| 电导率分段线性变化的水平层的点电源电场的数值解 |
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| 引用本文： | 徐世浙.电导率分段线性变化的水平层的点电源电场的数值解[J].地球物理学报,1986,29(1):84-90. |
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| 作者姓名： | 徐世浙 |
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| 作者单位： | 山东海洋学院 |
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| 摘 要： | 首先给出柱坐标系中电导率分段线性变化的水平层的点源电场的二维边值问题,然后用变分法将边值问题转变为变分问题。用有限单元法解变分问题,将区域剖分成矩形单元,在单元中进行双线性函数插值,将变分方程化为线性代数方程组。解方程组,得各节点的电位值,由此可计算地表的视电阻率。 算例表明,本方法计算结果与精确解十分符合。本文还举了一个定量分析视电阻率年变化的例子。 本方法占用计算机内存约100K数量级。在MV/6000超小型计算机上计算一条电测深曲线的时间为几十秒钟。
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| 关 键 词： | 点电源 分段线性 水平层 电导率 数值解 电场 视电阻率 徐世浙 年变 边值问题 |
| 收稿时间： | 1984-04-24 |
A NUMERICAL METHOD FOR SOLVING ELECTRIC FIELD OF POINT SOURCE ON A LAYERED MODEL WITH LINEAR CHANGE OF CONDUCTIVITY IN EACH LAYER |
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| XU SHI-ZHE.A NUMERICAL METHOD FOR SOLVING ELECTRIC FIELD OF POINT SOURCE ON A LAYERED MODEL WITH LINEAR CHANGE OF CONDUCTIVITY IN EACH LAYER[J].Chinese Journal of Geophysics,1986,29(1):84-90. |
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| Authors: | XU SHI-ZHE |
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| Institution: | Shandong College of Oceanology |
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| Abstract: | First, the 2-D boundary value problem o electric field of point source on a layered model with linear change of conductivity is given in cylindrical coordinate system. Then, the boundary value problem is converted into a variational equation by the variation method. We solve the variation equation by means of the finite element method. Dividing the entire region into many rectangular elements and interpolating with a bilinear function in each element. The variation equation is converted into a linear algebric equation system. Solving the equation system, we can obtain the electric potential value on nodes. According to these value, the apparent resistivity on ground surface can be calculated.The calculation example shows that the result calculated by this method is in agreement with the analytic solution. In addition, this paper gives an example of quantitative analysis of the annual variation of apparent resistivity.The capacity of memory needed for this method is about 100 K. The runtime for calculating a sounding curve on super smallcomputer MV/6000 is about several tens of seconds. |
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