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Prestack Stolt migration can be summarized (24)
as a succession of transformations from seismic data
to seismic images as follows:
| |
(29) |

where and are representations of the data and image
in the space domain,
while and are the equivalent
representations in the Fourier domain.
In stoltmain,
*t* stands for time,
for midpoint location,
for half-offset, and
for depth.
The central component of prestack Stolt migration
is the re-mapping from the domain to the domain, where
and represent,
the temporal frequency and the depth wavenumber respectively, and
and represent the
midpoint and offset wavenumbers.

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

| |
(30) |

where
and stand for, respectively, the receiver and the source
wavenumbers. From dsr-sg we can express
as a function of :
| |
(31) |

We can obtain an equation equivalent to ()
in midpoint-offset coordinates, if we make the usual change of
variables:

| |
(32) |

** Next:** Prestack Stolt residual migration
** Up:** Prestack residual migration
** Previous:** Introduction
Stanford Exploration Project

11/4/2004