三维直流电阻率有限元-无限元耦合数值模拟  

3D DC resistivity forward modeling by finite-infinite element coupling method

作　　者：汤井田[1] 公劲喆[1] 

机构地区：[1]中南大学信息物理工程学院,长沙410083

出　　处：《地球物理学报》2010年第3期717-728,共12页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(40874072)资助

摘　　要：为解决传统有限元截断边界所引起的问题,本文提出了一种新的三维直流电阻率有限元-无限元耦合数值模拟方法.首先推导了无限元三维单元映射函数,然后提出了一种全新的最优的无限元形函数并与多种其他形函数进行了对比,随后将其与非结构化四面体有限元相结合,取代了传统的混合边界条件,使得电位在无限域内连续并在无限远处衰减为零,最终形成的左端矩阵稀疏对称并与场源位置无关.数值计算表明,该方法可以在近似测区大小的计算范围内得到与混合边界条件相当的计算精度,优于相同计算范围下齐次边界条件的解,有利于减少计算节点数;由于左端矩阵不随场源位置改变,有利于加速反演计算.To solve the problems caused by artificial boundary conditions in conventional finite element modeling, a new 3D DC resistivity finite- infinite element coupling method was proposed. Firstly, the 3D mapping functions of infinite elements were derived. Then, a new type of shape functions was proposed and proved to be the optimal one in both accuracy and time consumption by comparing with several other shape functions. After that, we integrated infinite element method into conventional finite element method to replace the mixed boundary conditions, which made the electrical potential distribute continuously in half space and decay to zero at infinity. Meanwhile, the global system matrix was independent with the locations of source points but still sparse and symmetric. Finally, analyses of numerical tests showed that the finite--infinite coupling method presented in this paper could obtain reasonable numerical solutions in a relatively small meshing area, the accuracy of which was equivalent with that obtained by mixed boundary conditions and higher than that of Neumann boundary conditions. Due to the reduction of the discretization domain and the invariability of the global system matrix with variant source positions, this new method is able to alleviate the computational burden and speed up inversions.

关 键 词：三维 直流 电阻率 有限元 无限元 

分 类 号：P631[天文地球—地质矿产勘探]