Probabilistic geophysical inversion of complex resistivity measurements using the Hamiltonian Monte Carlo method

Geophysical Journal International, vol. 240, pp. 349–361

Abstract

SUMMARY In this work, we introduce the probabilistic inversion of tomographic complex resistivity (CR) measurements using the Hamiltonian Monte Carlo (HMC) method. The posterior model distribution on which our approach operates accounts for the underlying complex-valued nature of the CR imaging problem accurately by including the individual errors of the measured impedance magnitude and phase, allowing for the application of independent regularization on the inferred subsurface conductivity magnitude and phase, and incorporating the effects of cross-sensitivities. As the tomographic CR inverse problem is nonlinear, of high dimension and features strong correlations between model parameters, efficiently sampling from the posterior model distribution is challenging. To meet this challenge we use HMC, a Markov-chain Monte Carlo method that incorporates gradient information to achieve efficient model updates. To maximize the benefit of a given number of forward calculations, we use the No-U-Turn sampler (NUTS) as a variant of HMC. We demonstrate the probabilistic inversion approach on a synthetic CR tomography measurement. The NUTS succeeds in creating a sample of the posterior model distribution that provides us with the ability to analyse correlations between model parameters and to calculate statistical estimators of interest, such as the mean model and the covariance matrix. Our results provide a strong basis for the characterization of the posterior model distribution and uncertainty quantification in the context of the tomographic CR inverse problem.

Authors 4

1. Joost Hase corresponding

   University of Bonn

   Affiliation as printed

   Geophysics Section, Institute of Geosciences, University of Bonn , Meckenheimer Allee 176, D-53115 Bonn ,

   Geophysics Section, Institute of Geosciences, University of Bonn, Meckenheimer Allee 176, 53115 Bonn, Germany

2. Florian Wagner corresponding Aachen Geophysical Imaging and Monitoring

   RWTH Aachen University

   Affiliation as printed

   Geophysical Imaging and Monitoring, RWTH Aachen University , Wüllnerstraße 2, D-52062 Aachen ,

3. Maximilian Weigand

   University of Bonn

   Affiliation as printed

   Geophysics Section, Institute of Geosciences, University of Bonn , Meckenheimer Allee 176, D-53115 Bonn ,

   Geophysics Section, Institute of Geosciences, University of Bonn, Meckenheimer Allee 176, 53115 Bonn, Germany

4. Andreas Kemna corresponding

   University of Bonn

   Affiliation as printed

   Geophysics Section, Institute of Geosciences, University of Bonn , Meckenheimer Allee 176, D-53115 Bonn ,

   Geophysics Section, Institute of Geosciences, University of Bonn, Meckenheimer Allee 176, 53115 Bonn, Germany