Resolution enhancement from scattering in passive sensor imaging with cross correlations

It was shown in [Garnier et al., SIAM J. Imaging Sciences 2 (2009), 396] that it is possible to image re ectors by backpropagating cross correlations of signals generated by ambient noise sources and recorded at passive sensor arrays. The resolution of the image depends on the directional diversity of the noise signals relative to the locations of the sensor array and the reflector. When directional diversity is limited it is possible to enhance it by exploiting the scattering properties of the medium since scatterers will act as secondary noise sources. However, scattering increases the fluctuation level of the cross correlations and therefore tends to destabilize the image by reducing its signal- to-noise ratio. In this paper we study the trade-o in passive, correlation-based imaging between resolution enhancement and signal-to-noise ratio reduction that is due to scattering.

[1]  Josselin Garnier,et al.  Resolution analysis for imaging with noise , 2010 .

[2]  Josselin Garnier,et al.  Passive Sensor Imaging Using Cross Correlations of Noisy Signals in a Scattering Medium , 2009, SIAM J. Imaging Sci..

[3]  Josselin Garnier,et al.  Identification of Green's functions singularities by cross correlation of noisy signals , 2008 .

[4]  Y. D. Verdière,et al.  Semiclassical analysis and passive imaging , 2008, 0803.2436.

[5]  M. V. Rossum,et al.  Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion , 1998, cond-mat/9804141.

[6]  Paul A. Martin,et al.  Acoustic Scattering by Inhomogeneous Obstacles , 2003, SIAM J. Appl. Math..

[7]  D. Malacara-Hernández,et al.  PRINCIPLES OF OPTICS , 2011 .

[8]  G. Nemes.  Asymptotic Expansions of Integrals , 2004 .

[9]  K. Wapenaar,et al.  Green's function representations for seismic interferometry , 2006 .

[10]  Michel Campillo,et al.  A study of the seismic noise from its long-range correlation properties , 2006 .

[11]  George Papanicolaou,et al.  Transport equations for elastic and other waves in random media , 1996 .

[12]  P. Sheng,et al.  Introduction to Wave Scattering, Localization and Mesoscopic Phenomena. Second edition , 1995 .

[13]  Maarten V. de Hoop,et al.  Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis: I - Phase velocity maps , 2006 .

[14]  J. Berryman.  Stable iterative reconstruction algorithm for nonlinear traveltime tomography , 1990 .

[15]  Josselin Garnier,et al.  Cross Correlation and Deconvolution of Noise Signals in Randomly Layered Media , 2010, SIAM J. Imaging Sci..

[16]  J. Garnier,et al.  Passive imaging and detection in cluttered media , 2009, 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[17]  Michel Campillo,et al.  High-Resolution Surface-Wave Tomography from Ambient Seismic Noise , 2005, Science.

[18]  Biondo L. Biondi,et al.  3D Seismic Imaging , 2006 .

[19]  R. Weaver,et al.  Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies. , 2001, Physical review letters.

[20]  G. F. Roach,et al.  Inverse problems and imaging , 1991 .

[21]  Jon F. Claerbout,et al.  Imaging the Earth's Interior , 1985 .

[22]  W. Kuperman,et al.  Ambient noise cross correlation in free space: theoretical approach. , 2005, The Journal of the Acoustical Society of America.

[23]  V. Naroditsky.  Wave Propagation in Random Media , 1989 .

[24]  R. Snieder.  Extracting the Green's function from the correlation of coda waves: a derivation based on stationary phase. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  R. Weaver,et al.  Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise , 2008 .

[26]  Michel Campillo,et al.  Towards forecasting volcanic eruptions using seismic noise , 2007, 0706.1935.

[27]  Josselin Garnier,et al.  Wave Propagation and Time Reversal in Randomly Layered Media , 2007 .

[28]  Francisco J. Sánchez-Sesma,et al.  Cross‐correlation of random fields: mathematical approach and applications , 2008 .

[29]  Arogyaswami Paulraj,et al.  Correlation-based radio localization in an indoor environment , 2011, EURASIP J. Wirel. Commun. Netw..

[30]  Josselin Garnier,et al.  Effective Properties of Randomly Layered Media , 2007 .

[31]  Oleg A Godin.  Accuracy of the deterministic travel time retrieval from cross-correlations of non-diffuse ambient noise. , 2009, The Journal of the Acoustical Society of America.

[32]  George Papanicolaou,et al.  Self-Averaging from Lateral Diversity in the Itô-Schrödinger Equation , 2007, Multiscale Model. Simul..

[33]  Huajian Yao,et al.  Surface wave array tomography in SE Tibet from ambient seismic noise and two-station analysis - II. Crustal and upper-mantle structure , 2008 .

[34]  H. Yau,et al.  Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation , 1999 .