点电源二维起伏界面三层介质边界单元法

THE BOUNDARY ELEMENT METHOD FOR SOLVING THE 2-D GEOELECTRIC FIELD OF A POINT SOURCE IN THREE LAYERED MEDIUM WITH FLUCTUATED INTERFACES

摘要:

本文在文献[5]的基础上,以三层介质下边两层界面上隆模型为例,讨论了边界元法在解决层状介质中存在二维横向不均匀情况下点源场视电阻率计算问题方面的应用。在本文中,由于选取了适当的基本解,故在所导出的方程中避免了对水平层状界面的积分计算,只对起伏边界进行积分计算,并在理论推导中设法消除了位场在边界上的法向导数,因而最后形成的代数方程组规模相当小,从而大大减少了所需的边界部分点和未知量的数目,大量地节省了计算机内存,加快了计算速度。这给数值计算带来了很大的方便,并为向二维及三维多层介质中存有异常体的问题推广提供了便利条件。

Abstract:

Based on the paper[5], this paper takes the 2-D model of three layered medium, in which the second layer and the third layer are convex, and discusses the application of boundary element method for calculating apparent resistivity. The proper, basic solution is selected, so that the integral calculation along the horizontal parts in the integral equations are avoided, and the normal derivatives of electric potential on boundaries are managed to be eliminated in the theory. So the number of all needed boundary cut joints and unknowns are much less, algebraic equation sets are on a smaller scale, computer memory and time are saved a lot. This study supplies some convenient conditions for furtherly solving the 2-D and 3-D problems of multi-layered medium (e, g. more then three layered model) which contains inhomogeneities.