| In this study, a stochastic finite element method is used to solve an inverse problem in groundwater flow. The adjoint states method combined with cokriging method is used to estimate the distribution of hydraulic conductivities in an area where hydraulic heads and hydraulic conductivities are measured at some locations. This method starts with obtaining the expected hydraulic heads in the entire study domain at different times. Then, the adjoint states at different times are calculated. Using both calculated values as input, the Jacobians that are needed for the development of covariance matrices of hydraulic heads at different times and the cross-covariance matrices between hydraulic heads at different times and hydraulic conductivities in the aquifer are calculated. Using the maximum likelihood estimate method (MLE), which utilizes all covariance and cross-covariance matrices obtained from the previous step, the statistical parameters (mean, variance, and correlation scale) of the model are estimated. Using the statistical parameter values and all observed values of hydraulic heads at different times and all measured hydraulic conductivities, the distribution of hydraulic conductivity in the entire study domain is estimated.; An attempt is made in this thesis to verify the computer program by utilizing two hypothetical problems as verification cases. In some parts of the aquifer, mostly at locations around the observation wells, the resulting hydraulic conductivity distributions have the same pattern with the "true" distribution patterns in both cases of verification. The values of L2-norms calculated by using the "true" and estimated values of log hydraulic conductivity are 0.18 and 0.57 for Case 1 and 2, respectively.; Data from two field problems are analyzed as an application of the computer program. The estimated values of hydraulic conductivity are found to be within the range of the observed values given in the original reports. These applications can be considered as a part of the validation of the method.; Considering the results of both case studies, it appears that the computer program developed in this study can be used with reasonable success to estimate the hydraulic conductivity distribution in real aquifers. As will be explained in the discussion of the results, however, the effect of zonation needs to be investigated further. (Abstract shortened by UMI.)... |
