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Electrical impedance tomography using a point electrode inverse scheme for complete electrode data
Filtered Kirchhoff migration of cross correlations of ambient noise signals
1. | Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, site Chevaleret, case 7012, 75205 Paris Cedex 13 |
2. | Department of Mathematics, University of California at Irvine, Irvine, CA 92697 |
References:
[1] |
C. Bardos, J. Garnier and G. Papanicolaou, Identification of Green's functions singularities by cross correlation of noisy signals, Inverse Problems, 24 (2008), 015011.
doi: 10.1088/0266-5611/24/1/015011. |
[2] |
G. Beylkin, Imaging of discontinuities in the inverse scattering problem by the inversion of a causal Radon transform, J. Math. Phys., 26 (1985), 99-108.
doi: 10.1063/1.526755. |
[3] |
B. L. Biondi, "3D Seismic Imaging," no. 14 in Investigations in Geophysics, Society of Exploration Geophysics, Tulsa, 2006. |
[4] |
N. Bleistein, J. K. Cohen and J. W. Stockwell Jr, "Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion," Springer Verlag, New York, 2001. |
[5] |
L. Borcea, G. Papanicolaou and C. Tsogka, Interferometric array imaging in clutter, Inverse Problems, 21 (2005), 1419-1460.
doi: 10.1088/0266-5611/21/4/015. |
[6] |
L. Borcea, G. Papanicolaou and C. Tsogka, Coherent interferometric imaging, Geophysics 71 (2006), S1165-S1175.
doi: 10.1190/1.2209541. |
[7] |
M. Born and E. Wolf, "Principles of Optics," Cambridge University Press, Cambridge, 1999. |
[8] |
J. F. Claerbout, "Imaging the Earth's Interior," Blackwell Scientific Publications, Palo Alto, 1985. |
[9] |
Y. Colin de Verdière, Semiclassical analysis and passive imaging, Nonlinearity, 22 (2009), R45-R75.
doi: 10.1088/0951-7715/22/6/R01. |
[10] |
A. Curtis, P. Gerstoft, H. Sato, R. Snieder and K. Wapenaar, Seismic interferometry - turning noise into signal, The Leading Edge, 25 (2006), 1082-1092.
doi: 10.1190/1.2349814. |
[11] |
M. de Hoop and K. Sølna, Estimating a Green's function from field-field correlations in a random medium, SIAM J. Appl. Math., 69 (2009), 909-932.
doi: 10.1137/070701790. |
[12] |
J. Garnier, Imaging in randomly layered media by cross-correlating noisy signals, SIAM Multiscale Model. Simul., 4 (2005), 610-640.
doi: 10.1137/040613226. |
[13] |
J. Garnier and G. Papanicolaou, Passive sensor imaging using cross correlations of noisy signals in a scattering medium, SIAM J. Imaging Sciences, 2 (2009), 396-437.
doi: 10.1137/080723454. |
[14] |
O. I. Lobkis and R. L. Weaver, On the emergence of the Green's function in the correlations of a diffuse field, J. Acoustic. Soc. Am., 110 (2001), 3011-3017.
doi: 10.1121/1.1417528. |
[15] |
F. Natterer and F. Wubbeling, "Mathematical Methods in Image Reconstruction," Society for Industrial and Applied Mathematics, Philadelphia, 2001.
doi: 10.1137/1.9780898718324. |
[16] |
P. Roux and M. Fink, Green's function estimation using secondary sources in a shallow water environment, J. Acoust. Soc. Am., 113 (2003), 1406-1416.
doi: 10.1121/1.1542645. |
[17] |
K. G. Sabra, P. Gerstoft, P. Roux and W. Kuperman, Surface wave tomography from microseisms in Southern California, Geophys. Res. Lett., 32 (2005), L14311.
doi: 10.1029/2005GL023155. |
[18] |
N. M. Shapiro, M. Campillo, L. Stehly and M. H. Ritzwoller, High-resolution surface wave tomography from ambient noise, Science, 307 (2005), 1615-1618.
doi: 10.1126/science.1108339. |
[19] |
L. Stehly, M. Campillo and N. M. Shapiro, A study of the seismic noise from its long-range correlation properties, Geophys. Res. Lett., 111 (2006), B10306. |
[20] |
K. Wapenaar and J. Fokkema, Green's function representations for seismic interferometry, Geophysics, 71 (2006), SI33-SI46.
doi: 10.1190/1.2213955. |
[21] |
H. Yao, R. D. van der Hilst and M. V. de Hoop, Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis I. Phase velocity maps, Geophysical Journal International, 166 (2006), 732-744.
doi: 10.1111/j.1365-246X.2006.03028.x. |
show all references
References:
[1] |
C. Bardos, J. Garnier and G. Papanicolaou, Identification of Green's functions singularities by cross correlation of noisy signals, Inverse Problems, 24 (2008), 015011.
doi: 10.1088/0266-5611/24/1/015011. |
[2] |
G. Beylkin, Imaging of discontinuities in the inverse scattering problem by the inversion of a causal Radon transform, J. Math. Phys., 26 (1985), 99-108.
doi: 10.1063/1.526755. |
[3] |
B. L. Biondi, "3D Seismic Imaging," no. 14 in Investigations in Geophysics, Society of Exploration Geophysics, Tulsa, 2006. |
[4] |
N. Bleistein, J. K. Cohen and J. W. Stockwell Jr, "Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion," Springer Verlag, New York, 2001. |
[5] |
L. Borcea, G. Papanicolaou and C. Tsogka, Interferometric array imaging in clutter, Inverse Problems, 21 (2005), 1419-1460.
doi: 10.1088/0266-5611/21/4/015. |
[6] |
L. Borcea, G. Papanicolaou and C. Tsogka, Coherent interferometric imaging, Geophysics 71 (2006), S1165-S1175.
doi: 10.1190/1.2209541. |
[7] |
M. Born and E. Wolf, "Principles of Optics," Cambridge University Press, Cambridge, 1999. |
[8] |
J. F. Claerbout, "Imaging the Earth's Interior," Blackwell Scientific Publications, Palo Alto, 1985. |
[9] |
Y. Colin de Verdière, Semiclassical analysis and passive imaging, Nonlinearity, 22 (2009), R45-R75.
doi: 10.1088/0951-7715/22/6/R01. |
[10] |
A. Curtis, P. Gerstoft, H. Sato, R. Snieder and K. Wapenaar, Seismic interferometry - turning noise into signal, The Leading Edge, 25 (2006), 1082-1092.
doi: 10.1190/1.2349814. |
[11] |
M. de Hoop and K. Sølna, Estimating a Green's function from field-field correlations in a random medium, SIAM J. Appl. Math., 69 (2009), 909-932.
doi: 10.1137/070701790. |
[12] |
J. Garnier, Imaging in randomly layered media by cross-correlating noisy signals, SIAM Multiscale Model. Simul., 4 (2005), 610-640.
doi: 10.1137/040613226. |
[13] |
J. Garnier and G. Papanicolaou, Passive sensor imaging using cross correlations of noisy signals in a scattering medium, SIAM J. Imaging Sciences, 2 (2009), 396-437.
doi: 10.1137/080723454. |
[14] |
O. I. Lobkis and R. L. Weaver, On the emergence of the Green's function in the correlations of a diffuse field, J. Acoustic. Soc. Am., 110 (2001), 3011-3017.
doi: 10.1121/1.1417528. |
[15] |
F. Natterer and F. Wubbeling, "Mathematical Methods in Image Reconstruction," Society for Industrial and Applied Mathematics, Philadelphia, 2001.
doi: 10.1137/1.9780898718324. |
[16] |
P. Roux and M. Fink, Green's function estimation using secondary sources in a shallow water environment, J. Acoust. Soc. Am., 113 (2003), 1406-1416.
doi: 10.1121/1.1542645. |
[17] |
K. G. Sabra, P. Gerstoft, P. Roux and W. Kuperman, Surface wave tomography from microseisms in Southern California, Geophys. Res. Lett., 32 (2005), L14311.
doi: 10.1029/2005GL023155. |
[18] |
N. M. Shapiro, M. Campillo, L. Stehly and M. H. Ritzwoller, High-resolution surface wave tomography from ambient noise, Science, 307 (2005), 1615-1618.
doi: 10.1126/science.1108339. |
[19] |
L. Stehly, M. Campillo and N. M. Shapiro, A study of the seismic noise from its long-range correlation properties, Geophys. Res. Lett., 111 (2006), B10306. |
[20] |
K. Wapenaar and J. Fokkema, Green's function representations for seismic interferometry, Geophysics, 71 (2006), SI33-SI46.
doi: 10.1190/1.2213955. |
[21] |
H. Yao, R. D. van der Hilst and M. V. de Hoop, Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis I. Phase velocity maps, Geophysical Journal International, 166 (2006), 732-744.
doi: 10.1111/j.1365-246X.2006.03028.x. |
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