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With the forward modeling relation in mind, it is possible for
many processes to derive an analytical formulation for the inverse
of the modeling operator. Whenever an exact formulation of the imaging
operator is obtainable, it is referred to
as an amplitude-preserving transformation. A considerable volume
of literature establishes theory for deriving the inverse
based on asymptotic theory for Kirchhoff modeling and Born scattering.
The resulting algorithms are then applied to discrete seismic data
through the linear transformation

| |
(2) |

True amplitude imaging aims at deriving the proper weights along
the summation surfaces or impulse responses of
. A well studied example is the case of the migration
operator. Jaramillo and Bleistein 1997
derived amplitude-preserving
weights for migration and demigration based on the Kirchhoff modeling
formula. Then based on the superposition principle they derived two
alternative operators to perform migration as isochron superposition
and demigration as diffraction superposition. We find the two concepts
rather easier to understand using Claerbout's terminology for push
and pull operators defined below.

** Next:** Push and Pull operators
** Up:** DISCRETE KIRCHHOFF IMPLEMENTATIONS
** Previous:** DISCRETE KIRCHHOFF IMPLEMENTATIONS
Stanford Exploration Project

7/5/1998