Generalization of Kirchhoff reflectivity to go beyond modelling and inversion of first-order reflection data -- A review of the theory

Abstract

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.