Statistical Inversion Of Acoustical And Statistical Parameters Of Seafloor From Shallow Water Reverberation

Statistical inversion of seafloor parameters based on Bayesian inference is an interesting topic in the research of underwater acoustics. The goal of statistical inversion is to derive the posterior probability density (PPD) of the unknown seafloor parameters from the measured ocean acoustic fields. It is convenient to cauculate the posterior moments in terms of the PPD, such as the mean, covariance, and marginal probability distributions, which provide the maximum a posterior probability estimation and uncertainties of unkown parameters.Ocean reverberation, consisting of sounds returns from the sea surface, seafloor and water column, is an important phenomenon in the shallow water and can be used to inverse the acoustical (such as velocity, density, attenuation, et al.) and statistical (such as the variances of surface elevation and slope, et al.) parameters of seafloor. The results of seafloor parameters inverted from shallow-water reverberation (SWR) can be applied to predict the sound filed in shallow water, classfy the seafloor style, and other practical application areas. However, relative little work has been applied to the problem of estimate seafloor parameters from SWR.This paper briefly recalls the Bayesian formulation of inverse theory and the principal numerical approaches to estimate the PPD. Then, in the frame of Baysian inverse theory, we study the statistical inverse problems of retrivaling the surface statistical parameters from travel-time statistics of high-frequency reverberation signals and determining the acoustical parameters from reverberation vertical correlation (RVC). Futhermore, a novel approach based on support vector machine is proposed for the low dimensional matched-field inversion.The major contributions of this thesis are summaried as follows:â‘ Theory of Fuks and Godin [Waves Random Media, 14, 539-562 (2004)] on the travel-time statistics of high-frequency reverberation signals (backscattered pulses from a random surface) is extended in this paper. We not only consider the difference between"up-crossing"and"down-crossing"of the wave-front and the stochastic surface, but also extend the theoretical results of Fuks and Godin to the case of in which surface elevation and slope are correlated. And the probability density functions (PDF) of the travel times of the first and second backscattered pulses and the time delay between them are obtained explicitly. It is found that these PDFs above are functions of elevation-slope correlationρand a dimensionless parameter T = (γ₀²H)/(2πσ₀), whereσ₀² andγ₀² are the variance of the surface elevation and slope, and H is the altitude of wave source. Furthermore, the inverse problem of rough surface parameters estimation from travel-time statistics of backscattered pulses is investigated in this paper. A Bayes-theory-based matched-PDF statistical inversion schem is proposed, which may be applied to estimate the parametersρand T of random surface from travel-time statistics of backscattered pulses. The uncertainties of the parameter estimation are analysis in terms of the posterior probability distributions of inversion results. Numerical simulation illustrates that the algorithm is effective to inverse the parameters of random surface and the inversion result ofρbeing a higher accuracy with respect to T . And there is a strong parameter couple betweenρand T . It is suggested that the elevation-slope correlation (ρ) cannot be neglected as other previous authors, bothρand T should be considered at the same foot in this kind of inversion problem.â‘¡Statistical geoacoustic inversion results based on reverberation vertical correlation (RVC) data from 300Hz to 800Hz are presented. The data were obtained during Yellow Sea Experiment-2005 (YSE-05). An uncertainty analysis is carried out. It is found that the inversion sea bottom sound velocities decrease when the frequency increases. Similar phenomenon has been reported by other authors. So it is difficult to determine the sea bottom sound velocity. In order to solve this problem, a two-layer bottom model is assumed, and a multi-frequency inversion approach based on Bayesian theory is proposed in this paper. The approach is demonstrated using YSE-05 experiment data. Both RVC and normal modes depth functions (NMDFs) calculated using the inverted geoacoustic parameters are in good agreement with the experimental measurements.â‘¢This paper proposed a new approach to estimate the PPD based on support vector machine (SVM). The main advantage of this approach is the PPD can be estimated based on small samples rapidly. The key schem is to train a SVM model to approximate cost function using the set of input-output training samples, where, the input is the set of unknown seafloor parameters, and the output is the corresponding value of cost function. Then, during the sampling procedure of estimateing the PPD, the real value of objective function is replaced by the approximate value, which cauculate by the SVM trained model. And there is no need for any further forward model runs. Comparison of exhaustive searching, Markov Chain Monte Carlo, and nearest neighborhood interpolation approximate algorithm, SVMA reduces the number of forward model runs remarkably and require less computation time. Morever, the numerical and experimental examples validate the SVMA for low dimensional matched-field inversion. This paper first introduces SVM to the problem of estimating the PPD and provides a novel approach to estimate the PPD of unknown parameters efficiently. It is helpful to enlarge the scope of the applications of Bayesian inversion.