瞬变电磁三维FDTD正演多分辨网格方法

孙怀凤, 程铭, 吴启龙, 米德才, 李术才, 李貅, 李敦仁, 李凯, 骆俊晖. 2018. 瞬变电磁三维FDTD正演多分辨网格方法. 地球物理学报, 61(12): 5096-5104, doi: 10.6038/cjg2018L0659
引用本文: 孙怀凤, 程铭, 吴启龙, 米德才, 李术才, 李貅, 李敦仁, 李凯, 骆俊晖. 2018. 瞬变电磁三维FDTD正演多分辨网格方法. 地球物理学报, 61(12): 5096-5104, doi: 10.6038/cjg2018L0659
SUN HuaiFeng, CHENG Ming, WU QiLong, MI DeCai, LI ShuCai, LI Xiu, LI DunRen, LI Kai, LUO JunHui. 2018. A multi-scale grid scheme in three-dimensional transient electromagnetic modeling using FDTD. Chinese Journal of Geophysics (in Chinese), 61(12): 5096-5104, doi: 10.6038/cjg2018L0659
Citation: SUN HuaiFeng, CHENG Ming, WU QiLong, MI DeCai, LI ShuCai, LI Xiu, LI DunRen, LI Kai, LUO JunHui. 2018. A multi-scale grid scheme in three-dimensional transient electromagnetic modeling using FDTD. Chinese Journal of Geophysics (in Chinese), 61(12): 5096-5104, doi: 10.6038/cjg2018L0659

瞬变电磁三维FDTD正演多分辨网格方法

  • 基金项目:

    国家自然科学基金(41404104),广西科技基地和人才专项(桂科AD17129047)和山东省重点研发计划(2018GSF117020)联合资助

详细信息
    作者简介:

    孙怀凤, 男, 1982年生, 博士, 副教授, 博士生导师, 主要从事瞬变电磁正反演方面的教学与科研工作.E-mail:sunhuaifeng@gmail.com

  • 中图分类号: P631

A multi-scale grid scheme in three-dimensional transient electromagnetic modeling using FDTD

  • 瞬变电磁三维时域有限差分(FDTD)正演的网格剖分受最小网格尺寸、时间步长、边界条件、目标尺寸、模型尺寸等的影响,结构化网格一直存在最小网格尺寸受限于异常目标尺寸的矛盾;尽管非均匀网格能够在保证模型尺寸的前提下尽可能的降低网格数量,但由于Yee网格结构的限制,非均匀网格不能无限制的扩大单一方向的尺寸,这是为了避免边界网格区域出现长宽比过大的畸形网格,影响计算精度甚至导致结果发散.在非均匀网格剖分的基础上,本文提出了瞬变电磁三维FDTD正演的多尺度网格方法,即首先使用较大尺寸的粗网格进行第一次剖分,然后在希望加密的区域进行二次剖分,使计算域中包含粗、细两套网格.尽管细网格包含在粗网格内部,但其具有Yee网格的全部属性,因而可以在网格中设置不同的电性参数模拟不同形状的目标.基于Maxwell方程组推导了细网格内电场和磁场的迭代公式,基于泰勒展开给出了设置粗、细网格后产生的内部边界条件,使电磁场的传播在粗、细网格和时间步进上得到统一.采用均匀半空间中包含三维低阻异常的经典模型和三维接触带复杂模型进行精度验证,发现多分辨网格方法计算结果满足精度要求.使用"L"型异常模型计算采用多分辨网格方法和不采用多分辨网格的传统FDTD方法对比计算效率,发现多分辨网格算法能够显著提高计算效率,并能够保证计算精度.

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  • 图 1 

    FDTD网格长宽比示意图

    Figure 1. 

    The aspect ratio of FDTD grid

    图 2 

    Yee晶胞与多分辨网格Yee晶胞

    Figure 2. 

    Yee cell and multi-resolution grid Yee cell

    图 3 

    多分辨网格的边界处理

    Figure 3. 

    Boundary treatment of multi-resolution grid

    图 4 

    时间域与空间域统一流程图

    Figure 4. 

    Unified flow chart of time-domain and space-domain

    图 5 

    粗-细网格及电阻率取值示意图

    Figure 5. 

    Diagram of coarse and fine grid and the resistivity distribution

    图 6 

    多分辨网格方法剖分模型局部示意图

    Figure 6. 

    Localization diagram of multi-resolution grid method

    图 7 

    多分辨网格算法精度对比图

    Figure 7. 

    Computing precision comparison chart of multi-resolution grid method

    图 8 

    三维模型及计算结果对比(Li et al., 2017; Zhou et al., 2018)

    Figure 8. 

    3D model and the comparison results (Li et al., 2017; Zhou et al., 2018)

    图 9 

    模型主视图(a)和俯视图(b)

    Figure 9. 

    Front view (a) and top view (b) of the model

    图 10 

    三种网格剖分示意图

    Figure 10. 

    Diagram of three meshing grid

    图 11 

    多分辨网格不同剖分个数计算结果对比图

    Figure 11. 

    Calculation results comparison figure of different multi-grid number

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出版历程
收稿日期:  2017-10-19
修回日期:  2018-03-28
上线日期:  2018-12-05

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