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I obtain images comparable to shot-profile migration results by combining wave-equation datuming and Kirchhoff migration into a layer-stripping migration method. In this case, eikonal traveltimes produce satisfactory images because the velocity model is subdivided and traveltimes are calculated under conditions where finite-differencing the eikonal equation is valid. By dividing the imaging problem in this way, the traveltimes are better behaved and some multiple arrivals are accounted for.