Geoacoustic Inversion Research Articles

A Method for Reducing Transcendental Dispersion Relations to Nonlinear Ordinary Differential Equations in a Wide Class of Wave Propagation Problems

A class of problems of wave propagation in waveguides consisting of one or several layers that are characterized by linear variation of the squared refractive index along the normal to the interfaces between them is considered in this paper. In various problems arising in practical applications, it is necessary to efficiently solve the dispersion relations for such waveguides in order to compute horizontal wavenumbers for different frequencies. Such relations are transcendental equations written in terms of Airy functions, and their numerical solutions may require significant computational effort. A procedure that allows one to reduce a dispersion relation to an ordinary differential equation written in terms of elementary functions exclusively is proposed. The proposed technique is illustrated on two cases of waveguides with both compact and non-compact cross-sections. The developed reduction method can be used in applications such as geoacoustic inversion.

One track, two experiments four years apart: On the repeatability of geoacoustic inversion on the New England Mud Patch

Our current knowledge of the geoacoustic properties of the New England Mud Patch (NEMP) is mostly driven by data collected in 2017 as part of the Seabed Characterization Experiment (SBCEX17). In 2021, a modest geoacoustic inversion experiment was performed on the NEMP using a simple and low-cost pair of experimental assets: a “TOSSIT” passive acoustic mooring and an impulsive “RIUSS” (Rupture Induced, Underwater Sound Source). The TOSSIT/RIUSS data were collected on a track that was studied intensively during SBCEX17, but with fundamental differences in oceanographic conditions: a frontal intrusion was present at the experimental site in 2021, creating a strongly stratified sound speed profile (SSP) in the water column, while the water column was essentially iso-speed in 2017. The 2021 TOSSIT/RIUSS data are used to perform geoacoustic inversion using warping and Bayesian trans-dimensional methods. The geoacoustic properties estimated for the 2021 data compare favorably to results obtained with SBCEX17 data, even when the 2021 data are inverted jointly for water-column SSP and seabed parameters. This study demonstrates inversion repeatability on the NEMP using data sets collected years apart and under different (and potentially unknown) oceanographic conditions. [Work supported by the Office of Naval Research.]

Quantifying data information content to resolve seabed structure in geoacoustic inversion

This paper considers the importance of quantitative model selection and general parameterizations in estimating and interpreting seabed profiles in geoacoustic inversion, with application to data collected on the New England Mud Patch. In particular, the seabed structure that can be resolved depends on the information content of the acoustic data set under consideration, which varies with a number of factors, including the physics of the seabed acoustic interaction, frequency content of the data, and measurement and theory errors. Quantitative model selection applied to general parameterizations ensures the inclusion of seabed structure that is reliably sensed by the data while avoiding spurious structure. Data sets considered here include ship noise, modal dispersion, and wide-angle reflection coefficients. In each case, seabed models consistent with the data information content are estimated as part of the inversion using trans-dimensional and/or Bernstein-polynomial parameterizations. Results for all data sets indicate a low sound-speed mud layer over higher-speed sand; however, the ability to resolve structure within the mud layer, such as a transition to higher speeds near the mud base and possibly a weak positive gradient in the upper mud, depends on the information content of the various data sets. [Supported by the Office of Naval Research.]

Graduate programs in physical, engineering, and underwater acoustics at the Naval Postgraduate School

The Departments of Physics and of Electrical and Computer Engineering at the Naval Postgraduate School offer graduate programs in acoustics leading to MS and PhD degrees in applied physics and engineering acoustics. Engineering acoustics degrees can be completed in either traditional or distance learning modes. The departments also offer stand-alone academic certificate programs in fundamentals of engineering acoustics, underwater acoustics, and sonar system applications, with a set of three certificates leading to a MS degree in engineering acoustics. MS and PhD programs are interdisciplinary, with courses and laboratory work drawn principally from the fields of physics and electrical engineering. Subjects covered include waves and oscillations; fundamentals of physical and structural acoustics; the generation, propagation, and reception of sound in the ocean; civilian and military applications of sonar systems; and acoustic signal processing. Topics of recent theses and dissertations include development and field testing of novel sensors for atmospheric and ocean acoustics, modeling and measurements of ambient noise and sound propagation in the ocean, sound scattering in underwater waveguides, acoustic vector sensors and vector field properties, acoustic communications, noise interferometry, time reversal in acoustics, geo-acoustic inversion, acoustic remote sensing of the ocean, and acoustics of autonomous underwater and aerial vehicles.

Geo-acoustic inversion using ground waves of explosive sounds

The ground waves of explosive sounds exhibit strong dispersion in shallow water waveguides. Their travel time and amplitude are related to the geo-acoustic properties in the seabed and could be utilized to construct cost functions for geo-acoustic inversion. Following the analysis of the Airy phase [Wan et al., JASA, 143, EL199-205, (2018)], this research focuses on the extraction and utilization of ground waves, which propagate at frequencies below the corresponding Airy frequency. First, the ground waves of low order modes are identified in the received signals from explosive SUS charges deployed at various depths/ranges and recorded by vertical line arrays during the series of Seabed Characterization Experiments (SBCEX) conducted in the New England continental shelf and slope region. Then, the extracted ground waves, showing strong dispersive characteristics in a bandwidth of a few Hertz (i.e., between cut-off frequency and Airy frequency), are fed to a proposed inversion algorithm to obtain the estimated geo-acoustic parameters. Finally, the advantage of using ground waves rather than water waves is discussed and a physical explanation is provided. [Work supported by ONR Ocean Acoustics.]

Broadband core and resonance logger measurements of sound speed and attenuation in the New England mud patch

Extensive measurements of sound speed and attenuation have been performed on sandy sediments over the last few decades, which have motivated a variety of physical sediment acoustics models. Recently, the seabed characterization experiment (SBCEX) was performed in 2015–2017, in part, to quantify the geoacoustic properties of a clayey-silt accumulation, known as the New England Mud Patch (NEMP). Due to the variability and frequency range reported by the various direct measurements and geoacoustic inversions, the sound speed measured in the NEMP lacked any noticeable frequency dependence. In 2022, an additional coring cruise was completed in the NEMP area and included shipboard core and resonance logger (CARL) measurements, expanding upper limit of the band to 1 MHz. CARL measured sound speed and attenuation as a function of depth from 100 kHz to 1 MHz using a time-of-flight technique, and sound speed along the entire core length from 12 kHz to 16 kHz using a resonance technique. Positive dispersion and depth dependance was observed in the 200 kHz to 1 MHz band. The frequency and depth dependence of the CARL measurements will be presented and compared with previously published model fits to the 2015–2017 SBCEX dataset. [Work sponsored by ONR.]

Evidence of 3D effects for along shelf acoustic propagation during SBCEX21

The 2021 Seabed Characterization Experiment (SBCEX21) was performed on the New England Shelf Break (NESB) in May 2021 with the main objective of characterizing the NESB sediment geoacoustic properties. In this talk, we focus on low-frequency propagation (f<100 Hz) along the 200 m isobath line. Time-frequency dispersion of normal modes is estimated using a SUS charge signal recorded on a distant single hydrophone TOSSIT system. Geoacoustic inversion is performed, but two-dimensional (2D) acoustic propagation models fail to capture the observed behavior of higher order acoustic modes, and predict much shorter travel times than are seen in the data. By introducing a three-dimensional (3D) model environment, both parabolic equation and modal ray calculations confirm that the gradual shelf slope has a nontrivial influence on modal travel times. This comparison between 2D and 3D simulations of SBCEX21 acoustics and experimental data emphasizes the importance of 3D effects from sloped bathymetry on understanding propagation in a shelfbreak environment. These effects will need to be accounted for when doing geoacoustic inversion of SBCEX21 along-shelf low-frequency data.

Underwater acoustics and ocean engineering at the University of Rhode Island

Underwater acoustics is one of the primary areas of emphasis in the Ocean Engineering Department at the University of Rhode Island, the first Ocean Engineering program in the United States. The program offers Bachelors, Masters (thesis and non-thesis options) and PhD degrees in Ocean Engineering. These programs are based at the Narragansett Bay campus, providing access to a living laboratory for student learning. Some key facilities of the program are an acoustics tank and a 100-foot-long wave tank. At the graduate level, students are actively involved in research focused in areas such as acoustical oceanography, propagation modeling, geoacoustic inversion, marine mammal acoustics, ocean acoustic instrumentation, and transducers. An overview of classroom learning and ongoing research will be provided, along with information regarding the requirements of entry into the program.

Bayesian geoacoustic inversion of 1-2 kHz seabed reflection data for layered muddy sediments

This paper presents trans-dimensional Bayesian geoacoustic inversion of seabed reflection data for sub-bottom geoacoustic profiles and associated uncertainty estimation at the New England Mud Patch. The data considered here are wide-angle seabed reflection coefficients as a function of grazing angle and frequency measured during the 2017 Seabed Characterization Experiment. Chirp pulses over a frequency band of 1–6 kHz were transmitted by an omnidirectional acoustic source towed by a research vessel at a speed of about 4 knots and recorded at a bottom-moored hydrophone. High signal-to-noise-ratio reflection coefficients from 1–2 kHz and angular coverage of ∼15–25° are considered here for geoacoustic inversion. This frequency range is higher than for previous reflection-coefficient data sets on the Mud Patch. The angular range, although relatively narrow, includes strong Bragg resonances which provide information on the sediment layering properties. The inversion applies the viscous grain-shearing sediment acoustics model, which provides dispersive (frequency-dependent) results for sound speeds and attenuations. The seabed structure estimated here is compared to previous inversion results and to core measurements in the vicinity. [Work supported by the Office of Naval Research.]

Overview of the seabed characterization experiment

The seabed characterization experiment (SBCEX) is a multi-disciplinary, multi-institutional international research project devoted to the following scientific goals: (1) to understand the physical mechanisms that control acoustic propagation in fine-grained sediments, (2) to quantify uncertainties in the estimation of seabed parameters, (3) to correlate the observed horizontal variations in the acoustical field with the measured horizontal variability of the seabed, and (4) to assess the performance of the resulting geoacoustic models, inversions, and statistical inference methods. To facilitate these scientific goals, research cruises were undertaken in 2015, 2016, 2017, 2021, and 2022 primarily at a site known as the New England Mud Patch. The work of the project through 2019 was documented in a special issue of the IEEE Journal of Oceanic Engineering, Vol. 45, No. 1 that appeared in January 2020, as well as in peer-reviewed papers in other journals. Here a brief overview of the results through the 2020 special issue will be presented, as well as an overview of the new field work competed in 2021 and 2022. [Work supported by ONR.]

Broadband sound speed and attenuation of a mud layer from acoustic propagation experiments in the New England Mud Patch

A series of Seabed Characterization Experiments (SBCEX) have been conducted in the New England Mud Patch area, where a top mud layer overlays a sand sediment. Using broadband acoustic signals from the SBCEX, the sound speed and attenuation of the mud layer as a function of frequency (from a few tens of Hz up to around 1 kHz) have been estimated by various inversion algorithms based on (1) modal dispersion curves and transmission loss [reported at the ASA Spring meeting, 2016], (2) Airy phase [Spring, 2017], (3) modal amplitude [Fall, 2017], (4) spatial coherence measurements [Spring, 2018], (5) mid-frequency modal dispersion analysis [Fall, 2019], and (6) ground waves [Fall, 2022]. This paper summarizes these inverted sound speed and attenuation, which are obtained at various frequencies independently (without using the frequency dependent constraints from any geo-acoustic models), therefore the inverted results could be used to verify the validity of geo-acoustic models. The performances of these inversion methods are evaluated. The performance assessment is helpful for one to select appropriate inversion algorithms and to choose optimal acoustic data for geo-acoustic inversion. [Work supported by ONR Ocean Acoustics.]

Wind-driven underwater ambient noise for seabed remote sensing: A review of methods and results

Estimation of seabed geoacoustic parameters in shallow water by acoustic remote sensing remains a challenging task due to constraints on hardware, data collection and analysis, and cost of maritime surveys. The work of Lisa Zurk and Martin Siderius, among many others, inspired investigation of signal processing techniques to process wind-driven underwater noise for the estimation of seabed geoacoustics. This paper presents a summary of the work on Bayesian geoacoustic inversion of ambient noise carried out at University of Victoria and Portland State University, using fixed and drifting vertical line arrays (VLA). The Bayesian inversion framework is based on Markov-chain Monte Carlo sampling. It estimates a joint posterior probability density function, from which marginal density functions, moments and covariances between geoacoustic parameters of interest can be quantified. The approach was applied to simulated and experimental ambient noise data for the estimation of seabed layer thicknesses, sound speeds, densities, and sediment attenuations. The resolution of the method was explored as a function of experiment factors such as array design and wind speed, and a method for extending the aperture of a VLA by extrapolating the noise coherence was proposed.

A forward-backward filter for estimating mud properties in SBCEX 17

The goal of SBCEX 17 was to investigate properties of the mud layer at the experiment site. We perform geoacoustic inversion for the mud site, integrating data and estimates obtained on a track of a moving source. The transmitted sound signals were LFM pulses in a mid-frequency range. The sound was received at a vertical array comprising 16 phones. Arrival times of multiple paths were extracted from the received signals using particle filtering and a backward-moving smoother: forward filtering and smoothing were applied to the received signals for the estimation of path arrival times generated by sound interacting with the waveguide. The smoothing step corrected for outliers that provided erroneous geoacoustic estimates for some source positions. The forward-backward filter provided accurate arrival times with a significant uncertainty reduction. The obtained arrival times were linked with a ray tracer and linearization for source localization and estimation of other parameters that affect sound propagation such as water column depth and sound speed. Sediment sound speed and thickness were then computed. Inversion was carried out at every source location within the track; the results were combined into a single set of estimates and corresponding probability density functions. [Work supported by ONR.]

Shear Wave Velocity Estimation Based on Deep-Q Network

Geoacoustic inversion is important for seabed geotechnical applications. It can be formulated as a problem that seeks an optimal solution in a high-dimensional parameter space. The conventional inversion approach exploits optimization methods with a pre-defined search strategy whose hyperparameters need to be fine-tuned for a specific scenario. A framework based on the deep-Q network is proposed in this paper and the environment and agent configurations of the framework are specially defined for geoacoustic inversion. Unlike a conventional optimization method with a pre-defined search strategy, the proposed framework determines a flexible strategy by trial and error. The proposed framework is evaluated by two case studies for estimating the shear wave velocity profile. Its performance is compared with three global optimization methods commonly used in underwater geoacoustic inversion. The results demonstrate that the proposed framework performs the inversion more efficiently and accurately.

Selected Topics of the Past Thirty Years in Ocean Acoustics

This paper reviews some of the highlights of selected topics in ocean acoustics during the thirty years that have passed since the founding of the Journal of Theoretical and Computational Acoustics. Advances in computational methods and computers helped to make computational ocean acoustics a vibrant area of research during that period. The parabolic equation method provides an unrivaled combination of accuracy and efficiency for propagation problems in which the bathymetry, sound speed, and other environmental parameters vary in the horizontal directions. The extension of this approach to cases involving layers that support shear waves has been an active area of research throughout the thirty year period. Interest in basin-scale and global-scale propagation was stimulated by the Heard Island Feasibility Test for monitoring climate change in terms of changes in travel time that occur as the temperature of the ocean rises. Diminishing ice cover in the Arctic, which is one of the consequences of climate change, has stimulated renewed interest in Arctic acoustics during the past decade. Reverberation is a challenging problem that was the topic of a major research program during the beginning of the thirty year period. An innovative approach for making it feasible to solve such problems was applied to data for reverberation from the seafloor and from schools of fish, and some of the findings were featured in Science and Nature. Source localization is one of the core problems in ocean acoustics. When applied on a 2-D array of receivers, an approach based on the eigenvectors of the covariance matrix is capable of separating the signals from different sources from each other, determining when this partitioning step is successful, and tracking sources that cross each other in bearing; one of the advantages of this approach is that it does not require environmental information or solutions of the wave equation. Geoacoustic inversion for estimating the layer structure, wave speeds, density, and other parameters of ocean bottoms has also been a topic of interest throughout the thirty year period.

Application of Dual-Source Modal Dispersion and Variational Bayesian Monte Carlo Method for Local Geoacoustic Inversion in Weakly Range-Dependent Shallow Water

Application of Dual-Source Modal Dispersion and Variational Bayesian Monte Carlo Method for Local Geoacoustic Inversion in Weakly Range-Dependent Shallow Water

Use of a Vertical Receiving Array for Geoacoustic Inversion in a Shallow-Water Waveguide with an Ice Cover

Use of a Vertical Receiving Array for Geoacoustic Inversion in a Shallow-Water Waveguide with an Ice Cover

Hybrid Seabed Parameterization to Investigate Geoacoustic Gradients at the New England Mud Patch

This article applies Bayesian geoacoustic inversion with a hybrid seabed-model parameterization to modal-dispersion data from the New England Mud Patch to estimate gradient structure in the upper mud layer. The hybrid parameterization comprises an upper layer with general smooth (continuous) gradients represented by Bernstein polynomials (BPs) for the mud, above an unknown number of discrete (uniform) layers. The Bayesian information criterion is applied to estimate BP orders for sound-speed and density profiles in the mud, and trans-dimensional (trans-D) inversion is applied for the underlying layered structure. The data, collected during the 2017 Seabed Characterization Experiment, include high-order modes (up to mode 21) extracted via warping time-frequency analysis from recordings of a combustive sound source at a vertical hydrophone array. Inversion results for the hybrid parameterization are compared to those from trans-D inversion with no gradient layer. Hybrid-inversion results indicate a nearly iso-speed mud layer with a rapidly increasing gradient near its base, consistent with increasing sand content in the mud above a sand interface, as indicated by cores. The sound-speed ratio of surficial sediments to bottom seawater is found to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt;$</tex-math></inline-formula> 1 with high probability, which differs from trans-D inversion results, indicating the significance of the choice of parameterization in interpreting structure.

Seabed Classification Using a Convolutional Neural Network on Explosive Sounds

The Seabed Characterization Experiment 2017 yielded a rich set of environmental and acoustical data, and subsequent geoacoustic inversions have estimated seabed properties. Seventeen of these seabed parameterizations are now used to define seabed classes, and a convolutional neural network (CNN) is trained to select a seabed class using explosive sounds. The CNN is trained on synthetic 1-s pressure time series and then applied to measured data samples from a single pressure sensor. While the environmental variability in the training data impacts the seabed classification, physical insights are gained by considering the classification results as a function of the sound speed ratio across the sediment–water interface and the interval velocity of the top sediment layer. These results indicate that the selected seabed classes for the data samples with longer propagation distances consistently have similar sediment–water sound speed ratios that are less than unity, while the data samples with the shortest propagation distances consistently have higher interval velocities. These classification results indicate that the CNN has learned physical features associated with acoustic sound propagation and points to future work that needs to be considered if the seabed classes have acoustically distinct signatures in the data.

Transdimensional Inversion on the New England Mud Patch Using High-Order Modes

This article presents geoacoustic inversion results for modal-dispersion data collected during the 2017 Seabed Characterization Experiment on the New England Mud Patch, an area where the seabed is characterized by an upper layer of mud. The experiment utilized a combustive sound source and a vertical line array of receivers at 5.4-km range. Using a careful combination of source deconvolution and warping time–frequency analysis, modal dispersion data (arrival time as a function of frequency) are estimated for 18 modes between modes 1 and 21. The modal dispersion data are then used to estimate seabed geoacoustic profiles and uncertainties via transdimensional Bayesian inversion. This article demonstrates the capacity to estimate high-order modes using warping. Comparing inversion results obtained with subsets of (lower order) modes to those obtained with the full set of available modes highlights the rich data information content carried by high-order modes. The results suggest a small sound-speed increase over the first 8 m of the seabed, the upper portion of the mud layer, which some earlier studies found to be isospeed. Overall, the inversion results are consistent with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measurements, as well as with previous geoacoustic inversion results.