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Various authors have discussed approaches for normalizing
Kirchhoff-style operators based on principles such as
operator fold [e.g. Beasley and Klotz (1992); Chemingui (1999); Slawson et al. (1995)].
While these concepts are based on reasonable heuristic ideas, it is
difficult to identify exactly when these approximations are valid in
the context of depth migration.
Equation () provides a methodology for
calculating weighting functions that are appropriate for normalizing
any generic linear operators Claerbout and Nichols (1994).
However, this approach has the advantage that
we know it will provide the *ideal* weighting function
if we have the correct forward modeling operator,
and .
Operator fold is not well-defined for finite-frequency recursive
migration operators; however, it is closely connected to the ideas
developed in Chapter .
In this Appendix, I identify explicitly how Kirchhoff fold
normalization relates to equation ().

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Stanford Exploration Project

5/27/2001