3D finite-element modeling of Earth induced electromagnetic field and its potential applications for geomagnetic satellites

The accumulated large amount of satellite magnetic data strengthen our capability of resolving the electrical conductivity of Earth's mantle. To invert these satellite magnetic data, accurate and efficient forward modeling solvers are needed. In this study, a new finite-element based forward modeling solver is developed to accurately and efficiently compute the induced electromagnetic field for a realistic 3D Earth. Firstly, the nodal-based finite element method with linear shape function on tetrahedral grid is used to assemble the final system of linear equations for the magnetic vector potential and electric scalar potential. The FGMRES solver with algebraic multigrid (AMG) preconditioner is used to quickly solve for the final system of linear equations. The weighted moving least-square method is employed to accurately recover the electromagnetic field from the numerical solutions of magnetic vector and electric scalar potentials. Furthermore, a local mesh refinement technique is employed to improve the accuracy of estimated electromagnetic field. At the end, two synthetic models are used to verify the accuracy and efficiency of our newly developed forward modeling solver. A realistic 3D Earth model is used to simulate the induced magnetic field at 450 and 200 km altitudes which are the planned flying altitudes of Macau's geomagnetic satellites. The simulation indicates that (1) amplitude of the mantle-induced magnetic field can reach 10-30 nT at 450 km altitude, which is 10-30% of the primary magnetic field. The induced magnetic field at 200 km altitude has larger amplitudes. These mantle-induced magnetic fields can be measured by Macau geomagnetic satellites; (2) amplitude of the ocean-induced magnetic field can reach 5-30 nT at satellite altitudes, which needs to be carefully considered in the interpretation of satellite magnetic data. We are confident that our newly developed forward modeling solver will become a key tool for interpreting satellite magnetic data.