Correlation in ambient seismic noise and the reconstruction of Green function

Cross-correlations between long continuous records of ambient seismic noise at distant stations are investigated. The dominant part of the Green function, namely Rayleigh waves, are reconstructed in a broad period range. This property reminds of the fluctuation-dissipation theorem that relates the random fluctuations of a linear system and the system’s response to an external force. Ambient seismic noise is indeed not a thermal noise but it can be considered as a random and isotropic wave field both because the distribution of the ambient sources responsible for the noise randomizes when averaged over long periods and because of scattering from heterogeneities that occur within the Earth. The dispersion curves of Rayleigh waves for the paths between the stations are measured from the correlations. On paths where direct measurements between earthquake and station are available, we show that they are in good agreement with those deduced from noise correlation. The measurement of correlation along paths crossing different geological structures allows to differentiate them, opening the way for a passive imaging of the Earth structure. The dispersion measurements are applied to seismic tomography at the regional scale. They make it possible to image crustal structures with a resolution higher than conventional techniques.