关键词: 2.5维, 起伏地表, 直流电场, 坐标变换, 有限差分法

Abstract:

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.

Key words: 2.5-D, surface topography, DC electric field, coordinate transformation, finite difference method