Towards green’s function retrieval from imperfectly partitioned ambient wave fields: Travel times, attenuations, specific intensities, and scattering strengths

Recent theorems have established that fully diffuse wave fields permit, on cross-correlating the noisy signal detected at different positions, retrieval of the Green’s function, and in particular, retrieval of wave travel times. Application to seismology has led to the creation of maps of seismic surface wave velocity with exceptional resolution. What is perhaps perplexing is that the ambient seismic noise fields that are used for this are rarely fully diffuse; the conditions for the theorems are not satisfied. It is shown here that this may be understood theoretically by a simple asymptotic argument. It is further shown that incompletely diffuse noise fields may permit us to robustly recover more than just travel times, but also ray arrival amplitudes, the ambient field’s specific intensity, the strength and density of its scatterers if any, and most importantly attenuation. A theoretical basis for this is presented.