Uncertainty quantification for regularized inversion of electromagnetic geophysical data—Part I: motivation and theory

SUMMARY We present a method for computing a meaningful uncertainty quantification (UQ) for regularized inversion of electromagnetic (EM) geophysical data that combines the machineries of regularized inversion and Bayesian sampling with a ‘randomize-then-optimize’ (RTO) approach. The RTO procedure is...

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Bibliographic Details
Published in:Geophysical journal international Vol. 231; no. 2; pp. 1057 - 1074
Main Authors: Blatter, Daniel, Morzfeld, Matthias, Key, Kerry, Constable, Steven
Format: Journal Article
Language:English
Published: Oxford University Press 25.07.2022
Subjects:
Inversion
Statistical methods
Electromagnetic methods
Electrical resistivity
Inverse theory
ISSN:0956-540X, 1365-246X
Online Access:Get full text
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Summary:SUMMARY We present a method for computing a meaningful uncertainty quantification (UQ) for regularized inversion of electromagnetic (EM) geophysical data that combines the machineries of regularized inversion and Bayesian sampling with a ‘randomize-then-optimize’ (RTO) approach. The RTO procedure is to perturb the canonical objective function in such a way that the minimizers of the perturbations closely follow a Bayesian posterior distribution. In practice, this means that we can compute UQ for a regularized inversion by running standard inversion/optimization algorithms in a parallel for-loop with only minor modification of existing codes. Our work is split into two parts. In Part I, we review RTO and extend the methodology to estimate the regularization penalty weight on the fly, not unlike in the Occam inversion. We call the resulting algorithm the RTO-TKO and explain that it samples from a biased distribution which we numerically demonstrate to be nearby the Bayesian posterior distribution. In return for accepting this small bias, the advantage of RTO-TKO over asymptotically unbiased samplers is that it significantly accelerates convergence and leverages computational parallelism, which makes it highly scalable to 2-D and 3-D EM problems. In Part II, we showcase the versatility and computational efficiency of RTO-TKO and apply it to a variety of EM inversions in 1-D and 2-D, carefully comparing the RTO-TKO results to established UQ estimates using other methods. We further investigate scalability to 3-D, and discuss the influence of prior assumptions and model parametrizations on the UQ.
ISSN:0956-540X
1365-246X
DOI:10.1093/gji/ggac241