Physical properties of the lithospheric and upper mantle’s rock are determined by its composition and the in-situtemperature and pressure conditions; they have been referred to the thermochemical structure as a whole. 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 potentials to map the 3D variations on both of the regional and global scales. In general principle, the Earth’s curvature must be taken into account in both forward and inversion modeling. Techniques for investigation of the thermochemical structure in the spherical coordinates are hereby in need, including forward modeling the geophysical observables, calculating schemes of the thermophysical properties for the lithologies and ambient conditions in upper mantle, effective inversion algorithms, etc., which are more important for the large-scale applications. In this paper, an adaptive meshing architecture based on the tetrahedral mesh are demonstrated 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. Moreover, methodologies for constructing 3D thermochemical models and forward modeling geophysical observations, including an inversion sub-routine that can couple the lithostatic pressure and density variations to forward modeling, are introduced and examined using synthetic datasets in detail. Subsequently, limitations and further developments of the forward modeling techniques are discussed with concluding remarks.

joint inversion,spherical coordinates,thermochemical inversion