Water Sound Speed Profile Research Articles

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.

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.

Prediction of Shipping Noise in Range-Dependent Environments

A prediction model for shipping noise in range-dependent environments based on coupled-mode theory is presented, as an enhancement to existing adiabatic normal-mode approaches without a significant increase in computational effort. Emphasis is placed on the categorization of environmental changes and precalculation and storage of eigenvalues, eigenfunctions and coupling matrices, such that they can be looked up and restored to efficiently compute the acoustic field of arbitrary noise source distributions over a given sea area. Taking into account that the water depth is the primary factor determining the number of propagating modes for a particular frequency, coupling is applied only in the case of changing bathymetry, whereas changes in the water sound-speed profile and/or the geoacoustic characteristics are treated adiabatically. Examples of noise calculations are given for benchmark setups in the Eastern Mediterranean Sea and comparisons with fully adiabatic predictions are drawn. Moreover, the effect of applying range propagation limitations in a numerical propagation model for shipping noise predictions is demonstrated.

A CNN for Range and Seabed Estimation on Normalized and Extracted Time-Series Impulses

Deep learning techniques have the potential to address real-time source localization and seabed characterization from passive ocean acoustic signals. The challenge grows when considering single-sensor cases that lack absolute travel time with no known source or environmental parameters. To address this, convolutional neural networks (CNNs) are trained to predict the source–receiver range and the seabed type on extracted and normalized 1-s pressure time series from explosive charges measured during the 2017 Seabed Characterization Experiment. To investigate the impact of ocean variability, two training data sets containing different sets of water sound-speed profiles (SSPs) are used. CNNs trained on the first synthetic data set, which contains a static ocean depth but significant variability in water SSPs, predict seabed class more accurately than the second data set from the measured data. Conversely, CNNs trained on the second synthetic data set, which contains fewer SSPs (similar to those measured during the experiment) and multiple ocean depths, predict the source–receiver range more accurately than the first data set from the measured data. The CNNs, with a degree of uncertainty, predict the seabed type and the source range when trained on synthetic data that have been stripped of source–receiver information, such as arrival time and amplitude. The CNNs trained to only predict the seabed type also make more accurate predictions on the seabed type when compared to those for multiple prediction types. This study highlights the importance of accounting for ocean variability and prediction uncertainties in training deep learning algorithms for marine applications.

Three-dimensional modeling of T-wave generation and propagation from a South Mid-Atlantic Ridge earthquake.

A three-dimensional (3D) hybrid modeling method is used to study the generation and propagation of T waves in the ocean triggered by a Southern Mid-Atlantic Ridge earthquake. First, a finite-element method model named SPECFEM3D is used to propagate seismic waves in the crust and acoustic waves in the ocean for the T-wave generation in a 200 × 50 km area near the epicenter. A 3D parabolic equation (PE) method is then used to propagate the T waves in the ocean for about 850 km further to the hydrophone stations deployed by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) near Ascension Island. All of the simulations considered the realistic bathymetry and water sound speed profile. The SPECFEM3D results suggest that T waves with clear modal features could be generated by the concentration of reflected head waves in two depressions 40 km away from the epicenter. To compare with the hybrid modeling method for calculating T-wave propagation losses and arrival azimuths at the CTBTO hydrophones, point source simulations using the 3D PE model from the T waves source locations, identified with SPECFEM3D, were also implemented. The advantages and limitations of each approach are discussed.

Learning location and seabed type from a moving mid-frequency source.

While source localization and seabed classification are often approached separately, the convolutional neural networks (CNNs) in this paper simultaneously predict seabed type, source depth and speed, and the closest point of approach. Different CNN architectures are applied to mid-frequency tonal levels from a moving source recorded on a 16-channel vertical line array (VLA). After training each CNN on synthetic data, a statistical representation of predictions on test cases is presented. The performance of a single regression-based CNN is compared to a multitask CNN in which regression is used for the source parameters and classification for the seabed type. The impact of water sound speed profile and seabed variations on the predictions is evaluated using simulated test cases. Environmental mismatch between the training and testing data has a negative impact on source depth estimates, while the remaining labels are estimated tolerably well but with a bias towards shorter ranges. Similar results are found for data measured on two VLAs during Seabed Characterization Experiment 2017. This work shows the superiority of multitask learning and the potential for using a CNN to localize an acoustic source and detect the surficial seabed properties from mid-frequency sounds.

Application of elastic parabolic equation solutions to acoustic reverberation in ice-covered underwater environments

Parabolic equation solutions can be obtained for underwater acoustic environments where elastic boundaries affect the acoustic propagation. One example of this situation is in the Arctic where a (potentially rough) ice layer is on top of the water column. The parabolic equation method shown here rigorously applies the zero-traction and fluid-elastic interface boundary conditions to obtain full field Green’s function estimates near the ice-water interface. This solution is crucial for calculation of recently derived reverberation estimates that require both horizontal and vertical derivatives of the complex acoustic field. Monostatic reverberation estimates for a rough under-ice interface are calculated for an upward refracting water sound speed profile and an elastic ocean bottom with a nearly fluid mud layer. These calculations could be used, for example, to estimate areal distribution of the ice layer roughness from azimuth-time dependence of acoustic reverberation measured in Arctic environments. Performance of the Pade rational function approach in the presence of thin ice cover and low shear speed ocean bottom layers will be addressed.

Using ambient noise to evaluate the acoustic Green’s function for a passive geoacoustic inversion in a dynamic shallow-water environment

Cross-correlation functions (CCFs) of ambient and shipping noise recorded by two hydrophones approximate the deterministic Green’s function and contain information about the propagation environment. This paper employs the data collected in the Shallow Water 2006 experiment on the New Jersey continental shelf to investigate the factors that affect the emergence of approximate Green’s functions from noise CCF estimates and accuracy of the approximation. One month-long continuous records of noise obtained by moored single-hydrophone receivers are analyzed. Hydrophones are located in 80–100-m deep water at distances of several kilometers from each other. Rapid variations of the water sound speed profile, which are primarily due to propagation of trains of strong nonlinear internal gravity waves, limit useful noise-averaging time. Available water temperature data are used to guide the selection of time windows for noise averaging and improve CCF evaluation and retrieval of information on seafloor properties. Various approaches to coherent stacking of CCFs are compared. Time warping transform is applied to the resultant noise CCF to extract dispersion curves of acoustic normal modes. The results of the geoacoustic inversion based on the passively measured dispersion curves are compared with the earlier results obtained using controlled sound sources. [Work supported by NSF and BSF.]

Identification of interference normal mode pairs of low frequency sound in shallow water

The interference characteristics of normal modes in low-frequency broadband sound can be applied to source localization and environmental parameter inversion in shallow water. However, the identification ambiguity of interference normal mode pairs generally occurs in practical applications due to unknown source position, some weakly-excited normal modes, mismatched environmental model, etc. For the applications of a horizontal line array, a model-based processing approach is proposed to determine the orders of the interference normal mode pairs based on the intrinsic dispersion characteristics of interference normal mode pairs in the received signals and the range-independent properties of the array beam output angles. Firstly, the normal mode pair filtering is achieved by using the WARPING transform of the signal autocorrelation function in the element domain of the horizontal line array. Then, the arrival angles of the filtered interference normal mode pairs are estimated by using array beamforming. Finally, the estimated beam output angles are matched with the replica values computed by sound field model. The approach is verified by using the explosive pulse signals received by the seafloor-deployed 32-element horizontal line array at the North Yellow Sea in 2011. Furthermore, some simulations are involved to analyze the effects of environmental parameter mismatches including water sound speed profile, sea bottom parameters and water depth on the identification performance of interference normal mode pairs. The results show that the water depth is a major factor influencing the extracted values of the beam output angles of interference normal mode pairs. The approach might fail when the water depth mismatch exceeds 14% of the practical value. However, the effects of water sound speed profile mismatch and sea bottom parameters mismatch are negligible. The effect of signal-to-noise ratio in the element domain on a horizontal line array is also simulated in order to analyze the limitation of identification performance, which shows that the required signal-to-noise ratio in the element domain should be more than 2 dB.

A noval method of constructing shallow water sound speed profile based on dynamic characteristic of internal tides

In order to provide constraint to the number of inversion parameters, sound speed profile is often modeled by empirical orthogonal functions (EOFs). However, the EOF method, which is dependent on the sample data, is often difficult to apply due to insufficient real-time <i>in-situ</i> measurements. In this paper, we present a novel basis for reconstructing the sound speed profile, which can be obtained by using historical data without real-time sample. By deducing the dynamic equations and the state function of water particle, the hydrodynamic mode bases (HMBs) can be calculated from historical data without real-time in-situ measurement, and a method of constructing the sound speed profile is established by using the dynamic characteristics of seawater. The use of the World Ocean Atlas 2013 (WOA13) can obtain the seasonal profiles of temperature and salinity, and then the HMB which represents the dynamic characteristic of internal tides is obtained and analyzed. Unlike EOF, the HMB and its projection coefficients are directly related to the sea dynamic features and have a more explicit physical meaning. According to the orthogonality analysis of hydrodynamic mode, the first-order coefficient can be used to describe the depth change of sound speed iso-lines and the second-order coefficient can be used to describe the change of sound speed gradient. Based on the conductance-temperature-depth profiles and broadband data from underwater explosion collected in the East China Sea experiment of the Asian Seas International Acoustic Experiment, the HMB is tested and compared with the EOF in the sound speed profile reconstruction and matched field tomography. The results show that the sound speed profile in shallow water area can be expressed by the HMB with proper precision. By means of the conventional matched field tomography, the valid sound speed profile can also be obtained in the form of HMB coefficients. The result of transmission loss prediction and tomography from HMB are as good as those from EOF, while the HMB has less dependent on real-time <i>in-situ</i> measurement. The HMB is easy to obtain and closely related to the physical characteristics of seawater, it can be used as an efficient alternative to EOF for monitoring the marine dynamic phenomena in sea areas with insufficient real-time in-situ measurement.

Bowhead whale localization using asynchronous hydrophones in the Chukchi Sea.

This paper estimates bowhead whale locations and uncertainties using non-linear Bayesian inversion of their modally-dispersed calls recorded on asynchronous recorders in the Chukchi Sea, Alaska. Bowhead calls were recorded on a cluster of 7 asynchronous ocean-bottom hydrophones that were separated by 0.5-9.2 km. A warping time-frequency analysis is used to extract relative mode arrival times as a function of frequency for nine frequency-modulated whale calls that dispersed in the shallow water environment. Each call was recorded on multiple hydrophones and the mode arrival times are inverted for: the whale location in the horizontal plane, source instantaneous frequency (IF), water sound-speed profile, seabed geoacoustic parameters, relative recorder clock drifts, and residual error standard deviations, all with estimated uncertainties. A simulation study shows that accurate prior environmental knowledge is not required for accurate localization as long as the inversion treats the environment as unknown. Joint inversion of multiple recorded calls is shown to substantially reduce uncertainties in location, source IF, and relative clock drift. Whale location uncertainties are estimated to be 30-160 m and relative clock drift uncertainties are 3-26 ms.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

Bowhead whale localization and environmental inversion using asynchronous hydrophones

This paper estimates bowhead whale locations and environmental properties using Bayesian inversion of the modal dispersion of whale calls recorded on asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. Bowhead calls were recorded on a Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by up to 9.2 km. We use a warping time-frequency analysis to obtain frequency-dependent relative mode arrival times for nine frequency-modulated whale calls. Trans-dimensional inversion is applied to invert mode arrival times for the whale location, water sound-speed profile, subbottom layering and geoacoustic parameters, source instantaneous frequency (IF), relative recorder clock drifts, and residual error standard deviation, all with estimated uncertainties. Joint inversion of multiple calls is found to substantially reduce uncertainties on whale location, source IF, and clock drifts. Estimated whale location uncertainties are 30–160 m and clock drift uncertainties a...

Bayesian environmental inversion of airgun modal dispersion using a single hydrophone in the Chukchi Sea.

This paper presents estimated water-column and seabed parameters and uncertainties for a shallow-water site in the Chukchi Sea, Alaska, from trans-dimensional Bayesian inversion of the dispersion of water-column acoustic modes. Pulse waveforms were recorded at a single ocean-bottom hydrophone from a small, ship-towed airgun array during a seismic survey. A warping dispersion time-frequency analysis is used to extract relative mode arrival times as a function of frequency for source-receiver ranges of 3 and 4 km which are inverted for the water sound-speed profile (SSP) and subbottom geoacoustic properties. The SSP is modeled using an unknown number of sound-speed/depth nodes. The subbottom is modeled using an unknown number of homogeneous layers with unknown thickness, sound speed, and density, overlying a halfspace. A reversible-jump Markov-chain Monte Carlo algorithm samples the model parameterization in terms of the number of water-column nodes and subbottom interfaces that can be resolved by the data. The estimated SSP agrees well with a measured profile, and seafloor sound speed is consistent with an independent headwave arrival-time analysis. Environmental properties are required to model sound propagation in the Chukchi Sea for estimating sound exposure levels and environmental research associated with marine mammal localization.

Bayesian environmental inversion of airgun modal dispersion using a single hydrophone in the Chukchi Sea

This paper presents estimated water-column and seabed parameters and uncertainties for a shallow-water site in the Chukchi Sea, Alaska, from trans-dimensional Bayesian inversion of the dispersion of water-column acoustic modes. Pulse waveforms were recorded at a single ocean-bottom hydrophone from a small, ship-towed airgun array during a seismic survey. A warping dispersion time-frequency analysis is used to extract relative mode arrival times as a function of frequency for source-receiver ranges of 3 and 4 km, which are inverted for the water sound-speed profile (SSP) and subbottom geoacoustic properties. The SSP is modeled using an unknown number of sound-speed/depth nodes. The subbottom is modeled using an unknown number of homogeneous layers with unknown thickness, sound speed, and density, overlying a halfspace. A reversible-jump Markov-chain Monte Carlo algorithm samples the model parameterization in terms of the number of water-column nodes and subbottom interfaces that can be resolved by the data. The estimated SSP agrees well with a measured profile, and seafloor sound speed is consistent with an independent headwave arrival-time analysis. Environmental properties are required for anthropogenic noise modeling studies in the Chukchi Sea and for improving acoustic localization of marine mammals detected with passive acoustic monitoring systems.

T-wave generation and propagation: A comparison between data and spectral element modeling

T-waves are underwater acoustic waves generated by earthquakes. Modeling of their generation and propagation is a challenging problem. Using a spectral element code-SPECFEM2D, this paper presents the first realistic simulations of T-waves taking into account major aspects of this phenomenon: The radiation pattern of the source, the propagation of seismic waves in the crust, the seismic to acoustic conversion on a non-planar seafloor, and the propagation of acoustic waves in the water column. The simulated signals are compared with data from the mid-Atlantic Ridge recorded by an array of hydrophones. The crust/water interface is defined by the seafloor bathymetry. Different combinations of water sound-speed profiles and sub-seafloor seismic velocities, and frequency content of the source are tested. The relative amplitudes, main arrival-times, and durations of simulated T-phases are in good agreement with the observed data; differences in the spectrograms and early arrivals are likely due to too simplistic source signals and environmental model. These examples demonstrate the abilities of the SPECFEM2D code for modeling earthquake generated T-waves.

Focused sound from three-dimensional sound propagation effects over a submarine canyon

Ship noise data reveal an intensification of the near-surface sound field over a submarine canyon. Numerical modeling of sound propagation is used to study the effect. The noise data were collected during an ocean acoustic and physical oceanography experiment northeast of Taiwan in 2009. In situ measurements of water sound-speed profiles and a database of high-resolution bathymetry are used in the modeling study. The model results suggest that the intensification is caused by three-dimensional sound focusing by the concave canyon seafloor. Uncertainties in the model results from unsampled aspects of the environment are discussed.

Marginal probability distributions for seabed parameter values from simultaneous processing of vertical and horizontal apertures.

Information about the physical parameter values for the seabed in a littoral region can be extracted from acoustic measurements in the water column. While acoustic data from both horizontal line arrays (HLAs) and vertical line arrays (VLAs) have been processed successfully to infer seabed properties, the simultaneous signal processing of acoustic data recorded on both a vertical and a horizontal aperture for seabed properties is a new research area. Relative to only a bottom‐mounted horizontal aperture, an L‐array (bottom mounted HLA and a VLA) provides access to the sensitivity of the depth‐dependence of the acoustic field to seabed parameters. However, the utility of the additional information can be negated by uncertainty in the assumed water sound speed profile. Acoustic data collected on two L‐arrays deployed on the New Jersey continental shelf are examined for the additional information about the seabed that can be obtained relative to the case for a single aperture. The information from simultaneou...

Mode formulas for shallow water waveguides using a modified asymptotic approximation

Sound speed profiles in shallow water waveguides are small deviations from isospeed and often decrease monotonically with depth. Approximation formulas for the propagating modes are found using a modified form of the classical WKBJ method. The ocean bottom is taken as homogeneous. The approach is accurate for modes with phase speeds greater than, and even slightly less than, the maximum water sound speed. The validity and accuracy of the approximations over frequency and mode number are illustrated using benchmark numerical calculations. Comparisons with approximations from other methods, including previous WKBJ approaches, are described. The formulas here are typically more compact and convenient. The results demonstrate how changes in parameters, such as frequency, bottom sound speed, and water sound speed profile quantitatively affect the mode functions. Applications for representative waveguide profiles are provided. [Work supported by the Office of Naval Research.]

Geoacoustic inversion in range-dependent ocean environments using a plane wave reflection coefficient approach

A new, efficient, versatile ray-based model is presented that performs geoacoustic inversions in range-dependent ocean waveguides faster than alternative forward models for which the computation time becomes extremely long, especially for broadband inversions. The water propagation is approximately separated from the seabed interaction using predetermined bathymetry and a possibly range-dependent water sound speed profile. The geometrical optics approximation is used to calculate eigenrays between sources and receivers, including bottom reflecting paths. Modeled broadband pressure fields are obtained by computing the plane wave reflection coefficient at specific angles and frequencies and by then linking this result with the bottom reflected eigenrays. Each perturbation of the seabed requires a recalculation of the plane wave reflection coefficient, but not a recalculation of the eigenrays, resulting in a highly efficient method. Range-independent problems are treated as a limiting case of the approach. The method is first described and then demonstrated with a few simple range-independent theoretical models. The versatility of addressing range-dependence in the bottom seabed is demonstrated with a simulated data set. Finally, the new model is applied to inversion from a measured data set, taken with impulsive sources, for both range-independent and range-dependent continental shelf environments.