The homogeneous Green’s function (i.e., the Green’s function and its time-reversed counterpart) plays an important role in optical, acoustic and seismic holography, in inverse scattering methods, in the field of time-reversal acoustics, in reversetime migration and in seismic interferometry. Starting with the classical closed-boundary representation of the homogeneous Green’s function, we modify the configuration to two parallel boundaries. We discuss step-by-step a process that eliminates the integral along the lower boundary. This leads to a single-sided representation of the homogeneous Green’s function. Apart from imaging, we foresee interesting applications in inverse scattering, time-reversal acoustics, seismic interferometry, passive source imaging, etc. @en

Recent work on autofocusing with the Marchenko equation has shown how the Green's function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green's function from the location of the virtual source to the surface. The Green's function is retrieved using only the reflection response of the medium and an estimate of the first arrival at the surface from the virtual source. Current techniques, however, only include primaries and internal multiples. Therefore, all surface-related multiples must be removed from the reflection response prior to the Green's function retrieval. Here, we present a new scheme that includes primaries, internal multiples, and free-surface multiples. In other words, we retrieve the Green's function in the presence of the free surface. The information needed for the retrieval are the reflection response at the acquisition surface and an estimate of the first arrival at the surface from the virtual source. The reflection response, in this case, includes the free-surface multiples; this makes it possible to include these multiples in the imaging operator and it obviates the need for surface-related multiple elimination.@en