Convergence of the two-point correlation function toward the Green's function in the context of a seismic-prospecting data set

When considering direct waves in the correlation process, the Green's function is reconstructed when using an even distribution of seismic sources or when the source distribution is restricted to the direction close to the alignment of the sensors. On the other hand, when considering records of coda waves, the convergence is achieved for any source distribution, as expected theoretically. We extract the expected amplitude decay along a seismic profile from the correlation functions when an even distribution of sources is considered or when the time window includes scattered waves.