电阻率任意各向异性三维有限元快速正演  

Rapid finite element resistivity forward modeling for 3D arbitrary anisotropic structures

作　　者：王威[1] 吴小平[1] 

机构地区：[1]中国科学技术大学蒙城地球物理国家野外观测站,地球和空间科学学院,合肥230026

出　　处：《地球物理学进展》2010年第4期1365-1371,共7页Progress in Geophysics

基　　金：国家自然基金项目(41074048);中国科学院知识创新工程重要方向项目(KZCX2-YW-QN508)联合资助

摘　　要：电阻率各向异性由于其可能导致观测数据解释的很大偏差,受到越来越多的关注.由于其复杂性,三维各向异性研究国内尚未开展.本文先推导了各向异性介质中直流电法满足的控制方程并建立其变分问题,然后用有限元方法将问题转化为求解二次场电位的大型线性方程组,结合系数矩阵一维压缩存储技术和解大型线性方程组的对称超松弛预条件共轭梯度(SSOR-PCG)迭代算法,大大提高了计算速度,减少了内存需求.本文提出的算法可以任意调整介质的电阻率取向,从而实现了直流电阻率三维任意各向异性的有限元快速、精确正演计算.模型计算结果表明,各向异性介质响应相对于各向同性介质有明显差异,其介质取向对于视电阻率观测有明显影响.Anisotropy of electrical resistivity receiveds increasing attention as it may results in serious deviation in data explanation. However, the study of three-dimensional （3D） resistivity anisotropy is still a gap in China. In this paper, the governing equations of the secondary potentials are formulated for the direct current resistivity method with anisotropic media and the variation principle is established. The problem is then turned into a set of large linear equations by the finite element method. We introduce a symmetric successive over-relaxation preconditioned conjugate gradient （SSOR-PCG） algorithm, combined with row-indexed sparse storage mode, to solve the large linear system. Our algorithm is much quicker and requires much less storage compared with the direct method, and the orientation of the electrical resistivity can be changed arbitrarily. Thus, we present a fast and accurate finite element resistivity forward modeling for 3D arbitrary anisotropic structures. Our results show that the responses of anisotropic structures are quite different from the isotropic cases. The result also indicates that the apparent resistivity is obviously influnced by the orientations of media.

关 键 词：任意各向异性 三维有限元 二次场 对称超松弛 共轭梯度 

分 类 号：P631[天文地球—地质矿产勘探]