基于MLS形函数处理边界的电阻率法有限单元正演模拟  

FEM forward modeling of resistivity method with boundary conditions implemented by MLS shape function

作　　者：麻昌英 赵文学 汤文武[1,3] 柳建新 闫玲玲[3] 周聪 秦臻[1,3] 钟炜城 程流燕 MA ChangYing;ZHAO WenXue;TANG WenWu;LIU JianXin;YAN LingLing;ZHOU Cong;QIN Zhen;ZHONG WeiCheng;CHENG LiuYan(Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province,East China University of Technology,Nanchang 330013,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),Ministry of Education,Changsha 410083,China;School of Geophysics and Measurement-Control Technology,East China University of Technology,Nanchang 330013,China)

机构地区：[1]东华理工大学江西省防震减灾与工程地质灾害探测工程研究中心,南昌330013 [2]中南大学有色金属成矿预测与地质环境监测教育部重点实验室,长沙410083 [3]东华理工大学地球物理与测控技术学院,南昌330013

出　　处：《地球物理学报》2023年第3期1281-1297,共17页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41904097,41804097);江西省自然科学基金项目(20202BAB211011,20202BABL211017);江西省教育厅科技项目(GJJ180397);有色金属成矿预测与地质环境监测教育部重点实验室(中南大学)开放基金项目(2020YSJS05);江西省防震减灾与工程地质灾害探测工程研究中心开放基金项目(SDGD202104,SDGD202101);地球内部多尺度成像湖北省重点实验室开放基金项目(SMIL-2020-05);核资源与环境国家重点实验室开放基金项目(2020NRE28);东华理工大学博士科研启动基金(DHBK2018068);东华理工大学研究生创新项目基金(DHYC-202113)联合资助。

摘　　要：电阻率法有限单元正演模拟中,采用第三类边界条件时为保证精度仍要求较大范围的计算域.无单元法为地球物理领域的新兴正演模拟方法,其计算效率低,但其中采用的移动最小二乘(MLS)形函数相比于有限单元法形函数具有良好的连续性,模拟精度高.本文将MLS形函数应用于电阻率法有限单元2.5维正演的第三类边界条件处理,提出电阻率法有限单元-移动最小二乘(FEM-MLS)耦合正演方法.通过不同正演方法的模型算例模拟结果对比,验证了本文算法的有效性,并讨论了各个参数选择对模拟结果的影响.本文数值模拟结果表明采用第三类边界条件时,在同等计算精度前提下,FEM-MLS耦合法相比于有限单元法可进一步缩小计算域并提高了计算效率,相比于采用较大计算域满足边界条件的有限单元法计算效率提高了约一倍,相比于采用相同小范围计算域的有限单元法平均精度提高了约一倍.When the third type of boundary conditions are used for the forward modeling of resistivity method by finite element method(FEM), a large computational domain is required to ensure the computation accuracy. The element free method(EFM) is an emerging forward modeling method in the field of geophysics, although its computation efficiency is low, the moving least squares(MLS) shape function implemented in EFM has better continuity property and higher computation accuracy compared with the shape function used by FEM. In this work, the MLS shape function is implemented for the processing of the third type of boundary conditions in the 2.5D forward modeling framework of the resistivity method with the traditional finite element method. Therefore, we call the proposed method a finite element-moving least squares(FEM-MLS) coupled forward modeling algorithm. By numerical comparisons of different models with different forward modeling methods, the validity of this method is verified, and the influences of the parameters on simulation results are discussed. The numerical tests show that when the third type of boundary conditions are used, the computation domain can be reduced with the FEM-MLS coupling method and the computation efficiency is improved with the same accuracy reached. Compared with the FEM using a large-scale computation domain, computation efficiency of FEM-MLS coupling method is accelerated by about one times. When the same small-scale computation domain is used, the average accuracy of FEM-MLS coupling method is improved by about one times.

关 键 词：耦合法 MLS形函数 有限单元法 边界条件 电阻率 

分 类 号：P631[天文地球—地质矿产勘探]