UBC Theses and Dissertations
Computational methods in hydrogeophysics Steklova, Klara
Parameter and state estimation for groundwater models within a coupled hydrogeophysical framework has become common in the last few years as it has been shown that such estimates are usually better than those from a single data inversion. Different approaches have been suggested in literature to combine the essentially two different modalities in order to obtain better estimates for groundwater models, and improve monitoring of processes such as solute transport. However, the coupled approaches usually come at a price of higher computational cost and difficulties in coupling the geophysical and groundwater inverse problems. Unlike in other studies, we developed both the groundwater and geophysical models in the same computational environment in order to test different minimization strategies. When solving the coupled inverse problem, the objective function consists of data misfit and regularization terms as well as a coupling term that relates groundwater and geophysical states. We present a novel approach to solve the inverse problem using an Alternating Direction Method of Multipliers (ADMM) to minimize the coupled objective function. ADMM enables us to treat the groundwater and geophysical part separately and thus use existing software with minor changes. However, ADMM as well as many other coupled approaches relies on implementing some petrophysical relationship to couple the groundwater and geophysical variable. Such relationships are usually uncertain and hard to parametrize for a large region and can potentially produce solute mass errors in the final model estimates. Therefore, in this thesis we examine coupled approaches that replace the fixed petrophysical relationship by a more loose structure similarity constraint. Besides, we propose efficient computational methods to minimize the objective function when there is no explicit petrophysical constraint. All approaches were tested on 3D synthetic examples. In the solute tracer test we estimated hydraulic conductivity or solute distribution using a structure coupled inversion, and were able to reduce the errors compared to a single data inversion alone. For a more complex example of seawater intrusion we implemented the ADMM method, and obtained better estimates for the solute distribution compared to just considering each data separately, or solving the problem with a simple coupled approach.
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