基于自然单元法的2.5维直流电阻率数值模拟  

2.5-D DC resistivity numerical modeling by natural element method

作　　者：王佳新 崔益安[1,2,3] 谢静 罗议建[1,2,3] 柳建新 WANG Jiaxin;CUI Yian;XIE Jing;LUO Yijian;LIU Jianxin(School of Geosciences and Info Physics, Central South University, Changsha 410083,China;Hunan Key Laboratory of Non-ferrous Resources and Geological Hazard Detection, Changsha 410083,China;Key Laboratory of Metalorganic Prediction of Nonferrous Metals and Geological Environment Monitoring (Central South University), Ministry of Education, Changsha 410083,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083 [2]中南大学有色资源与地质灾害探查湖南省重点实验室,长沙410083 [3]中南大学教育部有色金属成矿预测重点实验室,长沙410083

出　　处：《物探化探计算技术》2022年第3期337-343,共7页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：国家自然科学基金项目(41874145)。

摘　　要：在直流电阻率法数值模拟研究中,常规数值模拟算法(如有限单元法、有限差分法等网格法)严格受网格约束,在具有复杂几何体或复杂地形的地电模型中需要大量前期剖分工作。针对该问题,笔者引入材料力学中常用的自然单元法开展直流电阻率法数值模拟研究,探究该数值算法在地球物理正演中的可行性。首先推导了点源场边值问题及其变分形式的基本方程,然后推导了自然单元法的数值实现过程,最后通过对层状模型以及三个含电阻率异常体的二维模型开展正演模拟研究,验证该算法的正确性及有效性。研究结果表明,自然单元法能在可接受精度条件下实现直流电阻率模型的有效数值模拟,能有效确定电阻率异常体的分布特征。同时该算法不受网格约束,自然节点布设灵活,有助于开展复杂地电模型数值模拟研究。In numerical modeling studies of DC resistivity models,conventional numerical algorithms such as the finite element method,the finite difference method,and other grid methods are strictly constrained by grids,which requires a lot of preliminary subdivision work in geoelectric models with complex geometry or terrain.Aiming at this problem,the natural element method,which is commonly used in material mechanics,was introduced in this work to conduct numerical modeling of DC resistivity models and to explore its feasibility in geophysical models.Firstly,the basic equations of the boundary value problem of the point source field and its variational form were derived,and then the numerical implementation process of the natural element method was derived.Finally,the correctness and effectiveness of the proposed algorithm were verified by a layered model and three DC resistivity models.The results show that the natural element method can be used to realize the effective numerical modeling of DC resistivity models with acceptable accuracy and can determine the distribution of resistivity anomalies.Moreover,this algorithm is free from grid constraints and the natural nodes can be laid out flexibly,which is helpful for numerical modeling of complex geoelectric models.

关 键 词：直流电阻率法 2.5维 数值模拟 自然单元法 可行性 

分 类 号：P631.3[天文地球—地质矿产勘探]