磁矢量势的全球电磁感应时间域三维有限元正演计算方法  

Three-dimensional time-domain finite-element modeling of global electromagnetic induction based on magnetic vector potential formulation

作　　者：杨聪[1,2,4] 任政勇 陈程[4,5] 姚鸿波 唐旭 汤井田 YANG Cong;REN ZhengYong;CHEN Cheng;YAO HongBo;TANG Xu;TANG JingTian(Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring Ministry of Education,Central South University,Changsha 410083,China;SinoProbe Laboratory,Ministry of Natural Resources,Beijing 100094,China;Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration,Changsha 410083,China;School of Geosciences and Info-physics of Central South University,Changsha 410083,China;Power China Zhongnan Engineering Corporation Limited,Changsha 410014,China)

机构地区：[1]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,长沙410083 [2]自然资源部深地科学与探测技术实验室,北京100094 [3]有色资源与地质灾害探查湖南省重点实验室,长沙410083 [4]中南大学地球科学与信息物理学院,长沙410083 [5]中国电建集团中南勘测设计研究院有限公司,长沙410014

出　　处：《地球物理学报》2024年第5期2015-2028,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(42250102,41830107,42142034,42130810,72088101);中南大学中央高校基本科研业务费专项资金资助(2023ZZTS0730);湖南省科技创新计划(2021RC4055);自然资源部深地科学与探测技术实验室开放课题(SinoProbeLab:202209)联合资助。

摘　　要：全球电磁感应测深方法能获得地球深部电导率结构分布,目前被广泛应用于地球内部结构与热状态研究.地磁台站与地磁卫星观测的电磁感应数据为时间序列信号,在时间域分析全球电磁感应数据,特别是分析频谱极宽的磁暴脉冲响应,具有天然的优势.然而,当前的全球电磁感应数据解释技术一般在频率域进行,缺少时间域中的研究成果.为了弥补缺少时间域全球电磁感应数据解释方法的问题,本文开发了一种基于磁场矢量势的全球电磁感应时间域三维有限元并行正演求解方法,具备高精度快速计算源于地球外部时变电流源的地球感应电磁场时间序列的能力,特别适合于计算与分析频谱极宽的磁暴脉冲电磁感应时变响应.首先,建立基于磁场矢量势的全球电磁感应时间域微分控制方程,结合磁层外部电流源的物理属性建立边界条件和初始条件,从而构建出全球电磁感应时间域初始边界值问题.然后,利用四面体矢量有限元技术和无条件稳定的隐式后退欧拉公式,分别实现磁场矢量势的空间域和时间域离散,进而获得不同时刻的实系数大型有限元线性方程组,借助于高性能并行直接求解器,快速高精度地求解不同时刻的磁场矢量势与感应磁场.最后,利用理论模型验证本文算法的正确性.利用Dst磁暴环电流指数建立的时间域电流源与真实地球三维电性模型,研究"澳科一号"后续卫星200 km轨道对中国和澳大利亚下方地幔转换带高导体的探测能力,结果表明这些地幔转换带异常体在200 km卫星轨道高度能产生明显异常.综上所述,本文开发的时间域全球电磁感应方法不仅具备精确快速计算全球感应电磁场时间序列响应的能力,还能为反演与解释"澳科一号"等我国地磁卫星观测数据提供技术支持.Global electromagnetic(EM)induction method can obtain the distribution of Earth's deep conductivity structure,it has been widely applied in the study of Earth's internal structure and thermal state.EM induction data are recorded as time series signals by geomagnetic observatories and satellites.Therefore,analyzing global EM induction data in the time domain has inherent advantages.However,the current interpretation techniques mainly focus on frequency domain analysis,lacking research results in the time domain.To address this limitation,this study develops a three-dimensional time-domain finite-element parallel forward modeling method for global electromagnetic induction based on magnetic vector potential.This method enables high-precision and fast computation of the time-series EM field induced by time-varying external currents in the Earth,particularly suitable for calculating and analyzing the time-varying responses of broad-spectrum geomagnetic storm pulses.First,the boundary value problem for time-domain global EM induction was derived by combining the magnetic field vector potential and the physical properties of external current sources in the magnetosphere.Then,the tetrahedral vector finite-element method and unconditionally stable implicit backward Euler formula were adopted to discretize the spatial and temporal variations of the magnetic vector potential,resulting in a large-scale system of finite-element linear equations at different time steps.With the help of a high-performance parallel direct solver,we solve the linear equation for the magnetic vector potential and induced magnetic field at different time steps quickly and accurately.Finally,the correctness of the proposed method is verified using theoretical models.Using the time-domain current source established by the geomagnetic storm ring current index(Dst)and realistic three-dimensional electrical conductivity model of the Earth,we studied the detection capability of"Macao Science Satellite 1"for high-conductivity anomalies in the mantle tran

关 键 词：时间域全球电磁感应 矢量有限元法 三维正演 地幔电性结构 

分 类 号：P631[天文地球—地质矿产勘探]