Theoretical Background for Estimating Attenuation Structures with Seismic Interferometry

Abstract

Seismic interferometry or the noise correlation method has provided passive methods for travel time tomography. However, it is not clear yet whether amplitudes of the retrieved Green’s functions can be reliably used for estimating attenuation structures. Recently, an equation was conjectured, which is thought to be an extension of the SPAC method to lossy media, and it was used to estimate attenuation structures from amplitudes of the retrieved Green’s functions. However, the conjecture is not clearly proved yet though numerical and analytical studies are being made. In this study, I initially prove a theoretical relation between the SPAC method and seismic interferometry for heterogeneous lossy media, and then develop a theory to support the conjecture by the help of the relation. The conjecture turns out to be derived for homogeneous lossy media under two assumptions of (1) weak attenuation and (2) larger station separations than a considered wavelength. Based on the results, applications of seismic interferometry to the estimation of attenuation structures should be conducted in relatively homogeneous regions with weak attenuation. Applications to attenuation tomography in heterogeneous regions still need to be investigated theoretically.