Equivalence of the virtual-source method and wave-field deconvolution in seismic interferometry

Seismic interferometry and the virtual-source method are related approaches for extracting the Green's function that accounts for wave propagation between receivers by making suitable combinations of the waves recorded at these two receivers. These waves can either be excited by active, controlled, sources, or by natural incoherent sources. We compare this technique with the deconvolution of the wave field recorded at different receivers. We show that the deconvolved wave field is a solution of the same wave equation as that for the physical system, but that the deconvolved wave forms may satisfy different boundary conditions than those of the original system. We apply this deconvolution approach to the wave motion recorded at various levels in a building after an earthquake, and show how to extract the building response for different boundary conditions. Extracting the response of the system with different boundary conditions can be used to enhance, or suppress, the normal-mode response. In seismic exploration this principle can be used for the suppression of surface-related multiples.