被动源电磁测深三维有限元数值模拟

Three dimensional finite element modeling for passive source electromagnetic sounding method

从基于电场的双旋度方程出发,针对被动源电磁测深法中的三维正演问题进行了有限元数值模拟。首先推导了被动源电磁法中电场所满足的矢量波动方程,然后从变分原理出发,得到其变分形式,通过有限元分析,最后形成大型复系数线性方程组。采用LDLT预处理共轭梯度法,降低了矩阵的条件数,提高了解方程组的速度。建立了一个典型的3层地电模型,得到了地表电磁场分布及其主测线视电阻率和阻抗相位,视电阻率平均相对误差为2.06%,阻抗相位平均相对误差为0.734%,满足实际要求,同时也验证了程序的正确性。

The vector wave equation about electric field for the passive source electromagnetic method is derived,and then,starting from the variational principle and by the final adoption of the finite element analysis,a large and complex coefficient equations are formed.Incomplete preconditioner LDLT and conjugate gradient method are introduced to accelerate the convergence rate of solving equations.The surface electromagnetic field distribution and the apparent resistivity and apparent phase are obtained.The results show that the average relative error of the apparent resistivity is 2.06% and the average relative error of apparent phase is 0.734%.They meet the actual requirements.At last,the electromagnetic response of the conductive anomaly body of homogenous half space is computed and the apparent resistivity curves of two modes are analyzed.