The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, whereas the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient since the seismic data are not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfied seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.
