Ocean Acoustic Propagation Models Research Articles

A Chebyshev collocation method for directly solving two-dimensional ocean acoustic propagation in linearly varying seabed.

It is one of the most concerning problems in hydroacoustics to find a method that can calculate the acoustic propagation accurately and adapt to the variation of the seabed. Currently, the one-dimensional spectral method has been employed to address the simplified ocean acoustic propagation model successfully. However, due to the model's application limitations and approximation error, it poses challenges when attempting to solve real-world ocean acoustic fields. Hence, there is a crucial need to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation, without relying on a simplified model. In previous work, we achieved successful solutions for the two-dimensional Helmholtz equation within a rectangular domain, utilizing a collocation-type spectral method. Taking into account the fluctuations in the actual seabed, we introduce a Chebyshev collocation spectral method to directly tackle the two-dimensional ocean acoustic propagation problem, which could solve the case of a seabed with linear variation, sound velocity variation and inhomogeneous medium situation. After comparative verification, the calculation result of the two-dimensional spectral method is more accurate than traditional mature models such as Kraken and COUPLE. By eliminating model constraints and enlarging the solution range, this spectral method holds immense potential in real marine environments.

Evaluation of data-driven neural operators in ocean acoustic propagation modeling

Various types of neural networks have been employed to tackle a wide range of complex partial differential equations (PDEs) and ordinary differential equations (ODEs). Notably, neural operators such as DeepONet and FNO show promise in handling these problems, offering potential real-time prediction capabilities. In contrast to physics-informed neural network (PINN) methods, neural operators primarily derive insight from extensive, well-prepared datasets. In the context of ocean acoustic propagation modeling, where the challenge involves solving the wave or Helmholtz equation given specific boundary conditions, this study focuses on assessing the performance of data-driven neural operators in predicting sound pressure. Unlike conventional approaches that map between finite-dimensional Euclidean spaces, neural operators excel in learning mappings between infinite-dimensional function spaces—a particularly advantageous feature in sound propagation modeling tasks. This research specifically delves into evaluating the generalization capabilities of neural operators when applied to sound propagation modeling in a range-independent shallow water environment. By exploring the neural operators' effectiveness in this domain, the study aims to contribute valuable insights into their potential applications for real-world ocean acoustics simulations.

Probabilistic acoustic predictions leveraging NESBA and ARGO measurements

Ocean acoustic propagation models used for sonar performance prediction often rely on global or regional ocean modeling and data assimilation, or monthly climatologic averages, for estimating the 4D ocean temperature and salinity (T/S) field. Ocean models rely heavily on satellite-based ocean surface measurements, e.g., sea surface temperature (SST) and height (SSH), plus typically vastly less resolved in space and time vertical water column measurements derived using ship-based and/or ARGO float instruments. Systems also exist that create 3D synthetic T/S fields from satellite SST/SSH measurements, e.g., the Modular Ocean Data Assimilation System (MODAS) and the more recent Improved Synthetic Ocean Profile (ISOP) system. It is unclear, however, how well these synthetic T/S fields capture significant ocean ducting conditions. Similarly, climatologic averages combine historical vertical T/S profile data in spatial cells by month; but the averaging process tends to blur out important features. This talk will address the use of 2021 New England Shelf Break Acoustics (NESBA) experiment and ARGO vertical profile data for: (1) testing the degree to which ocean models or climatology capture important acoustic features under a range of conditions; and (2) providing more realistic sonar performance prediction means and uncertainties. [Work supported by the Office of Naval Research].

Study on the effect of seafloor sound speed dispersion on sound propagation

As one of the boundaries of ocean waveguide, the acoustic properties of seafloor sediments have been a hot research problem in ocean acoustic propagation and acoustic field modeling. The existing research has shown that the sound velocity in seafloor sediment is frequency dependent. In order to solve the problem that the sedimentary sound speed dispersing often be ignored in actual applications, this article uses the parabolic Newton to iterate to solve the dispersion equation to obtain the characteristic value of the normal mode. And the impact of frequency dispersion of sediment sound speed through simulation are studied. The results show that the sound wave in the time domain will appear more obvious broadening phenomenon, and the propagation loss will be reduced after considering the sound velocity dispersion of the sediment. Also, with the increase of frequency, the more obvious the effect of sound velocity dispersion on the sound propagation in the frequency range of sound velocity dispersion.

Gaussian process model selection for parameter estimation in ocean acoustics

The dynamic nature of the ocean environment presents numerous challenges to parameter estimation in ocean acoustics. We present a variational Bayesian method which selects an optimal model for parameter estimation in ocean acoustics using Gaussian process (GP) regression. GP model selection is based on Bayesian model selection, which treats the parameters and kernel selection of the model as hyperparameters and uses Bayesian inference to compute a model’s likelihood with respect to its hyperparameters. However, in Bayesian model selection, the integrals over parameter space are often intractable and require approximation or sampling methods such as Markov chain Monte Carlo. GP renders these integrals tractable by treating hyperparameters as multivariate Gaussian distributions, which greatly speeds up the optimization. Furthermore, model selection using GPs allows for straightforward evaluation of uncertainty in the selected model’s likelihood. In this study, we compare results of acoustic parameter estimation from Bayesian and GP model selection using an ocean acoustic propagation model.

Using energy flux methods to derive a 3D ocean acoustic propagation model

The energy flux model is a direct source-to-receiver calculation that avoids the need for finding eigenvalues, but it averages out the modal interference structure as originally derived. It has been shown possible in the two-dimensional model to include the near-neighbor modal interference that resolves large-scale caustic features and shadow zones. So far limited work has been done to develop three-dimensional energy flux models for ocean acoustic propagation, but such a model may have significant computational advantages in complex environments or at high frequencies. We present current progress towards developing three-dimensional underwater acoustic propagation models that have been derived using energy flux principles. In particular we will discuss a vertical normal mode and horizontal energy flux model used to solve for the acoustic propagation in a wedge environment.

Sensitivity Analysis of Hybrid Split-Step Fourier/Finite Difference Parabolic Equation Models

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air interface.

Sensitivity Analysis of Hybrid Split-Step Fourier/Finite Difference Parabolic Equation Models

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air inter...

Model validation of rough surface scattering at a water/air interface using a hybrid parabolic equation model

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models. For propagation models based on the parabolic equation that utilize split-step Fourier (SSF) algorithms, previous work has involved field transformational techniques to treat the rough surface displacements. Such techniques assume small angle scattering at the interface, which may not produce adequate numerical accuracy. An alternative approach is to model the physical water/air interface, and allow the higher order propagator functions of the parabolic approximation to more accurately model the rough surface scatter. However, the introduction of such large interface discontinuities have been known to introduce phase errors in SSF-based models. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches, as well as the pressure release field transformational technique, for simple rough surfaces. A finite element model is utilized to provide a benchmark solution and comparisons are made for both standard Dirichlet and explicit mixed media treatments of the air-water interface. Tradeoffs between accuracy and stability are discussed, as well as transmission across the water/air interface.

Examination of rough surface scattering from water/air interface using hybrid parabolic equation model

Many ocean acoustic propagation models assume an idealized pressure-release boundary at the ocean surface. This is easily accomplished numerically using finite element, finite difference, and split-step Fourier techniques. For models based on the split-step Fourier algorithm, rough surfaces can also be treated, but require additional complexity in the definitions of the field and propagator functions through a field transformation technique. For this reason, it may be advantageous to model a rough water/air interface in a manner analogous to the bottom treatment by extending the calculation into the air medium, thereby simplifying the definitions of the propagator functions. However, standard approaches to treat density discontinuities in split-step Fourier algorithms invoke smoothing functions, which have been shown to introduce phase errors in range. In this work, the hybrid split-step/finite-difference approach introduced by Yevick and Thomson (1996) is implemented in the Monterey-Miami Parabolic Equation (MMPE) model for both the water/sediment and water/air interfaces. Particular attention is paid to comparisons between the rough surface scattering results from the field transformation technique (applied to a pressure release surface) and the hybrid split-step/finite-difference approach (applied to the water/air interface).Many ocean acoustic propagation models assume an idealized pressure-release boundary at the ocean surface. This is easily accomplished numerically using finite element, finite difference, and split-step Fourier techniques. For models based on the split-step Fourier algorithm, rough surfaces can also be treated, but require additional complexity in the definitions of the field and propagator functions through a field transformation technique. For this reason, it may be advantageous to model a rough water/air interface in a manner analogous to the bottom treatment by extending the calculation into the air medium, thereby simplifying the definitions of the propagator functions. However, standard approaches to treat density discontinuities in split-step Fourier algorithms invoke smoothing functions, which have been shown to introduce phase errors in range. In this work, the hybrid split-step/finite-difference approach introduced by Yevick and Thomson (1996) is implemented in the Monterey-Miami Parabolic Equat...

Deep seafloor arrivals in long range ocean acoustic propagation

Ocean bottom seismometer observations during the long-range ocean acoustic propagation experiment in the North Pacific in 2004 showed robust, coherent, late arrivals that were not observed on hydrophones suspended 750m and more above the seafloor and that were not readily explained by ocean acoustic propagation models. The DSFA arrival pattern on the OBSs near 5000m depth are a delayed replica, by about two seconds, of the arrival pattern on the deepest element of the DVLA at 4250m depth (DVLA-4250). Using a conversion factor from the seafloor vertical particle velocity to seafloor acoustic pressure, we have quantitatively compared signal and noise levels at the OBSs and DVLA-4250. Ambient noise and DSFA signal levels at the OBSs are so quiet that if the DSFA arrivals were propagating through the water column, perhaps on an out-of-plane bottom-diffracted-surface-reflected (BDSR) path, they would not appear on single, unprocessed DVLA channels. Nonetheless arrival time and horizontal phase velocity analysis rules out BDSR paths as a mechanism for DSFAs. Whatever the mechanism, the measured DSFAs demonstrate that acoustic signals and noise from distant sources can appear with significant strength on the seafloor at depths well below the conjugate depth.

Deep seafloor arrivals in long range ocean acoustic propagation

Ocean bottom seismometer observations at 5000 m depth during the long-range ocean acoustic propagation experiment in the North Pacific in 2004 show robust, coherent, late arrivals that are not readily explained by ocean acoustic propagation models. These "deep seafloor" arrivals are the largest amplitude arrivals on the vertical particle velocity channel for ranges from 500 to 3200 km. The travel times for six (of 16 observed) deep seafloor arrivals correspond to the sea surface reflection of an out-of-plane diffraction from a seamount that protrudes to about 4100 m depth and is about 18 km from the receivers. This out-of-plane bottom-diffracted surface-reflected energy is observed on the deep vertical line array about 35 dB below the peak amplitude arrivals and was previously misinterpreted as in-plane bottom-reflected surface-reflected energy. The structure of these arrivals from 500 to 3200 km range is remarkably robust. The bottom-diffracted surface-reflected mechanism provides a means for acoustic signals and noise from distant sources to appear with significant strength on the deep seafloor.

Information and linearity of time-domain complex demodulated amplitude and phase data in shallow water

Wave-theoretic ocean acoustic propagation modeling is used to derive the sensitivity of pressure, and complex demodulated amplitude and phase, at a receiver to the sound speed of the medium using the Born-Fréchet derivative. Although the procedure can be applied for pressure as a function of frequency instead of time, the time domain has advantages in practical problems, as linearity and signal-to-noise are more easily assigned in the time domain. The linearity and information content of these sensitivity kernels is explored for an example of a 3-4 kHz broadband pulse transmission in a 1 km shallow water Pekeris waveguide. Full-wave observations (pressure as a function of time) are seen to be too nonlinear for use in most practical cases, whereas envelope and phase data have a wider range of validity and provide complementary information. These results are used in simulated inversions with a more realistic sound speed profile, comparing the performance of amplitude and phase observations.

Bathymetric scattering and seafloor interface waves in long‐range ocean acoustic propagation.

Ocean bottom seismometer observations during a long‐range ocean acoustic propagation experiment in the North Pacific in 2004 showed robust, coherent, late arrivals that were not observed on hydrophones suspended 750 m and more above the seafloor and that were not readily explained by ocean acoustic propagation models. These deep seafloor arrivals were the largest amplitude arrivals on the vertical velocity channel for ranges from 500 to 3200 km. They appear to correspond to energy converted from ocean acoustic waves into seafloor interface (Scholte) waves at a small bathymetric high about 18 km from the receivers. Some problems with this model are the following: (a) It is rare to observe discrete Scholte waves propagating 18 km or so on the seafloor. It is usually assumed that Scholte and shear waves decay rapidly in and along the seafloor because of strong scattering and intrinsic attenuation. (b) There is apparently insignificant scattering back into the water column because this would have been observe...

Source range and depth estimation using passive sonar, horizontal arrays, and knowledge of the environment.

Target detection, classification, localization, and tracking (DCLT) using horizontal arrays and passive sonar is a well‐studied problem. Good detection results can be obtained using narrow beams that maximize signal to noise ratio. Beamforming also provides azimuth angle, but is generally not reliable for range and depth estimation. Matched field processing (MFP) makes use of environmental knowledge to predict the received signal at the array, and correlates predicted and received signals to estimate target range and depth. However, poor or inaccurate environmental knowledge degrades MFP performance, and in general, MFP suffers from high side lobes or ambiguity in the range/depth probability surface. Received signal amplitude statistics have been used to estimate source depth, but the method has not been studied extensively to date. Recently several methods have been developed involving received signal amplitude statistics predicted using environmental parameter statistics to construct statistically valid descriptions of the environment, which were then fed to an ocean acoustic propagation model (i.e., Monte Carlo simulation). Performance of the algorithms has been evaluated using data from the Swellex‐96 experiment. [Work sponsored by ONR Undersea Signal Processing.]

Source depth classification of passive sonar signals using amplitude statistics.

A number of at-sea measurements have shown that fluctuations in the amplitude of passive sonar signals are affected by source depth, range, and the propagation path from the source to the receiver. However, to date, received signal statistics have not been incorporated into passive sonar classification algorithms because the field results have not been accompanied by development of a statistics-based classifier architecture whose performance can be assessed using accepted signal processing metrics, e.g., a receiver operating characteristic curve. The performance of a statistics-based classifier depends critically upon statistical knowledge of the received signal, which in turn depends upon statistical knowledge of relevant environment parameters (sound speed in the water column and sediment, for example). Thus the classifier architecture must make use of the environmental information which in reality is only approximately known and must be described in statistical terms. Given a statistical description of the environment, an ocean acoustic propagation model and Monte Carlo simulation can be used to predict received signal statistics. Once received signal statistics are available for the different classes, a classifier can be designed. Here we examine a likelihood ratio binary source depth classifier for passive sonar. [Work sponsored by ONR Undersea Signal Processing.]

A Bayesian approach to incorporating maximum entropy-derived signal parameter statistics into the receiver operating characteristic (ROC) curves

Our goal is to develop a probabilistic sonar performance prediction methodology that can make use of limited knowledge of random or uncertain environment, target, and sonar system parameters, but does not make unwarranted assumptions. The maximum entropy method (MEM) can be used to construct probability density functions (pdfs) for relevant environmental and source parameters, and an ocean acoustic propagation model can use those pdfs to predict the variability of received signal parameter. At this point, the MEM can be used once again to produce signal parameter pdfs. A Bayesian framework allows these pdfs to be incorporated into the signal processor to produce ROC curves in which, for example, the signal-to-noise ratio (SNR) is a random variable for which a pdf has been calculated. One output of such a processor could be a range-dependent probability of detection for fixed probability of false alarm, which would be more useful than the conventional range of the day that is still in use in some areas. [Work supported by ONR Code 321US.]

Embedding uncertainty into ocean acoustic propagation models (L)

A probabilistic formalism is proposed for the direct inclusion of environmental uncertainty into an acoustic model that describes propagation in an ocean waveguide. Incomplete environmental knowledge is characterized by a spectral representation of uncertainty using expansions of random processes in terms of orthogonal random polynomials. A brief summary of the method is presented and a set of coupled differential equations describing the propagation of both the acoustic field and its associated uncertainty is derived for the case where the uncertain environment is attributed to a lack of complete information concerning the waveguide’s sound speed distribution.

Range-depth tracking of humpback whales using autonomous acoustic recorders

Matched-field processing (MFP) is a technique for tracking an acoustic source in range and depth by comparing the output of an ocean acoustic propagation model with measured acoustic data collected across multiple hydrophones [e.g., Thode et al., J. Acoust. Soc. Am. 107, 1286–1300 (2000)]. In October 2003 a MFP experiment was conducted using humpback whale sounds recorded during the spring migration off the Sunshine Coast in Queensland, in conjunction with a larger experiment conducted by the Humpback Acoustic Research Collaboration (HARC). Humpback whale sounds between 50 Hz to 1 kHz were recorded on a five-element vertical array deployed in 24-m-deep water. The vertical array consisted of a set of flash-memory autonomous recorders attached to rope with an anchor at one end, and a subsurface float at the other. Acoustic data were simultaneously collected and monitored on five sonobuoys deployed over approximately 2-km range. Using the range estimates from the sonobuoys as bounds on the matched-field processing, a geoacoustic inversion using the calls was performed on the vertical array data using a genetic algorithm. Preliminary results of the inversion and resultant 3-D position fixes are presented. [Work supported by ONR.]

Travel-time sensitivity kernels in ocean acoustic tomography

Wave-theoretic ocean acoustic propagation modeling is combined with the peak arrival approach for tomographic travel-time observables to derive the sensitivity kernel of travel times with respect to sound-speed variations. This is the Born–Fréchet kernel relating the three-dimensional spatial distribution of sound-speed variations with the induced travel-time variations. The derivation is based on the first Born approximation of the Green’s function. The application of the travel-time sensitivity kernel to an ocean acoustic waveguide gives a picture close to the ray-theoretic one in the case of high frequencies. However, in the low-frequency case, of interest in ocean acoustic tomography, for example, there are significant deviations. Low-frequency travel times are sensitive to sound-speed changes in Fresnel-zone-scale areas surrounding the eigenrays, but not on the eigenrays themselves, where the sensitivity is zero. Further, there are areas of positive sensitivity, where, e.g., a sound-speed increase results in an increase of arrival times, i.e., a further delay of arrivals, in contrast with the common expectation. These findings are confirmed by forward acoustic predictions from a coupled-mode code.