A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation

Abstract

Simulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. 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 3-D 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 parametrizations 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 3-D 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.