基于吸收边界条件的瞬变电磁法三维矢量有限元快速正演

张永超, 王光杰, 李宏杰, 廉玉广, 李文, 邱浩, 牟义. 2021. 基于吸收边界条件的瞬变电磁法三维矢量有限元快速正演. 地球物理学报, 64(3): 1106-1118, doi: 10.6038/cjg2021N0137
引用本文: 张永超, 王光杰, 李宏杰, 廉玉广, 李文, 邱浩, 牟义. 2021. 基于吸收边界条件的瞬变电磁法三维矢量有限元快速正演. 地球物理学报, 64(3): 1106-1118, doi: 10.6038/cjg2021N0137
ZHANG YongChao, WANG GuangJie, LI HongJie, LIAN YuGuang, LI Wen, QIU Hao, MOU Yi. 2021. Efficient 3D vector finite element modeling for TEM based on absorbing boundary condition. Chinese Journal of Geophysics (in Chinese), 64(3): 1106-1118, doi: 10.6038/cjg2021N0137
Citation: ZHANG YongChao, WANG GuangJie, LI HongJie, LIAN YuGuang, LI Wen, QIU Hao, MOU Yi. 2021. Efficient 3D vector finite element modeling for TEM based on absorbing boundary condition. Chinese Journal of Geophysics (in Chinese), 64(3): 1106-1118, doi: 10.6038/cjg2021N0137

基于吸收边界条件的瞬变电磁法三维矢量有限元快速正演

  • 基金项目:

    煤炭科学技术研究院科技发展基金(2018CX06),国家自然科学基金青年科学基金(51704162),国家科技重大专项(2016ZX05045001-004)资助

详细信息
    作者简介:

    张永超, 男, 1983年生, 助理研究员, 主要从事瞬变电磁法正反演研究及应用. E-mail: 120460817@qq.com

    通讯作者: 王光杰, 男, 1966年生, 中国科学院地质与地球物理研究所副研究员, 主要从事电磁法勘探研究和应用工作. E-mail: gjwang@mail.iggcas.ac.cn
  • 中图分类号: P631

Efficient 3D vector finite element modeling for TEM based on absorbing boundary condition

More Information
  • 瞬变电磁法的三维有限元正演通常采用齐次边界条件,为满足该边界条件,需要构建较大尺寸的模型,这降低了正演问题的求解速度.针对该问题,本文采用吸收边界条件代替齐次边界条件,以缩小模型体积,加快正演速度:首先,从时间域麦克斯韦方程组出发,推导了基于库伦规范的矢量势的微分控制方程,结合一阶吸收边界条件推导了相应的的弱形式方程;在此基础上采用一阶四面体矢量单元进行单元分析、Newmark法进行时间离散,实现了瞬变电磁法的快速三维正演.通过均匀半空间模型的解析解,H型地电断面的CR1Dmod解和相应模型有限元解的对比,验证了本文算法的正确性.均匀半空间模型分别采用吸收边界条件和齐次边界条件的正演结果对比表明:吸收边界条件确实可以提高三维正演的精度或者缩小模型尺寸、加快计算速度.

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  • 图 1 

    四面体矢量单元的节点和棱边示意图

    Figure 1. 

    Sketch map of nodes and edges in a tetrahedral vector unit

    图 2 

    发射回线示意图

    Figure 2. 

    Sketch map of transmitter loop

    图 3 

    电流关断波形

    Figure 3. 

    Waveform of the turn-off current

    图 4 

    均匀半空间数值解及其相对误差(σ=0.01 S·m-1, 6 km×6 km×6 km)

    Figure 4. 

    Numerical solution and relative errors of homogeneous half-space (σ=0.01 S·m-1, 6 km×6 km×6 km)

    图 5 

    均匀半空间数值解及其相对误差(σ=0.01 S·m-1, 10 km×10 km×10 km)

    Figure 5. 

    Numerical solution and relative errors of homogeneous half-space (σ=0.01 S·m-1, 10 km×10 km×10 km)

    图 6 

    H型地电断面的有限元解和CR1Dmod解及其相对误差

    Figure 6. 

    FEM solution and CR1Dmod solution of H type geoelectric section and their relative errors

    图 7 

    水平低阻异常体模型示意图

    Figure 7. 

    Sketchmap of horizontal low resistivity anomalous body model

    图 8 

    O点不同模型的瞬变电磁响应

    Figure 8. 

    TEM response of different models at point O

    图 9 

    水平低阻异常体的瞬变电磁响应时间切片

    Figure 9. 

    Time slice of TEM response of horizontal low resistivity anomalous body model

    图 10 

    XZ平面0.05~0.06 ms电流密度变化

    Figure 10. 

    Change of current density in XZ plane from 0.05 ms to 0.06 ms

    图 11 

    倾斜低阻异常体模型示意图

    Figure 11. 

    Sketch map of sloping low resistivity anomalous body model

    图 12 

    O点水平和倾斜低阻异常体模型的瞬变电磁响应

    Figure 12. 

    TEM response of models of horizontal and sloping low resistivity anomalous body at point O

    图 13 

    y=0线瞬变电磁多测道剖面

    Figure 13. 

    TEM multichannel profile of y=0 line

    图 14 

    倾斜低阻异常体的瞬变电磁响应时间切片

    Figure 14. 

    Time slice of TEM response of sloping low resistivity anomalous body model

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出版历程
收稿日期:  2019-04-04
修回日期:  2021-01-27
上线日期:  2021-03-10

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