You might wish to do migration in -space with lateral velocity variation. Then the thin-lens stage would be implemented by time shifting instead of by multiplying by .Time shifting is a delightfully easy operation when what is needed is to shift data by an integral number of sample units. Repetitive time shifting by a fractional number of digital units, however, is a nightmare. Multipoint interpolation operators are required. Even then, pulses tend to disperse. So the lens term is probably best left in the frequency domain.