郎超^1,,
仇楚钧²,
刘少林³,
申文豪³,
李小凡⁴,
徐锡伟^3,,
1. 北京信息科技大学理学院, 北京 100192
2. 清华大学数学科学系, 北京 100084
3. 应急管理部国家自然灾害防治研究院, 北京 100085
4. 中国地质大学(武汉)地球物理与空间信息学院, 武汉 430074

基金项目: 中国地震局地壳应力研究所中央级公益性科研院所基本科研业务专项资助项目(ZDJ2019-18)，国家自然科学青年基金(41804051)，北京市教委科技一般项目(KM202111232009)联合资助


详细信息

作者简介: 郎超, 男, 1988年生, 北京信息科技大学副教授, 主要从事地震波正反演的研究工作.E-mail: langc14@tsinghua.org.cn

通讯作者: 徐锡伟, 男, 研究员, 主要从事活动断层构造与地震关系研究.E-mail: xiweixu@vip.sina.com

中图分类号: P315

收稿日期:2020-11-24
修回日期:2020-12-27
上线日期:2021-08-10

A nearly discrete analytic method of wave-field simulation for elastic wave equations in the frequency domain

LANG Chao^1,,
QIU ChuJun²,
LIU ShaoLin³,
SHEN WenHao³,
LI XiaoFan⁴,
XU XiWei^3,,
1. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
2. Department of Mathematics, Tsinghua University, Beijing 100084, China
3. Institute of Natural Hazards, Ministry of Emergency Management of China, Beijing 100085, China
4. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China


More Information

Corresponding author: XU XiWei,E-mail:xiweixu@vip.sina.com

MSC: P315

--> Received Date: 24 November 2020
Revised Date: 27 December 2020
Available Online: 10 August 2021


摘要
摘要:为提高频率域弹性波动方程数值求解的计算效率，本文引入近似解析离散化(NAD)方法将其进行数值离散并得到大型线性代数方程组.在详细分析了相应系数矩阵的稀疏分块结构与数学性质之后，本文提出采用不精确旋转分块三角预处理子加速Krylov子空间迭代方法来快速求解该线性方程组，并利用数值试验证实这种方法在弹性波场模拟方面的数值效率.通过与另外两种经典数值方法(常规有限差分方法和交错网格有限差分方法)对多种介质模型进行波场模拟、数值频散分析以及与解析解的波形对比，NAD方法显示了其在压制数值频散和提高计算效率方面的优势以及对复杂介质模型弹性波场数值模拟的有效性.
关键词: 频率域弹性波动方程/
近似解析离散化/
预处理迭代方法/
波场模拟/
频散分析

Abstract:To improve the computing efficiency of numerically solving frequency-domain elastic wave equation, this paper introduces nearly analytic discrete (NAD) method for numerically discretizing the frequency-domain elastic wave equation to obtain a large-scale linear algebraic system. After the detailed analysis for sparse block structure and mathematical property of the corresponding coefficient matrix, the inexact rotated block triangular preconditioners are proposed to accelerate Krylov subspace iteration methods to solve the linear system and the numerical efficiency of such methods for elastic wave simulation is examined by numerical experiments. When comparing with the other two classical numerical schemes (ordinary finite difference method and staggered grid method) in wave-field simulation, numerical dispersion analysis and waveform comparison with analytic solution for various models, NAD method shows its advantages of increasing computing efficiency, suppressing numerical dispersion and the effectiveness of numerical simulation in complicated media.
Key words:Frequency-domain elastic wave equation/
Nearly analytic discrete/
Preconditioned iteration method/
Wave-field simulation/
Dispersion analysis



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