Ocean Acoustic Problems Research Articles

Learning source-receiver range in a laboratory tank with variable water temperature

Deep learning has great potential to be useful for ocean acoustics problems. However, uncertainty in an ocean environment must be taken into account, because it affects the ability of trained machine learning models to generalize. Because ocean measurements are costly, we are using a laboratory water tank to help develop our deep learning neural networks. In addition, using a water tank in a lab increases some level of control over the amount of uncertainty in data used to train neural networks. A residual convolutional neural network architecture is trained to identify source-receiver range in an underwater tank environment at room temperature. The model is then tested on data taken with variable water temperature. For comparison, two different source signals are used (sine waves and linear chirps) to analyze the usefulness of broadband sounds. These tests explore how environmental uncertainty impacts source localization and will lead to insights on how to develop robust machine learning for ocean acoustics problems. [Work supported by the Office of Naval Research.]

Accounting for Azimuthal Coupling in Long-Range Ocean Acoustics Calculations

The parabolic equation method is an accurate and efficient approach for solving nonseparable problems in ocean acoustics in which there are horizontal variations in the environmental parameters. Many range-dependent problems may be solved using 2-D parabolic equation models that ignore coupling of energy between planes of constant azimuth. When azimuthal coupling must be taken into account, the splitting method may be used to efficiently solve a 3-D parabolic equation that handles the depth operator to higher order but handles the azimuth operator only to leading order. Despite the fact that this approximation provides a favorable combination of accuracy and efficiency for 3-D problems, run times have generally been regarded as prohibitive for the long-range problems that are often of interest in ocean acoustics. It is demonstrated here that, when propagation paths from source to receiver are confined to a relatively narrow neighborhood of the vertical plane containing the source and receiver, it is practical to solve 3-D problems out to long ranges by using nonuniform azimuthal sampling, with fine sampling near the vertical plane and extremely coarse sampling elsewhere.

Application of a spectral method to simulate quasi-three-dimensional underwater acoustic fields

The calculation of a three-dimensional underwater acoustic field has always been a key problem in computational ocean acoustics. Traditionally, this solution is usually obtained by directly solving the acoustic Helmholtz equation using a finite difference or finite element algorithm. Solving the three-dimensional Helmholtz equation directly is computationally expensive. For quasi-three-dimensional problems, the Helmholtz equation can be processed by the integral transformation approach, which can greatly reduce the computational cost. In this paper, a numerical algorithm for a quasi-three-dimensional sound field that combines an integral transformation technique, stepwise coupled modes and a spectral method is designed. The quasi-three-dimensional problem is transformed into a two-dimensional problem using an integral transformation strategy. A stepwise approximation is then used to discretize the range dependence of the two-dimensional problem; this approximation is essentially a physical discretization that further reduces the range-dependent two-dimensional problem to a one-dimensional problem. Finally, the Chebyshev–Tau spectral method is employed to accurately solve the one-dimensional problem. We provide the corresponding numerical program SPEC3D for the proposed algorithm and describe several representative numerical examples. In the numerical experiments, the consistency between SPEC3D and the analytical solution/high-precision finite difference program COACH verifies the reliability and capability of the proposed algorithm. A comparison of running times illustrates that the algorithm proposed in this paper is significantly faster than the full three-dimensional algorithm in terms of computational speed.

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.

Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment

The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the finite difference method (FDM). In this paper, a Legendre collocation method (LCM) based on domain decomposition is proposed to solve this problem. A set of collocation points cannot penetrate multiple layers of media, thus necessitating domain decomposition and the use of multiple sets of collocation points. The solution process of this method proceeds entirely in physical space, requiring that the original differential equation be strictly established at the collocation points; thus, a dense matrix eigenvalue system is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained. Numerical experiments are presented to demonstrate the validity and applicability of this method. A comparison with other methods shows that the LCM proposed in this article is more accurate than the FDM and offers approximately the same accuracy as, but a faster calculation speed than, other types of spectral methods.

Parabolic Equation Techniques for Seismology, Seismo-Acoustics, and Arctic Acoustics

After the parabolic equation method was initially applied to scalar wave propagation problems in ocean acoustics and seismology, it took more than a decade before there was any substantial progress in extending this approach to problems involving solid layers. Some of the key steps in the development of the elastic parabolic equation are discussed here. The first breakthrough came in 1985 with the discovery that changing to an unconventional set of dependent variables makes it possible to factor the operator in the elastic wave equation into a product of outgoing and incoming operators. This innovation, which included an approach for handling fluid-solid interfaces, was utilized in the first successful implementations of the elastic parabolic equation less than five years later. A series of papers during that period addressed the issues of accuracy and stability, which require special attention relative to the scalar case. During the 1990s, the self-starter made it possible to handle all types of waves, rotated rational approximations of the operator square root made it possible to handle relatively thin solid layers, and there was some progress in the accurate treatment of sloping interfaces. During the next decade, an improved formulation and approach for handling interfaces facilitated the treatment of piecewise continuous depth dependence and sloping interfaces. During the last 10 years, the accuracy of the elastic parabolic equation was improved and tested for problems involving sloping interfaces and boundaries, and this approach was applied to Arctic acoustics and other problems involving thin layers. After decades of development, the elastic parabolic equation has become a useful tool for a wide range of problems in seismology, seismo-acoustics, and Arctic acoustics, but possible directions for further work are discussed.

Incidence of data augmentation in machine learning using broadband spectrograms

One of the main problems in ocean acoustics is the lack of training data that assist networks to generalize better understand undersea environments. In deep learning, data augmentation is commonly used to add variability to the data by applying small transformations to the samples with the purpose of improving the performance and generalization capabilities of the networks. Here, this definition is extended to broadband spectrograms from merchant ships collected during the Seabed Characterization Experiment in 2017. In this study, residual neural networks were used as the machine learning algorithm for performing source localization and environment classification. Additionally, nine different data augmentation techniques were considered for studying their performance predictions. Each of the transformations was applied to the data set during the training stage, and the results were compared to establish the effects in the performance for both regression and classification tasks. The metrics used were the root mean squared error for regression and accuracy in the case of seabed classification. The results show a favorable potential of residual-based deep learning models to differentiate the seabed types and the source position based on these types of data, in addition to the improvements in performance after applying complex transformations during the training. [Work supported by the Office of Naval Research, Contract No. N00014-19-C-2001.]

A convolutional neural network applied to measured time series for source range and ocean seabed classification

Source localization and environmental inference are common problems in ocean acoustics requiring computationally intensive algorithms and knowledge of the search space. Convolutional neural networks (CNNs) learn useful features for making predictions directly from a gridded input signal circumventing the costly practice of selecting features or comparisons to a forward propagation model. To take advantage of these benefits, a CNN was trained and validated on simulated pressure signals generated using four different environments (sandy, muddy, and mixed-sediment layers) for several ranges (2 to 12 km) to make environment class and range predictions. The trained network was then tested on recorded signals from the APL-UW Intensity Vector Autonomous Receiver system during SBC2017. We found that the network could make predictions with 99% accuracy on the simulated validation dataset but struggled to make unbiased predictions on the measured data. The struggles highlight the need to incorporate all significant features in the training data, such as time alignment and addition of noise. The CNN has the power to make predictions on this type and clearly see the differences in the data, but investigations for creating the proper training dataset or building a deeper network are required. [Work supported from Office of Naval Research.]

Ed Sullivan and model-based ocean acoustic signal processing

Ed Sullivan was a pioneer in model-based signal processing and his contributions have inspired numerous scientists in the fields of acoustic signal processing and ocean acoustics. Work by Ed and his colleagues is among the first efforts to formulate ocean acoustic inverse problems in a sequential filtering framework; methods were developed that overcome the destructive role of mismatch between assumed and true physics in inverse problems. In paper “Model-based ocean acoustic signal processing,” Acoustics Today, July 2011, Ed Sullivan identifies three main directions in signal processing, detection, classification, and estimation; he focuses on estimation and presents a study of model-based methods for inverse problems and how those methods can be successfully applied to the field of ocean acoustics. This presentation reviews these applications and discusses the impact of Ed Sullivan’s contributions on other advances in ocean acoustic signal processing.

Beam tracing for two- and three-dimensional problems in ocean acoustics.

Beam tracing is an extension of ray tracing that constructs beams around the central rays radiating from a source. Typically, a fan of such beams is used to represent a point source and the field at any given location is computed by coherently summing all contributing beams. On a slightly superficial level, one points to the following key benefits: (1) improved accuracy because the beams smooth out singularities of the ray-theoretic field, and (2) algorithmic advantages because eigenrays precisely connecting the source and the receiver do not need to be identified. One may argue about these considerations; however, beam tracing methods have emerged as a very important class of methods for computing ocean acoustic fields. Interestingly, the published literature has not kept up with the numerous advances in beam tracing, including algorithmic developments that are important to efficient and robust implementations. Furthermore, there are quite a few variants of beam tracing algorithms with very different characteristics. This article discusses these variants, significant advances in practical implementation, and performance characteristics.

Clay and Medwin: An intuitive approach to the math and physics

It is interesting to look back to the first encounter with a field that one would eventually make a career. This is frequently a combination of a mentor and some initial learning in an academic environment. Clarence (“Clay”) Clay and Herman (“Hank”) Medwin provided such an experience for numerous researchers in the field of ocean acoustics. Being active researchers and mentors, they published a sequence of two books, both entitled Acoustical Oceanography (1977 and the revised version in 1998), to introduce the field to those interested in using sound to remotely sense the oceans’ interior and boundaries. In addition to acousticians, readership includes marine biologists, geologists, and physical oceanographers. Although each book may look relatively simple at first glance, they present an intuitive approach to complex ocean acoustic problems with the right balance between physics, math, and real-world applications. There are also many references to more in-depth treatments of the topics. Each book provides a range of diverse topics including principles of underwater sound, sonar systems, signal processing, nonlinear acoustics, scattering from objects and creatures in the sea, the seafloor, acoustic waveguides, and many other subjects.

Results of matched-field inversion in a three-dimensional oceanic environment ignoring horizontal refraction

For some practical reasons, inverse problems in ocean acoustics are often based on 2-D modeling of sound propagation, hence ignoring 3-D propagation effects. However, the acoustic propagation in shallow-water environments, such as the continental shelf, may be strongly affected by 3-D effects, thus requiring 3-D modeling to be accounted for. In the present talk, the feasibility and the limits of an inversion in fully 3-D oceanic environments assuming 2-D propagation are investigated. A simple matched-field inversion procedure implemented in a Bayesian framework and based on the exhaustive search of the parameter space is used. The study is first carried out on a well-established wedge-like synthetic test case, which exhibits well-known 3-D effects. Both synthetic data and replica are generated using a parabolic-equation-based code. This approach highlights the relevance of using 2-D propagation models when inversions are performed at relatively short ranges from the source. On the other hand, important mismatch occurs when inverting at farther ranges, demonstrating that the use of fully 3-D forward models is required. Results of inversion on experimental small-scale data, based on a subspace approach as suggested by the preliminary study made on the synthetic test case, are presented.

Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions.

A normal mode solution to the ocean acoustic problem of the Pekeris waveguide with an elastic bottom using a Green's function formulation for a compressional wave point source is considered. Analytic solutions to these types of waveguide propagation problems are strongly dependent on the eigenvalues of the problem; these eigenvalues represent horizontal wavenumbers, corresponding to propagating modes of energy. The eigenvalues arise as singularities in the inverse Hankel transform integral and are specified by roots to a characteristic equation. These roots manifest themselves as poles in the inverse transform integral and can be both subtle and difficult to determine. Following methods previously developed [S. Ivansson et al., J. Sound Vib. 161 (1993)], a root finding routine has been implemented using the argument principle. Using the roots to the characteristic equation in the Green's function formulation, full-field solutions are calculated for scenarios where an acoustic source lies in either the water column or elastic half space. Solutions are benchmarked against laboratory data and existing numerical solutions.

Nonuniform depth grids in parabolic equation solutions

The parabolic wave equation is solved using a finite-difference solution in depth that involves a nonuniform grid. The depth operator is discretized using Galerkin's method with asymmetric hat functions. Examples are presented to illustrate that this approach can be used to improve efficiency for problems in ocean acoustics and seismo-acoustics. For shallow water problems, accuracy is sensitive to the precise placement of the ocean bottom interface. This issue is often addressed with the inefficient approach of using a fine grid spacing over all depth. Efficiency may be improved by using a relatively coarse grid with nonuniform sampling to precisely position the interface. Efficiency may also be improved by reducing the sampling in the sediment and in an absorbing layer that is used to truncate the computational domain. Nonuniform sampling may also be used to improve the implementation of a single-scattering approximation for sloping fluid-solid interfaces.

On the Feasibility of a Matched-Field Inversion in a Three-Dimensional Oceanic Environment Ignoring Out-of-Plane Propagation

Inverse problems in ocean acoustics are based on 2-D modeling of sound propagation, hence ignoring the effects of horizontal refraction, referred to as 3-D propagation effects. However, the acoustic propagation in shallow-water environments, such as the continental shelf, may be affected by 3-D effects requiring 3-D modeling to be accounted for. The aim of this work is to investigate the importance of the 3-D effects with respect to the performance and reliability of typical 2-D-model-based inversion procedures of ocean acoustics. The study is carried out on a well-established synthetic test case which exhibits well-known 3-D effects. A matched-field inversion procedure is implemented based on the exhaustive search over the parameter space. The feasibility and the limits of inverting low-frequency noisy 3-D synthetic data for some parameters describing the test case by matching replica from 2-D computations are explored. Both synthetic data and replica are generated using a parabolic-equation-based code. This approach highlights the relevance of using 2-D propagation models when inversions are performed at relatively short ranges from the source. On the other hand, important mismatch occurs when inverting at farther ranges, demonstrating that the use of fully 3-D forward models is required.

A summary of filtering approaches in ocean acoustics.

Sequential filtering provides an optimal framework for estimating and updating the unknown parameters of a system as data become available. Filtering is a powerful estimation tool, employing prediction from previous es‐timates and updates stemming from physical and statistical models that relate acoustic measurements to the unknown parameters. The foundations of sequential Bayesian filtering with emphasis on practical issues are presented covering both Kalman and particle filter approaches. Extended, unscented, and ensemble Kalman filters are compared to particle filtering approaches such as sequential importance resampling and advanced variants. Complex problems in ocean acoustics, where the state vector order is uncertain or the most suitable physical model for the problem at hand is not known a priori, are also addressed. Examples of model order selection and multiple model particle filters in underwater acoustic applications are given. Ocean acoustic examples are presented in target tracking, wave estimation, geoacoustic inversion, and frequency tracking.

The second order resolution operator of a nonlinear ocean acoustics inverse problem.

The resolution operator for a linear inverse problem indicates how much smearing exists in the map between the true model and the estimated model. The trace of the resolution operator provides an estimate of the number of model parameters model that are resolved. In a series representation of the resolution operator for a nonlinear problem, the higher‐order terms indicates how much spurious nonlinear leakage there is from the true model to the estimated model. In previous work, the solution of a simple nonlinear ocean acoustic inverse problem as a perturbation series in the horizontal wavenumber was constructed, and the linear data kernels were presented. This linear problem permitted the quantification of the magnitude of the perturbation and indicated when nonlinear effects must be taken into consideration. In this extension of previous work, the second order resolution kernel is constructed, which describes how effectively nonlinear effects can be removed from the reconstructed model. [Work supported by ONR.]

Resolution matrix perturbation series applied to a nonlinear ocean acoustic inverse problem.

The resolution operator for a nonlinear inverse problem is the product of the estimated inverse of the forward model operator and the forward model operator itself. If the inverse of the forward model operator were exact, then the resolution operator would be the identity, but in general the resolution operator describes the (noninvertible) transfer function between the unknown true environmental model and the limited‐resolution version, which can be estimated from measurements. The nonlinear model resolution operator can be computed iteratively from the Neumann series representation of an estimate of the inverse of the forward model operator with the assumption that both the data functional and the model perturbation functional possess regular perturbation expansions. An example of a problem that fits these criteria is normal mode acoustic propagation with “slow enough” perturbations such that the modes adjust adiabatically to the perturbations, and the mode eigenvalues are “far” from cutoff. We examine the effects of the nonlinear components of the model and the higher order components of the model resolution on the reconstruction of the model estimate for a simple ocean acoustic propagation problem. [Work supported by ONR.]

NURC/SACLANTCEN milestone experiments toward solving inverse problems in ocean acoustics

This paper reviews milestone experiments conducted by Saclant Undersea Research Centre to support the development and validation of techniques for obtaining and taking into account environmental information in sonar. The experiments brought together underwater acousticians, geophysicists and oceanographers with the aim to collect comprehensive acoustic and environmental ground-truth data. Environmental-adaptive signal processing was first demonstrated in a deep water area (WESTSARDINIA'89&90). From ducted propagation measurements, a model-based matched filter (MBMF) receiver that fully incorporates the physics of wave propagation determined a source range, depth and Doppler. For environmental inversion the broadband extension of matched-field processing was investigated in a shallow water area south of Elba island (YELLOWSHARK'94&95). Geoacoustic properties of the sea bottom were determined by finding the best fit between predicted and observed sound fields at multiple frequencies using genetic search algorithms. The same inversion results were obtained by MBMF processing of broadband linearly-frequency-modulated signals enabling the use of an array of a few hydrophones instead of a dense and large vertical array. This motivated the development of drifting acoustic buoys which were tested successfully over the southern continental shelf off Marettimo island, Sicily (ENVERSE'97&98). A recent experiment demonstrated an integrated concept of Rapid Environmental Assessment (MREA/BP'07) using sparse arrays of hydrophones and pressure/temperature sensors, hand-deployed from small vessels.

Tank experiment: The ultrasonic approach to ocean physics

Acoustic/elastic waves ranging from a few kHz to a few MHz are nowadays easy to emit/receive through the use of "key in hands" multi‐channel systems. These systems provide the instantaneous amplitude and phase of the deterministic wave propagating in the medium with a dynamic larger than 90 dB in some cases (16‐bit amplitude sampling). The use of a large number of channels (at least 64) is mandatory to simultaneously investigate the spatial and temporal aspect of wave propagation in complex media. The advantage of a laboratory‐scaled ocean model relies in the ease with which it can be build, modified, and/or controlled over time. Finally, the trend in ocean wave physics is now to study the dynamics of such medium (internal waves, turbulent flow, sensor motion) that requires the use of a real‐time acquisition system. Examples of the types of analog experiments that could be carried out with a laboratory‐scaled system are the study of nonuniform doppler shifted fields in reverberant environments, ocean acoustic tomography and similar inverse problems, coherent communications in complex moving environments, etc. After the description of the equipment, we give more specific examples of potential experiments to illustrate the versatility of the laboratory set‐up.