Matched-field Inversion Research Articles

Inversion in an uncertain ocean using Gaussian processes.

Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.

Uncertainty reduction in matched field inversion using Gaussian Processes

Gaussian Processes have been shown to be an effective tool for predicting an acoustic field in the ocean at a densely populated virtual array. This property is employed in this work for pre-processing acoustic data before these are used for source localization and geoacoustic parameter estimation using matched-field inversion (MFI). The process increases the accuracy of MFI as uncertainty in the estimation process is reduced. Via the application of Gaussian Processes, the data are denoised and interpolated and the new, enhanced fields are used as input to MFI along with replicas calculated at the virtual receivers at which field predictions are made. Kernel functions, implicit in the implementation of Gaussian Processes, quantify the correlation among field values at neighboring spatial points. Employing different kernels, the approach is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional Bartlett MFI in source localization and geoacoustic inversion. [Work supported by ONR.]

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.

Deep-learning geoacoustic inversion using multi-range vertical array data in shallow water.

A multi-range vertical array data processing (MRP) method based on a convolutional neural network (CNN) is proposed to estimate geoacoustic parameters in shallow water. The network input is the normalized sample covariance matrices of the broadband multi-range data received by a vertical line array. Since the geoacoustic parameters (e.g., bottom sound speed, density, and attenuation) have different scales, the multi-task learning is used to estimate these parameters simultaneously. To reduce the influence of the uncertainty of the source position, the training and validation data are composed of the simulation data of different source depths. Simulation results demonstrate that compared with the conventional matched-field inversion (MFI), the CNN with MRP alleviates the coupling between the geoacoustic parameters and is more robust to different source depths in the shallow water environment. Based on the inversion results, better localization performance is achieved when the range-dependent environment is assumed to be a range-independent model. Real data from the East China Sea experiment are used to validate the MRP method. The results show that, compared with the MFI and the CNN with single-range vertical array data processing, the use of geoacoustic parameters from MRP achieves better localization performance.

Matched-field geoacoustic inversion using Gaussian Processes for field prediction

Matched-field geoacoustic inversion is the process of maximizing a correlation measure between received data at deployed hydrophones and replica fields calculated via an acoustic model for a set of values for environmental parameters, frequently along with source range and depth. The values that produce the maximum correlation form the geoacoustic parameter and source location estimates. Matched-field inversion performance improves as the number of receiving hydrophones increases and the water column is sampled in a dense manner. In order to achieve dense water column sampling when only a few phones are available, we predict the field at a large number of virtual depths within a given aperture using Gaussian Processes. Similarly to classical matched-field inversion, the predicted field, computed after the choice of a suitable kernel and its hyperparameters, is correlated with replicas calculated at the same phone depths. It is demonstrated with both synthetic and real data that the Gaussian Process matched-field inversion approach outperforms conventional processing. The effect is more pronounced as the Signal-to-Noise Ratio attains lower values. [Work supported by ONR.]

Matched-field geoacoustic inversion based on radial basis function neural network.

Multi-layer neural networks (NNs) are combined with objective functions of matched-field inversion (MFI) to estimate geoacoustic parameters. By adding hidden layers, a radial basis function neural network (RBFNN) is extended to adopt MFI objective functions. Specifically, shallow layers extract frequency features from the hydrophone data, and deep layers perform inverse function approximation and parameter estimation. A hybrid scheme of backpropagation and pseudo-inverse is utilized to update the RBFNN weights using batch processing for fast convergence. The NNs are trained using a large sample set covering the parameter interval. Numerical simulations and the SWellEx-96 experimental data results demonstrate that the proposed NN method achieves inversion performance comparable to the conventional MFI due to utilizing big data and integrating MFI objective functions.

Spatial Diversity and Geoacoustic Inversion Using Distributed Sources and Receivers

Matched field inversion (MFI) has been studied extensively in shallow water environments to invert for the geoacoustic parameters using a vertical or horizontal linear array (VLA/HLA). Deploying VLA/HLA at sea is not easy, which limits the use of MFI in practice for large-area surveys. In the future, many inexpensive transceivers will likely be deployed in the ocean forming distributed networks. Geoacoustic parameters could potentially be inverted from signals received on the distributed sensors from distributed sources, such as that generated by a towed source or passing by ships, referred to as a multiple-input-multiple-output (MIMO) system. The data from each source can be processed like a virtual HLA; different virtual HLA geometries are generated for different source locations, providing propagation data along different azimuthal angles, referred to as spatial diversity. The signals between the distributed receivers may not be synchronized, hence only the frequency cost function will be used. The inversion performances using the MIMO system are evaluated using simulated data to compare with that obtained using the traditional methods with a VLA/HLA. Practical applications of this method are proposed. Some technical issues are studied using the Shallow Water 2006 data.

Ship source level estimation and uncertainty quantification in shallow water via Bayesian marginalization.

This paper applies a non-linear Bayesian marginalization approach to ship spectral source level estimation in shallow water with unknown seabed properties and uncertain source depth. The algorithm integrates the posterior probability density over seabed models sampled via trans-dimensional Bayesian matched-field inversion and over depths/ranges of multiple point sources (representing different noise-generating components of a large ship) via Metropolis-Hastings sampling. Source levels and uncertainty are derived from marginal distributions for source strength. The approach is applied to radiated noise due to a container ship recorded on a bottom-moored horizontal array in shallow water. The average uncertainty is 3.8 dB/Hz for tonal frequencies.

Geoacoustic Inversion Using an Autonomous Underwater Vehicle in Conjunction With Distributed Sensors

A midfrequency (2–6 kHz) geoacoustic parameter inversion approach is proposed using a moving source and single receiver. The source motion creates a synthetic horizontal line array (SHLA), and the received signals, by source–receiver reciprocity, can be used to estimate the sediment/bottom parameters using matched field inversion (MFI). Using a wideband signal, the arrival times of multipaths are estimated using compressive sensing, from which one can estimate the source–receiver range, water depth, sediment thickness, and sound speed. This information is difficult to get at low frequencies due to the limited bandwidth. MFI is carried out using the frequency-coherent cost function and does not require the data to be precisely synchronized. Sensitivities of inversion of geoacoustic parameters are also studied. Performance using the SHLA is shown to be comparable to that using the conventional horizontal and vertical line array, and is shown to be sensitive to sediment attenuation—one of the difficult parameters to estimate. The proposed scheme uses short range (50–150 m) data, and requires a low-level source that can be carried by an autonomous underwater vehicle (AUV). With the AUV traveling between nodes in a distributed sensors network, the inversion can be conducted over a large area.

Detection and Parameter Estimation of Solitary Internal Waves Using Distributed Acoustic Sensors

A method to detect solitary internal waves passing through the sensors area in shallow water and estimate their parameters is proposed in this paper using distributed acoustic sensors. The proposed detection method is based on cross correlation of the (envelop of) channel impulse responses estimated from broadband signals transmitted between the sensor nodes with the reference impulse responses in the absence of solitary internal waves. An iterative sequential parameter estimation method is proposed based on time domain matching of the measured channel impulse responses with modeled impulse responses. Simultaneous parameter estimation can be obtained using a global search method such as the matched field inversion. Simulation studies are carried out using environmental acoustic data collected in the northern South China Sea. The results show that the proposed method can effectively detect the existence of passing SIWs, and their parameters can be estimated with reasonable accuracy even under low signal-to-noise ratio conditions.

Geoacoustic inversion the Buckingham way

This paper examines the impact of Mike’s research on geoacoustic inversion for characterization of sea bed sediments. First is his paper in 1987 that reported the use of vertical coherence of ambient ocean noise for estimating critical angles of sea bed sediment. Apart from the novel use of ambient noise as a sound source, his work opened the idea to make use of information about the ocean bottom contained in spatial phase relationships in vertical hydrophone array data. The practice was quickly adapted and widely applied as matched field inversion. However, the inversions were generally carried out using visco-elastic theory of sound propagation, an approach that is not the most appropriate for applications with porous sediment material. Mike’s next contribution addressed this issue in his series of papers starting around 1997 on the grain-shearing and viscous grain-shearing models of sound propagation in porous media. His theory provided a physical basis for the model parameters that are used to describe the interaction of sound with porous sediment media in geoacoustic inversions. Recent examples are shown that indicate how these innovations have become standard practice in geoacoustic inversions.

Ship source level estimation in an uncertain environment via trans-dimensional Bayesian inversion

This paper considers the joint estimation of ship source spectral levels and environment parameters of a layered seabed via a trans-dimensional Bayesian matched-field inversion approach, with applications to shallow-water data collected with acoustic arrays in the 2017 Seabed Characterization Experiment conducted on the New England Shelf. The approach samples probabilistically over possible model parameterizations (number of seabed layers), and provides uncertainty estimates of ship source levels that include uncertainty due to the environment and source depth/range. Approaches to modeling of a distributed source (i.e., as multiple point sources) in the inversions will also be considered. The approach is applied to low-frequency tonal (propeller and machinery) noise in the 10–300 Hz frequency band due to large container ships passing near the arrays.This paper considers the joint estimation of ship source spectral levels and environment parameters of a layered seabed via a trans-dimensional Bayesian matched-field inversion approach, with applications to shallow-water data collected with acoustic arrays in the 2017 Seabed Characterization Experiment conducted on the New England Shelf. The approach samples probabilistically over possible model parameterizations (number of seabed layers), and provides uncertainty estimates of ship source levels that include uncertainty due to the environment and source depth/range. Approaches to modeling of a distributed source (i.e., as multiple point sources) in the inversions will also be considered. The approach is applied to low-frequency tonal (propeller and machinery) noise in the 10–300 Hz frequency band due to large container ships passing near the arrays.

Ship-of-Opportunity Noise Inversions for Geoacoustic Profiles of a Layered Mud-Sand Seabed

This paper considers the use of broadband noise from a ship-of-opportunity in statistical inference for estimating geoacoustic parameters of a layered mud-sand seabed model via trans-dimensional (trans-D) Bayesian matched-field inversion, with applications to data collected with a bottom-moored horizontal array in the 2017 Seabed Characterization Experiment conducted on the New England Shelf. The trans-D approach applied here samples probabilistically over possible model parameterizations (different numbers of seabed layer interfaces), and provides quantitative uncertainty estimates of seabed geoacoustic profiles. Inversions are carried out for acoustic data sets collected both when the ship-of-opportunity (a container ship) was oriented with its bow and with its stern towards the array. A third inversion involved combining data from a series of segments along the ship track. Inversion results image an upper sediment layer 3–7 m thick with low-sound speed (close to the water sound speed) over higher speed sediment, with indication of a transition layer above the interface. Sediment parameter estimates from the inversions are in good agreement with direct measurements from sediment cores and other geophysical data collected in the experiment area.

Range-dependent geoacoustic inversion for sound propagation in two seamounts environment

This paper presents a work of range-dependent geoacoustic inversion for two seamounts environment with negative gradient sound speed profiles based on the transmission losses (TLs), collected in an experiment in the South China Sea, 2016. Bombs of 200 m and the mooring vertical line array (VLA) is applied for recording. Typical characteristics of shadowing and reflecting by seamounts are confirmed by the fluctuations of TLs with respect to range, indicating the complexity of sound propagation within seamounts environment. In the framework of matched field inversion (MFI), the geoacoustic model of two layers and the range-dependent acoustic model (RAM) is applied to produce the replica TLs, which is used to compute the cost function in combination with the collected TLs in terms of the least mean variance. The simulated annealing (SA) is expected to augment the searching efficiency of geoacoustic parameters. Results of four models with different parameters within 120km are obtained, with which the simulated TLs are in good accordance with experiment results for several frequencies and receiving depths. Conclusion is drawn that the effects of range-dependence of geoacoustic parameters in seamounts environment are as important as those of bathymetry on sound propagation, which should be seriously considered especially with negative gradient sound speed profiles.

Inversion of range-dependent ocean environmental parameters using radiation noises of an Autonomous Underwater Vehicle

Moving platform is playing an increasingly important role in ocean observatories. We previously reported some field testing results of using the radiation noises of an Autonomous Underwater Vehicle (AUV) as the sound source to invert the range-independent SSP. To incorporate source motion effects, the forward model based on the waveguide Doppler and normal mode theory was applied to compute the replica field, and to resolve the adjacent Doppler shifted frequencies, an analytical solution of the forward model and its simplified version were obtained for arbitrary signal integration intervals with a monochromatic source. In this paper, we reformulate the matched-field inversion problem into a state-space model to track the range-dependent environmental parameters and moving source parameters along the AUV path with the constantly updated measurement equations. Performances of several sequential filters, including extended Kalman, unscented Kalman, and particle filters, are compared. Note that at each point of the track, the estimate is the average from the source to the receiver; by doing the inversion sequentially with AUV moving, one can get the parameter estimate at individual points (sections). This process is equivalent to iteration over space, while iteration over time is considered as a solution to an under-determined inverse problem.Moving platform is playing an increasingly important role in ocean observatories. We previously reported some field testing results of using the radiation noises of an Autonomous Underwater Vehicle (AUV) as the sound source to invert the range-independent SSP. To incorporate source motion effects, the forward model based on the waveguide Doppler and normal mode theory was applied to compute the replica field, and to resolve the adjacent Doppler shifted frequencies, an analytical solution of the forward model and its simplified version were obtained for arbitrary signal integration intervals with a monochromatic source. In this paper, we reformulate the matched-field inversion problem into a state-space model to track the range-dependent environmental parameters and moving source parameters along the AUV path with the constantly updated measurement equations. Performances of several sequential filters, including extended Kalman, unscented Kalman, and particle filters, are compared. Note that at each point ...

An Improved Numerical Computation of Hull Pressure Fluctuations Due to Unsteady Sheet Cavitation of a Propeller

An operating propeller is the main source of vibration on the ship hull, especially on the stern. In this article, an improved numerical scheme is presented to predict the pressure fluctuations on the ship hull due to the unsteady sheet cavitation of a propeller. The calculated results are compared with the published results and experimental data carried out in the hydrodynamics and cavitation tunnel of Hamburgische Schiffbau-Versuchsanstalt to verify the improvement. The present method is based on a two-cycle iterating scheme which satisfies the boundary integral equation in time domain. The hull pressure fluctuations calculated by the first-cycle iterations are treated as the initial values for the second-cycle iterations. The solid angles of the elements will deviate from the standard value, .5, as the dramatic variation in geometry appears, and accumulate numerical errors in the calculating process. During the second-cycle iterations, a filter based on the solid angles on hull elements is proposed to minimize the iterating error. A container ship is treated as the computing sample in this study, and evidence is offered regarding the 16% improvement achieved by the present method. 1. Introduction A propeller operating in a nonuniform wake field in the ocean is one of the prime sources of vibration and noise affecting the ship. The prediction of hull pressure fluctuations caused by propellers is an important consideration for many vessels and worthy of being researched. Hull pressure fluctuation caused by the marine propeller has been widely investigated since the 1980s. Huse and Guoqiang (1982) developed a semi-empirical prediction method, in which the cavitation volume on the propeller blade surface can be estimated using experimental data. Breslin et al. (1982) proposed a model based on the potential flow theory, which simulates the ship hull by means of a simple panel method and the propeller by means of a lifting surface vortex lattice method. Kinns and Bloor (2004) used an acoustic boundary element (BE) model to simplify the problem of hull vibration excitation due to propeller sources and dipoles. The convergence of results for a cruise liner model was demonstrated with different element distributions. Kehr and Kao (2004) derived the incident blade rate pressure induced by unsteady sheet cavitation (monopole) and unsteady forces (dipole) of an operating propeller, for calculating the hull pressure fluctuations. Brouwer (2005) applied a stationary set of rings of monopole and dipole sources in the frequency domain to solve the propeller-induced noise and vibrations. Lee et al. (2006) integrated computational fluid dynamics (CFD) and the finite difference method for the computation of propeller-induced hull vibration. It was recommended that the phase difference of the propeller-induced pressure should be considered for preventing overprediction. Kao and Kehr (2006) developed a time domain iteration method to calculate the hull pressure fluctuations induced by the operating propeller. The phase difference is included in the iterating scheme, and the computation is robustly convergent. Seol and Moon (2009) derived the governing equation of pressure fluctuation induced by sheet cavitation according to the Ffowcs Williams approach. In the study by van Wijngaarden (2011), a potential flow boundary element method (BEM) with measured hull pressure data as input was applied to solve the hull pressure fluctuations, and the model experiments were also carried out. It was concluded that the computed hull pressure fluctuations due to non-cavitating propellers is reasonably accurate compared with the experimental data. Kehr and Kao (2011) calculated the pressure fluctuations on ship hull due to propeller sheet cavitation by using the method presented in Kao and Kehr (2006). The numerical result is higher than the experimental data provided by the hydrodynamics and cavitation tunnel (HYKAT) of HSVA (Wiemer 1999) by approximately 27%. The pressure fluctuations on ship stern induced by cavitating propellers were solved by Kanemaru and Ando (2011) with a surface panel method. The maximum amplitude appears in the first blade frequency and overestimates the experimental data by about 30%. Kim et al. (2012) predicted the hull pressure fluctuations induced by marine propeller sheet cavitation, and the Doppler effect was considered at the same time. Wei and Wang (2013) employed CFD to simulate the propulsion of a submarine. The finite element method and BEM were then combined to solve the submarine's structure and acoustic responses under the propeller excitations. The matched-field inversion technique applied in Lee et al. (2014) uses the fluctuating hull pressure field measured by receivers and the acoustic field calculated by BEM to define the sheet cavitation noise, source strengths, source positions, and number of sources. The equivalent source model for the propeller can result in more accurately extrapolated hull pressure distribution. In Wei et al. (2016), the unsteady forces of a submarine propeller were predicted by CFD, and the hull pressure fluctuations due to the non-cavitation propeller were calculated by the method proposed in Kao and Kehr (2006).

Geoacoustic inversion using distributed sensors

Geoacoustic inversion is a method using sound to invert for the sediment/bottom properties. The method has been researched extensively using sound received on a vertical or horizontal line array (VLA/HLA). It requires usually a dedicated ship to deploy the array and source to collect the data. Conducting such experiments is costly and its use is limited in practical applications. It is anticipated in the future that many low-cost acoustic transceivers will be deployed in the ocean in the form of a distributed sensor network. It seems logical to use these distributed sensors as the receivers to conduct geoacoustic inversion using a ship-mounted source, thus covering a wide area wherever the distributed nodes are deployed. The question is how well can one estimate the bottom parameters using distributed sensors, compared with that using the traditional arrays. Note that the VLA/HLA data offers spatial coherence, thus one usually carries out geoacoustic inversion using the so called matched-field inversion. The signal received on the distributed data may not be coherent and one will conduct geoacoustic inversion using frequency-coherent inversion methods. The advantage of distributed receiver is spatial diversity, particularly when the source moves. Simulation results will be presented to compare their performance.

The Comparison of Bottom Parameter Inversion in Geoacoustic Space and in (P,Q) Space

The acoustical properties of the sea-bottom can be described by geoacoustic (GA) parameters or by reflective parameters: [Formula: see text] (phase shift parameter) and [Formula: see text] (absorption parameter). Both in GA space and in ([Formula: see text], [Formula: see text]) space, the parameters are difficult to measure and are instead estimated by inversion methods such as matched field inversion (MFI). In GA space, an assumed model is needed to mount the GA parameters for inverting (model dependent), while the reflective parameters ([Formula: see text], [Formula: see text] are model-free. In this paper, the efficiency and quality of matched field processing (MFP) in GA space as well as in ([Formula: see text]) space are compared and the potential possibility of bottom sound-speed-profile estimation is discussed.

Localization of incipient tip vortex cavitation using ray based matched field inversion method

Cavitation of marine propeller is one of the main contributing factors of broadband radiated ship noise. In this research, an algorithm for the source localization of incipient vortex cavitation is suggested. Incipient cavitation is modeled as monopole type source and matched-field inversion method is applied to find the source position by comparing the spatial correlation between measured and replicated pressure fields at the receiver array. The accuracy of source localization is improved by broadband matched-field inversion technique that enhances correlation by incoherently averaging correlations of individual frequencies. Suggested localization algorithm is verified through known virtual source and model test conducted in Samsung ship model basin cavitation tunnel. It is found that suggested localization algorithm enables efficient localization of incipient tip vortex cavitation using a few pressure data measured on the outer hull above the propeller and practically applicable to the typically performed model scale experiment in a cavitation tunnel at the early design stage.

Sound speed profile inversion using a horizontal line array in shallow water

It is better to use a simple configuration to enhance the applicability of ocean environment inversion in shallow water. A matched-field inversion method based on a horizontal line array (HLA) is used to retrieve the variation of sound speed profile. The performance of the inversion method is verified in the South China Sea in June, 2010. An HLA laid at bottom was used to receive signals from a bottom-mounted transducer. Inverted mean sound speed profiles from 9-hour long acoustic signals are in good agreement with measurements from two temperature chains at the sites of the source and receiver. The results show that an HLA can be used to monitor the variability of shallow-water sound speed profile.