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In shot-profile migration each record is
migrated independently.
The receiver wavefield *P*^{g} is downward continued
starting from the recorded data.
The source wavefield *P*^{s}is downward continued
starting from an assumed source wavelet.
In this case, we assume that the source is a delta
function in the space domain and a constant as a function
of frequency (impulse at time zero).
Each wavefield is propagated independently by
convolution with the Single Square Root operator (SSR).
At each depth level
that is;

| |
(1) |

and
| |
(2) |

where *x* and *y* are defined in the image (model)
space, and is the location of the shot.
The prefix in indicates that
the source function is an impulse.
Notice the negative sign in front of the exponential
in equation (1).
The negative sign is there because the source wavefield propagates downward,
as opposed to
propagate upward as the receiver wavefield does.
The image cube is formed by cross-correlating
along the time axis
the two wavefields shifted with respect to each other
along the horizontal axes.
In the frequency domain the cross-correlation is
performed by multiplication with the complex conjugate,
and it is evaluated at zero lag by
summation over frequencies.
The horizontal shift is the subsurface offset
.The image cube is thus computed as:

| |
(3) |

** Next:** Source-receiver migration
** Up:** THEORY
** Previous:** THEORY
Stanford Exploration Project

11/11/2002