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.

大地电磁（MT）法是一种重要的地球物理电磁感应勘探工具，通过适当的反演程序，我们可以对地球的电导结构进行成像。可靠的反演程序需要迭代调用求解地球电磁感应方程的前向建模求解器。在这项研究中，提出了一种用于二维 (2D) MT 有限元建模的新型混合亥姆霍兹-卷曲公式系统。在电导率较小的空气空间中，使用表现良好的亥姆霍兹方程来表示电磁场的传播。在电导率为正值的地球域中，良好的卷曲-卷曲电磁方程用于表示电磁场的感应和传播行为。在空气-地球界面上，对于任意表面地形，电磁场的连续性条件被强制执行以保证解的唯一性。几个具有包含地形的简单和复杂地电结构的合成模型用于验证和测试新开发的混合亥姆霍兹-卷曲公式系统的性能。数值试验表明，当在空气空间中使用低电导率值和使用低信号频率时，混合亥姆霍兹-卷曲公式系统在数值上是稳定的。混合 Helmholtz-curl 公式系统是开发 2D MT 正向建模求解器的替代算法。几个具有包含地形的简单和复杂地电结构的合成模型用于验证和测试新开发的混合亥姆霍兹-卷曲公式系统的性能。数值试验表明，当在空气空间中使用低电导率值和使用低信号频率时，混合亥姆霍兹-卷曲公式系统在数值上是稳定的。混合 Helmholtz-curl 公式系统是开发 2D MT 正向建模求解器的替代算法。几个具有包含地形的简单和复杂地电结构的合成模型用于验证和测试新开发的混合亥姆霍兹-卷曲公式系统的性能。数值试验表明，当在空气空间中使用低电导率值和使用低信号频率时，混合亥姆霍兹-卷曲公式系统在数值上是稳定的。混合 Helmholtz-curl 公式系统是开发 2D MT 正向建模求解器的替代算法。