Shallow Water Waveguide Research Articles

Analysis on the seismic wave caused by low frequency sound source in shallow sea based on multi-transmitting formula artificial boundary

The elastic waves propagating in seabed caused by sailing ships are called ship seismic waves, which can be used to identify ship targets. The wave components and the influences of source frequency, source depth and depth of seawater to the seismic waves are important to the application of seismic wave to detect ship targets. Thus, a forward numerical simulation of seismic waves in shallow sea excited by low frequency sources in time domain was carried out with finite element method based on the Multi-Transmitting Formula artificial boundary. The numerical results show that the body waves and conical waves decay faster in space, but the interface wave decays relatively slow. Multi-transmitting Formula (MTF) artificial boundary has achieved good transmitting effect for longitudinal wave, upstream and downstream acoustic wave and transverse wave. When the source frequency is very low and the seawater layer is shallow, due to the effect of low-frequency cutoff, there is no normal mode wave which can propagate without attenuation in the seawater waveguide, and only the interface wave is propagating near the sea bottom surface. When the frequency of the source or the depth of the seawater layer increases, the effect of low frequency cutoff in the shallow water waveguide is weakened, and the normal mode waves propagating in seawater layer are gradually excited. The intensity of the interface wave caused by low-frequency point sound source mainly depends on the distance between the source and the seafloor.

Resolution of matched field processing for a single hydrophone in a rigid waveguide.

This paper studies resolution of matched field processing for locating, in range and depth, a broadband underwater acoustic source from data measured at a single hydrophone receiver. For the case of an ideal rigid shallow-water waveguide with a pressure-release top boundary and a rigid bottom boundary, the paper derives approximations for the main-lobe widths of the ambiguity surface. The two cases studied in this paper are (1) when coherent measurements of the pressure are available, with the transmitted source waveform precisely known, and (2) when only measurements of the received-signal pressure magnitude-squared are available, such as might occur when the transmitted signal is random and unknown. The analysis uses the normal-mode expansion for the pressure field to derive approximate expressions for the ambiguity-surface main-lobe widths, as a function of the number of modes and frequency band, for both range and depth. Numerical results are presented corroborating the analytical analysis. Finally, the paper argues that this ambiguity analysis can also give insights into Pekeris waveguides under appropriate conditions and shows numerical simulations of matched-field localization ambiguity surfaces for some realistic shallow-water Pekeris environments.

Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water

The interference pattern of the sound field of a broadband source in a shallow water waveguide is studied theoretically and experimentally in this paper. In the ocean waveguide, the sound source generates the interference pattern of the intensity distribution (interferogram) in the frequency–time domain. The mathematical theory of the interferogram structure is developed. The source interferogram consists of a set of quasi-parallel interference fringes in the frequency–time domain. It is shown that the slope of the interference fringes depends on the distance, velocity, and direction of motion of the sound source. The relationship between the slope angle of the interference fringes in the interferogram and the source parameters is derived in the paper. The two-dimensional Fourier transform (2D-FT) is used to analyze the interferogram. The result of the 2D-FT is called the Fourier hologram (hologram). It is shown that the hologram consists of a few focal spots in a relatively small area. The presence of these focal spots is the result of the interference of acoustic modes with different wavenumbers. The mathematical theory of the hologram structure is developed in this paper. The relationship between the coordinates of the focal spots on the hologram and the source parameters is considered. Consequently, the position of the focal spots can be used to estimate the source parameters (range, velocity, and direction of motion). The theoretical conclusions are verified in the context of computer modeling and the results of the acoustic experiment on the Pacific shelf (Yellow Sea, April, 2004) in the band 180–220 Hz.

Hologram formation by using vertical antenna in a shallow water waveguide

Holographic signal processing method by using a vertical linear antenna in shallow water is presented in the paper. Offered method of moving source sound field hologram formation by using vertical antenna is based on holographic signal processing of each element of vertical antenna. Sound field of source moving in shallow water waveguide creates a stable interference pattern (interferogram) in the frequency-time domain on each element of vertical antenna. The 2D-FT (2D Fourier transform) of the interferogram is antenna element hologram (AEH). AEH allows to coherently accumulate the sound intensity of the interferogram in a relatively small area as focal spots for each element of antenna. It is shown that the focal spots coordinates on AEH depends upon the source range, velocity, and motion direction. The focal spots coordinates on AEH are same for each element of antenna. The output antenna hologram is formed by superposition AEH. Relationship between focal spot coordinates on the antenna hologram and the source range, velocity, and motion direction are derived in the paper. The results of the numerical experiment of antenna hologram formation for low-frequency (100200 Hz) sound field of source moving in shallow water are presented. The results presented in the paper significantly expand the efficiency of interferometric signal processing in shallow water. [This study was supported by RFBR 19-29-06075, МК-6144.2021.4, and МК-4846.2022.4.]

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.]

Inversion of ocean acoustic modal-dispersion and amplitude data for seabed geoacoustic models including attenuation

The long-range acoustic field due to an initial sound source in a shallow-water waveguide can be expressed as the sum of a number of dispersive, propagating modes. Modal-dispersion data (arrival time as a function of frequency), as extracted with warping time-frequency analysis, have been inverted to estimate seabed sediment sound-speed and density profiles. In this work, measurements of modal amplitudes as a function of frequency are combined with modal-dispersion data in a joint (simultaneous) inversion which also provides sensitivity to frequency-dependent sound attenuation coefficients in the sediment layers. Since the source signature (spectrum) is often unknown in practice, the relative amplitudes between modes can be considered as data, or the source spectrum can itself be included as additional unknowns in the inversion. Here, trans-dimensional Bayesian inversion is applied to modal-dispersion and amplitude data to estimate marginal probability profiles for sediment geoacoustic properties, including attenuation. The signal processing and inversion methods are demonstrated using modal-dispersion and amplitude data extracted from acoustic measurements made by a hydrophone-equipped underwater glider during the 2017 Seabed Characterization Experiment (Work supported by the Office of Naval Research).

Normal mode extraction using sparse Bayesian learning in shallow water

The low-frequency signals propagating in the shallow-water waveguides are dispersive. They are composed of several normal modes according to the normal mode theory. For the vertical array data, the horizontal wavenumbers and the associated multi-frequency modal depth functions were estimated using block sparse Bayesian learning (Niu et al., JASA 2020), while a priori knowledge of sea bottom, moving source, and source locations is not needed. For the impulsive or known-form signals received by one hydrophone, the sparse Bayesian learning (SBL) approach can be also used to extract the modes (Niu et al., JASA 2021). It uses the approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, to build the dictionary matrix for SBL. Different from warping transforms based on the group slowness (or group speed) dispersion curves, mode separation using SBL is performed in frequency domain based on the phase speed (or equivalently horizontal wavenumbers) dispersion relation. The simulation results demonstrate that the proposed approach is adapted to the environment where both the reflected and refracted modes coexist, whereas the performance of the time warping transformation degrades significantly in this scenario.

Research on the Range-Frequency Interference Characteristics of Target Scattering Field in a Shallow Water Waveguide

Based on the target scattering model and the normal mode theory in a shallow water waveguide, a mathematical model of the acoustic intensity under the coupling condition of the target and the environment was deduced, and the interference striations in the monostatic and bistatic configuration were obtained by simulations. Further, a field experiment was carried out in a lake, and the data were collected for a spherical target in two frequency bands, i.e., 20−40 kHz and 40−80 kHz. The experiment results showed good agreement with the simulations. The results of the simulation and the experiment showed that the existence of the target made the interference phenomenon in shallow water waveguides more complex, and the range-frequency interference characteristics were closely related to the configuration of the sonar system, the target scattering function, the frequency range, and the target movement trajectory. These interference phenomena were found and theoretically analyzed in the paper. The research results can be applied to target detection and recognition, signal parameter estimation, target tracking, and other fields.

Coupled-Mode Parabolic Equations for the Modeling of Sound Propagation in a Shallow-Water Waveguide with Weak Elastic Bottom

In this work, a mode parabolic equation method with interacting modes accounting for the weak elasticity at the bottom is developed. An important feature of the proposed method is that computations of elastic modes are avoided and that the solution is obtained in the form of expansion over acoustic modes. A numerical technique for solving resulting mode parabolic equations is developed, and the accuracy and efficiency of the resulting solution is validated by a direct comparison against source image solutions in the 3D wedge benchmark problem. Satisfactory agreement of the two solutions is achieved for sufficiently small values of shear wave speed that are typical for soft sediments of the sea bottom. The developed approach may be used for solving 3D problems of sound propagation with the elastic properties of bottom sediments taken into account.

The Striation-Correlation-Based Beamforming for Estimating the Green’s Function in a Shallow Water Waveguide

In shallow water, there exist regular interference striations on the structured sound intensity pattern versus frequency and element location of a horizontal array. Beamforming along the striation with frequency-shifted pressure can improve the correlation among array signals, but the beam focusing performance is limited by the source spectrum (e.g. random phase spectrum generated from ship-radiated noise) and signal truncation. In this paper, the cross-correlation phase relationship among the array signals is deduced, and striation-based beamforming with such cross-correlated data can produce a similar directivity to the conventional beamforming, while the effect from signal truncation and source spectrum can be eliminated. This striation-correlation-based beamforming also outputs the signal corresponding to the Green’s function between the source and the reference array element, moreover, recovers the interference structure that characters the channel. The striation-based array signal processing also provides the proposed Greens function estimation method with the ability to work effectively under the condition of low signal-to-noise ratio. Simulation results are presented and performance variations related to signal frequency, signal-to-noise ratio, striation slope estimation error, element number and array aperture are also analyzed numerically.

Shallow-water waveguide acoustic analysis in a fluctuating environment.

The Acoustic Laboratory for Marine Applications (ALMA) is a deployable and autonomous acoustic system, designed by DGA Naval Systems, to address problems in underwater acoustics, such as sound propagation in fluctuating environments. In this article, data from the ALMA-2016 at-sea campaign are used to analyze the ocean fluctuation's influence on sound propagation in a shallow-water waveguide. The experiment took place on the continental shelf of the island of Corsica in November 2016. A source and a receiver array were 9.3 km apart in a nearly constant water depth of 100 m. The source emitted a variety of signals from which the chirp (1-13 kHz) is used to extract the waveguide eigenrays. To do so, a time-domain beamforming is performed on the match-filtered received signals with an automatic detection of local maxima in the time of arrival/direction of arrival (TOA/DOA) domain. A 2 min acquisition period of more than 13 h duration shows significant fluctuations in eigenray TOAs/DOAs. Qualitative comparisons with synthetic signals obtained from simulations in two and three dimensions permit reproduction of the observed eigenray fluctuations without including range dependence of the sound-speed profile.

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

High-resolution modal wavenumber estimation in range-dependent shallow water waveguides using vertical line arrays

Estimation of modal wavenumbers is important for inference of geoacoustic properties and matched field processing in shallow water waveguides. However, it is challenging in a range-dependent environment, because modal content varies locally in response to changes in the environment. Moreover, the scales of the spatial variations in the waveguide may be on the same order as the range aperture required for resolvability of the individual modes. To this end, high-resolution (HR) wavenumber estimation methods have been widely used. In this paper, the matrix pencil and MUSIC algorithms are generalized to geometry involving a synthetic horizontal aperture (SHA) formed by a towed acoustic source and a fixed full-spanning vertical line array (VLA). The performance of the proposed methods is evaluated by simulated data in a noisy shallow water environment. Numerical results show that, when compared with the previous methods, the proposed methods significantly outperform the previous methods in terms of aperture requirement.

Three-dimensional higher-order raypath separation in a shallow-water waveguide.

Separating raypaths in a multipath shallow-water environment is a challenge due to the interferences between them and the colored noise that exists in an ocean environment, especially for two raypaths that arrive close to each other. Thus, in this paper, a three-dimensional (3D) higher-order raypath separation in an array to array configuration is proposed. Performance tests using simulation data in a multipath environment, real data obtained in an ultrasonic waveguide, and ocean shallow-water data, respectively, illustrate that the proposed algorithm achieves a higher resolution and a stronger robustness compared to the existing algorithms.

Retrieval of Dispersion Dependences of Waveguide Modes from Ship Noise Measurements Using Two Synchronized Arrays

An approach is proposed for estimating the dispersion characteristics of waveguide modes from analysis of ship noise recorded by two closely spaced and synchronized vertical arrays. This approach was used for an experimental study of the mode structure of a low-frequency sound field in a shallow-water waveguide with a gas-saturated bottom in a wide frequency band (from 20 to 250 Hz). The experiment was carried out in Lake Kinneret (Israel), known for its high methane bubble content in the sedimentary layer (~1%) and, consequently, for the low sound speed in this layer (~100 m/s). The maximum depth in the area of the experiment was 40.4 m. The receiving system consisted of two 27 m vertical arrays spaced 40 m from each other and covering part of the waveguide below the thermocline. The noise source, the R/V Hermona, moved along a straight line connecting the arrays at distances of up to 1 km from them. The approach made it possible to isolate the frequency dependences of the phase velocities for the first 12 modes; these dependences proved close to those for a waveguide with an perfectly soft bottom, except for the frequency region near the cutoff frequency. The limitations and possible development of the technique are discussed.

On Average Losses of Low-Frequency Sound in a Two-Dimensional Shallow-Water Random Waveguide

For a low-frequency sound signal propagating in a two-dimensionally inhomogeneous shallow-water waveguide, the influence of random bathymetry (fluctuating bottom boundary) was considered based on the local-mode approach and statistical modeling using first-order evolution equations. The study was carried out in shallow sea conditions corresponding to the coastal waveguides of the Russian Arctic seas. Here, a feature was the presence of an almost homogeneous water layer with various characteristics of seabed sediments. To describe the latter, a random model of the impedance was adopted. For the conditions of a strongly penetrable bottom boundary, on average, the calculations predicted adequate weak effects of bathymetry fluctuations on the average sound intensity compared to the effect of fluctuations in the sediment parameters and volumetric random inhomogeneities of the water column. In addition, it was shown that, in terms of statistics, the roughness of the bottom boundary perturbed the average sound intensity in a shallow-water waveguide differently than volumetric fluctuations in the speed of sound. The dependence of the statistical effects (the first and second moments of the signal intensity) on the parameters of the waveguide and the frequency range was studied. As a result of numerical modeling, comparative quantitative estimates of the influence of both the random roughness of the bottom interface and fluctuations of bottom sediment parameters on the average losses of the propagating signal, not presented in the literature, were obtained.

The holographic signal processing for the estimation of sound mode parameters in shallow water

The holographic method for estimation of the broadband sound field modes parameters by using a single receiver in shallow water is presented in the paper. The holographic method of signal processing is based on the two-dimensional Fourier transform (2D-FT) of the source moving in the shallow water waveguide. The sound field creates in waveguide a stable interference pattern (interferogram) in the frequency-time domain. The result of the 2D-FT of the interferogram is called the Fourier-hologram (hologram). It is shown in the paper that different sound field modes create different focal spots in the hologram domain. The filtering focal spots and applying the inverse 2D-FT to them allows restoring the field of the selected mode. In relation to the time-warping operator, the proposed method of signal processing provides a smaller error in the mode group velocity estimation. The results of the numerical simulation as well as the sound mode parameters estimation are presented and discussed in the paper. [Work supported by the RFBR (19-29-06075) and МК-6144.2021.4.]

Range estimation within a shallow-water waveguide via active and reactive acoustic intensity

The proposed ranging algorithm examines low-order modal variations in vertical reactive (Qz) and horizontal active (Ir) acoustic intensity and provides a gated estimate of the range from a receiver to a source. The receiver (measuring horizontal and vertical acoustic intensity) estimates range bins, for example, a source, which is confined within a range of 1 km to 2 km. Accurate initial range estimates provide key information for follow-on processors, such as tracking and depth classification algorithms. The technique relies on predictive broadband frequency characteristics between the superposition of low order trapped modes; modes which are restricted to the first few orders, for example, modes one through five. The binned range estimates can deliver, for example, initial values for higher level iterative and interpolative Detection, Classification and Localization (DCL) algorithms. Similarly, given an accurate opening estimate of a target’s range, neural networks techniques are enhanced. Existing at-sea shallow-water (<300 m), acoustic intensity data are compared to theoretical predictions to assess the feasibility and performance of the proposed algorithm.

Acquisition functions in Bayesian optimization of ocean acoustic waveguides using Gaussian processes

Geoacoustic model optimization and inversion are computationally expensive endeavors. In cases where a parameter grid search is prohibitively expensive, optimization produces an approximated solution through sampling techniques such as Markov chain Monte Carlo, simulated annealing, and genetic algorithms. More recent work proposes replacing such sampling with a Bayesian approach that uses a Gaussian process as a surrogate model of the objective function. The surrogate model represents the posterior on the objective function and is updated with each sample evaluation. As an alternative to sampling methods listed above, acquisition functions incorporate the uncertainty in the posterior to select the next point to be sampled and can greatly speed the optimization. In this study, four common acquisition functions are described encompassing approaches that use manual tuning (upper confidence bound), improvement criteria (probability of improvement and expected improvement), and information criteria (entropy search). Results are presented from an acoustic parameter search for a shallow water waveguide for each function. Expected improvement is found to be the preferred acquisition function for the simulations, converging on the optimal solution more quickly than the other acquisition functions.

Depth estimation as a sequential process following array invariant range estimation

Range estimation based on the array invariant concept exploits the inherent properties of shallow-water waveguide propagation. Multipath arrivals observed on a vertical line array, indexed on vertical arrival angle and time difference of arrival, form what is known as a beam migration pattern in the shape of an ellipse that is a function of source range and the acoustic invariant beta. Fitting the beam migration pattern to an ellipse yields the source range. A property of this beam migration pattern is that it is independent of source depth. Source depth determines how the multipath arrivals are distributed along that ellipse. We will extend previous work on estimating range and present how to estimate depth. This decouples the two estimates and reduces a 2D search process to two 1D processes. We will explore the CRLB structure of the range and depth estimates and demonstrate the results of processing experiment data from the RADAR 2007 experiment in shallow water off the coast of Portugal.