直流电阻率法三维各向异性多尺度有限元数值模拟  

3D anisotropic forward modeling for direct-current resistivity method based on multiscale finite-element algorithm

作　　者：齐彦福 伍亮 曹华科 李貅[1,2] 孙乃泉[1,2] 戚志鹏[1,2] 周建美[1,2] 刘文韬[1,2] QI YanFu;WU Liang;CAO HuaKe;LI Xiu;SUN NaiQuan;QI ZhiPeng;ZHOU JianMei;LIU WenTao(College of Geological Engineering and Geomatics,Chang'an University,Xi'an 710054,China;Integrated Geophysical Simulation Laboratory,Chang'an University,Xi'an 710054,China;Changjiang Geophysical Exploration&Testing Co.,Ltd(Wuhan),Wuhan 430010,China)

机构地区：[1]长安大学地质工程与测绘学院,西安710054 [2]长安大学地球物理场多参数综合模拟实验室,西安710054 [3]长江地球物理探测(武汉)有限公司,武汉430010

出　　处：《地球物理学报》2024年第9期3605-3617,共13页Chinese Journal of Geophysics

基　　金：国家重点研发计划项目(2021YFB2600402);国家自然科学基金项目(42004118,42074168,41830101);长江设计集团有限公司自主创新项目(CX2019Z39);长安大学中央高校基本科研业务费专项资金(300102264206,300102262101)联合资助.

摘　　要：在使用传统数值方法模拟大规模各向异性复杂地质模型三维直流电场分布时,需要进行大范围精细网格剖分,导致计算量巨大.为了提高计算效率,本文开发了直流电阻率法三维各向异性多尺度有限元正演模拟算法.通过在多尺度网格上并行求解局部偏微分方程的边值问题,构造多尺度基函数,将小尺度电性信息反映到大尺度上.然后,通过在大尺度粗网格上求解原电流传导问题,实现大规模复杂介质模型快速正演.针对由于网格大小与非均质目标尺寸相近引起的共振效应,本文采用过采样技术,压制共振误差,提高多尺度有限元法的计算精度.为了检验本文算法的准确性,我们首先建立了各向异性层状介质模型,通过与解析解进行对比,验证了本文算法的精度.在此基础上,建立了具有复杂结构的三维各向异性电阻率模型.通过与精细网格上传统有限元正演结果进行对比,我们发现本文算法在保证计算精度的同时具有更高的计算效率.最后,进一步分析了过采样技术以及多尺度网格粗细比对多尺度有限元算法的数值精度和计算效率的影响,进而为多尺度有限元最佳参数的设定提供指导.To handle the forward modeling problem of DC resistivity over anisotropic earth with large-area complex structures,the traditional numerical simulation methods need to generate fine mesh in large area,which leads to a huge amount of calculation.In order to improve the computational efficiency,we develop a 3D forward modeling method for DC resistivity over anisotropic earth based on multiscale finite-element algorithm.By solving the boundary value problem of local partial differential equations in parallel on multiscale meshes,we construct the multiscale basis functions to reflect small-scale electrical information to large scale.Then,by solving the original current conduction problem on a coarse mesh,the forward modeling is accelerated.Aiming at the resonance effect caused by the similarity between the grid size and the heterogeneous-target size,we adopt the oversampling technique to suppress the resonance error and improve its calculation accuracy.We first establish an anisotropic layered model,and verify the accuracy of our algorithm by comparing with the analytical solution.On this basis,we establish two 3D anisotropic resistivity models with complex structures.By comparing their forward modeling results obtained by our multiscale method with those obtained by the traditional finite-element method on fine mesh,we find that the proposed algorithm has higher computational efficiency while ensuring the calculation accuracy.Finally,we further analyze the influence of oversampling technique and coarse/fine ratio of the multiscale mesh on both the numerical accuracy and computational efficiency.It can provide guidance for setting optimal parameters of multiscale finite-element algorithm.

关 键 词：多尺度有限元 各向异性 直流电阻率 三维正演 过采样 

分 类 号：P631[天文地球—地质矿产勘探]