Computational considerations

The cost of downward continuing a 3-D wavefield one depth step in the Fourier domain is proportional to $N_{xy} \log (N_{xy})$. On the other hand, the cost of imaging with a 3-D version of equation (1) is proportional to N_xy N_h<<57>>xy. Clearly, if the number of offsets is large, then the cost of the imaging step may be comparable (or even greater) than the cost of the downward continuation.

This increase in computational cost is not a problem with shot-geophone migration. In that instance, the cost of the imaging step (proportional to N_xy N_h<<59>>xy), will always be less than the cost of the downward continuation [proportional to $N_{xy} N_{h_{xy}} \log (N_{xy} N_{h_{xy}})$].