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TY  - THES
AU  - Liang, Zhouji
TI  - Derivative-informed Bayesian inference for trainable geological modeling - in modern machine-learning framework
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2024-02206
SP  - 1 Online-Ressource : Illustrationen
PY  - 2023
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2024
N1  - Dissertation, RWTH Aachen University, 2023
AB  - Earth’s subsurface remains the most vital source of energy and minerals for humankind. However, these subsurface resources cannot be extracted without a comprehensive understanding of what lies beneath our feet. Geoscientists have dedicated significant efforts characterizing the subsurface to guide resource development decisions and have increasingly relied on computer modeling software. A 3D structural geological model serves as such a tool that encapsulates the knowledge of geoscientists and provides an efficient visualization, communication, and advanced analysis. Ensuring a faithful representation of the subsurface is a crucial task for the geological model, both from the financial point of view and for safety reasons. Conventionally, a single model is developed based on the modeler’s best knowledge. Yet, any criteria the model was based on beyond our actual observation is subject to certain uncertainties, for example, the input data, the interpolation, and the missing knowledge. A good quantification of these uncertainties is fundamental for the success of the application of geological models. The Bayesian framework offers a systematic approach to simultaneously consider the uncertainties in the prior knowledge and additional observations within the likelihood function. The inferred probability with the consideration of additional observations is referred to as the posterior probability. This inference problem often cannot be solved analytically. Evaluating the posterior distribution is equivalent to the exploration of the posterior space and is often solved using Markov Chain Monte Carlo (MCMC) methods. In the geosciences, geophysical data is widely used to characterize the subsurface through collection of observations of physical signals. The accumulated scientific expertise and collected geophysical surveys make geophysical data an attractive candidate for uncertainty quantification. However, integrating geophysical observations in the Bayesian Framework is challenging due to difficulties in calculating chained derivatives of geological followed by geophysical simulations. This thesis presents an end-to-end methodology to solve the problem of integrating potential field data, specifically gravity, into the Bayesian inference framework by leveraging advanced derivative-informed inference methods, implemented in a Machine Learning framework - TensorFlow. First, methods are introduced to simulate gravity data from a geological model using the implicit modeling method. The proposed kernel methods for gravity simulation take advantage of the value that can be queried at any position in space based on the implicit modeling methods to achieve a more efficient gravity calculation. In addition, a refinement strategy is proposed to achieve better accuracy in the probabilistic modeling framework. Then, methods to create trainable geological models are introduced. The proposed methods introduce a smooth slope function to bridge derivative discontinuities between geological modeling and gravity simulation. The proposed method enables meaningful derivatives to be calculated from a geological inversion to allow the application of advanced inference methods. A visualization method using the order-reduction technique is adopted to visualize the trainable posterior space. Finally, by combining the introduced gravity simulation methods and trainable geological modeling technique, this study is the first attempt to adopt advanced inference methods, including the Hessian-informed MCMC (generalized preconditioned Crank-Nicolson, gpCN) and gradient-informed variational method (Stein Variational Gradient Descent, SVGD) to the application of probabilistic geological modeling. The approach to efficiently evaluate Hessian information based on the trainable geological concept is introduced. The proposed methodology using gpCN has demonstrated the superior performance of posterior exploration compared to the state-of-the-art MCMC method in both synthetic examples and real case studies and shows the potential for more complex scenarios. The SVGD algorithm is proposed in an attempt to tackle the multimodal posterior, which is a challenge for many MCMC-type algorithms. Preliminary results show that the posterior space in geological inversion with gravity as the likelihood could be complex, and the multimodal distribution is difficult to resolve in the current configuration. This is intended to show the possibility of applying SVGD to solve the model-based inversion problem and indicates the need for further improvement.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2024-02206
UR  - https://publications.rwth-aachen.de/record/980351
ER  -