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Resolution enhancement from scattering in passive sensor imaging with cross correlations
1. | Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13, France |
2. | Mathematics Department, Stanford University, Stanford, CA 94305, United States |
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, 26 pp.
doi: 10.1088/0266-5611/24/1/015011. |
[2] |
J. Berryman, Stable iterative reconstruction algorithm for nonlinear travel time tomography, Inverse Problems, 6 (1990), 21-42.
doi: 10.1088/0266-5611/6/1/005. |
[3] |
B. L. Biondi, 3D Seismic Imaging, no. 14 in Investigations in Geophysics, Society of Exploration Geophysics, Tulsa, 2006. |
[4] |
N. Bleistein and R. Handelsman, Asymptotic Expansions of Integrals, Dover, New York, 1986. |
[5] |
M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, 1999.
doi: 10.1017/CBO9781139644181. |
[6] |
F. Brenguier, N. M. Shapiro, M. Campillo, V. Ferrazzini, Z. Duputel, O. Coutant and A. Nercessian, Towards forecasting volcanic eruptions using seismic noise, Nature Geoscience, 1 (2008), 126-130.
doi: 10.1038/ngeo104. |
[7] |
T. Callaghan, N. Czink, F. Mani, A. Paulraj and G. Papanicolaou, Correlation-based radio localization in an indoor environment, EURASIP Journal on Wireless Communications and Networking, 2011 (2011), 135p.
doi: 10.1186/1687-1499-2011-135. |
[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] |
L. Erdös and H.-T. Yau, Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation, Comm. Pure Appl. Math., 53 (2000), 667-735.
doi: 10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5. |
[11] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer, New York, 2007.
doi: 10.1007/978-0-387-49808-9_4. |
[12] |
U. Frisch, Wave Propagation in Random Media, in Probabilistic Methods in Applied Mathematics, edited by A. T. Bharucha-Reid, Academic Press, New York, 1 (1968), 75-198. |
[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] |
J. Garnier and G. Papanicolaou, Resolution analysis for imaging with noise, Inverse Problems, 26 (2010), 074001, 22pp.
doi: 10.1088/0266-5611/26/7/074001. |
[15] |
J. Garnier and K. Sølna, Cross correlation and deconvolution of noise signals in randomly layered media, SIAM J. Imaging Sciences, 3 (2010), 809-834.
doi: 10.1137/090757538. |
[16] |
O. A. Godin, Accuracy of the deterministic travel time retrieval from cross-correlations of non-diffuse ambient noise, J. Acoust. Soc. Am., 126 (2009), EL183-EL189.
doi: 10.1121/1.3258064. |
[17] |
P. Gouédard, L. Stehly, F. Brenguier, M. Campillo, Y. Colin de Verdière, E. Larose, L. Margerin, P. Roux, F. J. Sanchez-Sesma, N. M. Shapiro and R. L. Weaver, Cross-correlation of random fields: Mathematical approach and applications, Geophysical Prospecting, 56 (2008), 375-393. |
[18] |
P. A. Martin, Acoustic scattering by inhomogeneous obstacles, SIAM J. Appl. Math., 64 (2003), 297-308.
doi: 10.1137/S0036139902414379. |
[19] |
P. M. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill, New York, 1968. |
[20] |
G. Papanicolaou, L. Ryzhik and K. Sølna, Self-averaging from lateral diversity in the Ito-Schroedinger equation, SIAM Journal on Multiscale Modeling and Simulation, 6 (2007), 468-492.
doi: 10.1137/060668882. |
[21] |
P. Roux, K. G. Sabra, W. A. Kuperman and A. Roux, Ambient noise cross correlation in free space: Theoretical approach, J. Acoust. Soc. Am., 117 (2005), 79-84.
doi: 10.1121/1.1830673. |
[22] |
L. V. Ryzhik, G. C. Papanicolaou and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), 327-370.
doi: 10.1016/S0165-2125(96)00021-2. |
[23] |
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. |
[24] |
P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena, Academic Press, San Diego, 1995. |
[25] |
R. Snieder, Extracting the Green's function from the correlation of coda waves: A derivation based on stationary phase, Phys. Rev. E, 69 (2004), 046610.
doi: 10.1103/PhysRevE.69.046610. |
[26] |
L. Stehly, M. Campillo, B. Froment and R. Weaver, Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise, J. Geophys. Res., 113 (2008), B11306.
doi: 10.1029/2008JB005693. |
[27] |
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.
doi: 10.1029/2005JB004237. |
[28] |
M. C. W. van Rossum and Th. M. Nieuwenhuizen, Multiple scattering of classical waves: Microscopy, mesoscopy, and diffusion, Reviews of Modern Physics, 71 (1999), 313-371. |
[29] |
K. Wapenaar and J. Fokkema, Green's function representations for seismic interferometry, Geophysics, 71 (2006), SI33-SI46. |
[30] |
R. Weaver and O. I. Lobkis, Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies, Phys. Rev. Lett., 87 (2001), 134301.
doi: 10.1103/PhysRevLett.87.134301. |
[31] |
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, 26 pp.
doi: 10.1088/0266-5611/24/1/015011. |
[2] |
J. Berryman, Stable iterative reconstruction algorithm for nonlinear travel time tomography, Inverse Problems, 6 (1990), 21-42.
doi: 10.1088/0266-5611/6/1/005. |
[3] |
B. L. Biondi, 3D Seismic Imaging, no. 14 in Investigations in Geophysics, Society of Exploration Geophysics, Tulsa, 2006. |
[4] |
N. Bleistein and R. Handelsman, Asymptotic Expansions of Integrals, Dover, New York, 1986. |
[5] |
M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, 1999.
doi: 10.1017/CBO9781139644181. |
[6] |
F. Brenguier, N. M. Shapiro, M. Campillo, V. Ferrazzini, Z. Duputel, O. Coutant and A. Nercessian, Towards forecasting volcanic eruptions using seismic noise, Nature Geoscience, 1 (2008), 126-130.
doi: 10.1038/ngeo104. |
[7] |
T. Callaghan, N. Czink, F. Mani, A. Paulraj and G. Papanicolaou, Correlation-based radio localization in an indoor environment, EURASIP Journal on Wireless Communications and Networking, 2011 (2011), 135p.
doi: 10.1186/1687-1499-2011-135. |
[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] |
L. Erdös and H.-T. Yau, Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation, Comm. Pure Appl. Math., 53 (2000), 667-735.
doi: 10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5. |
[11] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer, New York, 2007.
doi: 10.1007/978-0-387-49808-9_4. |
[12] |
U. Frisch, Wave Propagation in Random Media, in Probabilistic Methods in Applied Mathematics, edited by A. T. Bharucha-Reid, Academic Press, New York, 1 (1968), 75-198. |
[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] |
J. Garnier and G. Papanicolaou, Resolution analysis for imaging with noise, Inverse Problems, 26 (2010), 074001, 22pp.
doi: 10.1088/0266-5611/26/7/074001. |
[15] |
J. Garnier and K. Sølna, Cross correlation and deconvolution of noise signals in randomly layered media, SIAM J. Imaging Sciences, 3 (2010), 809-834.
doi: 10.1137/090757538. |
[16] |
O. A. Godin, Accuracy of the deterministic travel time retrieval from cross-correlations of non-diffuse ambient noise, J. Acoust. Soc. Am., 126 (2009), EL183-EL189.
doi: 10.1121/1.3258064. |
[17] |
P. Gouédard, L. Stehly, F. Brenguier, M. Campillo, Y. Colin de Verdière, E. Larose, L. Margerin, P. Roux, F. J. Sanchez-Sesma, N. M. Shapiro and R. L. Weaver, Cross-correlation of random fields: Mathematical approach and applications, Geophysical Prospecting, 56 (2008), 375-393. |
[18] |
P. A. Martin, Acoustic scattering by inhomogeneous obstacles, SIAM J. Appl. Math., 64 (2003), 297-308.
doi: 10.1137/S0036139902414379. |
[19] |
P. M. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill, New York, 1968. |
[20] |
G. Papanicolaou, L. Ryzhik and K. Sølna, Self-averaging from lateral diversity in the Ito-Schroedinger equation, SIAM Journal on Multiscale Modeling and Simulation, 6 (2007), 468-492.
doi: 10.1137/060668882. |
[21] |
P. Roux, K. G. Sabra, W. A. Kuperman and A. Roux, Ambient noise cross correlation in free space: Theoretical approach, J. Acoust. Soc. Am., 117 (2005), 79-84.
doi: 10.1121/1.1830673. |
[22] |
L. V. Ryzhik, G. C. Papanicolaou and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), 327-370.
doi: 10.1016/S0165-2125(96)00021-2. |
[23] |
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. |
[24] |
P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena, Academic Press, San Diego, 1995. |
[25] |
R. Snieder, Extracting the Green's function from the correlation of coda waves: A derivation based on stationary phase, Phys. Rev. E, 69 (2004), 046610.
doi: 10.1103/PhysRevE.69.046610. |
[26] |
L. Stehly, M. Campillo, B. Froment and R. Weaver, Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise, J. Geophys. Res., 113 (2008), B11306.
doi: 10.1029/2008JB005693. |
[27] |
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.
doi: 10.1029/2005JB004237. |
[28] |
M. C. W. van Rossum and Th. M. Nieuwenhuizen, Multiple scattering of classical waves: Microscopy, mesoscopy, and diffusion, Reviews of Modern Physics, 71 (1999), 313-371. |
[29] |
K. Wapenaar and J. Fokkema, Green's function representations for seismic interferometry, Geophysics, 71 (2006), SI33-SI46. |
[30] |
R. Weaver and O. I. Lobkis, Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies, Phys. Rev. Lett., 87 (2001), 134301.
doi: 10.1103/PhysRevLett.87.134301. |
[31] |
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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