Retrieval of Green's function having coda from the cross-correlation function in a scattering medium illuminated by surrounding noise sources on the basis of the first order Born approximation

Abstract

SUMMARY The peak lag time of the cross-correlation function (CCF) of random noise at two receivers give the wave propagation velocity. This idea has been widely used for the velocity tomography analysis. Recently, there were reports on the temporal change in the coda portion of CCF or autocorrelation function of ambient noise as a measure of the medium property. Here, we propose a simple concrete model for the retrieval of Green’s function having a coda tail in a scattering medium without dissipation from the CCF of noise. The scattering medium is mathematically given by a distribution of velocity anomalies represented by delta functions. We suppose that waves are radiated from stationary noise sources, which are randomly distributed on a surrounding spherical shell with a large radius compared with the dimension of the scattering medium. Using the first order Born approximation, we show that the derivative of CCF with respect to lag time gives the antisymmetrized Green’s function having a coda tail in the framework of the single scattering approximation.