Passive tomography for elastic waves in solids

TL;DR

This paper develops methods to reconstruct Green's functions for elastic waves in solids from ambient noise cross-correlations, extending scalar wave techniques to vector waves in 3D media with viscous damping.

Contribution

It introduces two approaches for relating ambient noise correlations to Green's functions in 3D elastic media, extending scalar wave methods to vector waves with viscous damping.

Findings

Derived relations between noise cross-correlation and Green's function in viscous elastic media.

Extended scalar wave reconstruction techniques to 3D vector elastic waves.

Improved physical understanding of wave propagation via Fourier analysis.

Abstract

In this paper we derive relations between the cross-correlation of ambient noises recorded at two different points and the Green's function of the elastic waves in a medium with viscous damping. The Green's function allows to estimate physical parameters such as speeds or distances. Furthermore, this work is extended by introducing the Green's correlation function proposed by J-L. Lacoume in [Lacoume07]. Some recent works proved the possible reconstruction of the Green's function for scalar waves from the cross-correlation function of ambient noise. In this work, we consider vector waves propagating in a three dimensional solid medium. Two approaches are developed. Firstly, we extend theoretical derivations proposed by Y. Colin de Verdi`ere in [ColinDeVerdiere09], relating cross-correlation of scalar waves to 1D Green's function using linear operator theory. The second approach recasts the three dimensional problem in the framework of Fourier theory. This allows to improve physical understanding of the underlying physical processes as outlined in [Lacoume07].