<p>Multiobservable thermochemical tomography (MTT) is a recent computational approach to obtain estimates of the physical state (e.g. temperature distribution, compositional structure and rock properties) for the upper mantle [1]. It allows to jointly invert multiple independent datasets (e.g. gravity, seismic, magnetotelluric) within a thermodynamically-constrained and fully probabilistic framework. Evaluation of the plausibility of different physical states of the mantle with Markov Chain Monte Carlo (MCMC) simulations requires the solution of complex forward problems (e.g. Stokes flow, Maxwell&#8217;s equations, etc.) millions of times, making MTT computationally demanding for large-scale inverse problems. Furthermore, the number of parameters in a global study can easily reach several millions, making it increasingly difficult to 1) locate the regions of high probability and 2) sample these regions appropriately.</p><p>In order to overcome these limitations, we have combined and implemented a number of techniques, such as reduced-order modelling and efficient parallelization of both the forward problems and the MCMC algorithms, which dramatically accelerate the solution of the forward problems. Our software, LitMod1D_4INV and LitMod3D_4INV, allow to compute a proposal in less than 1 second, even when solving multiple complex forward problems together. We develop a multi-level parallel MPI driver for a collection of advanced MCMC sampling strategies to locate and sample high-probability regions efficiently. The massive amounts of data generated by large-scale MTT inversions need to be managed efficiently. We output results to open-source freeware formats, such as HDF5, TileDB, designed for big data problems. We emphasize that our methods and approaches are not only useful for MTT, but for any demanding inverse problem.</p><p>In this contribution, we will present applications of our software to complex, large-scale MTT problems and discuss its benefits, limitations and future improvements.</p><p>[1] J.C. Afonso, N. Rawlinson, Y. Yang, D. L. Schutt, A. G. Jones, J. Fullea, W. L. Griffin, 3&#8208;D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle: III. Thermochemical tomography in the Western&#8208;Central U.S., Journal of Geophysical Research, 121, doi:10.1002/2016JB013049, 2016</p>
3-D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle. I:a prioripetrological information and geophysical observables
