A Reduced Order Approach for Probabilistic Inversions of 3D Magnetotelluric Data I: General Formulation

Abstract

Simulation-based probabilistic inversions of 3D magnetotelluric (MT) data are arguably the best option to deal with the non-linearity and non-uniqueness of the MT problem. However, the computational cost associated with the modeling of 3D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT datasets. In this contribution, we present a novel and general inversion framework, driven by Markov chain Monte Carlo (MCMC) algorithms, which combines i) an efficient parallel-in-parallel structure to solve the 3D forward problem, ii) a reduced order technique to create fast and accurate surrogate models of the forward problem, and iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method.We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parameterizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.

A Reduced Order Approach for Probabilistic Inversions of 3D Magnetotelluric Data II: Joint inversion of MT and Surface-Wave Data

“…This means > 99.5 % gain in computational efficiency compared to the high-fidelity solution (∼ 30 secs). For the same model, and using the same number and type of processors, the RB+MCMC inversion of MT data only (see Manassero et al, 2020) took ∼ 30 days (an average of 1.03 seconds per the location of these columns (white small squares) and 96 column-parameters as a reference.…”

“…values of the maximum a posteriori and mean conductivity models, as well as the rms for the LAB structure, are included in Table 2. As a comparison, we have also included the rms values obtained for the same model after the RB+MCMC inversion of 3D MT data only (see Manassero et al, 2020), which are considerable higher than those obtained with the joint inversion.…”

“…In this section, we introduce the 3D magnetotelluric (MT) forward problem, the finite-element high-fidelity solver and the RB+MCMC approach to compute surrogate solutions. The reader is referred to Douglas Jr et al (1999 and Zyserman & Santos (2000) for an in-depth treatment of the theory behind the formulation of the 3D MT problem and to (Part I; Manassero et al, 2020) for a detailed description of the surrogate approach.…”

“…In these situations, an adaptive MCMC approach where the surrogate is refined online during the MCMC simulation is a more effective and efficient approach. A strategy to reduce the computational cost of the 3D MT forward solver and perform full probabilistic 3D MT inversions has recently been presented by Manassero et al (2020). This novel strategy, called RB+MCMC, combines i) an efficient parallel-in-parallel structure to solve the 3D MT forward problem, ii) a Reduced Basis Method to create fast and accurate surrogate models of the highfidelity solution, and iii) adaptive strategies for both the MCMC algorithm and the surrogate model.…”

“…This novel strategy, called RB+MCMC, combines i) an efficient parallel-in-parallel structure to solve the 3D MT forward problem, ii) a Reduced Basis Method to create fast and accurate surrogate models of the highfidelity solution, and iii) adaptive strategies for both the MCMC algorithm and the surrogate model. This paper builds on our previous work (Manassero et al, 2020) and presents the first joint inversion of 3D magnetotelluric and surface-wave data within the context of MCMC-driven, fully probabilistic inversions. Specifically, we focus on a realistic 3D mapping of the electrical conductivity structure of the lithosphere including the locus of deep thermochemical anomalies and fluid pathways.…”