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.
@article{SLSEDP_2011-2012____A1_0, author = {Josselin Garnier}, title = {Identification of {Green{\textquoteright}s} {Functions} {Singularities} by {Cross} {Correlation} of {Ambient} {Noise} {Signals}}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:1}, pages = {1--18}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2011-2012}, doi = {10.5802/slsedp.1}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.1/} }
TY - JOUR AU - Josselin Garnier TI - Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:1 PY - 2011-2012 SP - 1 EP - 18 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.1/ DO - 10.5802/slsedp.1 LA - en ID - SLSEDP_2011-2012____A1_0 ER -
%0 Journal Article %A Josselin Garnier %T Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals %J Séminaire Laurent Schwartz — EDP et applications %Z talk:1 %D 2011-2012 %P 1-18 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.1/ %R 10.5802/slsedp.1 %G en %F SLSEDP_2011-2012____A1_0
Josselin Garnier. Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 1, 18 p. doi : 10.5802/slsedp.1. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.1/
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