Three-dimensional Marchenko equation for Green's function retrieval “beyond seismic interferometry”

In recent work we showed with heuristic arguments that the Green's response to a virtual source in the subsurface can be obtained from reflection data at the surface. This method is called “Green's function retrieval beyond seismic interferometry”, because, unlike in seismic interferometry, no receiver is needed at the position of the virtual source. Here we present a formal derivation of Green's function retrieval beyond seismic interferometry, based on a 3-D extension of the Marchenko equation. We illustrate the theory with a numerical example and indicate the potential applications in seismic imaging and AVA analysis