电导率连续变化的线源FCSEM有限元正演模拟

Finite Element Forward Modeling on Line Source of FCSEM for Continuous Conductivity

为了更好地模拟地下介质连续变化及开展连续介质的反演,对二维电导率分块线性变化的线源频率域可控源电磁法进行了有限元正演模拟,在剖分单元内同时对电场及电导率参数线性插值,使电导率参数在剖分单元之间保持连续变化。首先,提出有限元正演模拟的边值问题及变分问题,并详细论述了有限元的剖分、插值、单元分析及总体合成的各个步骤;其次,采用稀疏存储及基于不完全IU分解的BICGSTAB算法求解复系数方程组,节省了内存并提高了计算速度;然后,对一个均匀半空间模型进行模拟,计算结果表明,低频及高频的有限元数值解都与解析解吻合,证明了算法的正确性;最后,对水平层状模型及垂直断层模型进行正演计算,视电阻率及相位的等值线图均较好地反映出了异常体,说明文中算法能够对电导率连续变化的线源可控源电磁法进行有效地模拟。

In order to simulate continuous conductivity of subsurface medium and inverse continuous medium, we worked on the finite element forward modeling on line source of FCSEM （frequency domain controlled-source electromagnetic） for two-dimensional block linear change of conductivity. In each unit, the linear interpolation both for electrical field and conductivity parameter was used, which would keep conductivity changing continuously between each unit. Firstly, boundary value problem and variational problem were given for finite element simulation. And the meshing, interpolation, unit analysis and total synthesis of FEM （finite element method） were discussed in detail. Secondly, sparse storage and BICGSTAB algorithm based on incomplete LU decomposition were used to solve complex equations, which had saved memory and improved compute speed. Then, a homogenous half space model was simulated and its result showed that the FEM numerical solutions of low and high frequency agreed with analytic solutions very well, which proved the correctness of this algorithm. Finally, a horizontal layered model and a vertical fault model were calculated, the contour maps both for apparent resistivity and phase reflected anomaly quite well. All of these had showed this algorithm can simulate the line source of FCSEM for continuous conductivity effectively.