Determination of finite-difference weights using scaled binomial windows

Handle URI:
http://hdl.handle.net/10754/597955
Title:
Determination of finite-difference weights using scaled binomial windows
Authors:
Chu, Chunlei; Stoffa, Paul L.
Abstract:
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 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/geo2011-0336.1 </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>Determination of finite-difference weights using scaled binomial windows</b></td></tr><tr><td>Chu,Chunlei et al.</td></tr><tr><td><i>GEOPHYSICS</i>(2012),77(3):W17</td></tr><tr><td><a href='http://dx.doi.org/10.1190/geo2011-0336.1'>http://dx.doi.org/10.1190/geo2011-0336.1</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/geo2011-0336.1><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/geo2011-0336.1><img src="/docs/iPage/images/gswbanner.gif" alt="GSW Logo"/></a> </div></div></body></html>
Publisher:
Society of Exploration Geophysicists
Journal:
GEOPHYSICS
Issue Date:
May-2012
DOI:
10.1190/geo2011-0336.1
Type:
Article
ISSN:
0016-8033; 1942-2156
Sponsors:
Stoffa would like to acknowledge the King Abdullah Universityof Science and Technology for their support of his research. We aregrateful to associate editor Stig Hestholm and the reviewers for theirconstructive comments which helped improve the original manuscript.We thank ConocoPhillips for permission to publishthis work.
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Full metadata record

DC FieldValue Language
dc.contributor.authorChu, Chunleien
dc.contributor.authorStoffa, Paul L.en
dc.date.accessioned2016-02-25T12:59:29Zen
dc.date.available2016-02-25T12:59:29Zen
dc.date.issued2012-05en
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/geo2011-0336.1 </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>Determination of finite-difference weights using scaled binomial windows</b></td></tr><tr><td>Chu,Chunlei et al.</td></tr><tr><td><i>GEOPHYSICS</i>(2012),77(3):W17</td></tr><tr><td><a href='http://dx.doi.org/10.1190/geo2011-0336.1'>http://dx.doi.org/10.1190/geo2011-0336.1</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/geo2011-0336.1><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/geo2011-0336.1><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/geo2011-0336.1en
dc.identifier.urihttp://hdl.handle.net/10754/597955en
dc.description.abstractThe finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.en
dc.description.sponsorshipStoffa would like to acknowledge the King Abdullah Universityof Science and Technology for their support of his research. We aregrateful to associate editor Stig Hestholm and the reviewers for theirconstructive comments which helped improve the original manuscript.We thank ConocoPhillips for permission to publishthis work.en
dc.publisherSociety of Exploration Geophysicistsen
dc.subjectDispersionen
dc.subjectFinite differenceen
dc.subjectFourier transformen
dc.titleDetermination of finite-difference weights using scaled binomial windowsen
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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