基于双二次插值的2.5维FCSEM有限元正演模拟

Finite element forward modeling of 2.5-D FCSEM based on biquadratic interpolation

首先给出2.5维频率域可控源电磁的有限元方程,并详细推导基于矩形剖分及双二次插值的有限元方程的刚度矩阵的求解过程;接着重点研究波数的选取并得到一组精度较高的波数选取方案;然后利用本文基于双二次插值的有限元算法对一个均匀半空间模型进行模拟计算,并将计算结果与解析解对比,验证本文算法的正确性;最后对2个二维地电模型进行有限元模拟,分别得到TE及TM模式下的视电阻率及相位等值线断面图,通过对比分析可知模拟结果均能在不同程度上反映出异常体,从而进一步说明本文算法能够对2.5维频率域可控源电磁进行有效地模拟。

Finite element equations were given for 2.5-D frequency domain controlled-source electromagnetic （FCSEM）, and the solving process of stiff matrix of finite equations was explained, based on rectangle meshing and biquadratic interpolation. The chosen schedule of wave number was researched and a high precision wave number select scheme was reached. Using this algorithm to compute for a homogenous half space model, comparison results between analytic solution and numerical solution verified the correctness of this algorithm. Finally, two 2-D geo-electric models were computed, and the contour maps both for apparent resistivity and phase of TE and TM mode were obtained. The results show that the forward modeling results can reflect anomaly on different levels, which furtherly verifies the effectiveness of this algorithm modeling for 2.5-D FCSEM.