An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

Gao, Kai; Fu, Shubin; Chung, Eric T.

doi:10.1785/0120170268

Title: An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

Abstract

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscale basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale methodmore »« less

Authors:

Gao, Kai ^[1]; Fu, Shubin ^[2]; Chung, Eric T. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Chinese Univ. of Hong Kong (China)

Publication Date:: Tue Feb 13 00:00:00 EST 2018

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE). Geothermal Technologies Office (EE-4G)

OSTI Identifier:: 1423976

Report Number(s):: LA-UR-17-27304
Journal ID: ISSN 1943-3573

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Bulletin of the Seismological Society of America (Online)

Additional Journal Information:: Journal Name: Bulletin of the Seismological Society of America (Online); Journal Volume: 108; Journal Issue: 2; Journal ID: ISSN 1943-3573

Publisher:: Seismological Society of America

Country of Publication:: United States

Language:: English

Subject:: 58 GEOSCIENCES; Earth Sciences

Citation Formats


                    Gao, Kai, Fu, Shubin, and Chung, Eric T. An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation.  United States: N. p., 2018. 
Web.  doi:10.1785/0120170268.

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                    Gao, Kai, Fu, Shubin, & Chung, Eric T. An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation.  United States.  https://doi.org/10.1785/0120170268

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                    Gao, Kai, Fu, Shubin, and Chung, Eric T. Tue .  
"An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation".  United States.  https://doi.org/10.1785/0120170268.  https://www.osti.gov/servlets/purl/1423976.

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@article{osti_1423976,

  title        = {An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation},

  author       = {Gao, Kai and Fu, Shubin and Chung, Eric T.},

  abstractNote = {The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscale basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.},

  doi          = {10.1785/0120170268},

  journal      = {Bulletin of the Seismological Society of America (Online)},

  number       = 2,

  volume       = 108,

  place        = {United States},

  year         = {Tue Feb 13 00:00:00 EST 2018},

  month        = {Tue Feb 13 00:00:00 EST 2018}

}

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Works referencing / citing this record:

Multiscale model reduction of the wave propagation problem in viscoelastic fractured media
journal, January 2019

Vasilyeva, M.; De Basabe, J. D.; Efendiev, Y.
Geophysical Journal International, Vol. 217, Issue 1
DOI: 10.1093/gji/ggz043

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