I present a layer-stripping Kirchhoff migration algorithm which is capable of obtaining accurate images of complex structures by downward continuing the data and imaging from a lower datum. I use eikonal traveltimes in a Kirchhoff datuming algorithm for the downward continuation. After downward continuation, I perform Kirchhoff migration. The method alternates steps of datuming and imaging. Because traveltimes are computed for each step, the adverse effects of caustics, headwaves, and multiple

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... rrivals do not develop. In principal, this method only requires the same number of traveltime calculations as a standard migration. Tests on the Marmousi data set produce excellent results.