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True-amplitude imaging

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
\begin{displaymath}
\bold m = \bold F \bold d.
\EQNLABEL{equ1}\end{displaymath} (49)
True amplitude imaging aims at deriving the proper weights along the summation surfaces or impulse responses of ${\bf F}$. A well studied example is the case of the migration operator. Jaramillo and Bleistein 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 up previous print clean
Next: Push and Pull operators Up: DISCRETE KIRCHHOFF IMPLEMENTATIONS Previous: DISCRETE KIRCHHOFF IMPLEMENTATIONS
Stanford Exploration Project
7/5/1998