基于异常场的2.5维电阻率有限元正演模拟  

Finite element method for 2.5D resistivity forward modeling based on anomaly electric field

作　　者：鲁杏[1,2,3] 张胜业[1] 崔先文[2,3] 

机构地区：[1]中国地质大学(武汉)地空学院,武汉430074 [2]安徽省勘查技术院,合肥230031 [3]安徽省电法勘探重点实验室,合肥230031

出　　处：《地球物理学进展》2014年第6期2718-2722,共5页Progress in Geophysics

基　　金：中国地质调查局"西准噶尔克拉玛依后山地区深部地质调查"(No.1212011220245);国家重大科学仪器专项大深度三维电磁探测技术工程化开发(No.2011YQ050060)联合资助

摘　　要：本文对2.5维直流电阻率正演进行了研究.通过傅立叶变换,推导了点电源2.5维直流电阻率的边值问题和变分问题.使用有限单元法对变分问题进行了求解,从模拟精度和计算效率两方面考虑,采用了对矩形单元再进行三角形剖分的网格剖分方法,从而降低了线性方程组的阶数,减少了计算量.在大型线性方程组的求解中,采用了紧缩矩阵存储的方式,并采用了不完全LU分解的稳定双共轭梯度算法,提高了运算速度.推导了异常场电位的偏微分方程,并给出了基于异常场算法的思路,采用异常场算法的正演模拟降低了点电源附近电位函数的奇异性,提高了正演精度.通过理论模型的计算和比较,验证了正演算法的正确性.In this paper,we describe the technique of the finite forward modeling for 2.5Ddirect current resistivity based on anomaly field.The variational problem of 2.5Ddirect current resistivity is deduced by the Fourier Transform.The finite element method is used to solve the variational problem equations.Considering the two aspects of simulation precision and computational efficiency,the area is divided into rectangular elements,and each element is divided by four triangles,so reduces the system of linear equations of order number and the amount of calculation.When solving the large linear equations,the algorithm with the compact storage scheme is given and using the method of BICGSTAB and improve the computing speed.The partial differential equation of the anomaly electric field is derived and introduce the idea of the method.The method reduces the singularity near the source,and improve the precision of the forward modeling.Verify the correctness of the forward modeling method by the theoretical model calculation.

关 键 词：有限单元法 正演模拟 异常场 正确性 

分 类 号：P631[天文地球—地质矿产勘探]