On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

Cross-correlation of ambient seismic noise recorded by two seismic stations may result in an estimate of the Green's function between those two receivers. Several authors have recently attempted to measure attenuation based on these interferometric, receiver-receiver surface waves. By now, however, it is well established that the loss of coherence of the cross-correlation as a function of space depends strongly on the excitation of the medium. In fact, in a homogeneous dissipative medium, uniform excitation is required to correctly recover attenuation. Applied to fundamental-mode ambient seismic surface waves, this implies that the cross-correlation will decay at the local attenuation rate only if noise sources are distributed uniformly on the Earth's surface. In this study we show that this constraint can be relaxed in case the observed loss of coherence is due to multiple scattering instead of dissipation of energy. We describe the scattering medium as an effective medium whose phase velocity and rate of attenuation are a function of the scatterer density and the average strength of the scatterers. We find that the decay of the cross-correlation in the effective medium coincides with the local attenuation of the effective medium in case the scattering medium is illuminated uniformly from all angles. Consequently, uniform excitation is not a necessary condition for the correct retrieval of scattering attenuation. We exemplify the implications of this finding for studies using the spectrally whitened cross-correlation to infer subsurface attenuation.