A numeric evaluation of attenuation from ambient noise correlation functions

The ambient noise correlation function (NCF) calculated between seismic stations contains, under appropriate conditions, accurate travel time information. However, NCF amplitudes are highly debated due to noise source intensity and distribution, seismic intrinsic attenuation, scattering, and elastic path effects such as focusing and defocusing. We prove with various numerical simulations that the NCFs calculated for a uniformly dispersive medium using the coherency method preserve accurate geometrical spreading and attenuation decay. We show that for a wide range of noise source distributions, the coherency of the noise correlation functions matches a Bessel function decaying exponentially with a specific attenuation coefficient. Conditions needed to obtain these results include averaging over long enough time intervals, a uniformly distributed seismic network, and a good distribution of far-field noise sources. We also show that the estimated attenuation coefficient corresponds to the interstation and not the noise-source-to-receiver structure.