  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.
