A Semi-classical calculus of correlations

TL;DR

This paper derives an explicit semi-classical formula for seismic noise correlations using phase-space methods, aiding in imaging the earth's crust with localized, non-homogeneous sources and surface guided waves.

Contribution

It introduces a semi-classical approach to compute seismic noise correlations, incorporating phase-space analysis and pseudo-differential calculus for improved earth crust imaging.

Findings

Explicit correlation formula in semi-classical regime

Inclusion of localized, non-homogeneous sources

Application to surface guided wave imaging

Abstract

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.