Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals

Josselin Garnier[1]

  • [1] Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions Université Paris VII Site Chevaleret 75205 Paris Cedex 13

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-18
  • ISSN: 2266-0607

Abstract

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In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain an estimate of the travel time between them. 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 identify the configurations under which travel time estimation by cross correlation is possible. We show that iterated cross correlations using auxiliary sensors can be efficient for travel time estimation when the support of the noise sources is spatially limited.

How to cite

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Garnier, Josselin. "Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-18. <http://eudml.org/doc/251184>.

@article{Garnier2011-2012,
abstract = {In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain an estimate of the travel time between them. 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 identify the configurations under which travel time estimation by cross correlation is possible. We show that iterated cross correlations using auxiliary sensors can be efficient for travel time estimation when the support of the noise sources is spatially limited.},
affiliation = {Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions Université Paris VII Site Chevaleret 75205 Paris Cedex 13},
author = {Garnier, Josselin},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {wave equation; noise; Green's function; cross correlation},
language = {eng},
pages = {1-18},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals},
url = {http://eudml.org/doc/251184},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Garnier, Josselin
TI - Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 18
AB - In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain an estimate of the travel time between them. 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 identify the configurations under which travel time estimation by cross correlation is possible. We show that iterated cross correlations using auxiliary sensors can be efficient for travel time estimation when the support of the noise sources is spatially limited.
LA - eng
KW - wave equation; noise; Green's function; cross correlation
UR - http://eudml.org/doc/251184
ER -

References

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