二维层状介质点电源边界单元解

本文用付氏变换将点源二维地电断面的三维边值问题变成二维边值问题,然后讨论了边界元法在解决层状介质中存在二维柱体时点源场视电阻率计算问题中的应用。由于选取的基本解避免了对水平层状界面的积分计算,从而大大减少了边界剖分节点数。在计算中设法略去了对边界上位场法向导数的求解,使未知量大为减少,从而便利了求解二维边值问题,并由付氏反变换求得三维空间中的位。本方法所需计算机内存少,原始数据的输入简单,且有较高的计算精度。

THE BOUNDARY ELEMENT METHOD FOR SOLVING ELECTRIC FIELD OF POINT SOURCE ON TWO-DIMENSIONAL LAYERED MEDIUM GEOELECTRICAL SECTION

Using Fourier transformation, the 3-D boundary value problem of electric field of point source on 2-D geoelectric section is converted into 2-D boundary value problem. Then we discussed the application of boundary element method for calculating apparent resistivity on layered medium which contains 2-D column body. The integral calculation of horizontal boundary is avoided because of the selection of basic solution. So, the number of all needed boundary cut joints are much less. Particularly, it need not calculate the partial derivative any more, unknown quantities are decreased very much, so that it calculates 2-D boundary value problem conveniently. And using Fourier inverse transformation, we can obtain electric potential in 3-D space. The mathod proposed in this paper requires less memory, less ariginal data needed for computer input, and has higher calculating accuracy.