A Bayesian approach to the groundwater inverse problem for steady state flow and heat transport

In this thesis the Bayesian approach proposed by Woodbury and Ulrych (2000) is extended to estimate transmissivity field of highly heterogeneous aquifers for two-dimensional steady state groundwater flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included.; This new algorithm is examined against a fictitious aquifer with both “high” and “extremely high” variations of ln (T). The addition of the hydraulic head data is shown to improve the ln (T) estimates, in comparison to simply interpolating the sparse ln (T) data alone. Forward solutions with the conditional-expected ln (T) field indicate that the conditional heads match the true heads better than the unconditional linearized approximation. This finding suggests that the Bayesian approach can be applied not only to the groundwater inverse problems for which linearized approximation is valid, but also to cases where linearized approximation may not be satisfactory due to high heterogeneity.; The new Bayesian code is employed to calibrate a high-resolution finite difference model of the Edwards Aquifer, Taxes. The posterior ln (T) fields from this application yield better fits when compared to the prior ln (T) determined from upscaling and co-kriging.; The methodology for the spatial inversion of transmissivity for two-dimensional steady state groundwater heat transport is developed based on the full-Bayesian approach. This new algorithm is examined against a generic example. It is found that the use of temperature data is showed to improve the ln (T) estimates, when compared to the updated ln (T) field conditioned on sparse ln (T) and head data. Also the addition of temperature data without head data to the update aids refinement of the In (T) field compared to simply interpolating the sparse ln (T) data alone.