Retrieving the Green's function in an open system by cross correlation: A comparison of approaches

We compare two approaches for deriving the fact that the Green's function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions. One approach is based on physical arguments, exploiting the principle of time-reversal invariance of the acoustic wave equation. The other,approach is based on Rayleigh's reciprocity theorem. Using a unified notation, we show that the result of the time-reversal approach can be obtained as an approximation of the result of the reciprocity approach. (c) 2005 Acoustical Society of America.