2.5D induced polarization forward modeling using the adaptive finite-element method  

一种激发极化法2.5维正演的自适应有限元方法（英文）

作　　者：叶益信[1,2] 李予国[1] 邓居智[2] 李泽林[2] 

机构地区：[1]中国海洋大学海底科学与探测技术教育部重点实验室,青岛266100 [2]东华理工大学放射性地质与勘探国防重点学科实验室,南昌330013

出　　处：《Applied Geophysics》2014年第4期500-507,511,共9页应用地球物理（英文版）

基　　金：financially supported by the National Natural Science Foundation of China(No.41204055,41164003,and 41104074);Opening Project(No.SMIL-2014-06) of Hubei Subsurface Multi-scale Imaging Lab(SMIL),China University of Geosciences(Wuhan)

摘　　要：The conventional finite-element（FE） method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization（IP）. In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4 % and 1.2 % for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models.传统的基于结构化网格有限元法采用的单元比较规则如矩形等,且网格剖分和加密要靠手动实现,所以传统的基于结构化网格有限元法不能准确和灵活地模拟复杂介质。本文采用易于模拟复杂介质模型的非结构化三角形网格进行剖分,且利用对偶加权后验误差估计指导网格自动细化过程,然后在电位模拟的基础上计算雅可比偏导矩阵,并依据Seigel(1959)理论实现激发极化法2.5维自适应有限元正演模拟算法。通过对垂直接触面模型进行正演分析,接收点附近网格得到了明显加密,电位数值解平均相对误差收敛到0.4%,视极化率平均相对误差收敛到1.2%,表明经自适应网格细化后,该算法数值解最终能收敛到精确解附近。最后对两个较复杂模型进行了正演计算与分析,进一步验证了该算法的准确性和灵活性。

关 键 词：Induced polarization（IP） dual error estimate weighting unstructured mesh ADAPTIVE finite-element（FE） 

分 类 号：P631.324[天文地球—地质矿产勘探]