王健^1,,
贺茜君²,
董兴朋¹,
杨顶辉^1,,,
李静爽³,
黄雪源²,
周艳杰²
1. 清华大学数学科学系, 北京 100084
2. 北京工商大学数学与统计学院应用统计系, 北京 100048
3. 中国矿业大学(北京)理学院, 北京 100083

基金项目: 国家自然科学基金地震联合基金项目（U1839206）和国家重点研发计划项目（2017YFC1500301）联合资助


详细信息

作者简介: 王健, 男, 1989年生, 博士, 主要研究方向为基于地震波动方程的正、反演方法.E-mail: wangjian012050@163.com

通讯作者: 杨顶辉, 教授, 主要从事计算地球物理、孔隙介质波传播理论、地震层析成像等研究.E-mail: ydh@mail.tsinghua.edu.cn

中图分类号: P631;P315

收稿日期:2020-12-24
修回日期:2021-04-21
上线日期:2021-11-10

A modified time-space optimized symplectic method for solving 3D elastic wave equations

WANG Jian^1,,
HE XiJun²,
DONG XingPeng¹,
YANG DingHui^1,,,
LI JingShuang³,
HUANG XueYuan²,
ZHOU YanJie²
1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2. School of Mathematics and Statistics, Beijing Technology and Business University(BTBU), Beijing 100048, China
3. School of Science, China University of Mining and Technology(Beijing), Beijing 100083, China


More Information

Corresponding author: YANG DingHui,E-mail:ydh@mail.tsinghua.edu.cn

MSC: P631;P315

--> Received Date: 24 December 2020
Revised Date: 21 April 2021
Available Online: 10 November 2021


摘要
摘要:正演计算是反演研究的基础，为了实现基于三维弹性波方程的全波形反演成像，发展准确、高效、低数值频散的三维正演模拟方法至关重要.为此，本文将修正保辛分部龙格-库塔格式与优化有限差分算子结合，发展了用于数值求解三维弹性波方程的修正时空优化保辛方法（MTSOS）.新方法使用二级龙格-库塔格式达到了三阶时间精度，且更适用于求解非均匀介质情况下的弹性波方程，数值频散误差小于同精度保辛分部龙格-库塔（SPRK）方法的误差，提高了计算精度.波场模拟结果表明，三维MTSOS方法可以精确给出数值模拟结果，能够清晰模拟地震波传播过程中产生的各种震相、有效压制数值频散.
关键词: 数值模拟/
三维弹性波方程/
非均匀介质

Abstract:Forward modeling is the basis of inversion research. In order to achieve full waveform inversion imaging based on 3D elastic wave equation, it is necessary to develop accurate and efficient 3D forward modeling methods with low numerical dispersion. For that reason, this paper combines the optimized finite difference operator with the modified symplectic partitioned Runge-Kutta (SPRK) scheme and extends it to 3D to develop a modified time-space optimized symplectic method (MTSOS) for solving the elastic wave equation in 3D inhomogeneous media. The method uses a second-order scheme to achieve third-order time accuracy, and is more suitable for solving the inhomogeneous medium model. The numerical dispersion error is smaller than the SPRK method, which improves the calculation accuracy. The numerical results show that the MTSOS method can give numerical simulation results accurately. The various phases in the inhomogeneous medium can be clearly seen, and there is no visible numerical dispersion, which shows the effectiveness of the new method.
Key words:Numerical simulation/
Three-dimensional elastic wave equation/
Inhomogeneous medium



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