复杂条件下3D电磁场有限元计算方法

黄临平; 戴世坤

复杂条件下3D电磁场有限元计算方法

石油大学资源与信息学院, 北京 102249

基金项目: 青海油田勘探开发研究院柴西地区综合物探技术攻关与评价项目

详细信息

作者简介:
黄临平(1964-), 男, 副教授, 现在石油大学做博士后研究, 主要研究方向为地球物理正、反演方法理论

中图分类号: O441
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出版历程
- 收稿日期: 2002-08-12
- 刊出日期: 2002-11-25

Finite Element Calculation Method of 3D Electromagnetic Field under Complex Condition

Resources and Information Institute, University of Petroleum, Beijing 102249, China

摘要

摘要: 从电磁场的Maxwell方程出发, 根据电磁场的边值问题及变分公式建立了有限元方程组.采用可以模拟较为复杂的空间地质构造和地形起伏的四面体单元离散计算区域; 单元中的插值函数选择了精度较高的十点双二次多项式; 并采用连续的双二次多项式插值函数来模拟计算区域内单元中电导率σ的空间变化.推导出了地下变电导率σ条件下计算三维电磁场的有限元单元方程的解析表达式; 采用伽辽金方法推导出了散度效正有限元方程组.根据所推导的公式, 编制了三维有限元的计算程序.数值计算结果表明, 上述公式推导正确, 为三维电磁场的数值计算提供了一条有效的新途径.
- 三维电磁场 /
- 有限元 /
- 电导率
Abstract: Based on the Maxwell's equations of electromagnetic field, this paper introduces equations of the finite element method for the boundary problem of the electromagnetic field and variation formula. In numerical calculation, the rectangular body elements fitted to simulate complex geology structure and topography relief were selected for discontinuity calculating areas. Ten points double secondary order interpolating functions were used in the finite element calculation and in the simulating calculation of the spatial variation of conductivity.The analytic expressions of the equations of finite elements of rectangular body elements for calculating three dimensions electromagnetic field in the spatial variation of conductivity were first deduced and the correction of the divergence equations of finite elements were deduced by the Galerkin method. The results of numerical calculation show that the deduced formulas are correct and a new way for three dimension electromagnetic field numerical calculation is proposed.
- D electromagnetic field /
- finite element /
- conductivity

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图 1 计算区域示意

Fig. 1. Sketch of calculation areas

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图 2 有限元剖分断面示意

a.常规有限元划分; b.网格收缩划分

Fig. 2. Sketch of cross section of finite elements

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图 3 三维不均匀模型示意

Fig. 3. Sketch of 3D model

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图 4 100 Hz (a), 1 Hz (b) 视电阻率分布立体图

Fig. 4. Map of resistance distribution under the frequency of 100 Hz (a), 1 Hz (b)

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表 1 模型垂向划分厚度

Table 1. Vertical thickness of models

表 2 100 Hz模型在中间一条剖面上的ρ_xy

Table 2. Values of ρ_xy at the middle profile under the frequency of 100 Hz

参考文献(4)

[1]	金建铭. 电磁场有限元方法[M]. 西安: 西安电子科技大学出版社, 1998. JIN J M. Finite elementmethod of electromagnetic field[M]. Xi'an: Xi'an Electronic University Press, 1998.
[2]	倪光正, 钱秀英. 电磁场数值计算[M]. 北京: 高等教育出版社, 1995. NI G Z, QIAN X Y. Numerical calculation of the electromagnetic field[M]. Beijing: Press of Higher Education, 1995.
[3]	徐世浙. 地球物理中的有限单元法[M]. 北京: 科学出版社, 1994. XU S Z. Finite element method of geophysics[M]. Beijing: Science Press, 1994.
[4]	Coggon J H. Electromagnetic and electric modeling by the finite element method[J]. Geophysics, 1971, 36: 132-155.