Conclusion

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.