Disclosed is a method for efficiently and accurately determining subsurface velocities for use in migration of seismic data. The method calls for restricting the number of traces considered to those lying upon that portion of the Kirchhoff summation curve wherein the integrand for Kirchhoff migration is smooth. In the preferred embodiment, only a random sample of traces within this aperture are used in the calculations. Improvements in efficiency on the order of a factor of 1000 can be realized with the preferred embodiment.
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