BAYESIAN INVERSE MODELING: ALGORITHMS AND APPLICATIONS IN GROUND WATER
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Inverse estimation of spatially-correlated parameter fields is essential in a variety of scientific disciplines, including hydrology, geology, geophysics, natural resources, environmental sciences and engineering, etc. Classical stochastic sampling approach, such as Markov Chain Monte Carlo (MCMC), and optimization approach, such as geostatistical approach (GA), are capable of solving inverse problems having a modest size of 103-104 unknowns with fast forward model evaluation. However, the computational cost becomes unaffordable for large-dimensional inverse problems with 106 unknowns on fine-resolution parameter fields. In this thesis, we develop new, efficient and accurate algorithms for both stochastic sampling approach and geostatistical approach within a Bayesian framework and test the efficacy using synthetic and field data for inverse estimation of large-dimensional hydrogeological parameter fields, including hydraulic conductivity and specific storage. For stochastic sampling, the stochastic Newton algorithm is employed to propose effective samples to speed up convergence, taking advantage of the local structure of posterior distribution. A quasi-Newton algorithm is incorporated into stochastic Newton to accelerate the sampling process by reducing the number of forward model evaluations. For the application of hydraulic tomography, an upscaling approach is applied to reduce the computational time of each forward model evaluation while still preserves the inverse accuracy. The proposed approach is validated via numerical experiments using synthetic datasets. For geostatistical approach, we reformulate the quasi-linear geostatistical approach onto principal component coefficients that significantly reduces the number of forward model runs, and benefits post-solution uncertainty analysis and generation of conditional realizations. This approach yields a more scalable normal equation system that is particularly advantageous for inverse problems with a large number of measurements, and therefore will potentially become popular in ‘big data’ era. The computational efficiency is improved further by combining an upscaling approach, which significantly lowers the running time of forward model evaluations. The proposed approach is successfully applied to both synthetic and field cases.