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

•A hybrid Helmholtz-curl formulae system is developed for magnetotelluric problems.•This formulae system can deal with arbitrary surface topographies.•It is numerically stable in the air space even at low frequencies. 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.