The inversion method is first applied on a perfect synthetic model defined by a sedimentary layer overlying a rocky basement. 
and 
values inside the two layers are plotted on figure 5.11(a) and 5.11(b) (black lines). We set up a 100 m aperture array with a quasi-circular shape characteristics of which are given in figure 3.24(a). From the azimuth-distance plot of figure 3.24(b), we selected five distinct rings including 7 to 12 station pairs each, with an average of ten. The limits of rings are arbitrary chosen. Parametric tests show that the final results are very little dependent on the ring selection. We introduce uncertainties into the original model assuming a normal distribution around the average model (black plain lines, figures 5.11(a) and 5.11(b)) with the standard deviation shown by dotted lines in the same figure. Theoretical auto-correlation ratios were computed for 5000 randomly generated models, keeping Poisson's ratio constant. Auto-correlation curves for the five rings are regularly distributed around the ones computed for the average model (black dots of figures 5.11(d) to 5.11(h)).