基于矢量位和标量位的空间波数混合域电磁三维正演模拟  

Forward modeling of 3D electromagnetic problems using vector and scalar potentials in a mixed space-wavenumber domain

作　　者：戴世坤[2,3] 赵东东 李昆[2,3] 张钱江[4] 凌嘉宣[2,3] 陈轻蕊[2,3] DAI ShiKun;ZHAO DongDong;LI Kun;ZHANG QianJiang;LING JiaXuan;CHEN QingRui(School of Electronic Engineering and Automation,Guilin University of Electronic Technology,Guilin 541004,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring,Ministry of Education,Central South University,Changsha 410083,China;School of Geosciences and Info-physics,Central Sounth University,Changsha 410083,China;College of Earth Sciences,Guilin University of Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学电子工程与自动化学院,桂林541004 [2]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 [3]中南大学地球科学与信息物理学院,长沙410083 [4]桂林理工大学地球科学学院,桂林541004

出　　处：《地球物理学报》2022年第1期404-416,共13页Chinese Journal of Geophysics

基　　金：国家重点研发计划专项(2018YFC0603602);广西自然科学基金创新研究团队项目(GXNSFGA380004);自然资源部中国地质调查局项目(DD20190301)联合资助.

摘　　要：高效、高精度电磁三维数值模拟是制约大规模电磁数据精细化三维反演成像、人机交互定量解释的核心问题.针对一问题,本文提出一种基于矢量位和标量位的空间波数混合域电磁场三维数值模拟方法.该方法利用沿水平方向的二维傅里叶变换将空间域矢量位和标量位耦合偏微分方程组转换为波数之间相互独立的常微分耦合方程组,将一个大规模三维问题分解为多个一维小问题,具有高度并行性,由此大大减少了计算量和存储量;保留垂向为空间域,浅层网格剖分适当加密,深层网格剖分适当稀疏,有效兼顾了计算精度与计算效率;采用有限单元法求解不同波数的常微分方程,充分利用追赶法求解定带宽线性方程组的高效性进一步提高数值模拟效率.在模型算例中,设计棱柱体模型验证了本文方法的正确性、计算精度和计算效率.数值试验结果表明本文方法具有数值精度高、并行度高、占用内存小、计算效率高的特性,比传统有限单元法三维数值模拟方法计算效率高1~2个数量级,且网格剖分规模越大,该方法计算效率优势越明显.Fast and accurate 3D electromagnetic(EM)forward modeling is the core problem of inversion and quantitative interpretation for field data.The computation and memory requirements of practical numerical modeling in space domain are enormous,which leads to the difficulty of deploying highly efficient and detailed inversions for large-scale models with complex geology.A new 3D EM forward modeling in a mixed space-wavenumber domain is proposed to mitigate the difficulty.By performing a two-dimensional Fourier transform along two horizontal directions,three-dimensional partial differential equations in the spatial domain are transformed into a group of independent 1D differential equations engaged with different wave numbers.Importantly,the computation and memory requirements of modeling are greatly reduced by this method,and the independent differential equations are highly parallel among different wave numbers.The method preserves the vertical component in the space domain,thus,a mesh for modeling can be fine at shallow depth and coarse at deep depth.Generally,the new method takes into account of both the calculation accuracy and efficiency.Finite element method is used to solve the transformed differential equations with different wave numbers,moreover the efficiency of solving fixed bandwidth linear equations is further improved by a chasing method.In a synthetic test,a model with prism-shaped anomaly is used to verify the accuracy and reliability of the proposed algorithm by the comparison between the proposed and classical IE solutions.Furthermore,The numerical experiments indicate that the proposed method not only has high accuracy,but also has charracteristics of high parallelism,small memory consumption and fast calculation speed.The calculation efficiency of about 1~2 orders of magnitude higher than the traditional 3D modeling by using FEM are obtained,and the larger the mesh size of the model,the more obvious the efficiency advantage of the proposed algorithm.

关 键 词：空间波数混合域 电磁 三维 数值模拟 

分 类 号：P631[天文地球—地质矿产勘探]