不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟

现代地质 ›› 2012, Vol. 26 ›› Issue (6): 1283-1288.

不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟

熊杰^1,2,3，邹长春^1,2，孟小红^1,2

1 中国地质大学地球物理与信息技术学院，北京100083; 2 地下信息探测技术与仪器教育部重点实验室
(中国地质大学，北京)，北京100083; 3 长江大学电子信息学院，湖北荆州434023

收稿日期:2012-06-12 修回日期:2012-08-20 出版日期:2012-10-24 发布日期:2012-10-31
作者简介:熊杰，男，副教授，1975年出生，地球探测与信息技术专业，主要从事地球物理正反演方法和石油软件开发研究。Email:xiongjie494@gmail.com。
基金资助:
中央高校基本科研业务费专项资金资助项目。

6Using the BICGSTAB Algorithm with the Incomplete LU Factorization Precondictioning to Implement 2D FDFD Induction Logging Fast Forward Modeling

XIONG Jie ^-1,2,3, ZOU Chang chun ^-1,2, MENG Xiao hong^-1,2

1 School of Geophysics and information technology, China University of Geosciences, Beijing100083, China;
2 Key Laboratory of Geodetection (China University of Geosciences, Beijing), Beijing100083，China；
3 School of Electron and Information, Yangtze University, Jingzhou, Hubei434023, China

Received:2012-06-12 Revised:2012-08-20 Online:2012-10-24 Published:2012-10-31

摘要/Abstract

摘要：

在柱坐标系下推导了二维感应测井差分格式，采用频率域有限差分方法求解感应测井正演问题。针对差分近似得到的线性方程组系数矩阵是大型稀疏复系数病态矩阵求解困难等问题，采用不完全LU分解预条件的稳定双共轭梯度(BICGSTAB)算法求解该线性方程组。研究结果表明，本算法具有速度快、精度高和稳定性好等优点，能有效提高感应测井正演模拟的效率和精度。

关键词: 感应测井, 频率域有限差分, 二维正演, 不完全LU分解, 稳定双共轭梯度法

Abstract:

The difference scheme of the 2D induction logging in cylindrical coordinates was derived, and the finite deference frequency domain method was employed to solve the induction logging forward modeling problem. Based on the fact that the coefficient matrix was a large sparse, complex and ill posed matrix and the linear system was difficult to solve, the bi-conjugate gradient stabilized (BICGSTAB) algorithm with incomplete LU factorization precondictioning was employed to solve this ill posed linear system. The results show that this algorithm has advantages of high performance, high precision and stability and can improve the performance and the precision of induction logging forward modeling.

Key words: induction logging, finite deference frequencydomain (FDFD), twodimensional forward modeling, incomplete LU factorization, biconjugate gradient stabilized method (BICGSTAB)

熊杰, 邹长春, 孟小红. 不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟[J]. 现代地质, 2012, 26(6): 1283-1288.

XIONG Jie, JU Chang-Chun, MENG Xiao-Gong. 6Using the BICGSTAB Algorithm with the Incomplete LU Factorization Precondictioning to Implement 2D FDFD Induction Logging Fast Forward Modeling[J]. Geoscience, 2012, 26(6): 1283-1288.