Single-receiver geoacoustic inversion using modal reversal

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.

Joint geoacoustic inversion based on Pearson correlation coefficient constraints

This Letter proposes a joint geoacoustic inversion method for modal group velocity dispersion and amplitudes of waveform by incorporating a Pearson correlation constraint. Numerical simulations show that this joint inversion leads to improved geoacoustic inversion performance with smaller uncertainties compared to separate inversion methods when applied to data from a single receiver. Additionally, the effective use of the Wasserstein metric from optimal transport theory is explored and compared to the more-common L2 norm misfit measure. The Letter also presents a qualitative representation of joint inversion convergence obtained through multiple independent runs of genetic algorithms. The algorithm is applied to simulated data.

Robust sparse reconstruction of attenuated acoustic field with unknown range of source

In this paper, we present a gridless algorithm to recover an attenuated acoustic field without knowing the range information of the source. This algorithm provides the joint estimation of horizontal wavenumbers, mode amplitudes, and acoustic attenuation. The key idea is to approximate the acoustic field in range as a finite sum of damped sinusoids, for which the sinusoidal parameters convey the ocean information of interest (e.g., wavenumber, attenuation, etc.). Using an efficient finite rate of innovation algorithm, an accurate recovery of the attenuated acoustic field can be achieved, even if the measurement noise is correlated and the range of the source is unknown. Moreover, the proposed method is able to perform joint recovery of multiple sensor data, which leads to a more robust field reconstruction. The data used here are acquired from a vertical line array at different depths measuring a moving source at several ranges. We demonstrate the performance of the proposed algorithm both in synthetic simulations and real shallow water evaluation cell experiment 1996 data.

Range-dependent geoacoustic inversion using equivalent environmental model in the presence of doppler effect

Geoacoustic inversion using moving sensors attracts lots of interest due to the ease of deployment and low cost. However, the well-established techniques, such as matched-field inversion (MFI), may run into difficulties when the sensors are in a range-dependent environment for mismatch issues and increasing unknown parameters. Given a range-dependent environment, the paper focuses on the inversion using a synthetic aperture created by moving sensors in the presence of the Doppler effect. The derivation is given to obtain an equivalent range-independent environmental model for fast inversion, instead of a range-dependent one. The received fields are modified using the Doppler-shifted wavenumbers. The simulations and results of the SWellEx-96 experimental data verify the effectiveness of the proposed inversion method.

Acoustic signal characterization based on hidden Markov models with applications to geoacoustic inversions

A probabilistic characterization scheme for acoustic signals with applications in acoustical oceanography is presented. This scheme aims at the definition of a set of stochastic observables that could characterize the signal. To this end, the signal is decomposed into several levels using the stationary wavelet packet transform. The extracted wavelet coefficients are then modeled by a hidden Markov model (HMM) with Gaussian emission distributions. The association of a signal with a representative HMM is performed utilizing the expectation-maximization algorithm. Eventually, the signal is characterized by the set of parameters that describe the HMM. The Kullback-Leibler divergence is employed as the similarity measure of two signals, comparing their corresponding HMMs. To validate the performance of the proposed characterization scheme, which is denoted as the probabilistic signal characterization scheme (PSCS), a simulated and a real experiment have been considered. The measured signal is characterized by the proposed PSCS method, and the model parameters of the seabed are estimated by means of an inversion procedure employing a genetic algorithm. The inversion results confirmed the reliability and efficiency of the proposed method when applied with typical signals used in applications of acoustical oceanography.

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.

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.

Grid-free compressive mode extraction

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.

An Efficient Time Reversal Method for Lamb Wave-Based Baseline-Free Damage Detection in Composite Laminates

Time reversal (TR) concept is widely used for Lamb wave-based damage detection. However, the time reversal process (TRP) faces the challenge that it requires two actuating-sensing steps and requires the extraction of re-emitted and reconstructed waveforms. In this study, the effects of the two extracted components on the performance of TRP are studied experimentally. The results show that the two time intervals, in which the waveforms are extracted, have great influence on the accuracy of damage detection of the time reversal method (TRM). What is more, it requires a large number of experiments to determine these two time intervals. Therefore, this paper proposed an efficient time reversal method (ETRM). Firstly, a broadband excitation is applied to obtain response at a wide range of frequencies, and ridge reconstruction based on inverse short-time Fourier transform is applied to extract desired mode components from the broadband response. Subsequently, deconvolution is used to extract narrow-band reconstructed signal. In this method, the reconstructed signal can be easily obtained without determining the two time intervals. Besides, the reconstructed signals related to a series of different excitations could be obtained through only one actuating-sensing step. Finally, the effectiveness of the ETRM for damage detection in composite laminates is verified through experiments.

Using nonlinear time warping to estimate North Pacific right whale calling depths in the Bering Sea

Calling depth distributions are estimated for two types of calls produced by critically endangered eastern North Pacific right whales (NPRWs) in the Bering Sea, using passive acoustic data collected with bottom-mounted hydrophone recorders. Nonlinear time resampling of 12 NPRW "upcalls" and 20 "gunshots" recorded in a critical NPRW habitat isolated individual normal mode arrivals from each call. The relative modal arrival times permitted range estimates between 1 and 40 km, while the relative modal amplitudes permitted call depth estimates, provided that environmental inversions were obtained from high signal-to-noise ratio calls. Gunshot sounds were generally only produced at a few meters depth, while upcall depths clustered between 10 and 25 m, consistent with previously published bioacoustic tagging results from North Atlantic right whales. A Wilcoxon rank sum test rejected the null hypothesis that the mean calling depths of the two call types were the same (p = 2.9 × 10^-5); the null hypothesis was still rejected if the sample set was restricted to one call per acoustic encounter (p = 0.02). Propagation modeling demonstrates that deeper depths enhance acoustic propagation and that source depth estimates impact both NPRW upcall source level and detection range estimates.

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.

Sequential inversion of modal data for sound attenuation in sediment at the New Jersey Shelf

This paper presents a method for estimating bottom geoacoustic properties especially the sediment attenuation from information contained in normal modes of a broadband signal. Propagating modes are resolved using the time-warping technique applied to signals from light bulb sound sources deployed at ranges of 5 and 7 km in the Shallow Water '06 experiment. A sequential inversion approach is designed that uses specific features of the acoustic data that are highly sensitive to specific geoacoustic model parameters. The first feature is the modal group speed, which is inverted for seabed sound speed, density, and sediment thickness. The second feature is the modal depth function for inverting receiver depths. The third feature is related to the modal coefficient spectra, and this is inverted for source depth and sediment attenuation. In each subsequent stage, estimates from the previous stage(s) are used as known values. The sequential inversion is stable and generates estimates for the geoacoustic model parameters that agree very well with results from other experiments carried out in the same region. Notably, the inversion obtains an estimated attenuation of 0.078 dB/λ in the band 120-180 Hz for the de-watered marine sediment characteristic of the continental shelf at the site.

Bayesian environmental inversion of airgun modal dispersion using a single hydrophone in the Chukchi Sea

This paper presents estimated water-column and seabed parameters and uncertainties for a shallow-water site in the Chukchi Sea, Alaska, from trans-dimensional Bayesian inversion of the dispersion of water-column acoustic modes. Pulse waveforms were recorded at a single ocean-bottom hydrophone from a small, ship-towed airgun array during a seismic survey. A warping dispersion time-frequency analysis is used to extract relative mode arrival times as a function of frequency for source-receiver ranges of 3 and 4 km which are inverted for the water sound-speed profile (SSP) and subbottom geoacoustic properties. The SSP is modeled using an unknown number of sound-speed/depth nodes. The subbottom is modeled using an unknown number of homogeneous layers with unknown thickness, sound speed, and density, overlying a halfspace. A reversible-jump Markov-chain Monte Carlo algorithm samples the model parameterization in terms of the number of water-column nodes and subbottom interfaces that can be resolved by the data. The estimated SSP agrees well with a measured profile, and seafloor sound speed is consistent with an independent headwave arrival-time analysis. Environmental properties are required to model sound propagation in the Chukchi Sea for estimating sound exposure levels and environmental research associated with marine mammal localization.

Recursive Bayesian synthetic aperture geoacoustic inversion in the presence of motion dynamics

A low signal to noise ratio (SNR), single source/receiver, broadband, frequency-coherent matched-field inversion procedure recently has been proposed. It exploits coherently repeated transmissions to improve estimation of the geoacoustic parameters. The long observation time improves the SNR and creates a synthetic aperture due to relative source-receiver motion. To model constant velocity source/receiver horizontal motion, waveguide Doppler theory for normal modes is necessary. However, the inversion performance degrades when source/receiver acceleration exists. Furthermore processing a train of pulses all at once does not take advantage of the natural incremental acquisition of data along with the ability to assess the temporal evolution of parameter uncertainty. Here a recursive Bayesian estimation approach is developed that coherently processes the data pulse by pulse and incrementally updates estimates of parameter uncertainty. It also approximates source/receiver acceleration by assuming piecewise constant but linearly changing source/receiver velocities. When the source/receiver acceleration exists, it is shown that modeling acceleration can reduce further the parameter estimation biases and uncertainties. The method is demonstrated in simulation and in the analysis of low SNR, 100-900 Hz linear frequency modulated (LFM) pulses from the Shallow Water 2006 experiment.

Range estimation of bowhead whale (Balaena mysticetus) calls in the Arctic using a single hydrophone

Bowhead whales generate low-frequency calls in shallow-water Arctic environments, whose dispersive propagation characteristics are well modeled by normal mode theory. As each mode propagates with a different group speed, a call's range can be inferred by the relative time-frequency dispersion of the modal arrivals. Traditionally, at close ranges modal arrivals are separated using synchronized hydrophone arrays. Here a nonlinear signal processing method called "warping" is used to filter the modes on just a single hydrophone. The filtering works even at relatively short source ranges, where distinct modal arrivals are not separable in a conventional spectrogram. However, this warping technique is limited to signals with monotonically increasing or decreasing frequency modulations, a relatively common situation for bowhead calls. Once modal arrivals have been separated, the source range can be estimated using conventional modal dispersion techniques, with the original source signal structure being recovered as a by-product. Twelve bowhead whale vocalizations recorded near Kaktovik (Alaska) in 2010, with signal-to-noise ratios between 6 and 23 dB, are analyzed, and the resulting single-receiver range estimates are consistent with those obtained independently via triangulation from widely-distributed vector sensor arrays. Geoacoustic inversions for each call are necessary in order to obtain the correct ranges.

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

Signals propagating in waveguides can be decomposed into normal modes that exhibit dispersive characteristics. Based on the dispersion analysis, the warping transformation can be used to improve the modal separability. Different from the warping transformation defined using an ideal waveguide model, an improved warping operator is presented in this paper based on the beam-displacement ray-mode (BDRM) theory, which can be adapted to low-frequency signals in a general shallow water waveguide. For the sake of obtaining the warping operators for the general waveguides, the dispersion formula is first derived. The approximate dispersion relation can be achieved with adequate degree of accuracy for the waveguides with depth-dependent sound speed profiles (SSPs) and acoustic bottoms. Performance and accuracy of the derived formulas for the dispersion curves are evaluated by comparing with the numerical results. The derived warping operators are applied to simulations, which show that the non-linear dispersion structures can be well compensated by the proposed warping operators.

Wideband dispersion reversal of lamb waves

Ultrasonic guided waves have been widely acknowledged as the most promising tools for nondestructive evaluation (NDE). However, because of the multimodal dispersion, the received guided modes usually overlap in both time and frequency, which highly complicates the mode separation and signal interpretation. The time-reversal technique can be used to realize the time recompression of the Lamb waves, but because of the multimode excitation and reception, it still may not be able to remove the mode ambiguity and achieve the pure pulse compression. With the goal of overcoming this limitation, a wideband dispersion reversal (WDR) technique is proposed. The technique makes use of a priori knowledge of the guided dispersion characteristics to synthesize the corresponding dispersion reversal excitations, which are able to selectively excite the self-compensation pure mode pulse. The theoretical basis of the technique is thoroughly described. A two-dimensional finite-difference time-domain (2D-FDTD) method is employed to simulate the propagation of two fundamental Lamb modes, the symmetrical S0 and antisymmetrical A0 modes in a steel plate. The proposed method was verified through experimental investigation. Finally, the advantages and potential applications of the method are briefly discussed.

Broadband synthetic aperture geoacoustic inversion

A typical geoacoustic inversion procedure involves powerful source transmissions received on a large-aperture receiver array. A more practical approach is to use a single moving source and/or receiver in a low signal to noise ratio (SNR) setting. This paper uses single-receiver, broadband, frequency coherent matched-field inversion and exploits coherently repeated transmissions to improve estimation of the geoacoustic parameters. The long observation time creates a synthetic aperture due to relative source-receiver motion. This approach is illustrated by studying the transmission of multiple linear frequency modulated (LFM) pulses which results in a multi-tonal comb spectrum that is Doppler sensitive. To correlate well with the measured field across a receiver trajectory and to incorporate transmission from a source trajectory, waveguide Doppler and normal mode theory is applied. The method is demonstrated with low SNR, 100-900 Hz LFM pulse data from the Shallow Water 2006 experiment.

Bayesian geoacoustic inversion of single hydrophone light bulb data using warping dispersion analysis

This paper presents geoacoustic inversion of a light bulb implosion recorded during the Shallow Water 2006 experiment. The source is low frequency and impulsive, the environment is shallow water, and the acoustic signal is recorded using a single receiver. In this context, propagation is described by modal theory, and inversion is carried out by matching modal dispersion curves in the time-frequency domain. Experimental dispersion curves are estimated using an advanced signal processing method called warping, allowing inversion to be carried out at a relatively short range (~/=7 km). Moreover, the inversion itself is performed using Bayesian methodology. This allows inference of the seabed structure from the data, including the number of seabed layers resolved, optimal estimates of the seabed parameters, and quantitative uncertainty estimates. Inversion results of the experimental data are in good agreement with both ground truth and estimates from other experimental data in the same region.