复杂地形下高密度激电法2．5维有限单元法数值模拟

摘要

目前三维有限元模拟计算量大，计算效率低，对计算机要求较高，2．5维模拟是三维问题的简化，较好地克服了上述问题。在高密度激电法模拟中，模拟的点数一般较大，要求程序计算效率高，因此对高密度激电法2．5维模拟研究是必要的。首先给出了2．5维稳定电流场的边值问题及对应的变分问题；为了能更好模拟复杂地形对极化率异常的影响，采用三角形网格，有利于模拟复杂地形又有利于将其应用于反演计算。推导了基于连续电性介质的2．5维稳定电流场的有限元法，利用等效电阻率法，编制了2．5维高密度激电法有限元模拟程序，计算了水平地形及起伏地形下的极化率异常模型，并验证了方法的可行性，分析得出了山谷地形比山脊地形对极化率观测的影响大的结果。%Currently,the 3D FEM simulation has the shortages of large computation,low computation efficiency and higher re-quirements on the computer.Therefore,2.5 dimensional simulation aims to simplify the 3D problem which can overcome the problems mentioned above.In the simulation of high density induced polarization method,IP 2.5 dimensional high density sim-ulation research deserves more attention since the points of simulation are too large and high computation efficiency is reques-ted.Firstly,in this paper we give the problems of 2.5 dimensional stable current field boundary value and the corresponding variable.Secondly,in order to simulate the abnormal effects of polarization exerted by complex terrain,we use triangle mesh which is conducive to the simulation of complex terrain and inverse calculation.Thirdly,we deduct the finite element method of 2.5 dimensional steady current field on the continuous electric medium and work out IP 2.5 dimensional high density finite ele-ment simulation program using the equivalent resistivity method.We then calculate the abnormal polarization model of level ter-rain and topography and verify the feasibility of the method.Finally we drown the conclusion that valley terrain exerts more in-fluence on the polarization observation than ridge terrain.