Mathematical models for passive imaging I: general background

TL;DR

This paper provides a mathematical framework for passive imaging, demonstrating how semi-classical analysis can be used to understand the asymptotic behavior of correlations in wave fields, with applications in seismology.

Contribution

It introduces a rigorous mathematical context for passive imaging and applies semi-classical analysis to analyze correlation asymptotics in wave propagation.

Findings

Correlation of noisy fields relates to Green functions

Semi-classical analysis reveals asymptotic behavior of correlations

Framework applicable to seismological imaging

Abstract

Passive imaging is a new technics which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields between different points is strongly related to the Green function of the wave propagation. The aim of this paper is to provide a mathematical context for this approach and to show, in particular, how the methods of semi-classical analysis can be be used in order to find the asymptotic behaviour of the correlations.