Block sparse Bayesian learning for broadband mode extraction in shallow water from a vertical array.

Estimation of modal wavenumbers is important for inference of geoacoustic properties and data-driven matched field processing in shallow water waveguides. This paper introduces a deep neural network called combining physical informed neural network (CPINN) for modal wavenumber estimation using a vertical linear array (VLA). Note that the sound field recorded by a VLA can be expressed as a linear superposition of finite modal depth functions, and the differential equations satisfied by the modal depth functions are related to the corresponding modal wavenumbers. CPINN can estimate the modal wavenumbers by introducing the proxies of the modal depth functions and constraining them to satisfy the corresponding differential equations. The performance of the CPINN is evaluated by simulated data in a noisy shallow water environment. Numerical results show that, when compared with the previous methods, CPINN does not need to know the exact horizontal distance between the sound source and the VLA. Moreover, CPINN can estimate the modal wavenumbers at the VLA position in the case where the range segment traversed by the source, i.e., the aperture in the range direction, is smaller than the maximum modal cycle distance and in a range-dependent waveguide.

According to the classical normal mode theory, low frequency acoustical signals propagating in shallow water are composed of several modal components associated with their own horizontal wavenumbers. In this paper, the horizontal wavenumbers are retrieved by the sparse Bayesian learning approach using a vertical line array. The modal depth functions derived from the Beam-Displacement-Ray-Mode theory are used as the dictionary. The proposed method does not require the prior of sea bottom information (e.g., sound speed). The performance is demonstrated by simulations in a shallow water environment.

This In order to reduce the difficulty of the practical application of the time reversal method (TRM), this paper proposed a new method of virtual TRM with a short vertical line array. The measurement field received by the short array is used to reconstruct an acoustic field of a virtual long vertical array. The method is mainly divided into three steps: Initially, using the modal decomposition to decompose the sound field received by the short vertical array into a modal function matrix and a modal coefficient vector. Furthermore, we obtain the estimated values of the modal coefficients of each order. In this paper, an iterative algorithm was used to obtain the modal coefficients of each order, and then the measured field of the long vertical line array is extended through the obtained modal coefficients. Finally, we use the extended vertical line array measurement field for time reversal processing. The results from the final computer simulation indicated that, due to the measurement field of the long vertical line after continuation contains more environmental information, the virtual time reverse processing method with the extended measurement field has superior focus positioning performance.

Various line array configurations are evaluated for the source localization performance based on the analysis of mode decomposition matrix in this paper. The guideline of array shape design focuses on improving the localization performance of matched filed processing, meanwhile reducing the difficulty of deploying equipment in practical experiments. In the shallow water environment, when the environment is well known, the source localization result can be obtained by matched field processing algorithms effectively, but the source localization performance is affected by the array parameters, such as array length, the number of sensors, and the configurations of various horizontal and vertical line arrays. The modal decomposition method provides a useful insight into the questions of how many modes are needed and how to design the array to resolve the modes. Therefore, the method of utilizing a normal mode acoustic propagation model to decompose mode is proposed by vertical line array, horizontal line array and combined array respectively. Then we can evaluate the source localization performance of various line array configurations by studying the characteristic of normal mode decomposition matrix, thus establishing a qualitative or even quantitative relationship between each other. The more the normal mode decomposition matrix tends to be diagonalized, the better performance of line array localization will be obtained. Simulation results show that the localization performance of matched field processing with the combined arrays will be severely degraded when the mode amplitudes cannot be accurately deduced by one of the sub-arrays. Considering the requirements for the practical experiments and various environments, the source localization performance of short vertical line array and combined array are mainly discussed in this paper. The combined array can increase the azimuth and depth information of the source and realize three-dimensional target detection while the vertical array provides range-depth information and the horizontal array provides bearing information. Simulation result indicates that the design guidelines based on the normal mode decomposition are appropriate for arrays employed for matched filed processing. Meanwhile, the combined arrays perform better than the short vertical array, which is benefited by the horizontal array's suppressing the side lobes, which leads the ratio of peak to sidelobe to increase, and thus improving the location accuracy. The values of localization accuracy of combined arrays are all above 90% according to the simulation experiment. Take the practical application into account, the combined array is undoubtedly a compromise choice for the localization performance and the test complexity.

Modal structure of shipping noise in a shallow water waveguide is studied experimentally and theoretically. Experiments were carried out in the Sea of Galilee (Lake Kinneret, Israel) having maximal depth of 40.5 m and remarkable concentration of methane bubbles in the upper sedimentary layer. Receiving system consisted of 27-m vertical line arrays (VLAs) with ten hydrophones at each. They spanned a lower part of the waveguide with interval ∼3 m. The VLAs were fixed in the centre of the lake with the distance ∼40 m between them. R/V “Hermona” was moving along a straight line connecting VLAs at the range of up to 1 km from the arrays. Modal filtration technique on two synchronized VLAs with a phase correction was proposed to extract complex eigenvalues of each mode, including modal attenuation, which strongly increase in the proximity of cut-off frequency for all normal modes. Based on frequency dependences of attenuation coefficients of lower modes, sound speed in gas-saturated bottom layer was estimated. For application of this technique, there is no need to know exact coordinate and speed of noise source, which seems to us to be an advantage of the method. [Work was supported by RFBR, Grant No. 20-05-00119.]

Bottom loss inference from ambient noise inversion has been shown to yield accurate and robust predictions of undersea sound propagation and sonar detection performance using vertical line arrays and a conventional beamformer [Arvelo, J. Acoust. Soc. Am., 123, 679, 2008]. However, any array with a vertical aperture should be good candidates for ambient noise inversion. The main problem with vertical line arrays is that they are not well suited to rapidly survey a large area. Platform translation with a vertical array is expected to cause extreme array shape distortions that could seriously limit the accuracy of the results. To mitigate array shape distortion, a smaller array with vertical aperture could be mounted on the survey platform, which would allow it to survey the area at greater speeds. The platform's diameter certainly limits the vertical aperture of the array. A limited vertical aperture limits the frequency range, resolution, and accuracy of the estimated bottom loss. Since the array is rigidly fixed to the platform's body, an aggressive adaptive beamformer may be adopted to increase the resolution and accuracy of the inverted bottom loss to very low frequencies. The performance is demonstrated via comparisons against conventional beamformers with numerical simulations and measurements.

The arriving-angle structure for the forward scattered wave on a vertical line array is obtained upon a modified scattering model in the Pekeris waveguide. The structure is investigated and interpreted by the array invariant theory combined with target induced modal coupling effect. Compared with that of the direct blast, the arriving-angle structure of the forward scattering wave owns multi-striations as well as an increased vertical array invariant. The forward scattered angle structure is dependent on the target position on the source-receiver line. Simulations indicate a potential separation for the forward scattered wave overwhelmed by the direct blast.

A grid-free compressive sensing (CS) based method for extracting the normal modes of acoustic propagation in the ocean waveguide from vertical line array (VLA) data is presented. Extracting the normal modes involves the estimation of mode horizontal wavenumbers and the corresponding mode shapes. Sparse representation of the waveguide propagation using modes at discrete horizontal wavenumbers enables CS to be applied. Grid-free CS, based on group total-variation norm minimization, is adopted to mitigate the issues of the wavenumber search grid discretization in the conventional CS. In addition, the suggested method can process multiple sensor data jointly, which improves performance in estimation over single sensor data processing. The method here uses data on a VLA from a source at several ranges, and processes the multiple sensor data at different depths jointly. The grid-free CS extracts the mode wavenumbers and shapes even with no a priori environmental knowledge, a partial water column spanning array data, and without the mode orthogonality condition. The approach is illustrated by numerical simulations and experimental SWellEx-96 (shallow water evaluation cell experiment 1996) data.

In deep water, multipath time delays or frequency-domain interference periods of the acoustic intensity combined with multipath arrival angles are typically used for source localization. However, depth estimate is hard to achieve for a narrowband source at a remote part of the direct arrival zone as the required bandwidth increases with the source range. In this paper, a passive source localization method with a vertical line array, suitable for both broadband and narrowband sources, is proposed. Based on the variation trends of multipath angles with source range and depth, source localization is achieved by only matching the measured angles of the direct path and surface-reflected path with model-based values of a predefined grid of potential source locations. Considering the angle resolution limited by the array aperture and the presence of coherent multipath, sparse Bayesian learning is used and compared with the conventional beamforming and the minimum-variance distortionless-response beamforming to resolve and estimate the multipath angles. Simulations and experimental data of explosive sources collected by a vertical line array in the South China Sea are carried out to illustrate the method and demonstrate the performance.

The spatial and energy resources available on small underwater platforms are limited, imposing strict restrictions on the structure, weight, and channel count of the sonar array they carry. To enhance the direction of arrival (DOA) estimation capabilities of small platform sonars under these constraints, this paper examines a combined vertical array (CVA), composed of a single vector hydrophone and pressure hydrophones. The vertical line array is insensitive to azimuthal variations, but the CVA is capable of horizontal direction estimation with better gain compared to a single vector hydrophone. A novel DOA estimation algorithm, based on the joint processing of sound pressure and particle velocity signals from a CVA, has been proposed: By jointly processing the sound pressure signals from the vertical array and the particle velocity signals from a single vector hydrophone, the method achieves gain transformation of the CVA in three-dimensional space, effectively enhancing the horizontal bearing estimation capability. Expressions for the horizontal gain of the CVA were derived, and the impact of array and signal parameters on the horizontal direction estimation accuracy of the CVA was simulated using the Monte Carlo method. Numerical simulations and experimental results indicate that the horizontal direction estimation accuracy of the CVA surpasses that of traditional vector hydrophones, with high-frequency gain stability unaffected by grating lobes in the elevation direction. This allows for high-precision, unambiguous estimation of target directions.

A survey is presented of recent related work (comprising numerical modeling and field experiments) on the determination of seafloor geoacoustic properties in shallow water from monochromatic pressure field measurements obtained using synthetic aperture and towed arrays. Two related techniques are discussed, their common foundation lying in the Hankel transform inversion of the pressure versus range data to obtain a depth-dependent Green's function versus horizontal wave number. Characteristic features of the Green's function, such as the peaks associated with normal mode propagation in the shallow water waveguide, are used to extract the geoacoustic properties (compressional and shear) as a function of depth in the bottom. INTRODUCTION Two related methods for determining geoacoustic properties in shallow water waveguides have recently been under development (Frisk and Lynch, 1984; Frisk et al., 1985; Kuperman et al., 1985; Werby and Tango, 1985). In both cases, the required input data are the magnitude and phase versus range of the pressure field due to a monochromatic (CW) point source. These data are numerically Hankel transformed to obtain the depth-dependent Green's function versus horizontal wave number. In the context of normal mode theory, the Green's function contains information about the nature of the discrete and continuous modal spectra as well as the plane-wave reflection coefficients of the waveguide boundaries. Specifically, the Green's function contains prominent peaks at horizontal wave numbers corresponding to the eigen-values for any trapped and virtual modes excited in the waveguide. The positions and magnitudes of these modal peaks are sensitive to the acoustic properties of the bottom, and this sensitivity is the basis of the two inverse methods for determining geoacoustic models in shallow water. The WHOI method utilizes an exact Hankel transform inversion of synthetic aperture array data obtained by towing a CW source away from two moored receivers. A geoacoustic model is obtained by computing the theoretical Green's function for various values of the bottom parameters and determining the parameter set which provides the best agreement with the experimental Green's function, particularly in the positions and relative magnitudes of the modal peaks. The NORDA technique involves an approximate Hankel transform inversion in which the beam formed output of a towed array due to the self-noise of the tow ship is computed. Layer sound velocity estimates are obtained from the identification of modal critical angles in the variable-offset beam former response. THEORY Consider a water column of thickness h, characterized by a constant density and a sound speed c(z), and bounded at the surface and bottom by horizontally stratified media as shown in Fig. 1. Then the spatial part of the acoustic pressure p, due to a point source at r =.0 and z = Zo with harmonic time satisfies the inhomogeneous Helmholtz equation(Mathematical equation available in full paper) The Green's function satisfies along with impedance boundary conditions at the surface and bottom. These boundary conditions can be ex pressed in terms of the plane-wave reflection coefficients RS(kr) and RB(kr) of the surface and bottom respectively (Frisk et al., 1980).

Estimating the depth of a moving source with unknown source range is always a challenging problem in shallow water waveguides. The method of estimating the current motion source depth is sensitive to the unknown initial range and requires the horizontal synthetic aperture length formed by the motion of the source to be much longer than the modal interference period. Presented in this work is a method to estimate the depth of moving source based on the incoherently matched beam-wavenumber. In the beam-wavenumber domain, each peak amplitude only contains the modal excitation related to source depth, and each peak position corresponds to the mode propagation angle and the horizontal wavenumber. In this method, the received data are first used to perform beam-formed transformation in the vertical depth and horizontal synthetic aperture direction, and transformed into the beam-wavenumber domain. Then beam-wavenumber peak amplitudes are extracted and incoherently matched with the modal depth function to estimate the source depth. The proposed method is used to eliminate the unknown distance dependent term and improves the mode resolution by performing mode separation in the beam-wavenumber two-dimensional domain. The prominent feature of this method lies in realizing the source depth estimation at the unknown initial range and the horizontal synthetic aperture length which is smaller than the mode interference period. The simulation and SWellEx-96 experimental data processing results validate the superior performance of the proposed method.

During the New Jersey Shelf RAGS03 experiment, acoustic signals emitted by ships of opportunity (merchant ships) are simultaneously recorded on three vertical line arrays (VLAs) and a horizontal line array (HLA). Recorded broadband (50–750 Hz) acoustic data sets are used to demonstrate the source localization capability as well as geoacoustic inversion capability. Waveguide invariant theory applied to beamforming by two vertical arrays that provided a range ratio of the source to the receivers. Beamforming by a horizontal array provided time‐evolving spectrum for a particular look direction (LOFARgram). The trajectories of the striations observed both in vertical array beamformer output and LOFARgrams are used to estimate the source speed, range, and azimuthal direction as well as bottom geoacoustic parameters. Trajectories of striations are identified by the Hough transform that converts a difficult global detection problem in the image domain into a simpler local peak detection problem. Analysis of both...

Acoustic propagation experiments have been carried out in the Florida Straits with a multi-frequency broadband source that transmitted m-sequence pulses over a range of 10 km to a sparse-filled vertical line array. This paper presents results of matched field inversions of the acoustic field data at low frequencies to estimate geoacoustic model parameters for the experimental site. Two approaches were taken for the inversions. The first was a conventional matched field inversion using multi-frequency data centered at 200 and at 400 Hz from the vertical array. The second approach was designed to model the low frequency waveform at a single hydrophone. For the very long range experimental geometry, the waveform was modeled in terms of modes. Each inversion was cast as an optimization problem using the adaptive simplex simulated annealing algorithm. The inversions provide a comparison between approaches that take advantage of the spatial coherence in one case, and the time coherence in the received signal in the other case. Both inversions give similar results for the parameters of a simple geoacoustic bottom model, and the sensitivities and relative uncertainties of the model parameters are consistent for the two approaches. Notably, the inversions are sensitive to compressional wave attenuation.

Source depth estimation is always a problem in underwater acoustic area, because depth estimation is a nonlinear problem. Traditional depth estimation methods use a vertical line array, which has disadvantage of poor mobility due to the size of sensor array. In order to estimate source depth with a horizontal line array, we propose a matched-mode depth estimation method based on autoregressive (AR) wavenumber estimation for a moving source in shallow water waveguides. First, we estimate the mode wavenumbers using the improved AR modal wavenumber spectrum. Second, according to the mode wavenumber estimation, we estimate the mode amplitudes by the wavenumber spectrum, which is obtained by generalized Hankel transform. Finally, we estimate source depth estimation by the peak of source depth function wherein the data mode best matches the replica mode that is calculated using a propagation model. Compared with synthetic aperture beamforming, the proposed method exhibits a better performance in source depth estimation under low signal-to-noise ratio or the small range span. The robustness of the proposed method is illustrated by simulating the performance in mismatched environment.