二维起伏地表直流电场插值法数值模拟

Numerical modeling of DC electrical field interpolation on two dimension undulate topography

本文提出了一种采用插值法实现边界条件的有限差分数值模拟新方法,地表函数通过三次样条插值能很好的拟合真实地表形状。其地表边界条件的实现思想是在地表法线方向上寻找一个与地表点位于同一等位线上的点,该点通过周围点插值来建立离散方程。采用不规则四边形距离加权插值法使插值形式统一化。在水平地表情况下做的数值解与解析解的对比分析表明:该方法的计算精度适合要求,对山谷模型的实例计算也得到了视电阻率与地形成镜像对称的结果。

This paper proposes a new method of finite-difference numerical modeling using interpolation to achieve boundary condition. Surface function can fit the true shape of geography well through 3 times spline interpolation. The interpolation method of surface boundary condition is to find a point in the normal line of surface which is located in its same equipotential line, and sets up discrete equation through the interpolation by around points. Irregular quadrilateral distance weighted interpolation is used to make interpolation models unified. Comparative a- nalysis of numerical solution and analytical solution in level surface shows that the calculation accuracy of this method is qualified, and the result of example calculation for valley model shows resistivity and topography as mirror symmetric.