagation in fluctuating environments. In this work, data from the ALMA-2016 at-sea campaign are used to analyze the ocean fluctuation's influence on sound propagation in a shallow-water waveguide. The experiment took place in November 2016 on the continental shelf of the eastern coast of the island of Corsica. A source and a receiver array were 9.3 km apart in a nearly constant water depth of 100 m. A thermistor chain was moored near the source to monitor sound speed fluctuations. The source emitted a variety of signals from which the chirp (1–13 kHz) is used to extract the waveguide eigenrays. To do so, a time-domain beamforming is performed on the match-filtered received signals with an automatic detection of local maxima in the time of arrival/direction of arrival (TOA/DOA) domain. A 2 min acquisition period of more than 13 h duration shows significant fluctuations in eigenray TOAs/DOAs. Qualitative comparisons with synthetic signals obtained from simulations permit reproduction of the observed eigenray fluctuations without including range dependence of the sound-speed profile. In addition, the joint analysis of the probability density function of the normalized acoustic intensity and of the thermistor chain data highlights the time dependence of the received signal characteristics.

A Method for Sound Speed Profile Prediction Based on CNN-BiLSTM-Attention Network

In response to the current challenges in efficiently acquiring sound speed profiles and ensuring their representativeness, considering the need to fully leverage historical sound speed profiles while accounting for their spatiotemporal variability, we introduce a model for sound speed profile prediction based on a CNN-BiLSTM-Attention network, which integrates a convolutional neural network (CNN), a bidirectional long short-term memory network (BiLSTM), and an attention mechanism (AM). The synergy of these components enables the model to extract the spatiotemporal features of sound speed profiles more comprehensively. Utilizing the global ocean Argo grid dataset, the model predicted the sound speed profiles of an experimental zone in the Western Pacific Ocean. In predicting sound speed profiles of a single point, the model achieved a root mean square error (RMSE), relative error (RE), and accuracy (ACC) of 0.72 m/s, 0.029%, and 0.99971, respectively, surpassing comparative models. For regional sound speed profile prediction, the mean RMSE, RE, and ACC of different water layers were 0.919 m/s, −0.016%, and 0.9995, respectively. The experimental outcomes not only confirm the high accuracy of the model, but also highlight its superiority in sound speed profile prediction, particularly as an effective compensatory approach when profile measurements are untimely or contain representational errors.

Sound Speed Inversion Based on Multi-Source Ocean Remote Sensing Observations and Machine Learning

Ocean sound speed is important for underwater acoustic applications, such as communications, navigation and localization, where the assumption of uniformly distributed sound speed profiles (SSPs) is generally used and greatly degrades the performance of underwater acoustic systems. The acquisition of SSPs is necessary for the corrections of the sound ray propagation paths. However, the inversion of SSPs is challenging due to the intricate relations of interrelated physical ocean elements and suffers from the high costs of calculations and hardware deployments. This paper proposes a novel sound speed inversion method based on multi-source ocean remote sensing observations and machine learning, which adapts to large-scale sea regions. Firstly, the datasets of SSPs are generated utilizing the Argo thermohaline profiles and the empirical formulas of the sound speed. Then, the SSPs are analyzed utilizing the empirical orthogonal functions (EOFs) to reduce the dimensions of the feature space as well as the computational load. Considering the nonlinear regression relations of SSPs and the observed datasets, a general framework for sound speed inversion is formulated, which combines the designed machine learning models with the reduced-dimensional feature representations, multi-source ocean remote sensing observations and water temperature data. After being well trained, the proposed machine learning models realize the accurate inversion of the targeted ocean region by inputting the real-time ocean environmental data. The experiments verify the advantages of the proposed method in terms of the accuracy and effectiveness compared with conventional methods.

Expendable Conductivity–Temperature–Depth-Assisted Fast Underwater Sound Speed Estimation by Convolutional Neural Network with Reduced Fully Connected Layers

Obtaining accurate sound speed profiles (SSPs) in near-real-time is of great significance for ocean exploration, underwater communication and improving the performance of sonar systems. In response to the problem that traditional sound speed estimation methods cannot obtain real-time sound speed distribution or rely too much on sonar observation data, we propose an SSP estimation method based on a convolutional neural network with reduced fully connected layers (RFC-CNN) in this paper. This method utilizes neural networks to extract the complex nonlinear features of various types of data. With the help of the historical SSPs and shallow seawater sound speed and temperature data obtained by expendable conductivity–temperature–depth probes (XCTDs), a more accurate estimation of the regional sound speed distribution can be realized quickly. This approach can save the observation cost and significantly improve the real-time performance of SSP estimation.

Fast estimation algorithm of sound field characteristics under the disturbance of sound speed profile in the marine environment

In the context of acoustics, underwater sound propagation is intricately influenced by conditions of the marine environment. These conditions dynamically alter the sound speed profile (SSP), introducing a high level of variability and uncertainty into SSP predictions. Such uncertainties are incorporated into the acoustical model, affecting the accuracy of forecasting sound propagation characteristics, including ray trajectory and propagation loss. This study introduces and applies a stochastic ray model designed to estimate the ray trajectory and propagation loss within the oceanic environment. We specifically examine the effects of SSP changes on sound propagation. Our approach integrates ray theory with an adaptive dynamic orthogonal differential equation to model stochastic evolution fields. Initially, this research utilizes SSPs gathered from the Philippine Sea and Kuroshio Extension region. We investigates the impact of SSP perturbation on the ray trajectory and propagation loss. Following this preliminary analysis, we present a stochastic ray model tailored for rapid estimation of sound field characteristics, premised on effects of the SSP disturbance. The proposed model achieves high accuracy while substantially diminishing the computational complexity compared with the Bellhop model.

Source Depth Discrimination Using Intensity Striations in the Frequency–Depth Plane in Shallow Water with a Thermocline

A source depth discrimination method based on intensity striations in the frequency–depth plane with a vertical linear array in a shallow water environment is proposed and studied theoretically and experimentally. To quantify the orientation of the interference patterns, a generalized waveguide variant (GWV) η is introduced. Due to the different dominance of the mode groups, the GWV distribution in the surface source is sharply peaked, indicating the presence of striations in the interferogram and the slope associated with the source–array range, while the distribution of the submerged source is more diffuse, and its interferogram is chaotic. The existence or lack of a distinct peak is used to separate the surface and submerged source classes. The method does not demand prior knowledge of the sound speed profile or the relative movement between the source and the array. In addition, it is the presence of the striations, not the value of η, that is exploited to separate the surface and submerged source classes, which means the source–array range can be unknown. The proposed method is validated using experimental data on the towing ship in SWellEx–96 and numerical modeling. The method’s performance under noise situations and for different source–array ranges is also investigated.

Performance study of ray-based ocean acoustic tomography methods for estimating submesoscale variability in the upper ocean.

Ocean acoustic tomography (OAT) methods aim at estimating variations of sound speed profiles (SSP) based on acoustic measurements between multiple source-receiver pairs (e.g., eigenray travel times). This study investigates the estimation of range-dependent SSPs in the upper ocean over short ranges (<5 km) using the classical ray-based OAT formulation as well as iterative or adaptive OAT formulations (i.e., when the sources and receivers configuration can evolve across successive iterations of this inverse problem). A regional ocean circulation model for the DeSoto Canyon in the Gulf of Mexico is used to simulate three-dimensional sound speed variations spanning a month-long period, which exhibits significant submesoscale variability of variable intensity. OAT performance is investigated in this simulated environment in terms of (1) the selected source-receivers configuration and effective ray coverage, (2) the selected OAT estimator formulations, linearized forward model accuracy, and the parameterization of the expected SSP variability in terms of empirical orthogonal functions, and (3) the duration over which the OAT inversion is performed. Practical implications for the design of future OAT experiments for monitoring submesoscale variability in the upper ocean with moving autonomous platforms are discussed.

Anomalous reflection from a two-layered marine sediment.

This paper concerns the theory of acoustic reflection from a two-layered marine sediment, the upper layer of which consists of a fine-grained material (mud). The seawater above and basement below the layer are treated as homogeneous half-spaces. Within the mud layer, the density is taken to be constant, and three sound speed profiles are considered: uniform, linear, and inverse-square. The reflection coefficient exhibits a background component that is similar in all three cases, exhibiting only a weak sensitivity to the gradient of the profile, the frequency, and the depth of the layer. Additionally, the two profiles with a non-zero gradient, linear and inverse-square, exhibit a sequence across grazing angle of narrow spikes of total reflection. The angular distribution of this acoustic glint is highly sensitive to the frequency and depth of the layer, and mildly so to the gradient. As the gradient approaches zero, the glint vanishes and the reflection coefficient reduces identically to the form of a uniform sound speed profile. If it were detectable, the angular distribution of the glint, observed at several frequencies, could constitute a unique, sensitive set of "fingerprints," allowing the depth and sound speed gradient of the mud layer to be inferred.

Through the sensor estimation of sound speed profiles.

A through-the-sensor method to sense the local sound speed profile (SSP) using measured acoustic wave numbers via an array of hydrophones is proposed. Ocean sounds can be treated as acoustic energy trapped as discrete modes within the water column. A Fredholm integral equation of the first kind relates the linearized (perturbative) sound speed corrections to the wave number differences between the measured values and those calculated from an acoustic kernel. Thus, a method to exploit environmental information deduced from different in situ sonar systems is proposed. Though this inversion can be unstable and non-unique, recent improvements in sparse inversions can lead to robust estimates even without an accurate starting SSP. An iterative algorithm using multiple acoustic frequencies is beneficial to achieve convergence and stability for larger sound speed corrections. This paper will compare broadband incoherent L2- and coherent L1-inversion results. Careful consideration must be made of the acoustic frequency, number of modes, a priori environmental information (e.g., water depth), and array length. The method will be first demonstrated on simulations and recordings from the Littoral Depth Discrimination Experiment 2012 (LIDDEX12) data set.

Source depth estimation with feature matching using convolutional neural networks in shallow water

A feature matching method based on the convolutional neural network (named FM-CNN), inspired from matched-field processing (MFP), is proposed to estimate source depth in shallow water. The FM-CNN, trained on the acoustic field replicas of a single source generated by an acoustic propagation model in a range-independent environment, is used to estimate single and multiple source depths in range-independent and mildly range-dependent environments. The performance of the FM-CNN is compared to the conventional MFP method. Sensitivity analysis for the two methods is performed to study the impact of different environmental mismatches (i.e., bottom parameters, water column sound speed profile, and topography) on depth estimation performance in the East China Sea environment. Simulation results demonstrate that the FM-CNN is more robust to the environmental mismatch in both single and multiple source depth estimation than the conventional MFP. The proposed FM-CNN is validated by real data collected from four tracks in the East China Sea experiment. Experimental results demonstrate that the FM-CNN is capable of reliably estimating single and multiple source depths in complex environments, while MFP has a large failure probability due to the presence of strong sidelobes and wide mainlobes.

Asteroseismic Inversions for Internal Sound Speed Profiles of Main-sequence Stars with Radiative Cores

The theoretical oscillation frequencies of even the best asteroseismic models of solar-like oscillators show significant differences from observed oscillation frequencies. Structure inversions seek to use these frequency differences to infer the underlying differences in stellar structure. While used extensively to study the Sun, structure inversion results for other stars have so far been limited. Applying sound speed inversions to more stars allows us to probe stellar theory over a larger range of conditions, as well as look for overall patterns that may hint at deficits in our current understanding. To that end, we present structure inversion results for 12 main-sequence solar-type stars with masses between 1 and 1.15 M ⊙. Our inversions are able to infer differences in the isothermal sound speed in the innermost 30% by radius of our target stars. In half of our target stars, the structure of our best-fit model fully agrees with the observations. In the remainder, the inversions reveal significant differences between the sound speed profile of the star and that of the model. We find five stars where the sound speed in the core of our stellar models is too low and one star showing the opposite behavior. For the two stars in which our inversions reveal the most significant differences, we examine whether changing the microphysics of our models improves them and find that changes to nuclear reaction rates or core opacities can reduce, but do not fully resolve, the differences.

GNSS-A Network Solution with Zenith Acoustic Delay Estimation

The ocean sound speed changes drastically with time and space. It is almost impossible to achieve centimeter-level-precision Global Navigation Satellite System (GNSS)-Acoustic (GNSS-A) positioning without regarding spatio-temporal variations of sound speed. Inspired by the atmospheric delay estimation, we define zenith acoustic delay (ZAD) as the zenith-direction ranging error sourced by the sound speed variations, and then it is decomposed into one temporal component and two horizontal components for the sound speed variations in time and space, respectively. We propose a network solution with the three ZAD components of each seafloor geodetic point as common parameters to be estimated, and then present a piece-wise estimation to characterize their time-varying nature. To remedy the ray bending effect this study is implemented in the context of the ray tracing algorithm based on a reference sound speed profile (SSP). Experimental tests show that the proposed network solution improves ZAD estimation and results in a better position determination as compared to the single-point positioning (SPP) solution. The proposed network solution for a single campaign can achieve a horizontal positioning precision better than 5 cm (1-sigma) for the seafloor geodetic array centroid. The temporal variation of ZAD is up to one meter while the horizontal variations vary within a few decimeters in the time domain and show an azimuthal asymmetry in space.

CRGAN-based turbo code interleaver for underwater acoustic communications

This paper proposes a channel response generative adversarial network (CRGAN)-based turbo code interleaver that estimates a channel response and interleaver indices at a transmitter by using a sound speed profile (SSP) and the ocean environments without feedback from a receiver. The interleaver indices are designed to allocate important bits from the turbo code to subcarriers with great channel gains, which reduces them from being affected by deep fading. Computer simulations and practical ocean experiments demonstrate that the proposed method estimates the channel response with low mean squared errors (MSEs) and improves bit error rate (BER) performances compared with the conventional method.

Semi-analytical solution for sound propagation from a moving directional source in a shallow-water waveguide

Understanding the waveguide fields produced by moving directional sources is of crucial importance in underwater acoustic detection. In practice, moving underwater targets often exhibit directionality, especially at high frequencies. Herein, we present a semi-analytical method to calculate the Doppler-shifted field (DSF) from a directional source moving horizontally in a range-independent, shallow-water waveguide. We develop a novel normal-mode model using a modal-projection approach with a perfectly matched layer. This comprehensively accounts for changes in modal shape, eigenvalue shifts, and the branch-integral contribution. We derive an analytical expression for the DSF based on Huygens’ principle, and the solution is presented 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 expression is valid for any type of radiator moving in a range-independent environment with a smoothly varying sound-speed profile. We then present a theoretical analysis of the Doppler beam shift produced by a piston-like radiator. This reveals that the observed angular offset of modal plane waves can be attributed to the Doppler beam shift and confirms that this is a new mechanism causing considerable differences between the fields generated by a directional moving source and by the same source at rest. This has potential value in various applications, particularly for underwater acoustic detection of moving targets.

Depth distribution law of polarization characteristics of vector acoustic field in shallow sea (Retracted)

The polarization of the acoustic field in the ocean waveguide environment is a unique property that can be measured by using a particle velocity sensor in the water column. It can provide new ideas for locating and detecting the underwater target, so it is interesting to study the polarization. The polarization of a monochromatic signal has been described by the Stokes parameters, a set of four real-valued quantities in previous work. In this work, the Stokes parameters are extended to the broadband form, and the expression is simplified by using the nonstationary phase approximation, which reduces the complexity of the theoretical derivation and reveals the physical mechanism behind the significant variations in polarization with source depth and symmetrical depth. Theoretical analysis shows that the polarization characteristics in the ideal waveguide vary significantly in the sea surface, the sea bottom, the depth of the sound source and symmetrical depth. In this work the numerical simulation is used to verify the theoretical analysis and study the relationship between range and integral bandwidth when nonstationary phase approximation method is effective. The numerical results demonstrate that the simplified expression using the nonstationary phase approximation is effective and can better characterize the depth distribution characteristics of the polarization. Additionally, by normalizing the broadband Stokes parameters, the effect of range on the depth distribution characteristics of polarization can be removed. It means that the normalized broadband Stokes parameters are in theory free of the range and depend on the environment, the receiver depth and the source depth, which have the potential to be used for source depth estimation. Subsequently, focusing on normalized broadband Stokes parameters, we analyzes the effects of parameters such as source frequency, source depth, sound speed profile and water depth on the depth distribution characteristics of polarization. The analysis results show that environmental factors have great influence on the depth distribution characteristics of polarization. In the end, the validity of the nonstationary phase approximation and the range-independent property of the normalized broadband Stokes parameters are verified by the results of the RHUM-RUM experimental data processing. The findings provide a theoretical basis for passive target depth estimation based on polarization.