Geodesic
Travel time estimation by cross correlation of noisy signals
Josselin Garnier1 ; George Papanicolaou2
1 Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 5
2 Mathematics Department, Stanford University, Stanford, CA 94305
ESAIM. Proceedings, Tome 27 (2009), pp. 138-155.

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In this review paper we consider the problem of estimating the singular support of the Green's function of the wave equation by using passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We show that the cross correlation of the recorded signals has enough information to identify the singular component of the Green's function, which provides an estimate of the travel time between the sensors. We consider different situations, such as when the support of the noise distribution extends over all space or is spatially limited, the medium is open or bounded, homogeneous or inhomogeneous, dissipative or not. We discuss the limitations of the cross correlation technique and identify configurations under which travel time estimation is possible. We show that iterated cross correlations using auxiliary sensors can be efficient for travel time estimation when the support of the noise source distribution is spatially limited.
DOI : 10.1051/proc/2009023

Josselin Garnier 1 ; George Papanicolaou 2

1 Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 5
2 Mathematics Department, Stanford University, Stanford, CA 94305 
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Josselin Garnier; George Papanicolaou. Travel time estimation by cross correlation of noisy signals. ESAIM. Proceedings, Tome 27 (2009), pp. 138-155. doi : 10.1051/proc/2009023. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009023/

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