On the amplitudes of correlations and the inference of attenuations, specific intensities and site factors from ambient noise

While techniques for retrieval of seismic velocities from wavelet arrival times in ambient noise correlations are now well established, interpretation of wavelet amplitudes remains unsatisfactory. It is clear that such amplitudes contain information on seismic attenuation, but they are also affected by ambient noise intensity, site amplification, and any nonlinear preprocessing that may have been applied to the noise signals. Disentangling these many factors in order to reliably recover seismic attenuation is challenging. It is argued here that noise intensity, while rarely isotropic or homogeneous, may nevertheless be modeled by a radiative transfer equation. It is then shown that this recognition sufficiently constrains the noise intensity that we may hope to fit measured correlation amplitudes to models for spatially varying attenuation and site amplification factors. One-bit preprocessing, it is shown, is not compatible with such fits except in the special case of spatially constant noise intensity. An alternative procedure for accelerating convergence is suggested. Numerical simulations for a case of homogeneous attenuation and homogeneous seismic velocity are presented in support of the assertions. Attenuation, site factors, and noise intensity are successfully retrieved from correlations of numerically simulated imperfectly diffuse waves measured on a linear array of sensors.