含地形起伏的MT模型非规则四边形FEM正演与反演  

MT finite element method forward modeling and inversion using irregular quadrilateral mesh of steep topography model

作　　者：冯德山[1,2] 刘金宝 王珣 FENG Deshan;LIU Jinbao;WANG Xun(School of Geosciences and Info-Physics,Central South University,Changsha 410083,China;Key Laboratory of Non-ferrous Resources and Geological Detection,Ministry of Hunan Province,Changsha 410083,China)

机构地区：[1]中南大学地球科学与信息物理学院,湖南长沙410083 [2]有色资源与地质灾害探查湖南省重点实验室,湖南长沙410083

出　　处：《中南大学学报（自然科学版）》2018年第3期626-632,共7页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(41574116);中南大学创新驱动项目(2015CX008);中南大学教师研究基金资助项目2014JSJJ001);中南大学升华育英人才计划项目(2012);湖湘青年创新创业平台培养对象共同资助项目(2013)~~

摘　　要：从大地电磁(MT)边值问题满足的变分方程出发,采用非规则四边形网格、双线性插值有限单元法(FEM)开展复杂起伏地形MT模型正演,探讨二维Jacobian变换行列式的计算方法,推导任意非规则四边形单元的插值方式及单元系数矩阵表达式,实现起伏地形MT模型的高精度正演。然后,介绍光滑约束的Tikhonov正则化反演算法,针对反演中正则化参数选取困难的问题,将广泛应用的L-curve法引入反演的正则化参数选取中。研究结果表明:L-curve法的曲线中曲率最大的拐点准确地指示了最优正则化参数;L-curve法选取的最优正则化参数对应的反演结果与原模型所示结果吻合度最高,反演效果最好。Based on the variational problem derived from magnetotelluric(MT)boundary value problems,the finite element method using irregular quadrilateral mesh and bilinear interpolation was used to solve MT forward problem of steep topography model.The detailed calculation of Jacobi transformation matrix was discussed and interpolation method of arbitrary irregular quadrilateral unit and unit coefficient matrix expression was derived which achieved high precision forward of steep topography MT model.Then,the smooth constrained Tikhonov regularization inversion algorithm was introduced.To overcome the difficulty in determination of regularization parameters for MT,L-curve method was used to calculate regularization parameters in MT inversion.The results show that inflection of L-curve can indicate the optimal regularization parameter accurately.Inversion results using optimal regularization parameter calculated by L-curve method is most similar to those of the original model,and better inversion results can be obtained.

关 键 词：大地电磁 非规则四边形网格 L-curve法 正则化约束反演 

分 类 号：P631[天文地球—地质矿产勘探]