司洁戈^1,2,3,,
李小凡^1,2,,
张欢^1,2,4,
李冰非^1,2,
马晓娜^1,2,
鹿璐^1,2,5,
陈世仲⁶
1. 中国科学院地质与地球物理研究所, 地球与行星物理重点实验室, 北京 100029
2. 中国科学院大学, 北京 100049
3. 中国电子科技集团公司第三研究所, 北京 100015
4. 中国船舶工业系统工程研究院, 北京 100094
5. 北京和德宇航技术有限公司, 北京 100085
6. 华北水利水电大学资源与环境学院, 郑州 450046

基金项目: 国家自然科学基金（41574053）资助


详细信息

作者简介: 司洁戈, 男, 在读博士研究生, 主要从事地震波数值模拟研究.E-mail:sijiege@126.com

通讯作者: 李小凡, 研究员, 主要从事地球物理非线性反演理论及应用研究、地震全波场、月震学、月球内部物理及结构的研究

中图分类号: P631;P315

收稿日期:2018-03-14
修回日期:2019-02-24
上线日期:2019-05-05

Frequency-domain acoustic wave modeling using regularized preconditioning iterative method

SI JieGe^1,2,3,,
LI XiaoFan^1,2,,
ZHANG Huan^1,2,4,
LI BingFei^1,2,
MA XiaoNa^1,2,
LU Lu^1,2,5,
CHEN ShiZhong⁶
1. Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. The 3^rd Research Institute of CETC, Beijing 100015, China
4. Systems Engineering Research Institute of CSSC, Beijing 100094, China
5. China Head Aerospace Technology Co., Ltd., Beijing 100085, China
6. School of Resources and Environment, North China University of Water Resources and Electric Power, Zhengzhou 450046, China


More Information

Corresponding author: LI XiaoFan

MSC: P631;P315

--> Received Date: 14 March 2018
Revised Date: 24 February 2019
Available Online: 05 May 2019


摘要
摘要:高精度及高效频率域声波数值模拟的关键在于高效求解声波方程经离散化后得到的大型稀疏线性方程组.该方程组系数矩阵具有很强的稀疏性，非对称性和非正定性等特征，常用的迭代算法难以准确、高效地求解.为了改善数值模拟迭代算法的收敛性与稳定性，在算法基础上添加预条件算子是求解该类方程的常用方案.本文基于以上思路，引入正则化技术来构造合适的预条件算子，提出正则化预条件迭代算法，以加速求解方程组.通过包含有均匀介质和高非均匀度介质（Marmousi）模型的数值模拟实验结果表明：与单独使用迭代算法相比，本文提出的正则化预条件迭代算法在计算量方面仅多了一次矩阵-矢量相乘，内存消耗未增加；同时，基于该算法的数值模拟结果能够满足精度要求，较单独使用迭代法能够有效改善收敛性质，加快收敛速度；而且，在二维模型算例下，与LU分解算法相比，基于该算法的内存消耗大幅下降.
关键词: 正则化预条件算子/
拟牛顿迭代算法/
频率域声波数值模拟

Abstract:One of the keys for efficient numerical modeling of frequency-domain acoustic wave modeling is to solve a large sparse and linear system, which the coefficient matrix have the character of non-symmetric and non-positive. To improve the convergence property and robustness of numerical modeling, we have developed a new regularized preconditioning iterative method that enforced the sparsity of solutions in frequency-domain. The construction of preconditioner requires the regularization for large sparse original problem firstly, which is called regularized system. Then we regarded the approximate iterative solution of the regularized system as initial value of original problem. The numerical computational experiments including the synthetic complex model indicate that the extra computation of the method is almost negligible. By comparison with the storage space of LU decomposition, the regularized preconditioning iterative algorithm is dramatically decreased. Besides, effectiveness and convergence rates of regularized preconditioning iterative solvers are greatly improved by regularized preprocessing.
Key words:Regularized preconditioning technique/
Quasi-Newton method/
Acoustic wave modeling



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