三维地电断面电阻率测深有限元数值模拟

阮百尧; 熊彬; 徐世浙

三维地电断面电阻率测深有限元数值模拟

1.
桂林工学院资源与环境工程系, 桂林 541004
2.
浙江大学地球科学系, 杭州 310027

基金项目:

国家自然科学基金 40064001

广西自然科学基金桂科自0007024

详细信息

中图分类号: P631.3⁺22
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- 文章访问数: 3254
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- 被引次数: 0
出版历程
- 收稿日期: 2000-08-29
- 刊出日期: 2001-01-25

FINITE ELEMENT METHOD FOR MODELING RESISTIVITY SOUNDING ON 3-D GEOELECTRIC SECTION

1.
Department of Resources and Environment Engineering, Guilin Institute of Technology, Guilin 541004, China
2.
Department of Earth Science, Zhejiang University, Hangzhou 310027, China

摘要

摘要: 用有限单元法进行了电导率分块均匀的三维点源电场电阻率测深的数值模拟.首先给出了三维构造中点源电场的边值问题、变分问题; 然后, 用有限单元法求解变分问题, 将区域剖分成六面体单元, 在单元中进行三线性函数插值, 将变分方程化为线性代数方程组; 最后解方程组, 得各节点的电位值, 进而计算出地表的视电阻率.对几例较典型的地电模型进行试算, 结果表明本方法是行之有效的
- 电阻率测深 /
- 三维地电断面 /
- 有限单元法 /
- 电导率分块均匀
Abstract: The finite element method is used for the numerical modeling of the resistivity sounding in a 3-D point-source electric field whose conductivities are homogeneous for each block. In this paper, the 3-D boundary value and variational equation concerning the point-source electrical field in the 3-D structure are both presented. Then the finite element method is used to solve the variational equation. The entire region is divided into many hexahedral units in each of which a trilinear function is interpolated. The variational equation is converted into a linear equation system. Finally the equation system is solved to obtain the potential value on each of the nodes, resulting in the calculation of the apparent resistivity on the ground surface. The test of several relatively typical geoelectric models shows that this finite element method is effective.
- resistivity sounding /
- 3-D geoelectric section /
- finite element method /
- homogeneous conductivity within each block

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图 1 区域Ω剖分及单元示意

Fig. 1. Division of region Ω including the finite element grid

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图 2 有限元法与数值滤波法结果对比

Fig. 2. Comparison of numerical filter wave and finite element method numerical solutions

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图 3 模型2偶极-偶极视电阻率等值线(单位: Ω·m)

Fig. 3. Dipole-dipole apparent resistivity contour of model 2

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图 4 模型3的平面及剖面示意

a.平面示意图; b.剖面示意图

Fig. 4. Plane and sectional sketch map of model 3

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图 5 模型3沿y方向断面视电阻率等值线(单位: Ω·m)

Fig. 5. Apparent resistivity contour of model 3 in the y direction

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参考文献(4)

[1]	Pridmore D F, HohmanG W, Ward S H, et al. An investigation of finite elementmodeling for electrical and electromagnetic data in three dimensions[J]. Geophysics, 1981, 46: 1009~ 1024. doi: 10.1190/1.1441239
[2]	Holcombe HT, JiracekG R. Three-dimensional terrain correction in resistivity surveys[J]. Geophysics, 1984, 49(4): 436 ~ 452. doi: 10.1190/1.1441679
[3]	徐世浙. 地球物理中的有限单元法[M]. 北京: 科学出版社, 1994. 178~ 183.
[4]	罗延钟, 张桂青. 电子计算机在电法勘探中的应用[M]. 武汉: 武汉地质学院出版社, 1987. 67~ 69.