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Spectral-element method with an optimal mass matrix for seismic wave modelling
Liu, Shaolin1,2; Yang, Dinghui3; Xu, Xiwei1; Wang, Wenshuai4; Li, Xiaofan5; Meng, Xueli1,4
2022-02-25
Source PublicationEXPLORATION GEOPHYSICS
ISSN0812-3985
Pages11
AbstractThe spectral-element method (SEM), which combines the flexibility of the finite element method (FEM) with the accuracy of spectral method, has been successfully applied to simulate seismic wavefields in geological models on different scales. One kind of SEMs that adopts orthogonal Legendre polynomials is widely used in seismology community. In the SEM with orthogonal Legendre polynomials, the Gauss-Lobatto-Legendre (GLL) quadrature rule is employed to calculate the integrals involved in the SEM leading to a diagonal mass matrix. However, the GLL quadrature rule can exactly approximate only integrals with a polynomial degree below 2N-1 (N is the interpolation order in space) and cannot exactly calculate those of polynomials with degree 2N involved in the mass matrix. Therefore, the error of the mass matrix originating from inexact numerical integration may reduce the accuracy of the SEM. To improve the SEM accuracy, we construct a least-squares objective function in terms of numerical and exact integrals to increase the accuracy of the GLL quadrature rule. Then, we utilise the conjugate gradient method to solve the objective function and obtain a set of optimal quadrature weights. The optimal mass matrix can be obtained simultaneously by utilising the GLL quadrature rule with optimal integration weights. The improvement in the numerical accuracy of the SEM with an optimal mass matrix (OSEM) is demonstrated by theoretical analysis and numerical examples.
KeywordSpectral-element method numerical integration seismic wave modelling forward modelling
DOI10.1080/08123985.2022.2043126
Funding OrganizationNational Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution
WOS KeywordDISCONTINUOUS GALERKIN METHOD ; FINITE-DIFFERENCE ; PROPAGATION ; SCHEME ; DISPERSION ; EQUATION ; SIMULATIONS ; STABILITY ; OPERATORS ; DYNAMICS
Language英语
Funding ProjectNational Institute of Natural Hazards, Ministry of Emergency Management of China[ZDJ2019-18] ; National Natural Science Foundation of China[U1839206] ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution[SKL-K202101]
Funding OrganizationNational Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Institute of Natural Hazards, Ministry of Emergency Management of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution ; Open Fund Project of the State Key Laboratory of Lithospheric Evolution
WOS Research AreaGeochemistry & Geophysics
WOS SubjectGeochemistry & Geophysics
WOS IDWOS:000766119000001
PublisherTAYLOR & FRANCIS LTD
Citation statistics
Document Type期刊论文
Identifierhttp://ir.iggcas.ac.cn/handle/132A11/104977
Collection岩石圈演化国家重点实验室
Corresponding AuthorYang, Dinghui
Affiliation1.Natl Inst Nat Hazards, Minist Emergency Management China, Beijing, Peoples R China
2.Chinese Acad Sci, Inst Geol & Geophys, State Key Lab Lithospher Evolut, Beijing, Peoples R China
3.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
4.Ningxia Univ, Sch Math & Stat, Yinchuan, Ningxia, Peoples R China
5.China Univ Geosci, Inst Geophys & Geomat, Wuhan, Peoples R China
First Author AffilicationInstitute of Geology and Geophysics, Chinese Academy of Sciences
Recommended Citation
GB/T 7714
Liu, Shaolin,Yang, Dinghui,Xu, Xiwei,et al. Spectral-element method with an optimal mass matrix for seismic wave modelling[J]. EXPLORATION GEOPHYSICS,2022:11.
APA Liu, Shaolin,Yang, Dinghui,Xu, Xiwei,Wang, Wenshuai,Li, Xiaofan,&Meng, Xueli.(2022).Spectral-element method with an optimal mass matrix for seismic wave modelling.EXPLORATION GEOPHYSICS,11.
MLA Liu, Shaolin,et al."Spectral-element method with an optimal mass matrix for seismic wave modelling".EXPLORATION GEOPHYSICS (2022):11.
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