| 三维地形频率域人工源电磁场的边界元模拟方法 |
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| 引用本文： | 阮百尧,王有学.三维地形频率域人工源电磁场的边界元模拟方法[J].地球物理学报,2005,48(5):1197-1204. |
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| 作者姓名： | 阮百尧 王有学 |
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| 作者单位： | 桂林工学院资源与环境工程系，桂林 541004 |
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| 基金项目： | 国家自然科学基金项目（40344022）资助. |
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| 摘 要： | 提出了一种用边界元法计算频率域人工源三维地形电磁场的数值模拟方法.首先用矢量积分理论和电磁场边界条件，将上半空间（空气）和下半空间（地下介质）两个区域电磁场边值问题变为仅对地形界面的两个矢量面积分方程.然后将对地形界面的积分剖分为一系列的三角单元积分.在三角单元积分中，假设单元中电磁场为无限大气空间电磁场与地形影响的叠加,并假设地形影响为常项,这样既保证了计算精度又使得计算方法简便.通过分解和计算，每一个矢量面积分方程分解为对应三个坐标方向的三个常量线性方程，这些线性方程组成了对角占优的线性方程组，可用SSOR方法求解.文中给出了垂直磁偶源的垂直磁场地形影响的例子.
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| 关 键 词： | 三维地形 人工源 频率域电磁法 数值计算 |
| 文章编号： | 0001-5733（2005）05-1197-08 |
| 收稿时间： | 2005-02-05 |
| 修稿时间： | 2005-02-052005-04-11 |
A boundary element modeling method for the electromagnetic field by artificial source in frequency domain with 3-D topography |
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| RUAN Bai-yao,WANG You-Xue.A boundary element modeling method for the electromagnetic field by artificial source in frequency domain with 3-D topography[J].Chinese Journal of Geophysics,2005,48(5):1197-1204. |
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| Authors: | RUAN Bai-yao WANG You-Xue |
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| Institution: | Department of Resources and Environment Engineering, Guilin University of Technology, Guilin 541004, China |
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| Abstract: | We propose a numerical method using boundary element to model the electromagnetic filed induced by artificial source in the frequency domain with 3-D topography. Firstly, by using the vector integral theory and boundary conditions of the electromagnetic filed, the boundary problem of two electromagnetic fields in the upper half space (air) and lower half space (earth medium) is transformed into two vector integral equations just related to the topography interface, i.e. one magnetic equation for computing the magnetic field and one electrical equation for computing the electrical field. Then, the topography interface integral is decomposed into a series of integrals of triangle elements. For the integral in a triangle element, we suppose that the electromagnetic filed in the triangle element is the stack of the electromagnetic field in the unlimited air space and the earth medium effect which is a constant, so the computing becomes simple and convenient with a high accuracy. By the decomposition and computation, each vector integral equation can be calculated by solving three linear equations which are related to three Cartesian directions, respectively. The matrix of these linear equations is of diagonally dominant, and can be solved by the SSOR method. As examples, the topography effects of vertical magnetic field induced by a vertical magnetic dipole source are analyzed by this method. |
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| Keywords: | 3-D topography Artificial source Electromagnetic method in frequency domain Numerical modeling |
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