A Semi-classical calculus of correlations

Details A Semi-classical calculus of correlations A Semi-classical calculus of correlations

2011-03-08

arxiv.org/abs/1103.1510v1

Physics

Mathematical Physics

To appear in a special issue "Imaging and Monitoring with Seismic Noise" of the series "Comptes Rendus G\'eosciences", from th

Scientific paper

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.

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