The derivation of Green's correlation naturally arises when identifying a linear propagation medium with uncontrolled random sources or ambient noise. As expected, this involves convolution of the well known Green's function with its time-reversed version. The purpose of this paper is to derive a general expression of Green's correlation function of a linear visco-acoustic propagation medium, in which the pressure field satisfies Stokes' equation. From the expression obtained for a visco-acoustic medium, the Ward identity that was recently obtained for unbounded media is extended to the case of bounded propagation media. This extension appears necessary as the unbounded model is not valid in many practical cases, as for acoustic rooms for example. It is illustrated with both simulations and real-world aerial acoustics experimental data recorded in a closed room and in the framework of passive identification. In these experiments, Green's correlation is estimated by the classical coda-based approach, and the performances are studied in this new context.