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In practice, 2-D Kirchhoff migration is carried out by summing the
amplitudes in (*x*,t) space along the diffraction curve that corresponds to
Huygen's secondary source at each point in (*x*,z) space. For
zero-offset
sections, the moveout at a source-receiver point a distance *x* from the
apex of a diffraction hyperbola at time *t*_{0} is given by:

| |
(2) |

while for common-offset sections, the moveout is given by:
| |
(3) |

where *s* is the value of offset and *v* is the velocity at
the apex of the hyperbola.
Before summation, each sample is scaled by the obliquity factor,
, and the spherical spreading factor (1/*vt*)^{1/2}.
After summation the output section is convolved with a filter
whose amplitude-frequency response is proportional to the square
root of frequency, with a constant phase delay of . The latter
corresponds to the half-derivative that was mentioned earlier on.

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Stanford Exploration Project

11/11/1997