Numerical accuracy of magnetotelluric modeling: A comparison of finite difference approximations

To solve for the induced electromagnetic fields in a conductive medium the quasi-static Maxwell's equations may be reduced to a second order elliptic system, formulated in terms of either the electric or magnetic vector fields. We show with 1-D and 3-D numerical experiments that solutions obtained from equations formulated in terms of the electric fields are less sensitive to grid resolution than those obtained from the magnetic formulation. On a fine enough mesh, solutions from both approaches are nearly identical, while on coarser meshes solutions form the electric field formulation tend to be closer to exact solutions (where available), or fully converged fine mesh solutions.