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物探与化探  2021, Vol. 45 Issue (3): 726-736    DOI: 10.11720/wtyht.2021.1539
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
三维磁场有限元—无限元耦合数值模拟
郭楚枫(), 张世晖(), 刘天佑
中国地质大学(武汉) 地球物理与空间信息学院,湖北 武汉 430074
3D magnetic field forward modeling by finite-infinite element coupling method
GUO Chu-Feng(), ZHANG Shi-Hui(), LIU Tian-You
Institute of Geophysics and Geomatics, China University of Geosciences(Wuhan), Wuhan 430074,China
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摘要 

利用传统有限单元法在有限空间范围内开展三维地球物理场正演模拟时,由于截断边界的影响,会引起局部异常的畸变,影响数值模拟的精度,对该问题通常采用扩边的办法加以解决,但需要的范围较大,从而大大增加运算成本,影响正演模拟效率。本文基于COMSOL Multiphysics软件,在求解域外部边界设置无限元以替代传统边界条件,达到减小计算区域目的。通过孤立球体和组合模型磁场正演模拟,考虑退磁、剩磁及地表起伏条件,与传统有限元方法相比,有限元—无限元耦合算法能够有效克服边界效应,提高计算精度,降低运算量,从而提高了有限单元法正演数值模拟效率。

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郭楚枫
张世晖
刘天佑
关键词 有限元—无限元三维正演磁法勘探COMSOL    
Abstract

Due to the influence of the artificial boundary condition, when the conventional finite element method is used to carry out the forward simulation of the three-dimensional geophysical field in a limited space, local abnormal distortion may occur, which affects the accuracy of the numerical simulation. This problem is usually solved by expanding the edge, but this requires a larger range, which greatly increases the computational cost and affects the efficiency of forward simulation. In this paper, on the basis of COMSOL Multiphysics software, infinite elements are set on the external boundary to replace the traditional boundary conditions so as to reduce the calculation area. Compared with the traditional finite element method, the finite element infinite element coupling method, by setting the isolated sphere and the combined body model and considering the conditions of demagnetization, remanence and surface undulation, can effectively overcome the boundary effect, improve the calculation accuracy and reduce the amount of calculation, thus improving the forward numerical simulation efficiency of the finite element method.

Key wordsfinite-infinite    3D forward modeling    magnetic prospecting    COMSOL
收稿日期: 2020-12-01      出版日期: 2021-07-27
:  P631  
基金资助:雄安新区深层地热资源探测评价技术示范项目(2018YFC0604303);深部资源预测系统技术研究与示范项目(2017YFC0601504)
通讯作者: 张世晖
作者简介: 郭楚枫(1996-),男,在读硕士研究生,研究方向为重磁勘探。Email: gcf2013@cug.edu.cn
引用本文:   
郭楚枫, 张世晖, 刘天佑. 三维磁场有限元—无限元耦合数值模拟[J]. 物探与化探, 2021, 45(3): 726-736.
GUO Chu-Feng, ZHANG Shi-Hui, LIU Tian-You. 3D magnetic field forward modeling by finite-infinite element coupling method. Geophysical and Geochemical Exploration, 2021, 45(3): 726-736.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2021.1539      或      https://www.wutanyuhuatan.com/CN/Y2021/V45/I3/726
Fig.1  非均匀介质分布(改自徐世浙,1994)
Fig.2  三维无限元映射(改自汤井田等,2010)
Fig.3  球体模型及网格剖分示意(蓝色为球体模型,红色直线代表测线,黄色为观测平面范围)
Fig.4  不同方法正演的球体平面ΔT磁异常及其平面误差分布
Fig.5  不同方法正演的球体磁异常曲线
Fig.6  绝对误差分布曲线
方法 有限元求
解域边长
/m
网格节
点数
平均网
格间距
/m
占用内存
/GB
计算时间
/s
最大绝
对误差
/nT
均方根
误差
/nT
平均相
对误差
/%
有限元—无限元 200 453751 1.5 4.85 70 73.83 17.49 0.78
传统有限元 200 383250 1.5 4.33 34 837.88 656.69 63.90
传统有限元 300 1255245 1.5 12.06 120 261.82 205.02 20.27
传统有限元 400 2951989 1.5 23.91 240 120.91 86.13 8.41
Table 1  不同算法模型计算效率及误差对比
Fig.7  组合形体模型及网格剖分示意(红色直线代表测线,黄色为观测平面范围)
Fig.8  有限元数值模拟结果及平面误差分布
方法 有限元求解
域边长/m
网格节
点数
平均网格
间距/m
占用内存
/GB
计算时间
/s
最大绝对
误差/nT
均方根误
差/nT
平均相对
误差/%
有限元—无限元 200 134853 5 3.67 109 35.22 12.53 1.68
传统有限元 200 114193 5 3.46 27 704.77 504.73 262.94
传统有限元 400 880751 5 10.98 60 159.25 114.61 18.02
传统有限元 600 2951638 5 28.46 262 98.21 50.32 7.62
Table 2  组合形体计算效率及误差对比
Fig.9  起伏地表模型(黄色为观测面范围)
Fig.10  起伏地形下有限元数值模拟结果及平面误差分布
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