Theoretical analysis of warping operators for non-ideal shallow water waveguides

Spatial domain dedispersion transform and its application extracting horizontal wavenumber structure

Dispersion and multipath effects contribute to the complexity of the shallow water acoustic field. However, this complexity contains valuable information regarding both the waveguide and the acoustic source. The horizontal wavenumber and relative amplitude of the modes comprising the acoustic field are crucial pieces of information for addressing acoustic inversion problems in shallow water. However, when employing a horizontal array to extract this information, limitations arise due to array aperture and signal-to-noise ratio constraints. To attempt to solve these challenges, the approach of spatial domain dedispersion transform and frequency domain accumulation is proposed. The objective can be attained by leveraging broadband source with slowly varying phase spectrum or known phase spectrum under the constraints of small aperture arrays and low signal-to-noise ratio. Additionally, the approach is validated on dual-hydrophone horizontal array by relaxing the signal-to-noise ratio requirement. In this paper, theoretical proof of the algorithms' performance is provided, accompanied by analysis of the impact of parameters such as acoustic source bandwidth, the number of elements and array aperture. The effectiveness of the algorithms are validated through simulations and experimental data.

Automated approach for recovering modal components in shallow waters

This paper proposes a fully automated method for recovering modal components from a signal in shallow waters. The scenario involves an unknown source emitting low-frequency sound waves in a shallow water environment, and a single hydrophone recording the signal. The proposed automated algorithm is based on the warping method to separate each modal component in the time-frequency space. However, instead of manually choosing a single arrival time for extraction, the method performs successive extractions with automated time selection based on an explicit quality factor. Modal component separation is achieved through a watershed algorithm, streamlining the process and eliminating the need for manual intervention. The proposed method is tested on experimental data of a right whale gunshot, a combustive sound source, and a bowhead whale upsweep, demonstrating its effectiveness in real-world scenarios.

Passive acoustic characterization of sub-seasonal sound speed variations in a coastal ocean

Acoustic noise interferometry is applied to retrieve empirical Green's functions (EGFs) from the ambient and shipping noise data acquired in the Shallow Water 2006 experiment on the continental shelf off New Jersey. Despite strong internal wave-induced perturbations of the sound speed in water, EGFs are found on 31 acoustic paths by cross-correlating the noise recorded on a single hydrophone with noise on the hydrophones of a horizontal linear array about 3.6 km away. Datasets from two non-overlapping 15-day observation periods are considered. Dispersion curves of three low-order normal modes at frequencies below 110 Hz are extracted from the EGFs with the time-warping technique. The dispersion curves from the first dataset were previously employed to estimate the seabed properties. Here, using this seabed model, we invert the differences between the dispersion curves obtained from the two datasets for the variation of the time-averaged sound speed profile (SSP) in water between the two observation periods. Results of the passive SSP inversion of the second dataset are compared with the ground truth derived from in situ temperature measurements. The effect of temporal variability of the water column during noise-averaging time on EGF retrieval is discussed and quantified.

Mode separation with one hydrophone in shallow water: A sparse Bayesian learning approach based on phase speed

An approach of broadband mode separation in shallow water is proposed using phase speed extracted from one hydrophone and solved with sparse Bayesian learning (SBL). The approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, is used to build the dictionary matrix for SBL. Given a multi-frequency pressure vector on one hydrophone, SBL estimates a set of sparse coefficients for a large number of atoms in the dictionary. With the estimated coefficients and corresponding atoms, the separated normal modes are retrieved. The presented method can be used for impulsive or known-form signals in a shallow-water environment while no bottom information is required. 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.

Observation and inversion of very-low-frequency seismo-acoustic fields in the South China Sea

Very-low-frequency (VLF) sound has significant potential for underwater detection and estimation of geoacoustic models of the ocean bottom structure. In marine settings, one type of VLF sound is the interface wave. These waves, trapped near the fluid-solid interface, are called Scholte waves, and this is the subject of this study. A field experiment was carried out in the South China Sea with the objective of exciting Scholte waves and investigating the propagation. The data were acquired by an ocean bottom seismometer, deployed on the seafloor. A large volume airgun array near the sea surface provided the sound source. The fundamental and three higher-order mode Scholte waves were excited. The Scholte waves are investigated by seismograms and a phase velocity inversion. The observed frequencies are in the range of 1.0-2.9 Hz. The energy attenuation is proportional to 1/r at the peak frequency 1.4 Hz. The shear wave speed structure, down to 600 m beneath the seafloor, is revealed from the dispersion curves by a least-squares inversion algorithm. The inversion result shows that the shear wave speed is below 300 m/s in the uppermost layer, which explains well the weak excitation of Scholte waves in this experiment.

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

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.

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.

Time-warping in underwater acoustic waveguides

The traditional way to isolate fixed mode number contributions to a transient wavefield in an underwater acoustic waveguide involves measuring the wavefield on a dense water-column-spanning vertical array and exploiting orthogonality over depth of the modes at each frequency. Recently it has been demonstrated that essentially the same goal can be accomplished in an ideal shallow water waveguide using measurements made on an isolated receiver by employing a signal processing technique known as time-warping. Time-warping makes use of a special nonuniform temporal sampling of the measured signal for which contributions from individual mode numbers are isolated in the frequency spectrum of the time-warped signal. The time-warping transformation in a general underwater acoustic waveguide is derived here. The general time-warping transformation is shown to reduce to the ideal shallow water waveguide time-warping transform as a special case. Use of the general time-warping transformation is illustrated with simulations in both a mid-latitude deep ocean environment and a high-latitude environment.

Characterizing the seabed in the Straits of Florida by using acoustic noise interferometry and time warping

Interferometry of ambient and shipping noise in the ocean provides a way to estimate physical parameters of the seafloor and the water column in an environmentally friendly manner without employing any controlled sound sources. With noise interferometry, two-point cross-correlation functions of noise serve as the probing signals and replace the Green's function measured in active acoustic remote sensing. The amount of environmental information that can be obtained with passive remote sensing and the robustness of the estimates of the seafloor parameters increase when contributions of individual normal modes are resolved in the noise cross-correlation function. Using the data obtained in the 2012 noise-interferometry experiment in the Straits of Florida, dispersion curves of the first four normal modes are obtained in this paper by application of the time-warping transform to noise cross correlations. The passively measured dispersion curves are inverted for unknown geoacoustic properties of the seabed. Resulting thickness of the sediment layer and sound speed are consistent with the geoacoustic models obtained earlier by other means.

A Passive Source Location Method in a Shallow Water Waveguide with a Single Sensor Based on Bayesian Theory

Bayesian methodology is a good way to infer unknown parameters in a marine environment. A passive source location method in a shallow water waveguide with a single sensor based on Bayesian theory is presented in this paper. The input of a Bayesian inversion algorithm is received different normal mode impulse signals, which are separated and extracted with a warping transformation from received broadband impulse signals. The source range, depth, and other seabed parameters were estimated without prior knowledge of the seabed information. Different normal mode impulse acoustic signals travelling at different group speeds arrived at the sensor at different times because of the dispersion characteristics of the shallow water waveguide. The time delay of different modes can be used for the passive source location. However, normal mode group speeds are greatly affected by the environmental parameters. The performance of the passive location becomes negative when parameters mismatch. In this paper, the source location was transformed to the inversion of the source location and environmental parameters, which can be estimated accurately based on the multi-dimensional posterior probability density (PPD). This method is less limited by environmental factors, and the accuracy of inversion results can be analyzed according to the PPD of inversion parameters, which has higher reliability and a wider application scope. The effectiveness and robustness of the algorithm were quantified in terms of the root mean squared error (RMSE) at a variety of signal-to-noise ratios (SNRs) in 50 simulation sets. The RMSE values decreased with the SNR. The validity and accuracy of the method were proved by the results of simulation and experiment data.

Waveguide mode amplitude estimation using warping and phase compensation

In shallow water, low-frequency propagation can be described by modal theory. Acoustical oceanographic measurements under this situation have traditionally relied on spatially filtering signals with arrays of synchronized hydrophones. Recent work has demonstrated how a method called warping allows isolation of individual mode arrivals on a single hydrophone, a discovery that subsequently opened the door for practical single-receiver source localization and geoacoustic inversion applications. Warping is a non-linear resampling of the signal based on a simplistic waveguide model. Because warping is robust to environmental mismatch, it provides accurate estimates of the mode phase even when the environment is poorly known. However, the approach has issues with mode amplitude estimation, particularly for the first arriving mode. As warping is not invariant to time shifting, it relies on accurate estimates of the signal's time origin, which in turn heavily impacts the first mode's amplitude estimate. Here, a revised warping operator is proposed that incorporates as much prior environmental information as possible, and is actually equivalent to compensating the relative phase of each mode. Warping and phase compensation are applied to both simulated and experimental data. The proposed methods notably improve the amplitude estimates of the first arriving mode.