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The cost of downward continuing a 3-D wavefield one depth step in the
Fourier domain is proportional to . 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
].

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Stanford Exploration Project

4/29/2001