Two-dimensional magnetotelluric finite element modeling by a hybrid Helmholtz-curl formulae system

The magnetotelluric (MT) method is an important geophysical electromagnetic induction exploration tool, with proper inversion routines, we can image the electrical conductivity structures of the Earth. A reliable inversion routine needs to iteratively call forward modeling solvers which solve the electromagnetic induction equations in the Earth. In this study, a novel hybrid Helmholtz-curl formulae system is presented for two-dimensional (2D) MT finite element modeling. In the air space with small values of conductivities, the well-behaved Helmholtz equation is used to represent the propagation of the electromagnetic field. In the Earth domain with positive values of conductivities, the well-behaved curl-curl electromagnetic equation is used to represent the inductive and propagating behaviors of the electromagnetic field. On the air-Earth interface, with arbitrary surface topographies, continuity conditions of the electromagnetic fields are enforced to guarantee the solution's uniqueness. Several synthetic models with both simple and complex geo-electrical structures incorporating topographies are used to verify and test the performance of the newly developed hybrid Helmholtz-curl formulae system. Numerical tests show that the hybrid Helmholtz-curl formulae system is numerically stable when using low conductivity values in the air space and using low signal frequencies. The hybrid Helmholtz-curl formulae system is an alternative algorithm to develop 2D MT forward modeling solvers.