基于有限元法的广域电磁法三维NLCG反演算法研究  

Research on Three-Dimensional NLCG Inversion Algorithm of Wide Field Electromagnetic Method Based on Finite Element Method

作　　者：徐星 

机构地区：[1]中南大学地球科学与信息物理学院,湖南 长沙

出　　处：《地球科学前沿（汉斯）》2023年第4期380-393,共14页Advances in Geosciences

摘　　要：广域电磁法(wide field electromagnetic method, WFEM)在资源勘探领域发挥着越来越重要的作用,但数据解释目前仍以一维二维反演为主,为了适应复杂的地质条件,提高广域电磁法的数据处理精度,本文开发了基于矢量有限元的三维非线性共轭梯度反演算法。把矢量有限元法用于广域电磁法三维正演,采用直接求解器Pardiso对大型稀疏线性方程组进行求解,使用非线性共轭梯度法(NLCG)进行三维反演,反演计算中,采用伴随正演隐式求取雅可比矩阵与向量的乘积,通过对多个地电模型的合成数据反演,反演结果能够很好地重现理论模型的电性结构,证明了本文算法的有效性。Wide field electromagnetic method (WFEM) plays an increasingly important role in the field of resource exploration, but data interpretation is still mainly based on one-dimensional and two-dimensional inversion, in order to adapt to complex geological conditions and improve the data processing accuracy of wide-area electromagnetic method, this paper develops a three-di- mensional nonlinear conjugate gradient inversion algorithm based on vector finite elements. The vector finite element method is used for the three-dimensional forward evolution of the wide-area electromagnetic method, the large sparse linear equation system is solved by the direct solver Pardiso, and the nonlinear conjugate gradient method (NLCG) is used for three-dimensional inversion, and in the inversion calculation, the product of the Jacobian matrix and the vector is implicitly obtained by adjoint forwarding, and the inversion results can reproduce the electrical structure of the theoretical model well by inverting the synthetic data of multiple geoelectric models, which proves the effectiveness of the proposed algorithm.

关 键 词：广域电磁法 矢量有限元法 非线性共轭梯度法 三维反演 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]