Bayesian multiple-source localization in an uncertain ocean environment

This paper considers simultaneous localization of multiple acoustic sources when properties of the ocean environment (water column and seabed) are poorly known. A Bayesian formulation is developed in which the environmental parameters, noise statistics, and locations and complex strengths (amplitudes and phases) of multiple sources are considered to be unknown random variables constrained by acoustic data and prior information. Two approaches are considered for estimating source parameters. Focalization maximizes the posterior probability density (PPD) over all parameters using adaptive hybrid optimization. Marginalization integrates the PPD using efficient Markov-chain Monte Carlo methods to produce joint marginal probability distributions for source ranges and depths, from which source locations are obtained. This approach also provides quantitative uncertainty analysis for all parameters, which can aid in understanding of the inverse problem and may be of practical interest (e.g., source-strength probability distributions). In both approaches, closed-form maximum-likelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. Examples are presented of both approaches applied to single- and multi-frequency localization of multiple sources in an uncertain shallow-water environment, and a Monte Carlo performance evaluation study is carried out.     

Effects of incoherent and coherent source spectral information in geoacoustic inversion

This paper examines the effect on matched-field geoacoustic inversion of including source spectral information, as can be available in controlled-source acoustic surveys. Source information can consist of relative or absolute knowledge of the source amplitude and/or phase spectra, and can allow frequency-coherent processing of spatial acoustic-field data. A number of multi-frequency acoustic processors, appropriate for specific types of source information, are defined based on the likelihood function for complex acoustic-field data with Gaussian noise. The information content of the various processors is quantified in terms of marginal probability distributions and highest-probability density intervals for the unknown geoacoustic and geometric parameters, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. The analysis is illustrated for incoherent and coherent processors corresponding to several types of source knowledge ranging from complete information to no information, and the results are considered as a function of the spatial and frequency sampling of the acoustic fields.     

Joint time/frequency-domain inversion of reflection data for seabed geoacoustic profiles and uncertainties

This paper develops a joint time/frequency-domain inversion for high-resolution single-bounce reflection data, with the potential to resolve fine-scale profiles of sediment velocity, density, and attenuation over small seafloor footprints (approximately 100 m). The approach utilizes sequential Bayesian inversion of time- and frequency-domain reflection data, employing ray-tracing inversion for reflection travel times and a layer-packet stripping method for spherical-wave reflection-coefficient inversion. Posterior credibility intervals from the travel-time inversion are passed on as prior information to the reflection-coefficient inversion. Within the reflection-coefficient inversion, parameter information is passed from one layer packet inversion to the next in terms of marginal probability distributions rotated into principal components, providing an efficient approach to (partially) account for multi-dimensional parameter correlations with one-dimensional, numerical distributions. Quantitative geoacoustic parameter uncertainties are provided by a nonlinear Gibbs sampling approach employing full data error covariance estimation (including nonstationary effects) and accounting for possible biases in travel-time picks. Posterior examination of data residuals shows the importance of including data covariance estimates in the inversion. The joint inversion is applied to data collected on the Malta Plateau during the SCARAB98 experiment.     

Bayesian Tracking in an Uncertain Shallow Water Environment

A Bayesian source tracking approach is developed to track a moving acoustic source in an uncertain ocean environment.This approach treats the environmental parameters(e.g.,water depth,sediment and bottom parameters) at the source location and the source parameters(e.g.,source depth,range and speed) as unknown random variables that evolve as the source moves.To track a target with low signal-to-noise ratio(SNR),acoustic signals from a series of observations are treated in a simultaneous inversion.This allows real-time updating of the environment and accurate tracking of the moving source.The noise signals radiated from a surface ship target are processed and analyzed.It is found that the Bayesian source tracking method could enhance the localization accuracy in an uncertain water environment and low SNR.     

Geoacoustic Inversion for Bottom Parameters via Bayesian Theory in Deep Ocean

We develop a new approach to estimating bottom parameters based on the Bayesian theory in deep ocean.The solution in a Bayesian inversion is characterized by its posterior probability density(PPD),which combines prior information about the model with information from an observed data set.Bottom parameters are sensitive to the transmission loss(TL)data in shadow zones of deep ocean.In this study,TLs of different frequencies from the South China Sea in the summer of 2014 are used as the observed data sets.The interpretation of the multidimensional PPD requires the calculation of its moments,such as the mean,covariance,and marginal distributions,which provide parameter estimates and uncertainties.Considering that the sensitivities of shallowzone TLs vary for different frequencies of the bottom parameters in the deep ocean,this research obtains bottom parameters at varying frequencies.Then,the inversion results are compared with the sampling data and the correlations between bottom parameters are determined.Furthermore,we show the inversion results for multifrequency combined inversion.The inversion results are verified by the experimental TLs and the numerical results,which are calculated using the inverted bottom parameters for different source depths and receiver depths at the corresponding frequency.     

利用拖船自噪声进行浅海环境参数贝叶斯反演

研究了以拖船自噪声为参考声源的浅海环境参数反演问题,并针对反演结果不确定性快速量化评估问题,提出了一种基于自适应重要性抽样的贝叶斯反演新方法。反演利用了拖船自噪声低频线谱成分,并采用混合高斯推荐函数自适应推荐声场模型样本,使得样本集中于参数高概率密度区域,实现后验概率密度快速收敛计算。仿真试验结果表明:拖船自噪声反演能够准确估计水深、沉积层及阵列参数等。所提自适应重要性抽样贝叶斯反演方法的计算效率优于快速吉布斯抽样方法。利用试验数据处理验证,反演得到试验海域声学环境参数,计算传播损失与各阵元接收线谱强度变化吻合,说明反演最优环境模型能准确表征声场传播特征。      

A Bayesian Approach to the Estimation of Parameters and Their Interdependencies in Environmental Modeling

We present a case study for Bayesian analysis and proper representation of distributions and dependence among parameters when calibrating process-oriented environmental models. A simple water quality model for the Elbe River (Germany) is referred to as an example, but the approach is applicable to a wide range of environmental models with time-series output. Model parameters are estimated by Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling. While the best-fit solution matches usual least-squares model calibration (with a penalty term for excessive parameter values), the Bayesian approach has the advantage of yielding a joint probability distribution for parameters. This posterior distribution encompasses all possible parameter combinations that produce a simulation output that fits observed data within measurement and modeling uncertainty. Bayesian inference further permits the introduction of prior knowledge, e.g., positivity of certain parameters. The estimated distribution shows to which extent model parameters are controlled by observations through the process of inference, highlighting issues that cannot be settled unless more information becomes available. An interactive interface enables tracking for how ranges of parameter values that are consistent with observations change during the process of a step-by-step assignment of fixed parameter values. Based on an initial analysis of the posterior via an undirected Gaussian graphical model, a directed Bayesian network (BN) is constructed. The BN transparently conveys information on the interdependence of parameters after calibration. Finally, a strategy to reduce the number of expensive model runs in MCMC sampling for the presented purpose is introduced based on a newly developed variant of delayed acceptance sampling with a Gaussian process surrogate and linear dimensionality reduction to support function-valued outputs.     

Maximum entropy approach to statistical inference for an ocean acoustic waveguide

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations.     

Bayesian localization in an uncertain ocean environment

In order to improve the ability to localize a source in an uncertain acoustic environment,a Bayesian approach,referred to here as Bayesian localization is used by including the environment in the parameter search space.Genetic algorithms are used for the parameter optimization.This method integrates the a posterior probability density(PPD) over environmental parameters to obtain a sequence of marginal probability distributions over source range and depth,from which the most-probable source location and localization uncertainties can be extracted.Considering that the seabed density and attenuation are less sensitive to the objective function of matched field processing,we utilize the empirical relationship to invert those parameters indirectly.The broadband signals recorded by a vertical line array in a Yellow Sea experiment in 2000 are processed and analyzed.It was found that,the Bayesian localization method that incorporates the environmental variability into the processor,made it robust to the uncertainty in the ocean environment.In addition,using the empirical relationship could enhance the localization accuracy.     

Regularized matched-mode processing for source localization

This paper develops a new approach to matched-mode processing (MMP) for ocean acoustic source localization. MMP consists of decomposing far-field acoustic data measured at an array of sensors to obtain the excitations of the propagating modes, then matching these with modeled replica excitations computed for a grid of possible source locations. However, modal decomposition can be ill-posed and unstable if the sensor array does not provide an adequate spatial sampling of the acoustic field (i.e., the problem is underdetermined). For such cases, standard decomposition methods yield minimum-norm solutions that are biased towards zero. Although these methods provide a mathematical solution (i.e., a stable solution that fits the data), they may not represent the most physically meaningful solution. The new approach of regularized matched-mode processing (RMMP) carries out an independent modal decomposition prior to comparison with the replica excitations for each grid point, using the replica itself as the a priori estimate in a regularized inversion. For grid points at or near the source location, this should provide a more physically meaningful decomposition; at other points, the procedure provides a stable inversion. In this paper, RMMP is compared to standard MMP and matched-field processing for a series of realistic synthetic test cases, including a variety of noise levels and sensor array configurations, as well as the effects of environmental mismatch.     

不确知海洋环境下的贝叶斯声源定位法

为了提高不确知海洋环境下的声源定位性能,贝叶斯声源定位法将环境参数与声源位置同时反演。该方法利用遗传算法在参数空间中寻优,将后验概率密度在环境参数起伏变化范围内积分,得到声源距离和深度的边缘概率分布,从中求得声源位置的最优值,并进行定位结果的不确定性分析。考虑到海底密度和衰减系数对匹配场处理代价函数的敏感性较弱,利用海底参数之间的经验关系实现这两个参数的间接反演。处理并分析了2000年的一次黄海声传播实验数据,研究表明,贝叶斯声源定位法对环境失配有较好的宽容性。采用经验公式可减少待反演参量维数,进一步提高定位的精度。      

Matched-field processing using measured replica fields

An approach for avoiding the problem of environmental uncertainty is tested using data from the TESPEX experiments. Acoustic data basing is an alternative to the difficult task of characterizing the environment by performing direct measurements and solving inverse problems. A source is towed throughout the region of interest to obtain a database of the acoustic field on an array of receivers. With this approach, there is no need to determine environmental parameters or solve the wave equation. Replica fields from an acoustic database are used to perform environmental source tracking [J. Acoust. Soc. Am. 94, 3335-3341 (1993)], which exploits environmental complexity and source motion.     

三维可穿透目标远场声波反演的一种指示器样本方法

提出了用时谐声散射场的远场信息来可视化三维可穿透目标的一种指示器样本方法,它是通过析取一个指示器函数在包含可穿透目标的某个样本区域中的支集来实现这种可视化的,其中,这个指示器函数在可穿透目标的内部和外部有显著不同的取值.这个算法的一个特别吸引人的性质是不需要关于障碍物的任何几何和物理的先验信息,并且只需要散射场在某个有限孔径中若干个入射和测量方向上的远场信息,即可得到可穿透目标的一个很理想的可视化.数值算例保证了这个可视化算法是有效和实用的 关键词： 声散射 反问题 物形反演     

A statistical geoacoustic inversion scheme based on a modified radial basis functions neural network

This paper addresses the task of recovering the geoacoustic parameters of a shallow-water environment using measurements of the acoustic field due to a known source and a neural network based inversion process. First, a novel efficient "observable" of the acoustic signal is proposed, which represents the signal in accordance with the recoverable parameters. Motivated by recent studies in non-Gaussian statistical theory, the observable is defined as a set of estimated model parameters of the alpha-stable distributions, which fit the marginal statistics of the wavelet subband coefficients, obtained after the transformation of the original signal via a one-dimensional wavelet decomposition. Following the modeling process to extract the observables as features, a radial basis functions neural network is employed to approximate the vector function that takes as input the observables and gives as output the corresponding set of environmental parameters. The performance of the proposed approach in recovering the sound speed and density in the substrate of a typical shallow-water environment is evaluated using a database of synthetic acoustic signals, generated by means of a normal-mode acoustic propagation algorithm.     

Hybrid geoacoustic inversion of broadband Mediterranean Sea data

This paper describes an acoustic experiment (PROSIM'97) carried out to investigate inversion for seabed properties at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. Acoustic fields were measured at a vertical hydrophone array due to a swept-frequency source towed over weakly range-dependent bathymetry. Based on the known geology, the seabed is modeled as a sediment layer overlying a semi-infinite basement with unknown model parameters consisting of the sediment thickness, sediment and basement sound speeds, source range and depth, water depth at the source and array, and array tilt. A hybrid inversion algorithm is applied to determine the model values that minimize the mismatch with the measured acoustic fields. Multiple data sets are analyzed to examine the consistency of the inversion results. It is found that the low sound speed of the sediment layer, together with a large uncertainty in bathymetry, leads to strong correlations between the water depths and sediment thickness. This precludes reliable estimation of these parameters individually; however, the total depth to the basement can be estimated reliably. In addition, the basement speed and geometric parameters are estimated consistently, and all parameters compare favorably with the geophysical ground-truth information and with previous inversion results.     

一种基于支持向量机的海底声学参数快速统计反演方法

匹配场统计反演海底声参数的根本目的是求解未知参数的后验概率分布(PPD)。针对现有各种求解参数PPD的数值方法如穷举搜索、Markov Chain Monte Carlo采样、最近邻域插值近似算法普遍存在计算速度慢、时间长、难以满足实际应用的问题,本文提出了一种基于支持向量机的快速求解参数PPD的新算法。该算法利用了支持向量机强大的小样本学习能力,通过训练学习拟合未知海底声参数和后验概率之间存在的函数关系,从而在求解参数PPD时简化了利用声场传播模型计算后验概率的复杂过程,减少了计算时间。数值仿真算例和海上实验数据的处理结果验证了该算法在低维匹配场统计反演海底声参数问题中的有效性。      

Geoacoustic inversion for bottom parameters in a thermocline environment in the northern area of the South China Sea

Bottom acoustic parameters have important influence on the application of underwater acoustic propagation and source location.The acoustic parameters of the seabed in the northern of the South China Sea(SCS) were inversed using the experiment data from an acoustic experiment in 2015.Based on the comprehensive analysis of the influence of the sound speed fluctuation and the geoacoustic model on seabed inversion,the multi-parameter hybrid acoustic inversion scheme is improved by selecting the equivalent mean sound speed profile(SSP) and half-infinite liquid bottom model to save the inversion dimensions in the matched field processing(MFP) inversion.The inverted bottom sound speed and density are in good agreement with the core sampling measurements.The nonlinear empirical relationship of the attenuation coefficient with frequency is given out.The inversion results are meaningful to the sound propagation research and application in the northern area of the SCS.     

Bayesian geoacoustic inversion using wind-driven ambient noise

This paper applies Bayesian inversion to bottom-loss data derived from wind-driven ambient noise measurements from a vertical line array to quantify the information content constraining seabed geoacoustic parameters. The inversion utilizes a previously proposed ray-based representation of the ambient noise field as a forward model for fast computations of bottom loss data for a layered seabed. This model considers the effect of the array's finite aperture in the estimation of bottom loss and is extended to include the wind speed as the driving mechanism for the ambient noise field. The strength of this field relative to other unwanted noise mechanisms defines a signal-to-noise ratio, which is included in the inversion as a frequency-dependent parameter. The wind speed is found to have a strong impact on the resolution of seabed geoacoustic parameters as quantified by marginal probability distributions from Bayesian inversion of simulated data. The inversion method is also applied to experimental data collected at a moored vertical array during the MAPEX 2000 experiment, and the results are compared to those from previous active-source inversions and to core measurements at a nearby site.     

An iterative implementation of rotated coordinates for inverse problems

A generalized inversion method is presented that uses a rotated coordinates technique [Collins and Fishman, J. Acoust. Soc. Am. 98, 1637-1644 (1995)] in simulated annealing to invert for both the location of an acoustic source and parameters that describe the ocean seabed. The rotated coordinates technique not only aids in the inversion process but also indicates the coupling of the source and environmental parameters and the relative sensitivities of the cost function to changes in the various parameters. The information obtained from the rotated coordinates provides insights into how the inversion problem can be effectively decoupled. An iterative process consisting of multiple simulated annealing runs that each use a different set of rotated coordinates is demonstrated. This multistep algorithm is called systematic decoupling using rotated coordinates and is especially helpful when inverting for a large number of unknown parameters. The cost function minimized in the inversion algorithm is model-data cross-hydrophone spectra summed coherently over frequency and receiver pairs. The results of applying this inversion method to simulated data are presented in this paper.     

Full wave-field reflection coefficient inversion

This paper develops a Bayesian inversion for recovering multilayer geoacoustic (velocity, density, attenuation) profiles from a full wave-field (spherical-wave) seabed reflection response. The reflection data originate from acoustic time series windowed for a single bottom interaction, which are processed to yield reflection coefficient data as a function of frequency and angle. Replica data for inversion are computed using a wave number-integration model to calculate the full complex acoustic pressure field, which is processed to produce a commensurate seabed response function. To address the high computational cost of calculating short range acoustic fields, the inversion algorithms are parallelized and frequency averaging is replaced by range averaging in the forward model. The posterior probability density is interpreted in terms of optimal parameter estimates, marginal distributions, and credibility intervals. Inversion results for the full wave-field seabed response are compared to those obtained using plane-wave reflection coefficients. A realistic synthetic study indicates that the plane-wave assumption can fail, producing erroneous results with misleading uncertainty bounds, whereas excellent results are obtained with the full-wave reflection inversion.