基于迭代有限元法的大地电磁二维正演  

Study of the magnetotelluric 2D forward based on the iterative finite element method

作　　者：王天意 侯征 杨进[4] 王万平 刘国辉 何胜 WANG TianYi;HOU Zheng;YANG Jin;WANG WanPing;LIU GuoHui;HE Sheng(Key Laboratory of Intelligent Detection and Equipment for Underground Space of Beijing-Tianjin-Hebei Urban Agglomeration,Ministry of Natural Resources,Hebei GEO University,Shijiazhuang 050031,China;Hebei Key Laboratory of Strategic Critical Mineral Resources,Hebei GEO University,Shijiazhuang 050031,China;School of Earth Sciences,Hebei GEO University,Shijiazhuang 050031,China;School of Geophysics and Information Technology,China University of Geosciences(Beijing),Beijing 100010,China;Qinghai 906 Engineering Survey and Design Institute Co.,Ltd.,Xining 810000,China)

机构地区：[1]京津冀城市群地下空间智能探测与装备重点实验室,石家庄050031 [2]河北省战略性关键矿产资源重点实验室,石家庄050031 [3]河北地质大学地球科学学院,石家庄050031 [4]中国地质大学(北京)地球物理与信息技术学院,北京100010 [5]青海九零六工程勘察设计院有限责任公司,西宁810000

出　　处：《地球物理学进展》2023年第1期328-336,共9页Progress in Geophysics

基　　金：国家重点研发计划项目“综合航空物探探测系统集成与方法技术示范研究”(2017YFC0602201);河北省自然科学基金项目“大地电磁三维非线性反演新技术研究”(D2018403090);青海省环境地质勘查局科技项目“青海省东部城镇区地下热水资源勘查地球物理方法试验研究”(青环地局[2021]43号)联合资助。

摘　　要：合理的模型剖分方案是影响大地电磁正演效率的一个重要因素,经典有限元算法为满足控制方程的无穷远边界条件,会在较大的计算空间内进行网格剖分,虽在边界区可以按等比例进行扩展,但依然会形成较高阶的线性方程组,在求解时计算效率较低.针对上述问题,本文开展了基于迭代有限元算法的大地电磁二维正演研究,首先阐述了迭代有限元算法的基本思想及实现过程,建立了基于迭代有限元算法的大地电磁正演模型;其次,结合理论模型的试算,通过与解析解及经典有限元算法的计算结果进行对比分析,验证了迭代有限元算法的准确性及鲁棒性;最后,分析了算法中不同参数对正演精度的影响.结果表明基于迭代有限元算法的大地电磁正演具有计算时间短,占用内存低,能更好的满足远边界条件的优点,可有效提高大地电磁的正演效率,也为后续的反演提供新思路.For the finite element method,a model division is one of the main factors affecting the efficiency of the Magnetotelluric(MT)forward calculation.The grid is usually divided into a sizeable computational space to satisfy the far boundary condition of the governing equation for the classical finite element method.Although the boundary region can be expanded in equal proportion,high-order linear equations are still formed,resulting in the low efficiency of forwarding calculation.Aiming at this problem,2D MT forward modeling was carried out based on the Iterative Finite Element Method(IFEM).The main idea for the boundary division is to divide the underground computing space into the inner and outer regions.The inner region is defined as the simulation region containing abnormal targets,and the traditional structured grid is used for subdivision.The outer zone is set up to satisfy the far boundary condition,and the order of the outer zone stiffness matrix can be reduced by using a specially designed ring band partition and iterative elimination.Finally,the internal and external zone matrices are combined to form a low-order total stiffness matrix to improve the forward efficiency.We illustrated the basic idea and realization process of IFEM,and established an MT forward model based on IFEM.The accuracy and robustness of the IFEM were verified by comparing the results of analytical and theoretical solutions for the 1D layered model and the 2D low-resistance model.Furthermore,the influence of different parameter values on the forward results was analyzed to further evaluate the performance of the IFEM.The results show that the 2D MT forward modeling based on the IFEM can better satisfy the far boundary condition,which effectively improves the computational efficiency of 2D MT forward modeling and provide new ideas for the subsequent inversion.

关 键 词：大地电磁 迭代有限元法 二维正演 

分 类 号：P631[天文地球—地质矿产勘探]