Estimating geoacoustic parameters using matched-field inversion methods

In this paper, we use matched-field inversion methods to estimate the geoacoustic parameters for three synthetic test cases from the Geoacoustic Inversion Techniques Workshop held in May 2001 in Gulfport, MS. The objective of this work is to use a sparse acoustic data set to obtain estimates of the parameters as well as an indication of their uncertainties. The unknown parameters include the geoacoustic properties of the sea bed (i.e., number of layers, layer thickness, density, compressional speed, and attenuation) and the bathymetry for simplified range-dependent acoustic environments. The acoustic data used to solve the problems are restricted to five frequencies for a single vertical line array of receivers located at one range from the source. Matched-field inversion using simplex simulated annealing optimization is initially used to find a maximum-likelihood (ML) estimate. However, the ML estimate provides no information on the uncertainties or covariance associated with the model parameters. To estimate uncertainties, a Bayesian formulation of matched-field inversion is used to generate posterior probability density distributions for the parameters. The mean, covariance, and marginal distributions are determined using a Gibbs importance sampler based on the cascaded Metropolis algorithm. In most cases, excellent results were obtained for relatively sensitive parameters such as wave speed, layer thickness, and water depth. The variance of the estimates increase for relatively insensitive parameters such as density and wave attenuation, especially when noise is added to the data.     

Quantifying data information content in geoacoustic inversion

This paper examines the information content in matched-field geoacoustic inverse problems as a function of a variety of experiment factors, with the aim of guiding data collection and processing to achieve the best possible inversion results. The information content of the unknown geoacoustic parameters is quantified in terms of their marginal posterior probability distributions, 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. When sampled to convergence, the marginal distributions are found to have simple, smooth shapes that facilitate straightforward comparisons. The approach is general; the specific examples considered here include factors such as the number of sensors in the receiving array, array length, source-receiver range, source frequency, number of frequencies, source bandwidth, and signal-to-noise ratio     

两种基于贝叶斯点估计理论的多声源定位方法研究

海洋环境参数失配是制约匹配场定位性能的主要因素之一。为了克服环境失配,本文基于贝叶斯理论,将环境参数与声源的距离和深度一起作为未知量进行反演。然而在进行多声源定位时,反演参数的维数几何增长,极大地增加了反演问题的复杂性和计算量。为此本文将声源强度和噪声方差表示成其极大似然估计值,从而将这些参数进行隐式采样,大大降低了反演的维数和难度。文章比较了两种贝叶斯点估计方法,最大后验概率密度方法和最大边缘后验概率密度方法。最大后验概率密度方法的解是令后验概率密度取得最大值的参数组合,可以利用优化算法快速获得。最大边缘后验概率密度法将其他参数积分,得到目标参数的一维边缘概率分布,分布的最大值为反演结果。该方法得到最优估计值的同时可以获取参数估计的不确定信息。在环境参数和声源参数都未知的情况下,利用蒙特卡洛法在不同信噪比情况下对两种声源定位方法进行分析,实验结果表明：(1)对于敏感参数,如声源距离、水深和海水声速,最大边缘后验概率密度法比最大边缘后验概率密度方法的性能好。(2)对于较不敏感的参数,如海底声速、海底密度和海底声衰减,当信噪比较低时,最大边缘后验概率密度方法能较好地平滑噪声,从而比最大边缘后验概率密度法具有更好的性能。由于声源距离和深度是敏感参数,研究表明最大边缘后验概率密度法提供了一种在不确知环境下更可靠的多声源定位方法。     

Perturbative inversion of geoacoustic parameters in a shallow waterenvironment

In many strategic shallow water areas, the geoacoustic properties of the sub-bottom are largely unknown. This paper demonstrates that inverse theory and measured data from a single hydrophone can be used to accurately deduce the geoacoustic properties of the sub-bottom, even when the initial background geoacoustic model is a highly inaccurate estimate. Since propagation in shallow water is very sensitive to the geoacoustic properties of the sub-bottom the inverse technique is a vitally important, practical, and inexpensive means to improve sonar performance prediction in a potentially hostile environment. To provide ground truth for the inverse technique, measured data collected during Project GEMINI were compared to the inverse solutions. Detailed, site-specific geoacoustic models were developed for two array locations and the finite-element parabolic equation (FEPE) model was used to estimate transmission loss (TL). The model estimates from FEPE compared well with the measured data and the detailed geoacoustic models were considered as “ground truth.” To test the efficacy of the technique, initial background geoacoustic models were constructed assuming no a priori information of the bottom. The resultant inverse solution was used to predict the geoacoustic properties at each of the sites. The final results were in excellent agreement with the measured data and the resulting TL estimates derived from the inverse technique were as good or better than the TL estimates obtained from the detailed, site-specific geoacoustic models     

浅海聚焦定位中简化地声模型的应用研究

为了提高定位算法的环境宽容性,聚焦法将环境参数纳入了寻优空间。聚焦法虽然降低了对环境测量的要求,但是反演参数的增加也增加了反演的复杂性。基于海底反射特性,用两个参数对海底进行建模。通过标准的反演测试问题对简化地声模型在浅海聚焦定位中的有效性进行了分析。结果表明:基于简化地声模型的聚焦定位是可行的。在获得正确定位结果的同时,随着地声参数个数的减少,匹配场处理的便捷性得到了提高。文中引入的简化地声模型是聚焦问题中参数最少的地声模型,它可以有效减少聚焦定位参数维数以提升反演的便捷性。同时,简化地声模型在参数敏感性和耦合性上有较好的表现,这些优点可以保证定位结果的稳健性。     

消频散变换反演海底地声参数

提出1种将消频散变换应用到海底地声参数反演的方法。对单一水听器接收声压信号进行消频散处理后,根据群延时差建立代价函数,反演得到主要海底参数,最后根据贝叶斯统计理论给出了待反演地声参数的边缘后验概率密度。对单层波导进行仿真证明这种新方法的有效性。     

Geoacoustic characterization of a range-dependent ocean environment using towed array data

This paper examines geoacoustic inversion over a range-dependent multiple-layer seabed using a towed acoustic source and towed horizontal array. The approach is based on combining the results of a series of short-range, range-independent inversions to form a range-dependent representation of the environment. The data were collected in the Strait of Sicily during the MAPEX 2000 experiment. Issues such as the resolvability of multilayer structure and the sensitivity of various geoacoustic parameters are investigated by inversion of simulated data and by comparison of the MAPEX 2000 inversion results to a high-resolution seismic profile and to sediment core measurements. It appears that two, and in some cases possibly three, sediment layers can be resolved.     

Rapid geoacoustic characterization: applied to range-dependent environments

The problem of rapid environmental assessment in a range-dependent environment is addressed. For rapid assessment, the exact geoacoustic parameters are not required, nor is it a requirement that the exact structure of the acoustic field (location of peaks and s) be matched by an acoustic prediction model. The parameters that are relevant are the overall transmission loss (incoherent TL), the time spread (/spl tau/), and the slopes of the range/frequency interference patterns (/spl beta/, the waveguide invariant). The rapid geoacoustic characterization algorithm uses a homogeneous single-sediment layer overlying a hard acoustic basement model to optimally match the predicted acoustic observables with those estimated from data. The approach is presented here and is applied to the range-dependent benchmark cases TC1 and TC2 from the Inversion Techniques Workshop held in Gulfport, MS, in May 2001. The technique successfully reproduces the acoustic observables and estimates the sediment sound-speed, density, and attenuation profiles, as well as the sediment thickness.     

基于Sobol法的海底反向散射模型参数敏感度分析

为了对海底声学参数反演中的估计精度做出预估,合理解释反演结果,本文基于Jackson海底声散射模型,利用Sobol算法,对该模型中的耗散系数、速度比等7个参数进行定量的敏感度分析。Sobol算法可以给出参数的一阶敏感度和参数间相互作用的敏感度,适用于分析散射强度的影响因子。仿真结果表明,所选择的声波频率对于参数的敏感度影响不大,模型各参数交互作用较为强烈,速度比的全局敏感度最大,而耗散系数敏感度很小。将参数划分为地声属性参数、粗糙度参数和非均匀性参数,地声属性参数敏感度最大。模型参数敏感度分析结果对于反演有一定的指导作用。     

Benchmarking geoacoustic inversion methods using range-dependent field data

Over the past decade, inversion methods have been developed and applied to acoustic field data to provide information about unknown ocean-bottom environments. An effective inversion must provide both an estimate of the bottom parameters and a measure of the uncertainty of the estimated values. This paper summarizes results from the Office of Naval Research (ONR)/Space and Naval Warfare Systems Command (SPAWAR) Geoacoustic Inversion Techniques Workshop, test cases 4 and 5. The workshop was held to benchmark present-day inversion methods for estimating geoacoustic profiles in shallow water. The format of the workshop was a blind test to estimate unknown geoacoustic profiles by inversion of measured acoustic transmission loss data in octave bands and reverberation envelopes. The data sets for test cases 4 and 5 were taken at two locations in shallow water, one in the East China Sea and the other along the southwest coast of Florida. The limitations of the data and the limits to the knowledge of the sites are discussed. In both cases, impulsive sources were used in conjunction with air-deployed sonobuoys. Since the measured data was incoherent, only methods consistent with total energy matching were applicable. Comparisons between the different inversion techniques presented at the workshop are discussed. For test cases 4 and 5, a precise metric was unavailable for comparison.     

Estimation of Transmission Loss in the Presence of Geoacoustic Inversion Uncertainty

A common problem in sonar system prediction is that the ocean environment is not well known. Utilizing probabilistic based results from geoacoustic inversions we characterize parameters relevant to sonar performance. This paper describes the estimation of transmission loss and its statistical properties based on posterior parameter probabilities obtained from inversion of ocean acoustic array data. This problem is solved by first finding an ensemble of relevant environmental model parameters and the associated posterior probability using a likelihood based inversion of the acoustic array data. In a second step, each realization of these model parameters is weighted with their posterior probability to map into the transmission loss domain. This approach is illustrated using vertical-array data from a recent benchmark data set and from data acquired during the Asian Seas International Acoustics Experiment (ASIAEX) 2001 in the East China Sea. The environmental parameters are first estimated using a probabilistic-based geoacoustic inversion technique. Based on the posterior probability that each of these environmental models fits the ocean acoustic array data, each model is mapped into transmission loss. This enables us to compute a full probability distribution for the transmission loss at selected frequencies, ranges, and depths, which potentially could be used for sonar performance prediction.     

Matched field inversion for geoacoustic model parameters usingadaptive simulated annealing

A method is described for the estimation of geoacoustic model parameters by the inversion of acoustic field data using a nonlinear optimization procedure based on simulated annealing. The cost function used by the algorithm is the Bartlett matched-field processor (MFP), which related the measured acoustic field with replica fields calculated by the SAFARI fast field program. Model parameters are perturbed randomly, and the algorithm searches the multidimensional parameter space of geoacoustic models to determine the parameter set that optimizes the output of the MFP. Convergence is driven by adaptively guiding the search to regions of the parameter space associated with above-average values of the MFP. The performance of the algorithm is demonstrated for a vertical line array in a shallow water enviornment where the bottom consists of homogeneous elastic solid layers. Simulated data are used to determine the limits on estimation performance due to error in experimental geometry and to noise contamination. The results indicate that reasonable estimates are obtained for moderate conditions of noise and uncertainty in experimental geometry     

Broad-band geoacoustic inversion in shallow water from waveguideimpulse response measurements on a single hydrophone: theory andexperimental results

The paper discusses an inversion method that allows the rapid determination of in situ geoacoustic properties of the ocean bottom without resorting to large acoustic receiving apertures, synthetic or real. The method is based on broad-band waterborne measurements and modeling of the waveguide impulse response between a controlled source and a single hydrophone. Results from Yellow Shark '94 experiments in Mediterranean shallow waters using single elements of a vertical array are reviewed, inversion of the bottom parameters is performed with an objective function that includes the processing gain of a model-based matched filter (MBMF) receiver relative to the conventional matched filter. The MBMF reference signals incorporate waveguide Green's functions for known geometry and water column acoustic model and hypothesized bottom geoacoustic models. The experimental inversion results demonstrated that, even for complex environmental conditions, a single transmission of a broad-band (200-800 Hz) coded signal received at a single depth and a few hundred forward modeling runs were sufficient to correctly resolve the bottom features. These included the sound speed profile, attenuation, density, and thickness of the top clay sediment layer, and sound speed and attenuation of the silty clay bottom. Exhaustive parameter search proved unequivocally the low-ambiguity and high-resolution properties of the MBMF-derived objective. The single-hydrophone results compare well with those obtained under identical conditions from matched-field processing of multitone pressure fields sampled on the vertical array. Both of these results agree with expectations from geophysical ground truth. The MBMF has been applied successfully to a field of advanced drifting acoustic buoys on the Western Sicilian shelf, demonstrating the general applicability of the inversion method presented     

Inversion for Time-Evolving Sound-Speed Field in a Shallow Ocean by Ensemble Kalman Filtering

In the context of the recent Maritime Rapid Environmental Assessment/Blue Planet 2007 sea trial (MREA/BP07), this paper presents a range-resolving tomography method based on ensemble Kalman filtering of full-field acoustic measurements, dedicated to the monitoring of environmental parameters in coastal waters. The inverse problem is formulated in a state–space form wherein the time-varying sound-speed field (SSF) is assumed to follow a random walk with known statistics and the acoustic measurements are a nonlinear function of the SSF and the bottom properties. The state–space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Surface measurements augment the measurement vector to constrain the range-dependent structure of the SSF. Realistic scenarios of vertical slice shallow-water tomography experiments are simulated with an oceanic model, based on the MREA/BP07 experiment. Prior geoacoustic inversion on the same location gives the bottom acoustic properties that are input to the propagation model. Simulation results show that the proposed scheme enables the continuous tracking of the range-dependent SSF parameters and their associated uncertainties assimilating new measurements each hour. It is shown that ensemble methods are required to properly manage the nonlinearity of the model. The problem of the sensitivity to the vertical array (VA) configuration is also addressed.      

基于正交匹配追踪的声层析方法

声速剖面的变化会对声传播产生较大的影响,经验正交函数模型经常用来实现对声速剖面数据的简化描述。然而在内波、湍流等海水不均匀性存在时,这种正则化操作会造成声速重构精度的大幅降低。本文利用字典学习生成声速剖面的非正交原子,在稀疏编码时采用正交匹配追踪（OMP,Orthogonal Matching Pursuit）算法,更新字典则使用KSVD （Kernel Singular Value Decomposition）的字典更新算法。由于字典学习不需要强制使用正交条件,对于训练数据更加灵活,从而可以使用少数的原子组合达到更高的重构精度。利用一次浅海声学实验多次测量的声速剖面研究了海水声速剖面的经验正交函数表示和字典学习,研究表明：相比于正交函数表示,学习字典可以利用少数原子（甚至一个原子）更好的解释声速剖面扰动。字典学习可以提高声速剖面的稀疏性,从而提高声速剖面的反演精度。     

Combined Geoacoustic Inversion of Propagation and Reverberation Data

Sonar performance predictions in shallow water are strongly dependent on good knowledge of the geoacoustic and scattering properties of the seabed. One technique to extract information about the bottom is to use a towed source and a towed horizontal array. This towed system has been shown to be applicable for characterizing the bottom properties locally by inversion of the acoustic signals received directly on the towed array at short ranges. The same towed system has also been applied to extract bottom properties from long-range reverberation data providing effective bottom properties over a large area. However, independent geoacoustic inversion of the short-range propagation and long-range reverberation data can introduce low sensitivity and uncertainty in the extracted bottom properties. An attempt to resolve this low sensitivity and ambiguity is made by a simultaneous geoacoustic inversion of short-range propagation and long-range reverberation data with the intention of constraining the possible solutions of the bottom properties.      

Geoacoustic Information Content of Horizontal Line Array Data

This paper examines the effectiveness of horizontal line arrays (HLAs) for matched-field inversion (MFI) by quantifying geoacoustic information content for a variety of experiment and array factors, including array length and number of sensors, source range and bearing, source-frequency content, and signal-to-noise ratio (SNR). Emphasis is on bottom-moored arrays, while towed arrays are also considered, and a comparison with vertical line array (VLA) performance is made. The geoacoustic information content is quantified in terms of marginal posterior probability distributions (PPDs) for model parameters estimated using a fast Gibbs sampler approach to Bayesian inversion. This produces an absolute, quantitative estimate of the geoacoustic parameter uncertainties which can be directly compared for various experiment and array factors.     

Geoacoustic seafloor exploration with a towed array in a shallowwater area of the Strait of Sicily

Acoustic propagation in shallow water is greatly dependent on the geoacoustic properties of the seabottom. This paper exploits this dependence for estimating geoacoustic sediment properties from the bottom acoustic returns of known signals received on a hydrophone line array. There are two major issues in this approach: one is the feasibility of acoustic inversion with a limited aperture line array, the other is related to the knowledge of the geometry of the experimental configuration. To test the feasibility of this approach, a 40-hydrophone-4-m spaced towed array together with a low-frequency acoustic source, was operated at a shallow water site in the Strait of Sicily. In order to estimate the array deformation in real time, it has been equipped with a set of nonacoustic positioning sensors (compasses, tilt-meters, pressure gauges). The acoustic data were inverted using two complementary approaches: a genetic algorithm (GA) like approach and a radial basis functions (RBF) inversion scheme. More traditional methods, based on core sampling, seismic survey and geophone data, together with Hamilton's regression curves, have also been employed on the same tracks, in order to provide a ground truth reference environment. The results of the experiment, can be summarized as follows: 1) the towed array movement is not negligible for the application considered and the use of positioning sensors are essential for a proper acoustic inversion, 2) the inversion with GA and RBF are in good qualitative agreement with the ground truth model, and 3) the GA scheme tends to have better stability properties. On the other hand, repeated in version of successive field measurements requires much less computational effort with RBF     

Data Uncertainty Estimation in Matched-Field Geoacoustic Inversion

This paper examines a variety of approaches to treating unknown data uncertainties in matched-field geoacoustic inversion. Both optimal parameter estimation via misfit minimization and parameter uncertainty estimation via Gibbs sampling are considered. The misfit is based on the likelihood function for Gaussian-distributed errors, which requires specification of the data variance at each frequency. Unfortunately, independent knowledge of variance is rarely available due to unknown theory errors. Many applications of matched-field minimization implicitly assume that variance effects are uniform over frequency; however, this can be a poor assumption as theory errors generally vary with frequency. Parameter uncertainty estimation to date has used fixed maximum-likelihood (ML) variance estimates, which does not account for the variance uncertainty in estimating parameter uncertainties. This paper considers two new approaches to treating data uncertainty in matched-field inversion: Including variances explicitly as additional (nuisance) parameters in the inversion, and treating variances as implicit unknowns by constraining the misfit according to an ML variance formulation (this includes variance uncertainty without increasing the number of unknown parameters). All of the above approaches are compared for realistic synthetic test cases and for shallow-water acoustic data measured in the Mediterranean Sea as part of the PROpagation channel SIMulator experiment (PROSIM'97).     

The structure of the incoherent sediments in the Ita Mai Tai Guyot (Pacific Ocean) based on geoacoustic profiling data

The results of geoacoustic studies carried out by the acoustic MAK-1M system in the southeastern Ita Mai Tai Guyot (Magellan Seamounts, Pacific Ocean) are discussed. The obtained geoacoustic sections characterize the incoherent part of the sedimentary sequence with high resolution. The geoacoustic stratification is well correlative with the deep-sea drilling data: the acoustic units are reliably correlated with the lithostratigraphic units defined in the cores of DSDP holes 200 and 202. Three geoacoustic units are distinguished in the sedimentary section (from the top downward): unit I corresponding in age to the terminal Miocene (Messinian)-Quaternary; unit II correlated with the Late Miocene (Tortonian); unit III accumulated in the Early Eocene-Early Miocene. The acoustic basement is composed of reefogenic limestones that were formed at different stages of the guyot’s development through the Aptian-Turonian to Late Paleocene-Eocene. The sonar images allow the distribution of the incoherent carbonate sediments to be contoured along the periphery of the summit’s plateau.