基于Fractal模型的复电阻率法2.5D有限元数值模拟  

Fractal model-based 2.5 D finite element modeling of complex resistivity method

作　　者：龙秀洁 陈汉波[2] 莫亚军 区小毅 卢胜辉 Long Xiu-Jie;Chen Han-Bo;Mo Ya-Jun;Ou Xiao-Yi;Lu Sheng-Hui(Guangxi Geophysical Investigation Institute,Liuzhou 545005,China;College of Earth Sciences,Guilin University of Technology,Guilin 541006,China)

机构地区：[1]广西壮族自治区地球物理勘察院,广西柳州545005 [2]桂林理工大学地球科学学院,广西桂林541006

出　　处：《物探与化探》2022年第4期887-896,共10页Geophysical and Geochemical Exploration

基　　金：桂林理工大学科研启动基金(RD2100002165);中国博士后科学面上基金(2021MD703820)。

摘　　要：复电阻率法在油气资源、矿产勘查中发挥了重要的作用,为了深刻认识复电阻率法异常特征变化规律,本文对复电阻率2.5D正演问题展开研究。首先直接给出复电阻率法2.5D有限元正演所满足的变分问题,并详细地推导相应的刚度矩阵的计算过程。引入Fractal模型作为等效模型研究频谱激电异常特征。对单元内的复电导率及复电位均进行线性插值,而后,采用不完全LU分解的稳定双共轭梯度算法求解有限元线性方程组,获得异常复电位值。设计3个典型的地电模型验证了本文算法的正确性及精确性,并分析了不同装置下,不同频率的2.5D复电阻率异常响应特征。数值模拟结果表明,采用Fractal模型研究激发极化异常特征是可行、有效的;不同装置、不同频率下的复电阻率法异常特征有着显著的差异。This study proposed the variational problem of 2.5D finite element forward modeling of the complex resistivity method and detailed the process of solving stiff matrix of finite equations.The Fractal model was introduced as a research model for studying the equivalent induced polarization anomalies of spectra.Furthermore,the complex conductivity and complex potential of a grid unit were linearly interpolated.Then,to obtain anomalous complex potential,finite element linear equations were solved using the biconjugate gradient stabilized method with incomplete LU decomposition.The results of three typical geoelectric models validated the correctness and accuracy of the algorithm proposed in this study.Furthermore,this study analyzed the abnormal response characteristics of 2.5D complex resistivity under different frequencies.

关 键 词：有限元 复电导率 Fractal模型 异常复电位 

分 类 号：P631[天文地球—地质矿产勘探]