Most migration methods are based on a variety of one-way approximations of the wave equation, one noticeable exception being the finite-difference, reverse-time, depth migration algorithm. Since this method requires enormous computer resources as compared to all other migration algorithms, its applications have been restricted primarily to 2-D synthetic data. Consequently, its potential for migrating poststack real data and imaging complex 3-D structures by constructive interference of wavefronts has not been exploited. Finite-difference depth migration is subject to the same conditions for avoiding grid dispersion and numerical instability as are forward modeling techniques. For field data, this can necessitate interpolation both in space and time. One can, however, exploit the fact that in forward modeling one tries to generate accurate reflection signals; whereas in migration, the primary objective is to accomplish imaging from the prerecorded signals, which may be attainable under less stringent conditions. Indeed our investigations indicate that accurate imaging can be clone without making rigid provisions for grid dispersion in the lateral direction, which reduces or eliminates the use of interpolated traces. In the case of 3-D data, the elimination of an interpolation step reduces the computational task by a factor of 50 or more, with similar reductions in memory requirements. Further efficiency can be achieved by using a nonuniform grid in the vertical direction that adapts to the expansion and contraction of the downward propagating wavelet in response to variations in velocity and frequency content of the input data. These steps reduce the time required to do high-resolution migration of large 3-D data volumes to several hours or less, depending on the machine and the size of the input data. Two applications on large, exploration-scale, 3-D field data carried out on a massively-parallel machine are presented. We compare our results with the results obtained by the Hale-McClellan algorithm.