Fourier-domain implementations of migration require that the medium to be laterally homogeneous (excluding some approximations used to handle smooth lateral velocity variation). However, this inherent limitation of time-migration results in implementations of migration in the Fourier domain, that are efficient. In addition, the assumption of lateral homogeneity allows, as mentioned above, for the two-parameter representation of P-waves in VTI media. Likely, through the combined action of gravity and sedimentation, velocity variation with depth represents the most important first-order inhomogeneity in the earth. This is one reason why time migration works well in so many places. The reader familiar with zero-offset time migration (Gazdag, 1978), and Popovici (1993) separate offset migration may prefer to skip this section, which is a summary of both methods. This section also introduces some notations used throughout this paper.