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For nearest neighbour interpolation, the inverse of the fold
produced by modeling and migrating a *model* vector full of ones
will be the ideal normalization operator.
Similarly, for linear interpolation it will be close to the ideal
normalization operator as long as the true model varies slowly on the
scale of the sampling interval.
For these interpolation operators, operator fold calculated from a
*data* vector full of ones is exactly equivalent to
the weighting function that can be derived from modeling and migrating
the a reference model full of ones.
For Kirchhoff operators, modeling and migrating a reference model full
of ones only produces a good normalization fold map if the true model
varies slowly on the scale of a bow-tie-shaped modeling/migration
impulse response.
In the special case of *v*(*z*) Kirchhoff operators, normalization by
the operator fold is incorrect dimensionally, but will approximate
the correct weighting functions for flat-events.

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Stanford Exploration Project

5/27/2001