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.

Joint inversions of two or more geophysical data sets are becoming common practice for imaging the Earth's interior and elucidating the physical state of the planet. When the inverted data sets have complementary sensitivities to the properties of interest, joint inversions significantly reduce the ambiguity inherent in single-data set inversions, achieve more stable solutions, increase identifiability of features and enhance model resolution. Perhaps more importantly, certain properties of the Earth's interior can only be revealed by combining observations from different techniques. An example is the bulk composition of the lithospheric mantle, which requires independent constrains on the bulk density (e.g., from gravity data sets) and shear-wave velocity (e.g., from surface-wave data). Recent discussions on the benefits and limitations of joint approaches for imaging the structure of the lithosphere and upper mantle can be found in, for example, Khan et al. (2006); Afonso, Fullea, Griffin,

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