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    Prestack wavefield approximations

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    Type
    Article
    Authors
    Alkhalifah, Tariq cc
    Date
    2013-09
    Permanent link to this record
    http://hdl.handle.net/10754/599397
    
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    Abstract
    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 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/geo2012-0532.1 </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>Prestack wavefield approximations</b></td></tr><tr><td>Alkhalifah,Tariq</td></tr><tr><td><i>GEOPHYSICS</i>(2013),78(5):T141</td></tr><tr><td><a href='http://dx.doi.org/10.1190/geo2012-0532.1'>http://dx.doi.org/10.1190/geo2012-0532.1</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/geo2012-0532.1><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/geo2012-0532.1><img src="/docs/iPage/images/gswbanner.gif" alt="GSW Logo"/></a> </div></div></body></html>
    Sponsors
    I thank Zedong Wu for generating the split-step Marmousi data set used here and for fruitful discussions. I thank KAUST for its support. I also thank the seismic wave analysis group for their support. I thank Jeff Shragge, Alexey Stovas, Bin Wang, and an anonymous reviewer for their helpful comments and suggestions.
    Publisher
    Society of Exploration Geophysicists
    Journal
    GEOPHYSICS
    ISSN
    0016-8033
    1942-2156
    DOI
    10.1190/GEO2012-0532.1
    ae974a485f413a2113503eed53cd6c53
    10.1190/GEO2012-0532.1
    Scopus Count
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