Problems In Underwater Acoustics Research Articles

Multi-frequency sparse Bayesian learning for matched field processing

Compressive sensing has been applied to underwater acoustic problems. Using multi-frequency sparse Bayesian learning (SBL), we present simulation and data results (SWellEx-96 Event S5) including mismatch. Mismatch is defined as a misalignment between the actual source field observed at the array and the modeled replica vector. Results for a multiple-source scenario indicate that SBL outperforms WNC and MUSIC when localizing a quiet source in the presence of a stronger source. Furthermore, simulations (including snapshots not corresponding exactly to replicas) and data results demonstrate that SBL offers robustness to mismatch including array-tilt. The array-tilt mismatch in the data varies over time and is especially pronounced at the closest point of approach, being 2 degrees. Because of its computational efficiency and performance, SBL is practical for real time applications requiring an adaptive and robust processor.

Application of iterative hill climbing to the sound speed profile inversion in underwater acoustics

An application of the iterative hill climbing algorithm to the solution of inverse problems of underwater acoustics is discussed. Modal dispersion data extracted from a recording of a pulse acoustical signal is used as the input for the geoacoustic inversion procedure. The mismatch of the dispersion curves extracted from experimental data and computed from a given set of waveguide parameters is minimized over the parameters space. The solution of two test inversion problems is considered. It is shown that the iterative launches of the hill climbing algorithm allow to locate either the global minimum or a local minimum which is reasonably close to the former. In the latter case a reasonable estimate of the waveguide parameters is obtained.

A sequential filtering algorithm for range estimation of a moving ship based on striation geometric features

There exist regular striation pattern in the broad-band noise field excited by a moving ship in shallow waters, whose time (range) frequency structure can be interpreted by the waveguide invariant theory. The striation characteristics have been exploited for underwater acoustic inversion problems, e.g., sediment geoacoustic parameter characterization. In this paper, the geometrical features of specific striations are observed for continuously ship ranging by a sequential algorithm. Comparing to matched-field processing techniques, this approach also has no requirements prior knowledge of environmental properties and burden of forward sound field calculation, which is similar to virtual receiver approach. The technique is tested on the striation fragments extracted from the ship noise data collected in Dalian 2008, and the outputs are in high agreement with in-situ GPS measurements. The results from independent runs with different initial values also suggest that this approach is robust to initial conditions in the sense of all runs can converge to the true values rapidly.

Robust multi-frequency sparse Bayesian learning: Theory and simulations

Compressive sensing based techniques have recently been applied successfully to underwater acoustics problems such as beamforming and matched field processing. Sparse Bayesian Learning (SBL) is one of the fast compressive sensing methods and is formulated using Bayesian statistics. In the SBL framework, source amplitudes are modeled as complex Gaussian random variables with unknown variance. Evidence maximization is performed to estimate the unknown source amplitude variance and source position. A major advantage of SBL over more commonly used methods such as basis pursuit is that it is computationally faster. In this work, we develop a robust sparse Bayesian learning algorithm that can account for model mismatch leading to errors in the replica vector dictionary. Specifically, the likelihood function is modified so that it takes into account the covariance matrix of error in replica vectors. We also extend the SBL algorithm to process observations from multiple frequencies. The derived update rule combines observations from all the frequencies in a holistic manner. We demonstrate the robust SBL algorithm with simulations. A comparison is done with other compressed sensing methods including basis pursuit and orthogonal matching pursuit.

Robust multi-frequency sparse Bayesian learning: Data results

Compressive sensing based techniques have been applied successfully to underwater acoustics problems. We present data results using a robust multi-frequency sparse Bayesian learning (SBL) algorithm that can account for model mismatch leading to errors in the replica vector dictionary. We use the SWellEx-96 Event S5 data set to demonstrate SBL capabilities for the beamforming and matched field processing (MFP) application. Beamforming results using the entire 64 element array (design frequency of 400 Hz) and source frequencies ranging from 50 to 400 Hz indicate that multi-frequency SBL outperforms Bartlett and WNC processors in identifying multipath arrivals over the approximately 10 km source track. MFP results in a multiple-source scenario indicate that SBL offers a degree of robustness in the presence of data-replica mismatch when tracking a quiet source. The data-replica mismatch is especially pronounced at the closest point of approach due to array tilt of approximately 2 degrees. Data results further indicate that the two SBL tuning parameters (diagonal loading of the replica vector covariance matrix and number of sources for the algorithm’s noise estimate) do not require excessive calibration.

Watermarking of linear frequency modulated pulses using chirplet graphs and stretch processing.

In many underwater acoustics problems such as search and rescue, it is desirable to establish the source of the sonar pings. In this paper a methodology is proposed to watermark sonar pulses prior to transmission by embedding them with a chain of low power chirplets represented by a graph. Watermark detection is formulated using stretch processing where chirplet energies are focused on a single beat frequency only if the graph is traversed along the same path used at the source. The algorithm is tested by simulation in shallow water at varying ranges.

Method of the spectral parameter power series in problems of underwater acoustics of the stratified ocean

The spectral parameter power series method is applied to problems of underwater sound propagation in the stratified ocean. This method is based on representations of solutions of vertical Sturm–Liouville problems of the form of power series with respect to the spectral parameter, and it gives an effective dispersion equation for wave numbers and explicit expressions for the propagating modes. Copyright © 2014 John Wiley & Sons, Ltd.

Simulation of underwater environments using the Discrete Huygens Modeling

The Discrete Huygens Modeling (DHM) is a numerical method that applies the Huygens principle to a discretized medium in order to provide time domain solutions to wave propagation problems. The method was originally conceived and applied in Electromagnetism, but previous works have shown that DHM is also a viable and promising approach for the simulation of acoustic problems. The main advantages of the method are its reduced computation cost when compared with other numerical methods and its relatively easy implementation and parallelization. However, little can be found in the literature about the use of DHM to underwater acoustic problems, and previous work have been limited to acoustic propagation only in the water column. In this work, a simple model of the acoustic field generated in the water column by a monopole was created, and the prediction of transmission, reflection, and scattering processes at the interface with the sediment were carried out. A DHM code has been fully implemented allowing the modeling of multiple media. The results obtained with the DHM model were compared with a Finite Element model yielding very good agreement, while the DHM approach proved to be much faster.

ANALYTICAL TIME DOMAIN NORMAL MODE SOLUTION OF AN ACOUSTIC WAVEGUIDE WITH PERFECTLY REFLECTING WALLS

Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run.

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

A finite difference method for the wide‐angle “parabolic” equation in a waveguide with downsloping bottom

AbstractWe consider the third‐order wide‐angle “parabolic” equation of underwater acoustics in a cylindrically symmetric fluid medium over a bottom of range‐dependent bathymetry. It is known that the initial‐boundary‐value problem for this equation may not be well posed in the case of (smooth) bottom profiles of arbitrary shape, if it is just posed e.g. with a homogeneous Dirichlet bottom boundary condition. In this article, we concentrate on downsloping bottom profiles and propose an additional boundary condition that yields a well‐posed problem, in fact making it L2 ‐conservative in the case of appropriate real parameters. We solve the problem numerically by a Crank–Nicolson‐type finite difference scheme, which is proved to be unconditionally stable and second‐order accurate and simulates accurately realistic underwater acoustic problems. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

Three-dimensional numerical modeling of sound propagation and scattering in the deep ocean with elastic (shear) bottoms

A major challenge in bottom-interacting ocean acoustics is to include an accurate description of environmental variability in a computationally feasible model. Wave field predictions are often difficult in environments with strong range dependence, with rapid bathymetric variations, with multiple scattering regions, with interface waves at fluid/solid boundaries, and/or with shear waves in the bottom. In this presentation, we are adapting an existing three-dimensional spectral-finite-element code (SPECFEM3D, distributed and supported by the NSF funded program, Computational Infrastructure for Geodynamics), originally developed for global seismology, to bottom interaction problems in underwater acoustics. Numerical results from SPECFEM3D are compared with the range-dependent acoustic/elastic wave propagation model based on the parabolic equation (PE) method, for a 10 Hz acoustic pulse propagating in the deep ocean. The importance of out-of-plane scattering and bottom shear properties on resulting wave fiel...

Effects of seismic source and environment parameters on elastic bottom parabolic equation solutions

Recently, two-types of elastic self-starters have been incorporated into parabolic equation solutions for range-dependent elastic bottom underwater acoustic problems. These source fields generate parabolic equation solutions that can be used to study development of oceanic T-phases via the process of downslope conversion. More general range-dependence has also been shown to scatter elastic wave energy into water column acoustic modes which then propagate as T-phases. In certain circumstances, sources in the elastic bottom can also cause interface waves at the ocean bottom that contribute to the ocean acoustic field. Both types of waves can propagate long distances and could be source mechanisms for unexplained acoustic signals recorded near the sea floor and below the ray-theoretic turning point. Parabolic equation solutions will be used to study effects of parameters such as frequency, source location, and source type on T-phase and interface wave generation and propagation.[Work supported by ONR.]

Vortex properties of the acoustic intensity vector in a shallow sea

We study the vortex properties of the field of the acoustic intensity vector as a function of distance and radiation frequency, determined using a combined acoustic system in Peter the Great Bay in the Sea of Japan. We present probability density histograms of the normalized intensity vector curl components at a frequency of 110 Hz for the distance interval between the source and receiver within the limits of 1200–1725 m. The vortex structure of the acoustic intensity vector was observed in the vertical plane at the full distance (4000 m) from the source to the receiver. The discovered vortex structures are of interest both for physical acoustics and for applied problems in underwater acoustics.

Comparison of the Vorticity of Acoustic Intensity Vector at 23 Hz and 110 Hz Frequencies in the Shallow Sea

This paper presents the results of vortex features research of the field of acoustic intensity vector depending on distance and frequency by the combined acoustic systems in Peter the Great Bay (Sea of Japan). The receiver was submerged to 70 m depth at the site depth of 120 m, sound velocity on the surface was higher than that of the bottom’s one. To determine the vorticity three components of curl of intensity vector were calculated. The work provides the distribution histograms of probability density in the normalized components of intensity vector curl at 110 Hz and 23 Hz frequencies for the distances interval between source and receiver within 1200 – 2000 m. The vortex structure of acoustic intensity vector was discovered in vertical plane along the entire researched distance (5000 m) between source and receiver. The described mechanism of acoustic energy transfer reveals new opportunities in the study of acoustic characteristics of the shallow sea. The disclosed vortex structures are of interest both for physical acoustics and for applied problems in underwater acoustics.

Comparison of parabolic equation and coupled mode solutions to seismo-acoustic problems

Parabolic equation methods that use the single scattering approximation and improved rotated coordinate methods generate accurate and efficient solutions for range-dependent underwater acoustic problems with elastic sediments. Recently these methods have demonstrated the conversion of acoustic energy in a fluid into shear propagation in an underlying elastic layer. Elastic coupled mode theory can also be used in a range-dependent environment and provides an accurate description of the conversion between fluid and elastic modes during propagation. The current parabolic equation approach will be augmented with an elastic version of the self-starter that includes both compressional and shear wave energy. Results from these two approaches will be compared for acoustic and elastic sources in both range-independent and range-dependent underwater environments. Propagation at the fluid–solid interface will be examined as a possible mechanism for the conversion of elastic layer shear energy into acoustic energy in...

A Hybrid Analytical‐Numerical Model Based on the Method of Fundamental Solutions for the Analysis of Sound Scattering by Buried Shell Structures

Several numerical and analytical models have been used to study underwater acoustics problems. The most accurate and realistic models are usually based on the solution of the wave equation using a variety of methods. Here, a hybrid numerical‐analytical model is proposed to address the problem of underwater sound scattering by an elastic shell structure, which is assumed to be circular and that is buried in a fluid seabed bellow a water waveguide. The interior of the shell is filled with a fluid that may have different properties from the host medium. The analysis is performed by coupling analytical solutions developed both for sound propagation in the waveguide and in the vicinity of the circular hollow pipeline. The coupling between solutions is performed using the method of fundamental solutions. This strategy allows a compact description of the propagation medium while being very accurate and highly efficient from the computational point of view.

Bayesian tracking and geoacoustic inversion

This paper describes a Bayesian approach to two related inverse problems in underwater acoustics: localizing/tracking an acoustic source when ocean environmental properties are unknown, and determining environmental properties using acoustic data from an unknown (moving) source. The goal of this work is not simply to estimate values for source and/or environmental parameters, but to determine parameter uncertainty distributions, thereby quantifying the state of knowledge and information content of the inversion. A common formulation is applied for both problems in which source parameters (location and spectrum) and environmental parameters are considered unknown random variables constrained by noisy acoustic data and by prior information on parameter values (e.g., physical limits for environmental properties) and on inter‐parameter relationships (limits on horizontal and vertical source speed). Given the strong nonlinearity of the inverse problem, marginal posterior probability densities are computed numerically using efficient Markov‐chain Monte Carlo importance sampling methods. Source tracking results are represented by joint marginal probability distributions over range and depth, integrated over unknown environmental parameters. The approach is illustrated with two examples representing tracking a quiet submerged source and geoacoustic inversion using noise from an unknown ship‐of‐opportunity. In both cases, source, seabed, and water‐column parameters are unknown.

Investigation of 3D benchmark problems in underwater acoustics: a uniform approach

In underwater acoustics, most of the three-dimensional effects on sound wave propagation are usually described by modelers considering one of the following shallow-water benchmark problems: a wedge-shaped waveguide, a canyon, a seamount, and a sinusoidal (corrugated) bottom. These test cases have been thoroughly analyzed individually considering both harmonic point sources (emitting at very low frequencies, for some obvious problems of CPU time and memory limitation) and broadband source pulses (with also very-low central frequencies). In the present work, we report numerical results corresponding to the propagation of broadband pulses in the four above-mentioned test cases. The numerical simulations are performed using a fully 3D parabolic equation based model coupled with a Fourier synthesis technique to handle the time dependence of the source signal. The objective is to propose a uniform representation of the numerical results so as to facilitate the comparison of the 3D effects present in each of the four benchmarks. Snapshots of the propagating pulses at very close successive times are compared with 2D results. In addition, movies of the propagating pulses are shown for each test case and compared to each other. Movies strongly facilitate the observation and thus the understanding of the 3D effects experienced by all the propagating waves.

Modeling of volume reverberation in the ray approximation

We propose a numerical model for the evaluation of the three-dimensional scattering of sound in the sea. The model is based on the construction of ray patterns both for the primary and secondary (scattered) radiation. The intensity of secondary radiation is expressed via the coefficient of backward volume scattering interpreted as the fraction of backward-scattered acoustic energy per unit length of the primary ray. It is shown that, in the first approximation, it suffices to consider the secondary rays repeating the paths of the primary rays in the opposite direction. The attenuation of the intensity of sound along the paths of the primary and secondary rays is taken into account. The results of numerical analysis of the reverberation signal as a function of time are presented for various conditions (different depths of immersion of the antenna and widths of the directional diagram and the presence of sound-scattering layers). The proposed approach can be used for the purposes of modeling of the surface and bottom reverberation and for the solution of the inverse problems of underwater acoustics.