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Prestack Stolt migration (PrSM) was summarized as
Claerbout (1985)
An important component of PrSM is the remapping from the domain to the (*k*_{z},*k*_{y},*k*_{h}) domain, where , *k*_{z} represent,
respectively, the frequency and the vertical wavenumber, and *k*_{y},*k*_{h}
represent the midpoint and offset wavenumbers.

If we consider the alternative representation of the input data in
shot-geophone coordinates, the mapping takes the form

| |
(1) |

where
*k*_{g} and *k*_{s} stand for, respectively, the geophone and the source
wavenumbers. It is desirable to implement the remapping as a pull
operator, to avoid numerical problems in the inverse Fourier
transform. A detailed discussion on the advantages and disadvantages
of the different mappings is done by Levin
1994.
We can, therefore, express
as a function of *k*_{z} from Equation (1) as:
| |
(2) |

or
| |
(3) |

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Stanford Exploration Project

6/30/1999