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The second step of shot-profile migration is forming a subsurface
image through extraction of appropriate information from the
independently extrapolated source and receiver wavefields.
Claerbout's imaging principle Claerbout (1971) asserts that energy
in the receiver
wavefield, *R*, that is spatially collocated with energy in the source
wavefield, *S*, at time *t*=0 originates from a reflector at that
model point. Mathematically, this is accomplished through the
extraction of the zero-lag of the cross-correlation of the two
wavefields. In practice, this translates to a summation over
frequency after the multiplication of the wavefields Claerbout (1985),
| |
(6) |

Here, *I*(*z*,*x*) represents the image point as a function of horizontal
distance and depth, ^{*} represents complex conjugation, and the subscript *s*
refers to individual shot-profile image results.
Additional subsurface reflectivity constraints are obtained by
extending (6) to include subsurface offset Rickett and Sava (2002). Offset domain common
image gathers (ODCIGs) are created by multiplication of the source and
receiver wavefields after a lateral shift of *h*:

| |
(7) |

** Next:** Angle domain common image
** Up:** Theory
** Previous:** Shot-profile wavefield continuation
Stanford Exploration Project

5/23/2004