Siwei Li and Sergey Fomel
Bureau of Economic Geology
John A. and Katherine G. Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8924
The computational efficiency of Kirchhoff-type migration can be enhanced by employing accurate
traveltime interpolation algorithms. We address the problem of interpolating between a sparse source
sampling by using the derivative of traveltime with respect to the source location. We adopt a
first-order partial differential equation that originates from differentiating the eikonal equation
to compute the traveltime source-derivatives efficiently and conveniently. Unlike methods that rely
on finite-difference estimations, the accuracy of the eikonal-based derivative does not depend on
input source sampling. For smooth velocity models, the first-order traveltime source-derivatives
enable a cubic Hermite traveltime interpolation that takes into consideration the curvatures of
local wave-fronts and can be straight-forwardly incorporated into Kirchhoff anti-aliasing schemes.
We provide an implementation of the proposed method to first-arrival traveltimes by modifying the
fast-marching eikonal solver. Several simple synthetic models and a semi-recursive Kirchhoff migration
of the Marmousi model demonstrate the applicability of the proposed method.
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