On seismic ambient noise cross-correlation and surface-wave attenuation

We derive a theoretical relationship between the cross correlation of ambient Rayleigh waves (seismic ambient noise) and the attenuation parameter a associated with Rayleigh-wave propagation. In particular, we derive a mathematical expression for the multiplicative factor relating normalized cross correlation to the Rayleigh-wave Green's function. Based on this expression, we formulate an inverse problem to determine a from cross correlations of recorded ambient signal. We conduct a preliminary application of our algorithm to a relatively small instrument array, conveniently deployed on an island. In our setup, the mentioned multiplicative factor has values of about 2.5-3, which, if neglected, could result in a significant underestimate of a. We find that our inferred values of a are reasonable, in comparison with independently obtained estimates found in the literature. Allowing a to vary with respect to frequency results in a reduction of misfit between observed and predicted cross correlations.