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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.

The acoustic propagation problem is modeled via the parabolic approximation. The physical domain consists of the water column with a horizontal water–bottom interface and the bottom region consists of N-strata with horizontal interfaces. The computational domain is restricted to the water column, while the stratified bottom region is modeled by a nonlocal boundary condition applied along the water–bottom interface, and having the form of a Neumann to Dirichlet map (NtD). The discrete analog of the NtD has been implemented in a finite difference scheme for the general wide angle PE model, and successfully tested for several benchmark problems. The stratification of the media can be either physical, e.g. sediment formulation in the bottom, or artificial/computational, e.g. forced by sparse distribution of environmental data measurements in the water column. It should be emphasized that the sound speed may vary from layer to layer, but is constant within each layer. The proposed NtD map can be used in geoacoustic inversion via the optimal control adjoint method.

Geoacoustic inversion is a very important issue in underwater acoustics, and the inversion method based on bottom reflection loss is a valid technique to invert bottom parameters. This paper describes a Bayesian method for estimating bottom parameters in the deep ocean based on inversion of reflection loss versus angle data which were obtained from an experiment conducted in South China Sea in 2013. The experimental data show that bottom loss depends on frequency. The Bayesian method can be applied in nonlinear inversion problems, and it provides useful indication about the quality of the inversion and parameter sensitivities. The bottom is modeled as a two-layer model, and each layer has constant parameters. The inverted parameters of sediment show a clay feature which is consistent with the core data. Furthermore, the inversion results are used to calculate transmission losses (TLs) along the experiment track which agree well with the direct measurements. Although the inversion results are limited to reveal exact structures of bottom, they are still useful for forecasting propagation losses in this area.

The characteristic acoustic impedance is a favorable observation variable for geoacoustic inversion (GI) owing to its higher sensitivity than that of pressure or particle velocity. However, no theoretical explanations have been provided for it. As an attempt to understand the underlying physical mechanism, interpretations based on the normal mode theory are conducted in this study. Moreover, synthetic Bayesian geoacoustic inversion with two recording scenarios of a vertical line array and single receiver are also performed, both of which proved that the impedance can provide improved estimation.

The bottom parameters of the deep ocean are difficult to obtain through in situ measurement. These parameters demonstrate a significant physical meaning for predicting sound field accurately. Thus, geoacoustic inversion is required. An acoustic experiment was performed on a reliable acoustic path (RAP) in the Philippine Sea in 2013. A single bottom-moored hydrophone was deployed as the receiver, and the explosive charges were chosen as the sources. The experimental bottom loss (BL) versus angle was obtained with the water depth above 5000m for bottom parameter inversion. The inversion sediment parameters show a clay-silt feature. The marginal probability distributions (MPDs) represent that the inversion results have a high credibility. This method provides a feasible solution for the inversion of the bottom parameters in the deep ocean.

The acoustic propagation problem in the ocean is modeled via the wide angle parabolic equation with a Neumann to Dirichlet map bottom boundary condition. An environment consisting of the water column, a sediment layer and the semi-infinite sub-bottom region is considered. The derivatives of a new cost function with respect to the unknown environmental parameters are calculated analytically via the adjoint operator and incorporated numerically in an inversion scheme. Full geoacoustic inversion for eight bottom parameters is performed successfully, using experimental field data from the Yellow Shark experiment, for the first time according to the authors’ knowledge. Adjoint inversion for the water SSP, using the EOFs, is also presented and validated with simulated data.

This paper reviews the progress in geoacoustic inversion over the past several decades. The review is separated into two parts. The first part reviews developments in model-based inversion methods that have led to present day usage of Bayesian inference. Theoretical foundations for the inversion methods are outlined, and limitations of model-based approaches are discussed. Examples are briefly described of applications of model-based inversion with different types of experimental data. The second part reviews recent developments in model-free inversion methods, focusing on discussion of distortion of estimated geoacoustic model parameters caused by model mismatch. It is shown that distortions in estimated model parameters lead to errors in interpreting characteristics of dispersion in the ocean waveguide, in particular the frequency dependence of sound attenuation in marine sediment. This review concludes with perspectives on new directions in research that promise improvement in inversion performance.

An inversion scheme based on time-warping is presented for estimating the attenuation coefficient of a sediment bottom using a single vector sensor, restricted to shallow water and using low-frequency impulsive sources. The attenuation information is extracted from the modal phase difference between pressure and vertical velocity. The method is derived from Pekeris waveguide theoretical equations and the eigen values are obtained using the normal mode model Kraken. Some changes are made to the time-warping process to mitigate the inherent interference between adjacent modes, which improves the phase extraction capabilities. Results are presented for a two-layer, homogeneous environment using the RAM propagation model for depth-dependent sound speed profile simulations. This version of RAM was updated to provide radial and vertical velocities. For additional generality, the technique is evaluated in the presence of white noise.

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.

This paper discusses the value added by using a single vector sensor over a conventional pressure-only hydrophone for geoacoustic inversions. Inversion methods based on genetic algorithms are used to estimate the seabed properties. Synthetic signals of impulsive arrivals first are modeled using KRAKEN and RAM propagation models, each being modified to predict components of the vector field. While KRAKEN is utilized to directly compute dispersion curves, RAM provides full-field results that require the application of time warping to separate the modal arrivals. Combinations of dispersion curves utilizing all vector sensor channels are compared to curves estimated with the pressure-only channel. Within the time warping analysis, both binary masking and band-pass filter masking methods are applied to compare stability of results. The environment modeled for the synthetic analysis and inversion method utilize sound speed profiles measured during the Monterey Bay 2019 at-sea experiment and assume a sediment layer of constant thickness overlying a deeper sub-bottom type. White noise is added to the synthetic data at different signal-to-noise ratios to evaluate the impact of signal excess on the results. A hybrid optimization approach is used to improve the results of the genetic algorithm method. The analysis with synthetic data is consistent with the analysis of broadband, impulsive data collected from the experiment, indicating that the additional information from the vertical velocity channel further improves the geoacoustic parameter estimates.

Broadband signals interacting with deep ocean fine-grained sediment are crucial in shaping the acoustic field of the geometric shadow zone. These signals travel through both the seabed reflected path and the refracted path. In this article, a sequential inversion scheme is employed to estimate the geoacoustic parameters in abyssal clay sediments. This inversion is based on seabed reflection loss data at different frequencies, as well as travel time difference data between refractions and reflections obtained from the South China Sea Experiment in 2018. Depth-dependent profiles of geoacoustic parameters are formulated using Bernstein polynomials. The polynomial coefficients and their posterior probability density functions are efficiently estimated using the adaptive simplex simulated annealing method and an approximate variational inference technique known as Variational Bayesian Monte Carlo. This technique demonstrates superior efficiency and comparable accuracy to Markov Chain Monte Carlo sampling. The inversion results indicate that the abyssal clay sediments in this area exhibit a positive sound speed gradient and relatively low attenuation, both with high probabilities. The deduced seabed model accurately predicts the transmission loss, aligning well with the experimental data.

This tutorial demonstrates the use of information geometry tools in analyzing environmental parameter sensitivities in underwater acoustics. Sensitivity analyses quantify how well data can constrain model parameters, with application to inverse problems like geoacoustic inversion. A review of examples of parameter sensitivity methods and their application to problems in underwater acoustics is given, roughly grouped into “local” and “non-local” methods. Local methods such as Fisher information and Cramér-Rao bounds have important connections to information geometry. Information Geometry combines the fields of information theory and differential geometry by interpreting a model as a Riemannian manifold, known as the model manifold, that encodes both local and global parameter sensitivities. As an example, 2-dimensional model manifold slices are constructed for the Pekeris waveguide with sediment attenuation, for a vertical array of hydrophones. This example demonstrates how effective, reduced-order models emerge in certain parameter limits, which correspond to boundaries of the model manifold. This example also demonstrates how the global structure of the model manifold influences the local sensitivities quantified by the Fisher information matrix. This paper motivates future work to utilize information geometry methods for experimental design and model reduction applied to more complex modeling scenarios in underwater acoustics.