The acoustic reverberation in a solid plate can be conveniently modeled through a nonstationary random process based on the image-sources method. The interest of such a statistical model is to allow the prediction of a general behaviour (in the form of mathematical expectations) from a limited set of experimentally accessible parameters. Contrary to previous works, the model presented here takes into account the dispersive nature of plate waves (Lamb waves). Then, the relations between the average signal envelopes or correlation functions and the reverberation properties of the medium and the relative positions of the noise source, the sensor(s) and, possibly, the defect are derived. Two kinds of possible applications of these theoretical results will be illustrated: (1) parameter extraction such as source-receiver distance, structural dimensions or propagation velocities through curve-fitting; (2) imaging potentialities from ambient acoustic noise correlation