三维广域电磁法自适应有限元正演  

Adaptive finite element forward modeling for three⁃dimensional wide⁃field electromagnetic method

作　　者：周峰[1,2] 徐锦通 张志勇 蓝泽鸾[1,2] 陈辉[1,2] 汤洪志 ZHOU Feng;XU Jintong;ZHANG Zhiyong;LAN Zeluan;CHEN Hui;TANG Hongzhi(State Key Laboratory of Nuclear Resources and Environment,East China University of Technology,Nanchang,Jiangxi 330013,China;Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province,Nanchang,Jiangxi 330013,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),Ministry of Education,Changsha,Hunan 410083,China)

机构地区：[1]东华理工大学核资源与环境国家重点实验室,江西南昌330013 [2]江西省防震减灾与工程地质灾害探测工程研究中心,江西南昌330013 [3]中南大学有色金属成矿预测与地质环境监测教育部重点实验室,湖南长沙410083

出　　处：《石油地球物理勘探》2023年第4期1017-1029,共13页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目“基于A‑φ势三维CSEM高阶自适应有限元正演”(42004061);江西省自然科学基金项目“频率域电磁法三维快速正反演研究及统一平台建设”(20204BCJL23058);江西省教育厅科学技术研究项目“花岗岩型铀矿的三维可控源电磁法反演研究”(GJJ2200749);自然资源部地球物理电磁法探测技术重点实验室开放基金项目“深部井巷频率聚焦观测技术有限元研究”(KLGEPT202004)联合资助。

摘　　要：为了进一步提高广域电磁法正演求解精度,采用基于电流密度法向连续为依据的后验误差估计策略的自适应有限元技术,实现了三维广域电磁法正演模拟。首先,从麦克斯韦方程出发,推导了可控场源满足的电场方程,采用非结构四面体网格的矢量有限元技术对电场方程进行离散,从而形成大型稀疏复线性方程组;其次,设计电流密度法向连续的后验误差估计策略,并将其融入大型稀疏复线性有限元方程组,实现了高精度三维广域电磁法正演计算;最后,采用一种优化Brent‑Dekker求根算法,提高广域视电阻率计算的稳定性,并利用层状介质模型验证了自适应算法的正确性,同时设计了典型的地形和球状地电模型,分析广域电磁响应特征。研究结果表明,自适应有限元法能够避免人为设计网格带来的低效率问题,通过对重点区域进行局部网格加密提升正演模拟精度;同时,在同等收发距情况下,广域电磁法相比可控源音频大地电磁(CSAMT)具有更大勘探深度与勘探范围,受非平面波的影响更小。In order to improve the solving accuracy of wide‑field electromagnetic method forward modeling,an adaptive finite element technique of a posterior error estimation strategy based on normal continuity of current density is used to realize three‑dimensional(3D)wide‑field electromagnetic method forward modeling.Firstly,based on Maxwell’s equations,the electric field equations satisfied by the controlled field source are derived.The vector finite element technique with unstructured tetrahedral meshes is used to discretize the electric field equations,which results in large and sparse complex linear equations.Then,a posterior error estimation strategy based on normal continuity of current density is designed and incorporated into large and sparse complex linear finite element equations,and a highprecision 3D wide‑field electromagnetic method forward calculation is achieved.Finally,an optimized Brent‑Dekker root‑finding algorithm is used to improve the stability of wide‑field apparent resistivity,and the correctness of the adaptive algorithm is verified by using a layered media model.At the same time,typical terrain and spherical geo‑electric models are designed to analyze the response characteristics of the wide‑field electromagnetic method.The results show that the adaptive finite element method can reduce the low efficiency caused by artificial mesh design and improve the accuracy of forward modeling by mesh refinement in key regions.In addition,compared with CSAMT(controlled source audiofrequency magnetotellurics),the wide‑field electromagnetic method has a larger exploration depth and range and is less affected by non‑plane waves under the same transmit/receive distance.

关 键 词：广域电磁法 自适应有限元 非结构化网格 正演模拟 

分 类 号：P631[天文地球—地质矿产勘探]