An eikonal-based formulation for traveltime perturbation with respect to the source location
Abstract
Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. The relationship between the eikonal solution and its perturbations is analyzed with respect to the source location and a partial differential equation is developed that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depends on lateral changes in velocity and in another form is independent of the velocity field and relies on second-order derivatives of the original traveltime field. For stable finite-difference calculations, this requires the velocity field to be smooth in a sense similar to ray-tracing requirements. Our formulation for traveltime perturbation has several potential applications, such that as traveltime calculation by source-location perturbation, velocity-independent interpolation including datuming, and velocity estimation. Additionally, higher-order expansions provide parameters necessary for Gaussian-beam computations. © 2010 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: 10.1190/1.3490390 </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>An eikonal-based formulation for traveltime perturbation with respect to the source location</b></td></tr><tr><td>Alkhalifah,Tariq et al.</td></tr><tr><td><i>GEOPHYSICS</i>(2010),75(6):T175</td></tr><tr><td><a href='http://dx.doi.org/10.1190/1.3490390'>http://dx.doi.org/10.1190/1.3490390</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/10.1190/1.3490390><img src="/docs/iPage/images/segdl_logo.gif" alt="SEGDL Logo"/></a> </div> <div id="second"> <a href=http://geophysics.geoscienceworld.org/cgi/doi/10.1190/1.3490390><img src="/docs/iPage/images/gswbanner.gif" alt="GSW Logo"/></a> </div></div></body></html>Sponsors
The first author thanks KACST and KAUST for their support of this research. We also thank the associate editor and the reviewers for their fine review of the paper.Publisher
Society of Exploration GeophysicistsJournal
GEOPHYSICSISSN
0016-80331942-2156