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Starting from the prestack migration equation in common midpoint
and offset coordinates, I find a partial differential equation
that can be used to transform prestack data to zero-offset data
in a constant velocity medium.
The PDE can be extended to depth variable velocity via an algorithm
similar to Gazdag's phase-shift downward continuation. The
synthetic results show a very good match between the
actual zero-offset section and the output of the depth
variable velocity MZO.
The obvious drawback is the fact that the MZO defined in this
paper does an implicit summation over offset. I need to
understand better this partial differential equation, so there
will be more work on this subject in the next SEP report.

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** Up:** Popovici : PDE for
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Stanford Exploration Project

11/17/1997