From closed-boundary to single-sided homogeneous Green's function representations

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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.