Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem |
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Authors: | Juan Luis Fernández‐Martínez Shan Xu Colette Sirieix Zulima Fernández‐Muniz Joëlle Riss |
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Institution: | 1. Group of Inverse Problems, Optimization and Machine Learning, Department of Mathematics, University of Oviedo, Oviedo, Spain;2. Université de Bordeaux, CNRS, Pessac, France |
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Abstract: | In this paper, we present the uncertainty analysis of the 2D electrical tomography inverse problem using model reduction and performing the sampling via an explorative member of the Particle Swarm Optimization family, called the Regressive‐Regressive Particle Swarm Optimization. The procedure begins with a local inversion to find a good resistivity model located in the nonlinear equivalence region of the set of plausible solutions. The dimension of this geophysical model is then reduced using spectral decomposition, and the uncertainty space is explored via Particle Swarm Optimization. Using this approach, we show that it is possible to sample the uncertainty space of the electrical tomography inverse problem. We illustrate this methodology with the application to a synthetic and a real dataset coming from a karstic geological set‐up. By computing the uncertainty of the inverse solution, it is possible to perform the segmentation of the resistivity images issued from inversion. This segmentation is based on the set of equivalent models that have been sampled, and makes it possible to answer geophysical questions in a probabilistic way, performing risk analysis. |
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Keywords: | Uncertainty analysis 2D nonlinear inversion Resistivity inversion |
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