计算直流电测深曲线的有限差分法

本文阐述了用点源二维有限差分法计算电测深曲线的原理、数学模型及计算实例。此法采用不等间隔的网格，将置于柱坐标系中的半无限介质进行离散化。由于原点放在点源的位置上，仅须在四分之一空间对电场作二维有限差分数值模拟。为了不漏掉那些厚度小于网格间距的“薄层”对电场分布的影响，利用各电性层的纵向电导和横向电阻等所谓DarZarrouk参数计算差分方程中的系数，从而取得“差分网格疏而不漏”的效果。用逐次超松弛（SOR）法求解差分方程组，每迭代五次优选一次松弛系数，直至相继两次系数值的变化小于10^-2。计算结果表明，有限差分法较之数字滤波法要占用较长的计算时间，它不仅适用于对称四极梯度装置形式，而且也能解决各向异性介质的电阻率数值的模拟问题。

Finite difference method for calculating D. C. sounding curve

The purpose of this paper is to detail the principle and mathematic model for calculating electric sounding curve by point source 2-D finite difference method,and present some calculation examples. According to this method, a half infinite medium located in cylindrical coordinate system is made discrete by adopting unequal interval mesh. Because the point source is superposed on the origin of the coordinate system, we need only to make 2-D finite difference simulation of a electric field within 1/4 space. In order not to neglect the effect of the bed thinner than mesh interval on field distribution, we compute the coefficients of difference equation by Iangitudinai conductivity and lateral resistance of each layer, called Dar Zarrouk parameter, thus making the difference mesh thin but not Leaky. Difference equation spstem can be estabiiished by applying successive over-relaxation method. Relaxation coefficient is optimized once every five iterations until two coefficients running are less than 10. The calculation shows that although the finite difference method takes more computing time than digital filtering method, it can help to simulate the resistivity value of anisotropic medium, and that the finite difference method is not limited to symmetric four pole gradient pattern.