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The algorithm described by equations 4 and 5 is
theoretically attractive because it shows in one equation that downward
extrapolation can be done entirely in the -
domain, even for arbitrary spatial velocity variations. From the practical
point of view, however, the algorithm is proportional, at each depth step and
each frequency, to the cube of the spatial dimensions.
Clearly, the cost is associated with the unreasonable
demand that we extrapolated, at each depth step, as many wavefields as spatial
positions. This is not really necessary, as we will see below.