二维起伏地表条件下坐标变换法直流电场数值模拟  

2D DC Electric Field Numerical Modeling Including Surface Topography Using Coordinate Transformation Method

作　　者：孙章庆[1,2] 孙建国[1,2] 张东良[1,2] 

机构地区：[1]吉林大学地球探测科学与技术学院,长春130026 [2]国土资源部应用地球物理综合解释理论开放实验室,长春130026

出　　处：《吉林大学学报（地球科学版）》2009年第3期528-534,共7页Journal of Jilin University：Earth Science Edition

基　　金：国家高新技术研究发展计划'863'探索导向类课题(2006AA06Z109)

摘　　要：针对有限差分方法处理不规则边界难的问题,引入曲化平的思想,实现了一种新的基于坐标变换法的起伏地表条件下直流电场数值模拟方法。通过坐标变换,将物理空间的直流电场满足的基本方程和边界条件变换到计算空间;在计算空间内,利用有限差分方法对变换后的方程和边界条件进行数值分析;最后,将计算结果由计算空间映射回物理空间。精度分析及计算实例表明:本文提出的算法精度高,计算误差主要集中在源附近,且当源离地表较近时平均相对误差在1.0%以下;计算结果满足起伏地表条件下电位及视电阻率的分布规律。It is difficult to deal with the irregular boundary using finite-difference method in the DC electric field numerical modeling including surface topography. To solve this problem, we introduce a coordinate transformation idea that transforms curved surface into horizontal topography and realize a new finite-difference method basing on the transform. We firstly transform the basic equations and boundary conditions of DC electric field from physical space to computation space, and then resolve the DC fields in computation space using finite-difference method. Finally, we retransform the computation results from computation space into physical space by coordinate mapping. Accuracy analysis and nume- rical tests show that the computation error congregates around the source, and the average relative error is less than 1% if the source is close enough to the irregular surface. Therefore, the new method has high accuracy, and the computation results can reveal the distribution characteristics of DC electric field and apparent resistivity including surface topography.

关 键 词：起伏地表 直流电场 坐标变换 有限差分 

分 类 号：P631.3[天文地球—地质矿产勘探]