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ESAIM: Proc., 2009, Vol. 27, pp. 138-155
DOI: 10.1051/proc/2009023
Travel time estimation by cross correlation of noisy signals
Josselin Garnier1 and George Papanicolaou21 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
Published online: 25 June 2009
Abstract
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.
© EDP Sciences, ESAIM 2009
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