Green's function representations for seismic interferometry

Using Rayleigh’s reciprocity theorem and the principle of time-reversal invariance, we derive representations for the Green’s function of an inhomogeneous medium in terms of cross-correlations of wave fields at two observation points. First we consider the hypothetical situation in which the primary sources are located at a closed surface. We carefully analyze the contributions from inhomogeneities inside as well as outside this surface. Next we consider the more realistic situation of an inhomogeneous medium below a free surface and primary sources on an open surface. Finally we illustrate the method with a numerical example.