On the retrieval of attenuation from the azimuthally averaged coherency   of a diffuse field
  It has been suggested that seismic attenuation \alpha can be inferred from comparisons of empirical coherencies (the cross spectra of pre-whitened ambient seismic noise records) with attenuated Bessel functions Jo(\omega r/c) exp(-\alpha r). Analysis shows here, however, that coherency depends strongly on the directionality of ambient noise intensity. Even if coherency is azimuthally averaged, the suggested attenuation dependence exp(-\alpha r) does not apply. Indeed in highly directional noise fields, coherency is independent of attenuation. It is also argued that spatial and azimuthal averages of coherency can incur phase cancellations related to variations in wavespeed that may mimic factors like exp(-\alpha r). Inference of attenuation from comparison of empirical coherencies to Jo(\omega r/c) exp(-\alpha r) is problematic. 
Richard L. Weaver
physics.geo-ph