2.5维起伏地表条件下坐标变换法直流电场数值模拟

2.5-D DC Electric Field Numerical Modeling Including Surface Topography Based on Coordinate Transformation Method

研究起伏地表对视电阻率分布的影响是进行地形校正的基础。由于很难处理不规则边界,计算简洁且效率高的有限差分方法很少用于解决起伏地表问题。为了解决该问题,引入曲化平思想,实现了一种基于坐标变换法的起伏地表条件下的直流电场数值模拟方法。方法从传统的2.5维基本方程及边界条件出发,通过坐标变换将起伏地表问题转化为水平地表问题,并利用有限差分法求解水平地表问题,最后再通过坐标映射得到起伏地表条件下的电位和视电阻率分布。精度分析及计算实例表明:本方法实现简洁,计算误差主要集中在震源附近,整个计算区域内的平均相对误差为1.39%,计算结果满足起伏地表条件下的电位和视电阻率的分布规律。

Research for the distribution characteristics of apparent resistivity including surface topography is the basis of topographic correction.For the difficulty of dealing with the irregular boundary,the finite-difference method,a concise and efficient method,is seldom used to solve the surface topography problem.For the sake of solving this problem,we introduced a method to transform the surface topography into horizontal topography and that realizes a new numerical modeling method for 2.5-D DC electric field base on coordinate transformation and finite-difference method.We firstly transformed the basic equations and boundary conditions of DC electric field by coordinate transformation,and then did the numerical analysis in computation space by finite-difference method.Finally,we transformed the computation results from computation space to surface topography space by the same coordinate mapping.Accuracy analysis and numerical tests show that the new method is concise,the computation error congregates around the source and the average relative error is 1.39%.The computation results are also able to meet the distribution characteristics of DC electric field and apparent resistivity including surface topography.