2维和2.5维起伏地表直流电法有限差分数值模拟  

Finite-difference DC electrical field modeling on 2D and 2.5D undulate topography

作　　者：张东良[1,2] 孙建国[1,2] 孙章庆[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：《地球物理学报》2011年第1期234-244,共11页Chinese Journal of Geophysics

基　　金：国家高技术研究发展计划(863)探索导向类课题(2006AA06Z109);教育部骨干教师自主计划资助

摘　　要：起伏地表直流电场数值模拟现多采用有限元法,主要是因为其有灵活的处理曲边界的能力,然而有限元法比有限差分法要复杂,如果让有限差分法也同样具有较好的处理曲边界的能力,那数值模拟将变得更为简单.本文通过在非正则内点处采用不等距差分,在起伏地表点处直接实现边界条件,克服转移法人为改变地表形状的弊端,使得基于笛卡尔网格的有限差分法有了较强的处理曲边界的能力.通过2维和2.5维的水平地表数值解和解析解的对比,以及2维起伏地表情况下数值解和保角变换理论解的对比,均说明该方法的有效性.最后例举了一些数值计算实例.Undulate surface DC field numerical simulation using finite element method is commonly used, mainly because of its flexible curved boundary treatment capacity. However, finite element is more complex than the finite difference. If we allow the finite difference to have also similar ability to deal with the curved boundary, that simulation will become easy. In this paper, non-equidistant difference is used at non-regular interior points and the boundary conditions are directly implemented to the undulate surface points, which overcomes the drawback of transfer method to change the shape of the surface, making finite-difference based on the Cartesian grid have a strong ability to deal with the boundary. Through the comparison of numerical and analytical solutions of the level surface in two-dimension and 2.5 dimension, as well as the two-dimensional numerical solution for undulate surface and the solution of conformal mapping theory, it is shown that the method is effective. Finally, we give some numerical examples.

关 键 词：起伏地表 曲边界 数值模拟 有限差分 

分 类 号：P631[天文地球—地质矿产勘探]