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Resolution enhancement from scattering in passive sensor imaging with cross correlations. (English) Zbl 1316.35298

In this paper, the framework for the analysis of cross correlations of noise signals is presented. Imaging by cross correlation of noise signals is reviewed briefly for a homogeneous background. The main result of the paper addresses cross correlation based passive array imaging in a weakly scattering medium. Also, a case is considered in which scattering is not generated by random inhomogeneities but by a deterministic reflecting interface in medium. The authors show how the use of iterated (fourth-order) cross correlations and appropriate imaging functionals can improve the resolution and the signal-to-noise ratio of passive sensor imaging in a scattering medium. Numerical simulations to illustrate the results of the paper are carried out.

MSC:

35R30 Inverse problems for PDEs
35R60 PDEs with randomness, stochastic partial differential equations
86A15 Seismology (including tsunami modeling), earthquakes
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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[1] C. Bardos, Identification of Green’s functions singularities by cross correlation of noisy signals,, Inverse Problems, 24 (2008) · Zbl 1145.35307 · doi:10.1088/0266-5611/24/1/015011
[2] J. Berryman, Stable iterative reconstruction algorithm for nonlinear travel time tomography,, Inverse Problems, 6, 21 (1990) · Zbl 0708.65065 · doi:10.1088/0266-5611/6/1/005
[3] B. L. Biondi, <em>3D Seismic Imaging</em>, no. 14 in Investigations in Geophysics,, Society of Exploration Geophysics (2006)
[4] N. Bleistein, <em>Asymptotic Expansions of Integrals</em>,, Dover (1986) · Zbl 0191.12403
[5] M. Born, <em>Principles of Optics</em>,, Cambridge University Press (1999) · Zbl 1430.78001 · doi:10.1017/CBO9781139644181
[6] F. Brenguier, Towards forecasting volcanic eruptions using seismic noise,, Nature Geoscience, 1, 126 (2008) · doi:10.1038/ngeo104
[7] T. Callaghan, Correlation-based radio localization in an indoor environment,, EURASIP Journal on Wireless Communications and Networking, 2011 (2011) · doi:10.1186/1687-1499-2011-135
[8] J. F. Claerbout, <em>Imaging the Earth’s Interior</em>,, Blackwell Scientific Publications (1985)
[9] Y. Colin de Verdière, Semiclassical analysis and passive imaging,, Nonlinearity, 22 (2009) · Zbl 1177.86011 · doi:10.1088/0951-7715/22/6/R01
[10] L. Erdös, Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation,, Comm. Pure Appl. Math., 53, 667 (2000) · Zbl 1028.82010 · doi:10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
[11] J.-P. Fouque, <em>Wave Propagation and Time Reversal in Randomly Layered Media</em>,, Springer (2007) · Zbl 1386.74001 · doi:10.1007/978-0-387-49808-9_4
[12] U. Frisch, Wave Propagation in Random Media,, in Probabilistic Methods in Applied Mathematics, 1, 75 (1968)
[13] J. Garnier, Passive sensor imaging using cross correlations of noisy signals in a scattering medium,, SIAM J. Imaging Sciences, 2, 396 (2009) · Zbl 1179.35344 · doi:10.1137/080723454
[14] J. Garnier, Resolution analysis for imaging with noise,, Inverse Problems, 26 (2010) · Zbl 1197.35320 · doi:10.1088/0266-5611/26/7/074001
[15] J. Garnier, Cross correlation and deconvolution of noise signals in randomly layered media,, SIAM J. Imaging Sciences, 3, 809 (2010) · Zbl 1200.35326 · 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) · doi:10.1121/1.3258064
[17] P. Gouédard, Cross-correlation of random fields: Mathematical approach and applications,, Geophysical Prospecting, 56, 375 (2008)
[18] P. A. Martin, Acoustic scattering by inhomogeneous obstacles,, SIAM J. Appl. Math., 64, 297 (2003) · Zbl 1063.76091 · doi:10.1137/S0036139902414379
[19] P. M. Morse, <em>Theoretical Acoustics</em>,, McGraw-Hill (1968)
[20] G. Papanicolaou, Self-averaging from lateral diversity in the Ito-Schroedinger equation,, SIAM Journal on Multiscale Modeling and Simulation, 6, 468 (2007) · Zbl 1143.35390 · doi:10.1137/060668882
[21] P. Roux, Ambient noise cross correlation in free space: Theoretical approach,, J. Acoust. Soc. Am., 117, 79 (2005) · doi:10.1121/1.1830673
[22] L. V. Ryzhik, Transport equations for elastic and other waves in random media,, Wave Motion, 24, 327 (1996) · Zbl 0954.74533 · doi:10.1016/S0165-2125(96)00021-2
[23] N. M. Shapiro, High-resolution surface wave tomography from ambient noise,, Science, 307, 1615 (2005) · doi:10.1126/science.1108339
[24] P. Sheng, <em>Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena</em>,, Academic Press (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) · doi:10.1103/PhysRevE.69.046610
[26] L. Stehly, Reconstructing Green’s function by correlation of the coda of the correlation (C3) of ambient seismic noise,, J. Geophys. Res., 113 (2008) · doi:10.1029/2008JB005693
[27] L. Stehly, A study of the seismic noise from its long-range correlation properties,, Geophys. Res. Lett., 111 (2006) · doi:10.1029/2005JB004237
[28] M. C. W. van Rossum, Multiple scattering of classical waves: Microscopy, mesoscopy, and diffusion,, Reviews of Modern Physics, 71, 313 (1999)
[29] K. Wapenaar, Green’s function representations for seismic interferometry,, Geophysics, 71 (2006)
[30] R. Weaver, Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies,, Phys. Rev. Lett., 87 (2001) · doi:10.1103/PhysRevLett.87.134301
[31] H. Yao, Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis I. Phase velocity maps,, Geophysical Journal International, 166, 732 (2006) · doi:10.1111/j.1365-246X.2006.03028.x
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