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The original surface seismic data are usually shot gathers. A typical seismic shot gather
(the receiver wavefield of a shot at the surface) is
a five dimensional object: *R*(*s*_{y},*s*_{x},*r*_{y},*r*_{x},*z*=0,*t*),
where (*s*_{y},*s*_{x}) is the source location,
(*r*_{x},*r*_{y}) is the receiver location and *t* is the travel time.
After a Fourier transformation in *t*, we have the receiver wavefield in the frequency
domain , where is the angular frequency.
Each shot represents a real physical experiment.
The most straight forward way to obtain the image of the subsurface
is shot-profile migration, in which we obtain
the local image of each experiment independently and form the final image
of the subsurface by stacking all the local images.
A typical shot-profile migration algorithm includes two steps. First, source and receiver wavefields
are extrapolated into the subsurface using one-way wave equations. In isotropic media they are defined as follows:

| |
(1) |

| (2) |

where *v*=*v*(*x*,*y*,*z*) is the velocity of the media, is the source wavefield,
which is an impulse at the surface and is the receiver wavefield.
Second, the image is formed by cross-correlating
the source and receiver wavefields:
| |
(3) |