Application of the reduced basis method in geophysical simulations: concepts, implementation, advantages, and limitations

  • Anwendung der reduzierten Basismethode in geophysikalischen Simulationen: Konzepte, Implementierung, Vorteile und Einschränkungen

Degen, Denise Melanie; Wellmann, Jan Florian (Thesis advisor); Veroy-Grepl, Karen (Thesis advisor); Regenauer-Lieb, Klaus (Thesis advisor)

Aachen : RWTH Aachen University (2020, 2021)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2020

Abstract

Renewable and sustainable energy sources are becoming more and more important. To retrieve these earth's resources, we require reliable simulations. This is, however, a major challenge because of huge uncertainties related to geophysical simulations. Therefore, in this thesis, we focus on improving numerical simulations, to enable the usage of computationally demanding inverse processes, such as Markov Chain Monte Carlo, for complex sedimentary basins that are prohibitive with state-of-the-art finite element solvers. We demonstrate that the reduced basis method is a powerful tool, especially for parameter estimation studies, in the field of Geosciences. We use simple benchmark examples, of a three-layer and a fault model, to better illustrate the employed methods and then use the same methods for the real-case basin-scale models of the Upper Rhine Graben and Brandenburg. For both models, we obtain speed-ups of four to six orders of magnitude, while maintaining an approximation accuracy higher than the measurement accuracy. Hence, we generate approximations that can be equally well used for model predictions and parameter studies as the original full model. We illustrate how the obtained speed-up can be used to perform both deterministic and probabilistic inverse processes as, for instance, global sensitivity studies, model calibrations, and Markov Chain Monte Carlo studies. For these analyses, we are able to reduce the compute time from ten to hundreds of core years to a couple of core hours. The reduced basis method has the advantage that it provides the full state variable, and not only the quantities of interest, such as many other surrogate models. This allows the generation of 2D and 3D uncertainty quantification maps, providing us with interesting insights into the influence of the kind of boundary conditions on the overall spatial distribution of the uncertainties. Opposed to many machine learning approaches, we use a physics-based approach. This allows to incorporate our physical knowledge and to compensate for problems as data sparsity. For the here presented problems, we are able to use the certified reduced basis method. Hence, we obtain error bounds. These error bounds give us a guarantee of our approximation quality and allow for an effective basis construction. We focus in this thesis on geothermal conductive heat transfer problems. However, we also present and discuss the benefits of the reduced basis method for groundwater flow, and electrical resistivity tomography problems. For the transient simulations of the groundwater flow problems, we are able to show that the gained speed-ups are several orders of magnitude higher than those for the steady-state problems. In addition to the parameter estimation studies, we furthermore demonstrate under which conditions the reduced basis method can be used for data assimilation in groundwater studies.

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