Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

Handle URI:
http://hdl.handle.net/10754/598096
Title:
Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method
Authors:
Chu, Chunlei; Stoffa, Paul L.
Abstract:
Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.
Citation:
OCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html><head> <title>Current Links for doi: 10.1190/geo2011-0415.1 </title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <!--geophysics.html--></head><style> body { font-size: 100%; font-family: arial, times; } #prime { padding: 5px; } #second { padding: 5px; } #links { padding: 5px; } #data { padding:5px; } #top { padding:5px; }</style><body><div id="top"> <img src="/docs/iPage/images/SEG_corp_logo.jpg" alt="SEG Corp Logo"/> <p> The Society of Exploration Geophysicists is a not-for-profit organization that promotes the science of applied geophysics and the education of geophysicists. SEG, founded in 1930, fosters the expert and ethical practice of geophysics in the exploration and development of natural resources, in characterizing the near surface, and in mitigating earth hazards. The Society, which has more than 33 000 members in 138 countries, fulfills its mission through its publications, conferences, forums, Web sites, and educational opportunities. </p> <hr/></div><div id="data"> <table width="450"> <tr><td><b>Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method</b></td></tr><tr><td>Chu,Chunlei et al.</td></tr><tr><td><i>GEOPHYSICS</i>(2012),77(4):T117</td></tr><tr><td><a href='http://dx.doi.org/10.1190/geo2011-0415.1'>http://dx.doi.org/10.1190/geo2011-0415.1</td></tr> </table> <hr/></div><div id="links"> <p> This article is available from multiple sources. <br/>Please click on the logo of the service to which you have a subscription, or click any logo to obtain pay-per-view access. </p> <div id="prime"> <a href=http://library.seg.org/doi/abs/10.1190/geo2011-0415.1><img src="/docs/iPage/images/segdl_logo.gif" alt="SEGDL Logo"/></a> </div> <div id="second"> <a href=http://geophysics.geoscienceworld.org/cgi/doi/10.1190/geo2011-0415.1><img src="/docs/iPage/images/gswbanner.gif" alt="GSW Logo"/></a> </div></div></body></html>
Publisher:
Society of Exploration Geophysicists
Journal:
GEOPHYSICS
Issue Date:
Jul-2012
DOI:
10.1190/GEO2011-0415.1
Type:
Article
ISSN:
0016-8033; 1942-2156
Sponsors:
Stoffa would like to acknowledge the King Abdullah University of Science and Technology (KAUST) for their support of his research. We are grateful to associate editor Jeff Shragge and the reviewers for their constructive comments which helped significantly improve the original manuscript. We also thank ConocoPhillips for permission to publish this work.
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Full metadata record

DC FieldValue Language
dc.contributor.authorChu, Chunleien
dc.contributor.authorStoffa, Paul L.en
dc.date.accessioned2016-02-25T13:12:36Zen
dc.date.available2016-02-25T13:12:36Zen
dc.date.issued2012-07en
dc.identifier.citationOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html><head> <title>Current Links for doi: 10.1190/geo2011-0415.1 </title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <!--geophysics.html--></head><style> body { font-size: 100%; font-family: arial, times; } #prime { padding: 5px; } #second { padding: 5px; } #links { padding: 5px; } #data { padding:5px; } #top { padding:5px; }</style><body><div id="top"> <img src="/docs/iPage/images/SEG_corp_logo.jpg" alt="SEG Corp Logo"/> <p> The Society of Exploration Geophysicists is a not-for-profit organization that promotes the science of applied geophysics and the education of geophysicists. SEG, founded in 1930, fosters the expert and ethical practice of geophysics in the exploration and development of natural resources, in characterizing the near surface, and in mitigating earth hazards. The Society, which has more than 33 000 members in 138 countries, fulfills its mission through its publications, conferences, forums, Web sites, and educational opportunities. </p> <hr/></div><div id="data"> <table width="450"> <tr><td><b>Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method</b></td></tr><tr><td>Chu,Chunlei et al.</td></tr><tr><td><i>GEOPHYSICS</i>(2012),77(4):T117</td></tr><tr><td><a href='http://dx.doi.org/10.1190/geo2011-0415.1'>http://dx.doi.org/10.1190/geo2011-0415.1</td></tr> </table> <hr/></div><div id="links"> <p> This article is available from multiple sources. <br/>Please click on the logo of the service to which you have a subscription, or click any logo to obtain pay-per-view access. </p> <div id="prime"> <a href=http://library.seg.org/doi/abs/10.1190/geo2011-0415.1><img src="/docs/iPage/images/segdl_logo.gif" alt="SEGDL Logo"/></a> </div> <div id="second"> <a href=http://geophysics.geoscienceworld.org/cgi/doi/10.1190/geo2011-0415.1><img src="/docs/iPage/images/gswbanner.gif" alt="GSW Logo"/></a> </div></div></body></html>en
dc.identifier.issn0016-8033en
dc.identifier.issn1942-2156en
dc.identifier.doi10.1190/GEO2011-0415.1en
dc.identifier.urihttp://hdl.handle.net/10754/598096en
dc.description.abstractFrequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.en
dc.description.sponsorshipStoffa would like to acknowledge the King Abdullah University of Science and Technology (KAUST) for their support of his research. We are grateful to associate editor Jeff Shragge and the reviewers for their constructive comments which helped significantly improve the original manuscript. We also thank ConocoPhillips for permission to publish this work.en
dc.publisherSociety of Exploration Geophysicistsen
dc.subject3Den
dc.subjectFourier transformen
dc.subjectModelingen
dc.titleEfficient 3D frequency response modeling with spectral accuracy by the rapid expansion methoden
dc.typeArticleen
dc.identifier.journalGEOPHYSICSen
dc.contributor.institutionConocoPhillips, Houston, United Statesen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
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