The spatial auto-correlation techniques take advantage of the random distribution of sources in time and space to link auto-correlation ratios to phase velocities. In the case of a single-valued phase velocity per frequency band, Aki (1957) demonstrated that these ratios have the shape of Bessel functions of order 0, the argument of which is dependent upon the dispersion curve values and the array aperture. Bettig et al. (2001) brought some slight modifications to the original formula to extend the method for irregular arrays. Those concepts are briefly recall in the next section. An original inversion strategy has been developed for auto-correlation ratios during this thesis (section 3.3). Examples for synthetic and real cases are discussed in sections 5.2, 6.1.5, and 6.2.5.