On the relation between Moho and sub-crustal stress induced by mantle convection

Abstract

The sub-crustal stress components due to mantle convection have a direct relation with the spherical harmonic coefficients of the Earth's disturbing potential like those of the Moho model, developed by the Vening–Meinesz–Moritz theory. In this paper, the relation between the stress components and the global and local models of Moho is mathematically developed in three different ways. Here, we present the S function (S) with a numerical differentiation approach to generate the stress components and we show that its spherical harmonic series is convergent to a degree of about 600 based on a mean global Moho depth of 23 km. An integral approach is developed for integration of a local Moho model for the stress recovery, but the kernels of this integral are not likely to be convergent and should be generated by their spectral forms to a limited degree. Another method is developed based on integral inversion, which is free of any mathematical problem and suitable for recovering S from an existing model of Moho. Our numerical presentation shows that the stress has a good agreement with the tectonic boundaries and the places at which the curvature of the Moho surface changes.