刘少林^1,4,,
杨顶辉^2,,,
徐锡伟¹,
李小凡³,
申文豪¹,
刘有山⁴
1. 应急管理部国家自然灾害防治研究院, 北京 100085
2. 清华大学数学科学系, 北京 100084
3. 中国地质大学地球物理与空间信息学院, 武汉 430074
4. 中国科学院地质与地球物理研究所, 岩石圈演化国家重点实验室, 北京 100029

基金项目: 应急管理部国家自然灾害防治研究院基本科研业务专项(ZDJ2019-18)，岩石圈演化国家重点实验室开放课题(SKL-K201804)，国家重点研发计划项目课题(2017YFC1500301)和国家自然科学基金(42064004)联合资助


详细信息

作者简介: 刘少林, 应急管理部国家自然灾害防治研究院研究员, 主要从事地震波正反演研究.E-mail: shaolinliu88@163.com

通讯作者: 杨顶辉, 清华大学数学科学系教授, 从事计算地球物理研究.E-mail: ydh@tsinghua.edu.cn

中图分类号: P315

收稿日期:2020-10-27
修回日期:2020-12-26
上线日期:2021-03-10

Three-dimensional element-by-element parallel spectral-element method for seismic wave modeling

LIU ShaoLin^1,4,,
YANG DingHui^2,,,
XU XiWei¹,
LI XiaoFan³,
SHEN WenHao¹,
LIU YouShan⁴
1. National Institute of Natural Hazards, Ministry of Emergency Management of China, Beijing 100085, China
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
3. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China
4. State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China


More Information

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

MSC: P315

--> Received Date: 27 October 2020
Revised Date: 26 December 2020
Available Online: 10 March 2021


摘要
摘要:高效地震波场正演模拟对于复杂模型中地震波传播与成像研究至关重要.本文在谱元法原理框架内，对已有逐元谱元法改进，提出一种新的逐元并行谱元法求解三维地震波运动方程，并得到地震波场.逐元并行谱元法的核心思想在于在单元上进行质量矩阵与解向量的乘积运算，并将此运算平均分配至每一个CPU计算核心，此处理有利提升谱元法的并行计算效率.同时，根据Gauss-Lobatto-Legendre (GLL)数值积分点与插值点重合的特点，将稠密单元刚度矩阵的存储转化成单元雅克比矩阵行列式的值及其逆的存储，大幅减少谱元法计算内存开销.此外，在模型边界上利用逐元并行谱元法求解二阶位移形式完美匹配层(PML)吸收边界条件，消除边界截断而引入的虚假反射.通过逐元并行谱元法得到的数值解与解析解对比，以及实际地震波场模拟，数值结果证实了逐元并行谱元法用于地震波场模拟的高效性.
关键词: 地震波/
谱元法/
正演模拟/
PML吸收边界条件

Abstract:High-efficient seismic wave forward modeling is important for the investigation of seismic wave phenomenon in complex media and the imaging of subsurface structures of the Earth. In the framework of spectral-element method (SEM),we improve the computation efficiency of the previous element-by-element method and propose a new element-by-element parallel spectral-element method (EBE-SEM) for solving 3D seismic wave equation to obtain seismic wavefield. The essential idea of EBE-SEM is that the products of stiffness matrix and solution vector are operated on element level,and the products are equally distributed to each CPU processor. This strategy can greatly increase the parallelization of SEM. Because Gauss-Legendre-Lobatto integration points coincide with the interpolation points in SEM,the storage of dense element stiffness matrix can be transformed to the storage of the determinant and inversion of element Jacobian matrix,and therefore the efficiency of EBE-SEM can be further increased. To eliminate the reflected wave from truncated boundary,we solve the second-order perfectly matched layer (PML) absorbing boundary condition that is constructed at the boundary of the computational domain. The validity and efficiency of the EBE-SEM are demonstrated by two numerical examples.
Key words:Seismic wave/
Spectral-element method/
Forward modeling/
PML absorbing boundary condition



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