Geoacoustic Parameters Research Articles

Geoacoustic inversion using Bayesian optimization with a Gaussian process surrogate model.

Geoacoustic inversion can be a computationally expensive task in high-dimensional parameter spaces, typically requiring thousands of forward model evaluations to estimate the geoacoustic environment. We demonstrate Bayesian optimization (BO), an efficient global optimization method capable of estimating geoacoustic parameters in seven-dimensional space within 100 evaluations instead of thousands. BO iteratively searches parameter space for the global optimum of an objective function, defined in this study as the Bartlett power. Each step consists of fitting a Gaussian process surrogate model to observed data and then choosing a new point to evaluate using a heuristic acquisition function. The ideal acquisition function balances exploration of the parameter space in regions with high uncertainty with exploitation of high-performing regions. Three acquisition functions are evaluated: upper confidence bound, expected improvement (EI), and logarithmically transformed EI. BO is demonstrated for both simulated and experimental data from a shallow-water environment and rapidly estimates optimal parameters while yielding results comparable to differential evolution optimization.

Using the phase characteristic for source depth discrimination with a horizontal line array for a broadband source

A solution to the problem of source depth discrimination in a shallow water waveguide is proposed for the case of a horizontal line array and low-frequency broadband sources. The method divides the horizontal line array into two subarrays with the same number of elements and then calculates the cross-power spectrum of beamforming pressure outputs of the subarrays. Depth-dependent features of phase fluctuation in the cross-power spectrum are analyzed using longitudinal correlation, and depth-separable decision metrics are defined. These decision metrics are poorly impacted by the energy distribution of the signal spectrum. Depth discrimination relies on the phase variation of the cross-power spectrum, and thus does not require mode space information or geoacoustic parameters as the prior knowledge, but sufficient effective horizontal apertures. Due to the application of beamforming, array gain can be obtained to improve the input signal-to-noise ratio of the phase feature-based discriminators. Simulations and Monte Carlo methods are applied to performance predictions and method comparison. The impact on the performance of signal-to-noise ratio, horizontal aperture, and array overlap is numerically studied. Finally, the method is experimentally demonstrated with data from a bottom-mounted horizontal line array deployed in the South China Sea, and the applicability of array overlap is illustrated.

On the Dependence of Acoustic Modes on Media Parameters in the Pekeris-Airy Waveguide

A waveguide consisting of an isospeed water layer overlying a halfspace with a sound speed gradient is considered. The dependence of horizontal wavenumbers of normal modes in such a waveguide on the sound frequency, water depth and geoacoustic parameters of the bottom are investigated. It is shown that these dependencies are described by ordinary differential equations that can be solved numerically at very low computational cost providing a substantial increase in the efficiency of broadband modelling of sound propagation. The explicit formulae for the derivatives of horizontal wavenumbers with respect to the bottom parameters can be also used in dispersion-based geoacoustic inversion methods. This approach can be extended to the case of a waveguide consisting of several layers of Airy-type media. We also propose a new and concise proof that the spectrum of the Sturm-Liouville problem from which the modes are found for this waveguide is purely discrete.

Bottom Multi-Parameter Bayesian Inversion Based on an Acoustic Backscattering Model

The geoacoustic and physical properties of the bottom, as well as spatial distribution, are crucial factors in analyzing the underwater acoustic field structure and establishing a geoacoustic model. Acoustic inversion has been widely used as an economical and effective method to obtain multi-parameters of the bottom. Compared with traditional inversion methods based on acoustic propagation models, acoustic backscattering models are more suitable for multi-parameter inversion, because they contain more bottom information. In this study, a Bayesian inversion method based on an acoustic backscattering model is proposed to obtain bottom multi-parameters, including geoacoustic parameters (the sound speed and loss parameter), partial physical parameters of the sediment, and statistical parameters of the seafloor roughness and sediment heterogeneity. The bottom was viewed as a kind of fluid medium. A high-frequency backscattering model based on fluid theory was adopted as the forward model to fit the scattering strength between the model prediction and the measured data. The Bayesian inversion method was used to obtain the posterior probability density (PPD) of the inversion parameters. Parameter estimation, uncertainty, and correlation were acquired by calculating the maximum a posterior (MAP), the mean values, the one-dimensional marginal distributions of the PPD, and the covariance matrix. Finally, the high-frequency bottom backscattering strength from the Quinault Range site was employed for inversion tests. The estimated values and uncertainties of various bottom parameters are presented and compared with the directly measured bottom parameters. The comparison results demonstrate that the method proposed herein can be used to estimate the sediment/water sound speed ratio, the sediment/water density ratio, and the spectral exponent of the roughness spectrum effectively and reliably.

Bayesian optimization for geoacoustic inversion

Geoacoustic inversion of high-dimensional parameter spaces is a computationally intensive procedure, often necessitating thousands of forward model evaluations to accurately estimate the geoacoustic environment, such as Markov chain Monte Carlo sampling. This study introduces Bayesian optimization (BO), an efficient global optimization technique, to estimate geoacoustic parameters with significantly fewer evaluations, typically on the order of hundreds. BO involves an iterative search within the parameter space to locate the global optimum of an objective function; in this study, the Bartlett power is used. BO consists of fitting a Gaussian process surrogate model to existing evaluations of the objective function, followed by selecting a new data point for evaluation using a heuristic acquisition function. The effectiveness of BO is showcased through its application to both simulated and real-world data from a shallow-water environment for multidimensional parameter space encompassing source location, array tilt, and seabed properties.

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.

Seabed Analysis on the New England shelf break using ambient sound data and trans-dimensional geoacoustic inversion

The New England Shelf Break Acoustics (NESBA) Signals and Noise experiment was conducted in April-May 2021. Ambient sound data were collected over several days in the mud-patch area as well as in deeper water closer to the shelf break. A 16-hydrophone vertical array was used to measure the natural sound of breaking waves on the sea-surface. Using beamforming in the 500–700 Hz band, these data were used to obtain an estimate of the bottom reflection coefficient as well as the seabed layering. The reflection coefficient data were subsequently used with trans-dimensional inversion techniques to produce a geoacoustic model for the seabed (e.g., sound speed, density, and layering). Results show the ambient sound data can be used to produce well resolved geo-acoustic parameters, especially in the upper part of the seabed (e.g., <10 m). These results are compared between several locations on the New England Shelf Break area and are also compared with other published results using different estimation techniques. In addition, some of the issues related to the impacts of data errors and preferred measurement geometries will also be presented. [Work supported by the Office of Naval Research.]

Geoacoustic inversion using 3D modal rays on the New England Shelf Break

During the Seabed Characterization Experiment in 2021 (SBCEX21), hydrophones deployed on the seabed of the New England Shelf Break recorded acoustic signals from SUS charge explosions. Acoustic data from one of these TOSSIT hydrophones displays evident modal structures which cannot be fully captured with 2D propagation models. In this presentation, 3D acoustic modal ray tracing is shown to provide a stronger match for recorded modal travel times, and is used to invert for geoacoustic parameters of the seabed. Performance of 2D and 3D modal propagation models are presented, and limitations of the methods are shown in the context of large parameter space inversion efforts. [This research is supported by The Office of Naval Research.]

Parallel tempering in trans-dimensional Bayesian inversion for seabed geoacoustic models with many parameters per layer

Trans-dimensional (trans-D) Bayesian inversion is a powerful tool for estimating seabed geoacoustic models from ocean-acoustic data, combining quantitative model selection with parameter/uncertainty estimation. The approach applies reversible-jump Markov-chain Monte Carlo methods to sample probabilistically over the number of seabed layers and the corresponding geoacoustic parameters for each layer. Layers are added and removed during sampling, referred to as birth and death moves, respectively, changing the dimension of the model. However, the probability of accepting birth and death moves can approach zero for formulations that include many parameters per layer. This paper considers the use of parallel tempering to mitigate this degradation in efficiency. Parallel tempering employs a series of interacting Markov chains with successfully-relaxed acceptance criteria, achieved by raising the likelihood to powers of 1/T, with T greater than or equal to 1 referred to as the sampling temperature. While only the T = 1 chain provides unbiased sampling, probabilistic interchange between chains provides a robust ensemble sampler that mixes more readily over the trans-D model space. The approach is illustrated for wide-angle reflection-coefficient inversion including compressional and shear parameters in the seabed model, resulting in a total of 5 unknown parameters per layer.

Low frequency inversion method based on multi-layer holizontal variation shallow seafloor model

Sound propagation in shallow water is significantly influenced by geoacoustic properties. Estimating these geoacoustic parameters is essential for sound field analysis and sonar performance assessment. As a common practice, the seafloor is often treated as a single-layer or two-layer range-independent geoacoustic model to reduce the number of involved parameters. However, acoustic parameters inverted through these two geoacoustic models are typically limited in their applicability to a specific frequency range, thus posing challenges when applied across a broader frequency range. A range-dependent multi-layer geoacoustic model based on experimental measurements obtained with a sub-bottom profiler is proposed in this study. The inversion scheme combines three inversion methods to estimate geoacoustic parameters, considering the different sensitivities of geoacoustic parameters to different physical parameters within the acoustic field. Firstly, modal dispersion is used to invert the geoacoustic parameters of each layer, with the dispersion curve obtained through warping transform and the Wigner-Ville distribution. After that, both the localization using matched field processing and the dispersion curve fitting demonstrate the effectiveness of the inversion results for each layer, although the peak of the probability distribution of sound speed in the first layer is broader than in others. Secondly, matched field processing is employed to invert the geoacoustic parameters of the first layer. This method is based on the theory that as frequency increases, the depth of sound rays penetrating the seabed decreases, revealing changes in the first layer's sound speed with the seabed depth. Lastly, bottom attenuation coefficients at different frequencies are inverted by the transmission loss (TL), and a fitting relationship between the attenuation coefficient and the frequency is derived. The inversion results obtained by using the range-dependent multi-layer geoacoustic model are compared with results estimated by the single-layer geoacoustic model. The findings indicate that the transmission loss (TL) error from the range-dependent multi-layer geoacoustic model in this study is smaller than that from the single-layer geoacoustic model, especially in the lower frequency band. The range-dependent multi-layer geoacoustic model proves to be suitable for a broader frequency range, providing better precision in explaining various acoustic phenomena.

Observation and Modelling on the Shipping Noise in Shallow Waters with Complex Islands and Reefs of the East China Sea

The impact of the noise radiated from merchant ships on marine life has become an active area of research. In this paper, a methodology integrating observation at a single location and modelling the whole noise field in shallow waters is presented. Specifically, underwater radiated noise data of opportunistic merchant ships in the waters of Zhoushan Archipelago were collected at least one day in each month from January 2015 to November 2016. The noise data were analyzed and a modified empirical spectral source level (SSL) model of merchant ships was proposed inspired by the RANDI-3 model (Research Ambient Noise Directionality) methodology. Then combining the modified model with the realistic geoacoustic parameters and AIS data of observed merchant ships, the noise mappings in this area were performed with N×2D of Normal Mode calculations, in which the SSL of each ship was estimated using the modified model. The sound propagation at different receiving positions is different due to the shielding effect of islands and bottom topography. The methodology proposed in this paper may provide a reference for modelling shipping noise in shallow waters with islands and reefs.

Comparative Review and Outlook of Research Progress in Backscatter-based Seafloor Substrate Classification Methods

Background: The seafloor is an essential ocean boundary, and the detection of seafloor information is necessary basis for seafloor scientific research. The classification and identification of seafloor geological types is necessary for researchers to conduct seafloor research, military activities, and marine platform construction. Objective: The purpose of this paper is to summarize the progress of seafloor substrate classification research based on backscattering and to seek a new development direction for seafloor substrate classification research. Method: The literature on various types of submarine sediment attenuation geoacoustic models, backscatter intensity calculations, and submarine substrate classification is summarized, and the progress of theoretical research required for the positive and negative problems of submarine substrate classification is described that include the geoacoustic parameter models based on fluid theory, elastomer theory and poroelastic theory and submarine acoustic scattering models, including the small roughness perturbation approximation model, the Kirchhoff approximation model, the Kirchhoff approximation model and the Kirchhoff approximation model. Result: The development of the Kirchhoff approximation model, the slight slope approximation model, the volume scattering model, and the inversion methods for seafloor substrate classification are summarized, and breakthroughs in seafloor substrate classification are sought by summarizing previous studies. Conclusion: The classification of seafloor substrate based on backscattering intensity needs the support of a perfect geoacoustic model and scattering model, and the current research of low and medium-frequency scattering models and multi-layer seafloor scattering models are the further development direction in the future. Currently, the better performance of the prediction model, geo-acoustic parameter inversion results are more than 90% accuracy, sound velocity ratio and other parameters in the high-frequency band inversion accuracy of 98%, are able to better meet the measured data. Finally, some patented technologies are also reported.

A Multi-Objective Geoacoustic Inversion of Modal-Dispersion and Waveform Envelope Data Based on Wasserstein Metric

The inversion of acoustic field data to estimate geoacoustic parameters has been a prominent research focus in the field of underwater acoustics for several decades. Modal-dispersion curves have been used to inverse seabed sound speed and density profiles, but such techniques do not account for attenuation inversion. In this study, a new approach where modal-dispersion and waveform envelope data are simultaneously inversed under a multi-objective framework is proposed. The inversion is performed using the Multi-Objective Bayesian Optimization (MOBO) method. The posterior probability densities (PPD) of the estimation results are obtained by resampling from the exploited state space using the Gibbs Sampler. In this study, the implemented MOBO approach is compared with individual inversions both from modal-dispersion curves and the waveform data. In addition, the effective use of the Wasserstein metric from optimal transport theory is explored. Then the MOBO performance is tested against two different cost functions based on the L2 norm and the Wasserstein metric, respectively. Numerical experiments are employed to evaluate the effect of different cost functions on inversion performance. It is found that the MOBO approach may have more profound advantages when applied to Wasserstein metrics. Results obtained from our study reveal that the MOBO approach exhibits reduced uncertainty in the inverse results when compared to individual inversion methods, such as modal-dispersion inversion or waveform inversion. However, it is important to note that this enhanced uncertainty reduction comes at the cost of sacrificing accuracy in certain parameters other than the sediment sound speed and attenuation.

Estimates of geoacoustic parameters and source range using airgun sound in the East Siberian Sea, Arctic Ocean

In a shallow-water waveguide, low-frequency sound propagating over several kilometers has dispersive properties and thus the dispersion curves can be used for the inversion of geoacoustic parameters. In September 2019, seismic survey was conducted by the icebreaking research vessel Araon, operated by Korea Polar Research Institute. A single hydrophone was moored at East Siberian Shelf, a nearly range-independent shallow water (<70 m), to receive seismic airgun sounds generated from the R/V Araon. It was observed that the arrivals corresponding to the first two modes were clearly dispersed in the spectrogram of the received signal. In order to use these dispersion curves for the geoacoustic inversion, the dispersion curves corresponding to the first two modes were extracted using the warping transform combined with the wavelet synchrosqueezing transform. Geoacoustic parameters including sound speed and density in the sediment and the distance between the source and receiver were then estimated by comparing the extracted dispersion curves to the model replicas predicted by the KRAKEN normal-mode acoustic propagation model. Finally, the inversion results and their error analysis will be discussed in this talk. [This research was a part of the project titled ‘Korea-Arctic Ocean Warming and Response of Ecosystem (K-AWARE, KOPRI, 1525011760)’, funded by the Ministry of Oceans and Fisheries, Korea and supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C2007772).]

Application of trans-dimensional particle filtering for geoacustic inversion

The acquiring geoacoustic model and associated geoacoustic parameters is vital for sound propagation modelling in a range-dependent environment. Conventional sequential methods, e.g., particle filtering and Kalman filtering have been widely used for geoacoustic inversion in range-dependent environment, which encounter challenges when confronted with unknown geoacoustic models that intrinsically varying with range. As an attempt to estimate geoacoustic model and associated geoacoustic parameters as well, a trans-dimensional particle filtering method is presented here. This method integrates birth-death rules into the filtering process, enabling automatic selection of appropriate geoacoustic models and estimating geoacoustic parameters in the same time. Numerical simulations were conducted based on an environment model of the South China Sea, where a sea trial was conducted in 2022. Numerical results demonstrate the efficiency in accurately estimating the geoacoustic model variations and associated parameters. Preliminary results of sea trial data processing are also presented here.

Geoacoustic inversion of wide-angle reflection-coefficient data to estimate sediment shear properties

This paper considers Bayesian geoacoustic inversion of broadband, wide-angle reflection-coefficient data including shear parameters in the seabed model to investigate the ability to estimate these parameters as well as effects on the estimation of other geoacoustic parameters, particularly compressional-wave attenuation. The seabed parameterization is based on the viscous grain-shearing (VGS) sediment-acoustic model, including the grain-to-grain shear modulus as an unknown parameter. VGS sediment parameters are transformed to density and frequency-dependent compressional- and shear-wave speeds and attenuations. Data prediction involves spherical-wave reflection-coefficient calculations. Trans-dimensional inversion, which samples probabilistically over the number of layers in the seabed model, is applied to combine quantitative model selection with parameter/uncertainty estimation. The inversion is applied to reflection-coefficient data sets collected on the New England Mud Patch, and inversion results are compared to those obtained under the common assumption of negligible shear effects (i.e., inverting for a fluid sediment model).

The Influence of the A Priori Uncertainty of the Shallow Sea Sound Channel Model on the Vertical Array Gain

The purpose of this paper is to numerically demonstrate and comparatively analyze the critically strong and ambiguous impact of the a priori uncertainty of a shallow sea waveguide model in its main physical parameters on the output performance of model-based methods for spatial processing of multimode signals received by a vertical antenna array. The scenario is specified when a relatively weak signal of a remote underwater source is received against the background of intensive interference excited by a subsurface source (like a ship, for example) and ambient sea noise excited by wind waves. The considered array processing methods include matched-signal processing, optimal processing of the signal on the background of interference and noise, and suboptimal processing based on matched-mode array filtering of one of the signal-carrying modes with adaptive selection of its number. Quantitative estimates are obtained from above for the environment uncertainties, or model errors, with respect to the sound velocity in the water column and geoacoustic parameters of the underlying bottom, at which the array gain loss does not exceed a given level. It is shown that such estimates are very different both for different environmental parameters and for processing methods, with the determining role played by the conditions of useful signal reception, namely, the modal composition and intensity levels of the interference and sea noise at the array input. The problem statement and results are considered to be useful to detail the requirements for operational oceanography tools designed to support the effective operation of sonar antenna systems in real sea environments.

A robust array geometry inversion method for a deep-towed multichannel seismic system with a complex seafloor

Deep-towed multichannel seismic exploration technology has better applicability and more development potential when utilized to invert the geoacoustic properties of deep-sea sediment. The accurate geometric inversion results of the receiving array are crucial for fine submarine sediment imaging and physical property parameter inversion based on deep-towed multichannel seismic data. Thus, this study presents an array geometry inversion method suitable for complex seafloors to address the challenge of precise source-receiver positioning. The objective function of the deep-towed seismic array geometry inversion is built using the shortest path algorithm according to the traveltimes of direct waves and seafloor reflections, and the particle swarm optimization algorithm is used to achieve high-precision inversion of the source-receiver position. The results showed that the proposed method is shown to have incomparable applicability and effectiveness in obtaining exact source-receiver positions for deep-towed multichannel seismic systems. Regardless of the complexity of the seabed morphology, seismic image processing techniques using the source-receiver position data obtained by the suggested method produce fine seismic imaging profiles that clearly and accurately reflect the structural characteristics of sediments. These findings provide insights for the accuracy and reliability of the proposed geometric shape inversion method for deep-towed seismic arrays in practical applications to meet the requirements of near-bottom acoustic detection for fine imaging of deep-sea seabed strata and precise inversion of geoacoustic parameters.

The Influence of the A Priori Uncertainty of the Shallow Sea Sound Channel Model on the Vertical Array Gain

The purpose of this paper is to numerically demonstrate and comparatively analyze the critically strong and ambiguous impact of the a priori uncertainty of a shallow sea waveguide model in its main physical parameters on the output performance of model-based methods for spatial processing of multimode signals received by a vertical antenna array. The scenario is specified when a relatively weak signal of a remote underwater source is received against the background of intensive interference excited by a subsurface source (like a ship, for example) and ambient sea noise excited by wind waves. The considered array processing methods include matched-signal processing, optimal processing of the signal on the background of interference and noise, and suboptimal processing based on matched-mode array filtering of one of the signal-carrying modes with adaptive selection of its number. Quantitative estimates are obtained from above for the environment uncertainties, or model errors, with respect to the sound velocity in the water column and geoacoustic parameters of the underlying bottom, at which the array gain loss does not exceed a given level. It is shown that such estimates are very different both for different environmental parameters and for processing methods, with the determining role played by the conditions of useful signal reception, namely, the modal composition and intensity levels of the interference and sea noise at the array input. The problem statement and results are considered to be useful to detail the requirements for operational oceanography tools designed to support the effective operation of sonar antenna systems in real sea environments.