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Published as Geophysics, 78, no. 4, S211-S219, (2013)

Kirchhoff migration using eikonal-based computation of traveltime source-derivatives

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

Abstract:

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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2013-07-26