Understanding deep-water striation patterns and predicting the waveguide invariant as a distribution depending on range and depth

Sources depth estimation for a tonal source by matching the interference structure in the arrival angle domain

A publication by McCargar and Zurk [J. Acoust. Soc. Am. 133(4), EL320-EL325 (2013)] introduced a passive source depth estimation method for a moving tonal source with a vertical line array (VLA), utilizing the depth-dependent modulation in the arrival angle domain caused by the interference between the direct and surface-reflected acoustic arrivals. Under the isovelocity approximation, this method can estimate the depth of sources at close ranges, but the depth estimation error will increase with the increase in source range, as the impact of the sound speed profile on sound propagation is ignored. This paper presents a theoretical formula for calculating the modeled interference structure in the arrival angle domain with the knowledge of the sound speed profile. By matching the measured interference structure obtained from the beamforming of the acoustic data received by the VLA with the modeled structure under different assumed source depths, the tonal source depth estimation is achieved, even for sources at the remote part of the direct arrival zone. The performance of this method is verified by simulation data, as well as experimental data radiated from a towed source and a non-cooperative passing ship.

Passive source depth estimation using beam intensity striations of a horizontal linear array in deep water

Source depth estimation is an important yet very difficult task for passive sonars, especially for horizontal linear arrays (HLAs). This paper proposes an efficient two-step depth estimation scheme using narrowband and broadband constructive and deconstructive striation patterns due to interference between the direct (D) and sea surface reflected (SR) arrivals at an HLA on the bottom of deep water. First, the horizontal source-array ranges are derived from triangulation results of solid angle estimates by subarray beamforming. The applicable areas of the method in deep water are investigated through Mento Carlo simulations, assuming different subarray partitioning ways of a given HLA aperture. Second, cost functions are built to match the measured beam intensity striations with modeled ones. To mitigate the spatial smoothing effect of the beam intensity striations during beamforming, a criterion of the largest subarray aperture is established, and a computationally efficient way is presented to model the replicas by the D-SR time delay templates at a single element of the array calculated by ray theory. The performance degradation due to limited source range spans, the distortion of the beam intensity striations, and range estimation errors has been analyzed. Two experimental datasets verify the effectiveness of the proposed method.

Range estimation of a moving source using interference patterns in deep water

The frequency-range interference patterns of the acoustic field in the shadow zone of deep water correlate with the source location. However, extraction of such interference structure requires a broadband source and fails for narrowband signals. In this work, the narrowband depth-time interference patterns of the acoustic field from a moving source are investigated. Two types of time intervals in the observed patterns are derived based on the ray theory. These time intervals are correlated with the multipath arrival angles, which in turn imply the source range. The simulations and the experimental results demonstrate stable range estimations using the interference patterns.

An overview of array invariant for source-range estimation in shallow water

Traditional matched-field processing (MFP) refers to array processing algorithms, which fully exploit the physics of wave propagation to localize underwater acoustic sources. As a generalization of plane wave beamforming, the "steering vectors," or replicas, are solutions of the wave equation descriptive of the ocean environment. Thus, model-based MFP is inherently sensitive to environmental mismatch, motivating the development of robust methods. One such method is the array invariant (AI), which instead exploits the dispersion characteristics of broadband signals in acoustic waveguides, summarized by a single parameter known as the waveguide invariant β. AI employs conventional plane wave beamforming and utilizes coherent multipath arrivals (eigenrays) separated into beam angle and travel time for source-range estimation. Although originating from the ideal waveguide, it is applicable to many realistic shallow-water environments wherein the dispersion characteristics are similar to those in ideal waveguides. First introduced in 2006 and denoted by χ, the dispersion-based AI has been fully integrated with β. The remarkable performance and robustness of AI were demonstrated using various experimental data collected in shallow water, including sources of opportunity. Further, it was extended successfully to a range-dependent coastal environment with a sloping bottom, using an iterative approach and a small-aperture array. This paper provides an overview of AI, covering its basic physics and connection with β, comparison between MFP and AI, self-calibration of the array tilt, and recent developments such as adaptive AI, which can handle the dependence of β on the propagation angle, including steep-angle arrivals.

Interferometric processing of hydroacoustic signals for the purpose of source localization

An interferometric signal processing method for localizing a broadband moving sound source in an oceanic waveguide is proposed and studied theoretically and experimentally. The field of a moving sound source in waveguide creates a stable interference pattern of the intensity distribution (interferogram) I(ω,t) in the frequency-time domain. Sound intensity is accumulated along interference fringes over the observation time. The two-dimensional Fourier transform (2D-FT) is applied to analyze the interferogram I(ω,t). The result of the 2D-FT F(τ,ν) is called the Fourier-hologram (hologram). The mathematical theory of hologram structure F(τ,ν) is developed in the present paper. It is shown that the hologram F(τ,ν) allows the coherent accumulation of sound intensity of the interferogram in a relatively small area focal spots. The presence of these focal spots is the result of interference of acoustic modes with different wave numbers. The main result of this paper is a simple relationship between the focal spots coordinates on the hologram and the source range, velocity, and motion direction. The proposed interferometric signals processing method for source localization is validated using experimental observations and numerical modeling in the band 80-120 Hz. The estimations of source range, velocity, and motion direction are performed for different cases of source motion.

Application of Waveguide Invariant Theory to Analysis of Interference Phenomenon in Deep Ocean

When a hydrophone is deployed under the critical depth in deep ocean, the interference pattern will be complex and variable. The waveguide invariant is no longer constant and is treated as a distribution. The interference pattern is impacted by refracted and surface reflected (RSR) modes, as well as surface reflected and bottom reflected (SRBR) modes together. This phenomenon is illustrated by numerical simulation and explained by the waveguide invariant theory in this paper. The theory demonstrates: (1) The interference pattern in zone-b corresponds to the waveguide invariant βRSR that varies quickly and leads to the slope change, which is contributed by RSR modes whose phase velocity is less than the sound velocity at seafloor; (2) The interference pattern in zone-a1 and zone-c1 is corresponding to the βSRBRWS that is the approximately 0.7 and leads to the stable slope, which is contributed by SRBR modes whose phase velocity is between the sound velocity at seafloor and sediment velocity; (3) The interference pattern in zone-a2 and zone-c2 is corresponding to the βSRBRSH which hardly varies at low frequency but varies fiercely with source frequency increasing, so the striations are complex with high frequency, which is contributed by SRBR modes whose phase speed is between sediment speed and half space speed.

Nonlinear time-warping made simple: A step-by-step tutorial on underwater acoustic modal separation with a single hydrophone

Classical ocean acoustic experiments involve the use of synchronized arrays of sensors. However, the need to cover large areas and/or the use of small robotic platforms has evoked interest in single-hydrophone processing methods for localizing a source or characterizing the propagation environment. One such processing method is "warping," a non-linear, physics-based signal processing tool dedicated to decomposing multipath features of low-frequency transient signals (frequency f < 500 Hz), after their propagation through shallow water (depth D < 200 m) and their reception on a distant single hydrophone (range r > 1 km). Since its introduction to the underwater acoustics community in 2010, warping has been adopted in the ocean acoustics literature, mostly as a pre-processing method for single receiver geoacoustic inversion. Warping also has potential applications in other specialties, including bioacoustics; however, the technique can be daunting to many potential users unfamiliar with its intricacies. Consequently, this tutorial article covers basic warping theory, presents simulation examples, and provides practical experimental strategies. Accompanying supplementary material provides matlab code and simulated and experimental datasets for easy implementation of warping on both impulsive and frequency-modulated signals from both biotic and man-made sources. This combined material should provide interested readers with user-friendly resources for implementing warping methods into their own research.