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Séminaire Laurent Schwartz — EDP et applicationsTable of contents for this volume | Next articleJosselin Garnier Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 1, 18 p., doi: 10.5802/slsedp.1 Article PDF Résumé - 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. Bibliography [2] Aki K and Chouet B 1975 Origin of coda waves: Source, attenuation and scattering effects J. Geophys. 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E 69 046610 [27] Stehly L, Campillo M, and Shapiro N M 2006 A study of the seismic noise from its long-range correlation properties Geophys. Res. Lett. 111 B10306 [28] Stehly L, Campillo M, Froment B, and Weaver R 2008 Reconstructing Green’s function by correlation of the coda of the correlation (C3) of ambient seismic noise, J. Geophys. Res. 113 B11306. [29] Wapenaar K and Fokkema J 2006 Green’s function representations for seismic interferometry Geophysics 71 SI33-SI46. [30] Yao H, van der Hilst R D, and de Hoop M V 2006 Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis Ð I. Phase velocity maps Geophysical Journal International 166 732-744 |
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