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

TL;DR

This paper reviews the theory behind extending Kirchhoff reflectivity to model and invert complex seismic data beyond first-order reflections, emphasizing the generalized reflectivity concept's potential in advanced seismic imaging techniques.

Contribution

It introduces the generalized reflectivity concept, connecting Kirchhoff and Born modeling, to enable modeling and inversion of complex seismic phenomena beyond first-order reflections.

Findings

Generalized reflectivity links Kirchhoff and Born modeling.

It allows modeling of higher-order effects like diffractions.

The approach enhances seismic imaging and interpretation.

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.