Evaluating RJ MCMC for parameter dimensionality adjustment in geological models

Abstract

Uncertainty quantification is integral in geological modeling for mining, exploration and civil engineering projects. Workflows for uncertainty estimation for model input in implicit structural geological modeling and inversion are well-established when the parameter space is fixed. These approaches require a priori known or chosen number of parameters. In many cases, this may not be justified given the data, as the system’s number of layers or the number of phases is not known, resulting in overly complex or too simple models. Trans-dimensional Markov chain Monte Carlo methods can be crucial to model selection in pursuing parsimonious models in complex geological settings with large uncertainty. Reversible jump Monte Carlo (RJ-MCMC) algorithms yield excellent solutions for inverse problems with varying dimensionality. In this study, we evaluate how far RJ-MCMC concepts can be applied to parameters of geological interpolation functions. Using the RJ-MCMC algorithm, we can automatically determine the optimal number of parameters for a given problem, reducing the need for subjective user input. We simulate geophysical measurements for simple structural geological models built with GemPy to create a ground truth. In the second step, we create an ensemble of prior structural models, which are updated using geophysical inversion. We can address models’ likelihood in this probabilistic framework and enable further probabilistic inference given new data. We evaluate the performance of the trans-dimensional RJ-MCMC compared to standard, fixed-dimensional methods.

Authors 5

1. Nils Chudalla Aachen Computational Geoscience

   RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics, RWTH Aachen University, Aachen, Germany (chudalla@cgre.rwth-aachen.de)

2. Florian Wellmann corresponding Aachen Computational Geoscience

   Fraunhofer Research Institution for Energy Infrastructures and Geotechnologies IEG · RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics, RWTH Aachen University, Aachen, Germany (chudalla@cgre.rwth-aachen.de)

   Fraunhofer Research Institution for Energy Infrastructures and Geothermal Systems IEG, Am Hochschulcampus 1, 44810 Bochum, Germany

3. Christin Bobe corresponding Aachen Computational Geoscience

   RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics, RWTH Aachen University, Aachen, Germany (chudalla@cgre.rwth-aachen.de)

4. Sofia Brisson Aachen Computational Geoscience

   RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics, RWTH Aachen University, Aachen, Germany (chudalla@cgre.rwth-aachen.de)

5. Zhouji Liang corresponding Aachen Computational Geoscience International Research Training Group Modern Inverse Problems

   RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics, RWTH Aachen University, Aachen, Germany (chudalla@cgre.rwth-aachen.de)

   International Research Training Group – Modern Inverse Problems (IRTG-MIP), Aachen, Germany