基于二次场的二维大地电磁有限元法数值模拟

Secondary Field-Based Two-Dimensional Magnetotelluric Numerical Modeling by Finite Element Method

引入基于计算二次场响应的方法,将其用于二维大地电磁数值模拟.导出了二维大地电磁二次场的表达式,在使用有限元法解偏微分方程时,利用二次场偏微分方程与总场偏微分方程的相似性,直接采用总场法中的系数矩阵作为二次场的合成矩阵.将根据此原理所编制的二次场有限元法模拟软件,对几个典型模型进行了试算,并与传统总场模拟法作了比较分析.结果表明,直接计算二次场的结果精度更高,更接近真实解.

This paper presents an efficient method named secondary finite element method （FEM） for two-dimensional magnetotelluric numerical modeling, which provides solution for secondary variations in the field, To deduce the rationale of the new procedure, the total field is divided into primary and secondary field. Only the secondary field equations which need to be solved for the primary field can be obtained easily, The equations of the secondary field can be solved effortlessly by finite element method when the boundary conditions are simple. The effect of resolution is analysed to study the response of synthetic model by the secondary field and a comparison is conducted between the results of secondary FEM and the total field FEM. It is concluded that the new arithmetic of numerical modeling can be used to derive more precise results in calculating the secondary field and is almost not affected by the density of mesh. It is expected to be used widely for the inversion of magnetotelluric data.