This presentation discusses the identification of some statistical properties of an elastic random medium based on surface measurements. The influence of two fundamental factors in the diffusion regime, i.e. the ratio between the dominant wavelength and the correlation length of the heterogeneities, and the ratio between P and S wave speeds is studied. The influence of the correlation model is also assessed. The global diffusion time of the medium is then used as a key parameter to identify the correlation length of the random medium.