|本期目录/Table of Contents|

[1]李孟洋,刘少林,杨顶辉,等.谱元法模拟地震波传播地震点源处理方法[J].地震研究,2025,(03):401-412.[doi:10.20015/j.cnki.ISSN1000-0666.2025.0042 ]
　LI Mengyang,LIU Shaolin,YANG Dinghui,et al.The Approximation Approaches for Seismic Point Sources with Spectral Element Method When Simulating Seismic Wavefields[J].Journal of Seismological Research,2025,(03):401-412.[doi:10.20015/j.cnki.ISSN1000-0666.2025.0042 ]
点击复制

谱元法模拟地震波传播地震点源处理方法(PDF/HTML)

《地震研究》[ISSN:1000-0666/CN:53-1062/P]

卷:
期数:
2025年03期
页码:
401-412
栏目:
出版日期:
2025-04-15

文章信息/Info

Title:
The Approximation Approaches for Seismic Point Sources with Spectral Element Method When Simulating Seismic Wavefields
作者:
李孟洋1; 2; 刘少林2; 杨顶辉3; 李小凡4
(1.中国科学院大学 地球与行星科学学院,北京 100049; 2.应急管理部国家自然灾害防治研究院,北京 100085; 3.清华大学 数学科学系,北京 100084; 4.中国地质大学 地球物理与空间信息学院,武汉 430074)
Author(s):
LI Mengyang1; 2; LIU Shaolin2; YANG Dinghui3; LI Xiaofan4
(1.College of Earth and Planetary Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)(2.National Institute of Natural Hazards,Ministry of Emergency Management of China,Beijing 100085,China)(3.Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China)(4.Institute of Geophysics and Geomatics,China University of Geosciences,Wuhan 430074,Hubei,China)
关键词:
谱元法;  地震波运动方程;  数值模拟;  δ函数
Keywords:
the spectral element method;  seismic wave function;  numerical simulation;  δ function
分类号:
P315.3
DOI:
10.20015/j.cnki.ISSN1000-0666.2025.0042
摘要:
在利用谱元法求解地震波运动方程时需要对方程进行离散,然而由于震源项常包含δ函数,该函数是奇异函数,通过数值近似具有一定难度,因此需要采用特殊方式处理震源项。引入δ函数的2类离散形式,以谱元法求解地震波运动方程为例,详细给出了震源项离散形式。为了验证这种震源处理方法的有效性,开展了多组数值模拟实验。首先在规则网格下,模拟了δ函数离散形式处理单极震源和矩张量震源的情况; 其次在非规则网格下,模拟了δ函数离散形式处理地震点源情况。数值实验表明,在谱元法模拟地震波传播时,利用δ函数离散形式近似地震点源项,可得到高精度数值模拟结果。
Abstract:
When solving the seismic wave equation with the spectral element method,it is necessary to discretize the equation.However,due to the presence of the δ function in the source term,which is a singular function,achieving accurate numerical approximation poses certain challenges.Therefore,special techniques are required to handle the source term.Two types of discrete forms of delta function are introduced in this paper.Using the spectral element method for numerical solution of seismic wave propagation,the discretized form of the source term is presented in detail.To validate the effectiveness of this source treatment approach,several numerical experiments were conducted.Firstly,the discrete form of the δ function was simulated for handling single-force and moment tensor sources on regular grid models.Secondly, the discrete form of the δ function was simulated for handling seismic point sources on an irregular grid model. The numerical experiments demonstrate that when simulating seismic wave propagation with the spectral element method,approximating the point source term with the discrete form of delta function can help to obtain high-precision results from numerical simulation.

参考文献/References:


李冰非,董兴朋,李小凡,等.2019.基于辛-谱元-FK混合方法的保结构远震波场模拟[J].地球物理学报,62(11):4339-4352.
Li B F,Dong X P,Li X F,et al.2019.Structure-preserving modeling of teleseismic wavefield using symplectic SEM-FK hybrid method[J].Chinese Journal of Geophysics,62(11):4339-4352.(in Chinese)
刘璐,刘洪,刘红伟.2013.优化15点频率-空间域有限差分正演模拟[J].地球物理学报,56(2):644-652.
Liu L,Liu H,Liu H W.2013.Optimal 15-point finite difference forward modeling in frequency-space domain[J].Chinese Journal of Geophysics,56(2):644-652.(in Chinese)
刘少林,杨顶辉,徐锡伟,等.2021.模拟地震波传播的三维逐元并行谱元法[J].地球物理学报,64(3):993-1005.
Liu S L,Yang D H,Xu X W,et al.2021.Three-dimensional element-by-element parallel spectral-element method for seismic wave modeling[J].Chinese Journal of Geophysics,64(3):993-1005.(in Chinese)
刘玉柱,黄鑫泉,万先武,等.2019.各向异性介质弹性波多参数全波形反演[J].地球物理学报,62(5):1809-1823.
Liu Y Z,Huang X Q,Wan X W,et al.2019.Elastic multi-parameter [HJ2.15mm]full-waveform inversion for anisotropic media[J].Chinese Journal of Geophysics,62(5):1809-1823.(in Chinese)
孟雪莉,刘少林,杨顶辉,等.2022.基于优化数值积分的谱元法模拟地震波传播[J].石油地球物理勘探,57(3):602-612.
Meng X L,Liu S L,Yang D H,et al.2022.Spectral-element method based on optimal numerical integration for seismic waveform modeling[J].Oil Geophysical Prospecting,57(3):602-612.(in Chinese)
王光文,卢占武,李文辉,等.2023.深地震反射剖面探测技术发展现状[J].地球与行星物理论评,54(2):120-139.
Wang G W,Lu Z W,Li W H,et al.2023.Development status of deep seismic reflection profile detection technology[J].Reviews of Geophysics and Planetary Physics,54(2):120-139.(in Chinese)
杨尚倍,白超英,周兵.2018.起伏地表下基于改进BISQ模型双相介质中曲线网格有限差分法波场模拟[J].地球物理学报,61(8):3356-3373.
Yang S B,Bai C Y,Zhou B.2018.Wavefield modeling in two-phase media including undulated topography based on reformulated BISQ model by Curvilinear Grid FD method[J].Chinese Journal of Geophysics,61(8):3356-3373.(in Chinese)
Bielak J,Ghattas O,Kim E J.2005.Parallel octree-based finite element method for large-scale earthquake ground motion simulation[J].Computer Modeling in Engineering and Sciences,10(2):99.
Chen Z Y,Wu T T,Yang H Q.2011.An optimal 25-point finite difference scheme for the Helmholtz equation with PML[J].Journal of Computational and Applied Mathematics,236(6):1240-1258.
Cho Y C,Gibson R L.2019.Reverse time migration via frequency-adaptive multiscale spatial grids[J].Geophysics,84(2):S41-S55.
De Hoop A.1959.The surface line source problem[J].Applied Scientific Research,8(4):349-256.
Feng Z C,Schuster G T.2017.Elastic least-squares reverse time migration[J].Geophysics,82(2):S143-S157.
Herrmann R.1979.SH-wave generation by dislocation sources-a numerical study[J].Bulletin of the Seismological Society of America,69(1):1-15.
Hicks G.2002.Arbitrary source and receiver positioning in finite-difference schemes using Kaiser windowed sinc functions[J].Geophysics,67(1):156-166.
Jung J H.2009.A note on the spectral collocation approximation of some differential equations with singular source terms[J].Journal of Scientific Computing,39:49-66.
Komatitsch D,Tromp J.1999.Introduction to the spectral element method for three-dimensional seismic wave propagation[J].Geophysical Journal International,139(3):806-822.
Komatitsch D,Tromp J.2002.Spectral-element simulations of global seismic wave propagation-I[J].Validation,Geophysical Journal International,149(2):390-412.
Lay T.1992.Seismology,theoretical[M]//Nierenberg W A.Encyclopedia of earth system science(Volume 4):San Diego:Academic Press,inc.Harcourt Brace jovanovich,Publishers,153-174.
Lei W,Liu Y T,Li G,et al.2023.2D frequency-domain finite-difference acoustic wave modeling using optimized perfectly matched layers[J].Geophysics,88(2):F1-F13.
Lin Y Z,van Leeuwen T,Liu H S,et al.2023.A fast wavefield reconstruction inversion solution in the frequency domain[J].Geophysics,88(3):R257-R267.
Liu S L,Li X F,Wang W S,et al.2014.A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling[J].Journal of Geophysics and Engineering,11(5):055009.
Lyu C,Capdeville Y,Zhao L.2020.Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation[J].Geophysics,85(1):T33-T43.
Mazzieri I,Stupazzini M,Guidotti R,et al.2013.SPEED:SPectral elements in Elastodynamics with discontinuous galerkin:A non-conforming approach for 3D multi-scale problems[J].International Journal for Numerical Methods in Engineering,95(12):991-1010.
Seriani G.1997.A parallel spectral element method for acoustic wave modeling[J].Journal of Computational Acoustics,5(1):53-69.
Shen W H,Yang D H,Xu X W,et al.2022.3D simulation of ground motion for the 2015 MW7.8 Gorkha earthquake,Nepal,based on the spectral element method[J].Natural Hazards,112(3):2853-2871.
Tape C,Liu Q,Maggi A,et al.2010.Seismic tomography of the southern California crust based on spectral-element and adjoint methods[J].Geophysical Journal International,180(1):433-462.
Tong P,Komatitsch D,Tseng T L,et al.2014.A 3-D spectral-element and frequency-wave number hybrid method for high-resolution seismic array imaging[J].Geophysical Research Letters,41(20):7025-7034.
Tromp J,Komatitsch D,Liu Q.2008.Spectral-element and adjoint methods in seismology[J].Communications in Computational Physics,3(1):1-32.
Tromp J,Tape C,Liu Q.2005.Seismic tomography,adjoint methods,time reversal and banana-doughnut kernels[J].Geophysical Journal International,160(1):195-216.
Yao G,da Silva N V,Debens H A,et al.2018.Accurate seabed modeling using finite difference methods[J].Computational Geosciences,22:469-484.
Yi J,Liu Y K,Yang Z Q,et al.2019.A least-squares correlation-based full traveltime inversion for shallow subsurface velocity reconstruction[J].Geophysics,84(4):R613-R624.
Zang N,Zhang W,Chen X F.2021.An overset-grid finite-difference algorithm for simulating elastic wave propagation in media with complex free-surface topography[J].Geophysics,86(4):T277-T292.


备注/Memo

备注/Memo:
收稿日期:2024-05-20.
基金项目:国家自然科学基金(42174111); 北京市自然科学基金(8222033); 上海佘山地球物理国家野外科学观测研究站开放基金项目(SSOP202203).
第一作者简介:李孟洋(1995-),博士研究生在读,主要从事地震数值模拟、地震层析成像方面的研究.E-mail:limengyang22@mails.ucas.ac.cn.
通信作者简介:刘少林(1988-),研究员,主要从事地震波正反演研究.E-mail:shaolinliu88@163.com.
更新日期/Last Update: 2025-04-15