摘要
本文建立了在二维复杂地电断面上点电源势场问题的边界积分方程。用付氏变换将点源三维边值问题转换为二维边值问题,采用边界单元法解出付氏电位,然后利用付氏反变换和互换原理求得视电阻率测深曲线。研究了用边界单元法解积分方程中点源和无穷边界的处理方法。给出了典型二层断面、水平地面下的低阻水平圆拄体和山脊地形下的高阻水平圆柱体的电阻率测深曲线计算结果。结果表明,这种方法输入数据简便,计算时间和计算机内存均比有限元法少得多。因此,边界单元法可以成为计算二维复杂地电断面电阻率测深曲线的实用方法。
In this paper, the bouadary integral equation of point source poten tial problem on two-dimensional(2-D)geoelectric sections is established。Transfer 3-D value problem of point source to 2-D problem with Fourier transform, using boundary element method (BEM) to solve the Fourier transfer potential, and obtain the apparent resistivity sounding curves (ARSC)by the reversal Fourier transform and the principle of iexchangeability. The treatment of point source and infinite boundary in solving the integral equation by BEM are developed. The calculation results of ARSC on typical two-layer section, horizontal conductive cylinder beneath a flat surface and horizontal insulating cylinder below the ridge are given. The results indicate that this method is simple and convenient for input data, and both the computing time and computer storage are much less than the finite element method. Therefore, BEM may be able to become a practical technique applied to calculation of ARSC on 2-D complicated geoelectric sections.
