Simulation of Satellite Observations of Induced Magnetic Fields using Scripted Finite Element Methods

Scripted finite element methods allow flexible investigations of the influence of asymmetric external source fields and 3-dimensional (3D) internal electrical conductivity structure in the problem of global geomagnetic depth sounding. Our forward modeling is performed in the time and frequency domains via FlexPDE, a commercial finite element modeling package, and the technique has been validated against known solutions to 3D steady state and time-dependent problems. The induction problem is formulated in terms of the magnetic vector potential and electric scalar potential, and mesh density is managed both explicitly and through adaptive mesh refinement. We investigate the effects of 3D Earth conductivity on both satellite and ground-based magnetic field observations in the form of a geographically varying conductance map of the crust and oceans overlying a radially symmetric core and mantle. This map is used in conjunction with a novel boundary condition based on Ampere's Law to model variable near-surface induction without the computational expense of a 3D crust/ocean mesh and is valid for magnetic signals in the frequency range of interest for satellite induction studies. The simulated external magnetic field is aligned with Earth's magnetic pole, rather than its rotational pole, and increases in magnitude along the Earth/Sun axis. Earth rotates through this field with a period of 24 hours. Electromagnetic c-responses estimated from satellite data under the assumption that the primary and induced fields are dipolar in structure are known to be biased with respect to local time. We investigate the influence of Earth's rotation through the non-uniform external field on these c-responses, to determine whether this can explain the observed local time bias.