  We remind and emphasize the connections and differences between Kirchhoff and
Born modelling. We discuss how they lead to a general expression for the
conversion of a velocity model perturbation into a reflectivity through the
"generalized reflectivity" concept. We seize the opportunity to clarify some
aspects related to possibly non-smooth propagating media and the linearity
approximation on reflectors. The generalized reflectivity offers opportunities:
on FWI approaches that include a reflectivity or least squares migration
approaches that can be based on Kirchhoff or Born modelling; in the framework
of traditional Kirchhoff modelling scheme, to model first-order effects that go
beyond first-order reflections (like first-order diffractions); in the
framework of traditional Kirchhoff inversion or true amplitude migration, i.e.
for the interpretation of seismic-migrated images.
