Introduction

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 ${\bf m}_{\rm ref}={\bf m}_{\rm true}$.

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 ().