Fluctuations of correlations and Green's function reconstruction: role of scattering

Correlations of ambient seismic or acoustic vibrations are now widely used to reconstruct the impulse response between two passive receivers as if a source was placed at one of them. This provides the opportunity to do imaging without a source, or \textsl{passive imaging}. Applications include terrestrial and solar seismology, underwater acoustics, and structural health monitoring, to cite only a few. Nevertheless, for a given set of data, correlations do not only yield the Green's function between the sensors. They also contain residual fluctuations that result from an imperfect time or source averaging that might eventually blur the images. In this article, we propose a heuristic model to describe the level of fluctuations of the correlations in the case of non-stationary wavefields, and more particularly in the case of scattering media. The work includes theoretical derivations and numerical simulations. The role of multiple scattering is quantitatively evaluated. The level of fluctuations decreases when the duration and intensity of the diffuse waves increase. The role of absorption is also discussed: absorption is properly retrieved by correlation, but the level of fluctuations is greater, thus degrading the Green's function reconstruction. Discrepancies of our simple model in the case of strong multiple scattering ($k\ell^*\leq 18$) are discussed.