  The method of passive imaging in seismology has been developped recently in
order to image the earth crust from recordings of the seismic noise. This
method is founded on the computation of correlations of the seismic noise. In
this paper, we give an explicit formula for this correlation in the
"semi-classical" regime. In order to do that, we define the power spectrum of a
random field as the ensemble average of its Wigner measure, this allows
phase-space computations: the pseudo-differential calculus and the ray theory.
This way, we get a formula for the correlation of the seismic noise in the
semi-classcial regime with a source noise which can be localized and non
homogeneous. After that, we show how the use of surface guided waves allows to
image the earth crust.
