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The derivation of the forward-modeling operator provides insight into the
form of the inversion operator. In generating the seismic model, each trace
is modeled as a weighted sum of image sources on a reflector.
Therefore, Kirchhoff imaging of seismic data
involves a weighted sum of filtered
surface-recorded traces where the weights
are deduced from inversion theory.
The resulting algorithms are then applied to the discrete seismic data
through the linear transformation

| |
(40) |

True amplitude imaging aims at deriving the proper weights along
the summation surfaces or impulse responses of
.
In the previous chapter, I
presented detailed derivations for true-amplitude weights for the azimuth
moveout operator.
Using a similar approach, Jaramillo and Bleistein 1997
derived amplitude-preserving
weights for migration and demigration based on the Kirchhoff modeling
formula. Then using the superposition principle they derived two
alternative operators to perform migration as isochron superposition
and demigration as diffraction superposition. I find the two approaches
rather easier to understand using Claerbout's terminology for push
and pull operators defined below.

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Stanford Exploration Project

1/18/2001