Retrieval of the Green function having coda for a scattering medium from noise correlation: the Born approximation

Résumé: Noise correlation method is now widely used for the retrieval of the Green function of the earth medium. Some geophysicists pay attention not only to the peak lag of the cross correlation function (CCF) but also to its coda portion. Recently there are reports on the temporal change in the coda phases of the CCF of ambient noises before and after a crustal earthquake. These observations suggest the importance of the retrieval of Green function having a tail from noise CCF in a scattering medium. Here, using specific mathematical models for a scattering medium, I will show how the Green function having a tail is retrieved from noise CCF for different types of noise source distributions. One is a randomly homogeneous distribution of stationary noise sources, and the other is a random distribution of stationary noise sources in a spherical shell surrounding the scattering medium. I will also discuss about the Green function retrieval from the CCF of coda waves of a single source in a scattering medium.