Three-dimensional time-domain finite-element modeling of global electromagnetic induction based on magnetic vector potential formulation

Global electromagnetic (EM) induction method can obtain the distribution of Earth's deep conductivity structure, it has been widely applied in the study of Earth's internal structure and thermal state. EM induction data are recorded as time series signals by geomagnetic observatories and satellites. Therefore, analyzing global EM induction data in the time domain has inherent advantages. However, the current interpretation techniques mainly focus on frequency domain analysis, lacking research results in the time domain. To address this limitation, this study develops a three-dimensional time-domain finite-element parallel forward modeling method for global electromagnetic induction based on magnetic vector potential. This method enables high-precision and fast computation of the time-series EM field induced by time-varying external currents in the Earth, particularly suitable for calculating and analyzing the time-varying responses of broad-spectrum geomagnetic storm pulses. First, the boundary value problem for time-domain global EM induction was derived by combining the magnetic field vector potential and the physical properties of external current sources in the magnetosphere. Then, the tetrahedral vector finite-element method and unconditionally stable implicit backward Euler formula were adopted to discretize the spatial and temporal variations of the magnetic vector potential, resulting in a large-scale system of finite-element linear equations at different time steps. With the help of a high-performance parallel direct solver, we solve the linear equation for the magnetic vector potential and induced magnetic field at different time steps quickly and accurately. Finally, the correctness of the proposed method is verified using theoretical models. Using the time-domain current source established by the geomagnetic storm ring current index (Dst) and realistic three-dimensional electrical conductivity model of the Earth, we studied the detection capability of "Macau Science Satellite 1" for high-conductivity anomalies in the mantle transition zone beneath China and Australia. The results show that these mantle transition zone anomalies body can produce significant anomalies at the altitude of 200 km in the satellite's orbit. In summary, the time-domain global EM induction method developed in this article not only can accurately and quickly calculate the global EM induction fields but also provides technical support for inverting and interpreting observation data from China's geomagnetic satellites such as "Macau Science Satellite 1".