Reliable Acoustic Path and Direct-Arrival Zone Spatial Gain Analysis for a Vertical Line Array.

A recent publication by McCargar and Zurk [(2013). J. Acoust. Soc. Am. 133(4), EL320-EL325] introduced a modified Fourier transform-based method for passive source depth estimation using vertical line arrays deployed below the critical depth in the deep ocean. This method utilizes the depth-dependent modulation caused by the interference between the direct and surface-reflected acoustic arrivals, the observation of which is enhanced by propagation through the reliable acoustic path. However, neither the performance of this method nor its limits of applicability have yet been thoroughly investigated. This paper addresses both of these issues; the first by identifying and analyzing the factors that influence the resolution and ambiguity in the transform-based depth estimate; the second by introducing another, much simpler depth estimation method, which is used to determine the target trajectories required for observation of the interference pattern and the array requirements for accurate depth estimation.

Reliable Acoustic Path (RAP) is one of the special physical phenomenon in the deep ocean sound propagation, in a certain extent, it can reflect the deep-ocean sound propagation characteristics. In this paper, the sound propagation characteristics in RAP are analyzed, and the transmission loss is calculated by Bellhop acoustic software, which is used to determine if the network nodes can connect. In this article, with the dynamic grid planning algorithm, the node layout scheme for the optimal path in deep-ocean underwater acoustic network based on the deep-ocean underwater acoustic network node.

The Green's function retrieval in media with horizontal boundaries usually only considers the extraction of direct and reflected waves but ignores the virtual head waves, which have been observed experimentally from ocean ambient noise and used to invert for geometric and environmental parameters. This paper derives the extraction of virtual head waves from ocean ambient noise using a vertically spaced sensor pair in a Pekeris waveguide. Ocean ambient noise in the water column is a superposition of direct, reflected, and head waves. The virtual head waves are produced by the cross-correlations between head waves and either reflected waves or other head waves. The locations of sources that contribute to the virtual head waves are derived based on the method of stationary phase. It is the integration over time of contributions from these sources that makes the virtual head waves observable. The estimation of seabed sound speed with virtual head waves using a vertical line array is also demonstrated. The slope of the virtual head waves is different from that of direct and reflected waves in the virtual source gather; it is therefore possible to constructively stack the virtual head waves. The predictions are verified with simulations.

In this study, sediment profiling using the passive fathometer and the head-wave phenomenon are investigated. Head waves are created by waves propagating in sediments parallel to the water-sediment interface (possibly at a speed higher than the water sound speed), and propagating back in the water at critical angles. Ocean ambient noise recorded by a vertical line array is processed using a generalization of the known “passive fathometer.” The technique can detect coherent time-separated arrivals at specific angles that are consistent with the propagation of head waves. The arrivals structure detected at endfire provides information on the sediment layering, while the head wave can be used to estimate the sediment sound speed, and may provide information about the attenuation. The technique is demonstrated using simulation and data from the Santa Barbara Channel Experiment of 2016, using both natural noise generated at the surface, and—for the first time—the noise generated by a ship. [Work supported by the Office of Naval Research, Ocean Acoustics Program.]

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.

Wind-generated noise is ubiquitous in ocean environments and highly influences the passive sonar performance. Since it originates from sources near the ocean surface, one of its physical features is that it largely represents only the intermediate- and high-order modes. The array-level signal-to-noise ratio (SNR), which includes the array-sampled sound intensity, background noise power, and array gain, is an essential quantity determining the sonar array performance. What is investigated in this work is how the array-level SNR of the vertical line array (VLA) varies with the source depth in downward-refracting shallow water, contributed by the modal structure of the surface noise. On the assumption that the modes are well sampled, it is theoretically demonstrated that the SNR varying with the source depth can be approximated as a linear combination of the lower-order mode-amplitude intensities varying with the water depth. Particularly, when the surface noise especially dominates and the water channel is highly downward refractive, this variation can be represented nearly only by the 1<sup>st</sup>-order mode-amplitude intensity varying with depth. The structure is meaningful in practice. It suggests the SNR will be inherently larger when the source is submerged than it is near the ocean surface, and will be maximized at a source depth slightly below the 1<sup>st</sup>-order mode peak across different source ranges. The above assertions are demonstrated in a typical downward-refracting shallow-water channel; the effects from the dominant degree of the surface noise, sound speed gradient in water column, and array aperture are investigated numerically. The obtained results are shown below. 1) Under certain circumstances, the variation of SNR with source depth is nearly irrelevant to the source range. 2) When the surface noise is more significant, the largest SNR in a certain source range will be more significantly larger than the SNR for the source near the surface, the corresponding source depth will be closer to that presenting the 1<sup>st</sup>-order mode’s peak, and the variation of SNR with source depth is increasingly irrelevant to the source range. 3) A stronger downward-refracting sound speed also enhances this SNR superiority and irrelevance to the source range, but causes the source depth presenting the largest SNR to be more deviated from the 1<sup>st</sup>-order mode’s peak. 4) Although the structure is unraveled on the assumption that the VLA spans the full water column, it can be seen when the VLA does not but covers the low-order modes' main part; when the array aperture is insufficiently large it will become approximately periodic in the source range, with the source depth presenting the largest SNR fluctuating lightly and nearly periodically around the 1<sup>st</sup>-order mode peak.

The sound field interference structure is analyzed in the reliable acoustic path (RAP) duct based on ray theory. We give the interference striation, which is defined as the line predicted by the approximate formulae and Bellhop model used in this paper (see e.g., Fig. 3 for more information). We observe that interference striation is resulted from time delay difference between the direct (D) path and the surface-reflected (SR) path of the broadband noise radiated from the underwater moving source. And interference striations turn to be tight with the increase of the source depth. Based on these observations, we propose a source depth estimation method by using a single hydrophone in the RAP duct. We set up a cost function which measures the matching degree between the interference striations (predicted by the approximate formulae and Bellhop model) and the sound field range-frequency interference structure (extracted from the sampled data of a single hydrophone). And we take the peak location of the outputted matching degrees as the source depth estimate. Numerical simulations show the effectiveness of the proposed source depth estimation method.

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.

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 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.

Distributed vertical line array (DVLA) measurements of a controlled towed source were made as part of the Office of Naval Research Philippine Sea 2009 experiment (PhilSea09). The vertical line array consisted of two 1000 m sections, one spanning the sound channel axis (∼1000 m) and the other spanning the surface conjugate depth (∼5000 m). The source transmitted a combination of narrowband tones and LFM signals ranging between 20 and 450 Hz was towed at ranges from 3 to over 100 km from the DVLA. In this paper, matched field localization methods, developed in the 1990s are applied to the pair of DVLA receivers. A comparison of the detection and localization skill of each array is made as a function of source range and source receiver. Deep-water propagation for shallow sources is dominated by convergence zone propagation and, therefore, the axial and deep receivers will be illuminated by the source at different times. Narrowband and broadband geo-acoustic inversion results will be presented. Seafloor roughness is shown to be a significant feature of the bottom bounce paths and a beam-based matched field processing technique is applied to mitigate for the spreading of bottom interacting ray-paths.

Several studies have been directed towards the development of both numerical and analytical expressions of ambient noise directionality. In this paper, the results of a simplified ambient noise model are employed to examine the response of sonar arrays to directional noise fields. Expressions are found for the array gain against wind noise for near-surface arrays, employing vertical and horizontal line arrays as examples. The results are compared in each case with array gain against isotropic noise (i.e., directivity index). Array response is found as a function of array orientation, frequency (or size), and steering angle. For the broadside steered line array, a simplified beam response pattern is used to find array gain for these simple analytical noise models. Results compare very well with array gains computed using more precise models of the ambient noise field and exact array response patterns. The implications on sonar design and performance studies are discussed, as well as similar estimates for the response of more complex array configurations. [Study supported by NAVSHIPS, PMS 302-4.]

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.

Depth estimation of deep water moving source based on ray separation

The horizontal wavenumbers and modal depth functions are estimated by block sparse Bayesian learning (BSBL) for broadband signals received by a vertical line array in shallow-water waveguides. The dictionary matrix consists of multi-frequency modal depth functions derived from shooting methods given a large set of hypothetical horizontal wavenumbers. The dispersion relation for multi-frequency horizontal wavenumbers is also taken into account to generate the dictionary. In this dictionary, only a few of the entries are used to describe the pressure field. These entries represent the modal depth functions and associated wavenumbers. With the constraint of block sparsity, the BSBL approach is shown to retrieve the horizontal wavenumbers and corresponding modal depth functions with high precision, while a priori knowledge of sea bottom, moving source, and source locations is not needed. The performance is demonstrated by simulations and experimental data.