SEG 1994 Expanded abstracts: pp 1175-1178 In principle, downward continuation of 3-D prestack data should be carried out in a 5-D computational space. Therefore 3-D prestack migration methods based on the solution of the one-way wave equation would be computationally inefficient for most 3-D data geometries and uncompetitive with Kirchhoff methods. To overcome this limitation, we present a method for downward continuing common-azimuth data in the frequency-wavenumber domain in the original 4-D space of the common-azimuth geometry. The method is based on a stationary-phase approximation of the one-way wave equation and can be applied to both phase-shift and Stolt migrations. The proposed migration methods are exact for constant velocity, and approximate for velocity varying with depth. However, results of some numerical experiments on synthetic data show that the approximation is good even in presence of strong vertical velocity gradients.