Stochastic Multi‐Observables Inversion for the 3D Thermochemical Structure of Lithosphere in Spherical Coordinates: Theory and Synthetic Examinations

Abstract The physical properties of the lithospheric and upper mantle's rock are determined by its composition and the in situ temperature and pressure conditions. Together, they have been referred to as the thermochemical structure. Information about the upper mantle's thermochemical structure could be obtained using methods from different disciplines of the earth sciences, in which the geophysical approaches show potential to map the 3D variations on both the regional and global scales. Thus, techniques for investigating the thermochemical structure in the spherical coordinates are needed, including forward modeling of the geophysical observables, calculating schemes of the thermophysical properties for the lithologies, and effective inversion algorithm, which is particularly important for large‐scale applications. This paper first demonstrates an adaptive meshing architecture based on the tetrahedral mesh by the sophisticated constructions in a spherical shell. Techniques that enable rapid calculations of the thermophysical properties of the upper mantle's rocks are introduced in length. Methodologies for constructing 3D thermochemical models and forward modeling geophysical observations, including an inversion sub‐routine that couples the lithostatic pressure and density variations to forward modeling, are introduced and examined in detail using synthetic data sets. We then introduce methods for determining 3D thermochemical structures of the upper mantle. The inverse problem is treated as a multi‐task evaluation process and solved using advanced stochastic optimizing techniques. Estimated uncertainties of the resultant thermochemical models are obtained simultaneously for error analysis. The proposed forward modeling and inversion techniques are validated using synthetic data sets in both forward and inversion circumstances. Limitations and further developments are discussed in the subsequent concluding remarks.