Role of Scattering in Virtual Source Array Imaging

We consider imaging in a scattering medium where the illumination goes through this medium but there is also an auxiliary, passive receiver array that is near the object to be imaged. Instead of imaging with the source-receiver array on the far side of the object, we image with the data of the passive array on the near side of the object. The imaging is done with travel time migration using the cross correlations of the passive array data. We showed in [J. Garnier and G. Papanicolaou, Inverse Problems, 28 (2012), 075002] that if (i) the source array is infinite, (ii) the scattering medium is modeled by either an isotropic random medium in the paraxial regime or a randomly layered medium, and (iii) the medium between the auxiliary array and the object to be imaged is homogeneous, then imaging with cross correlations completely eliminates the effects of the random medium. It is as if we imaged with an active array, instead of a passive one, near the object. The purpose of this paper is to analyze the resolu...

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

[2]  E. Slob,et al.  Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances , 2010 .

[3]  H. Georgi,et al.  The Physics of Waves , 1992 .

[4]  G. Papanicolaou,et al.  Interferometric array imaging in clutter , 2005 .

[5]  G. Ross.  The Elements of Wave Propagation in Random Media , 1978 .

[6]  Hongkai Zhao,et al.  Super-resolution in time-reversal acoustics. , 2002, The Journal of the Acoustical Society of America.

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

[8]  Roux,et al.  Robust Acoustic Time Reversal with High-Order Multiple Scattering. , 1995, Physical review letters.

[9]  Maarten V. de Hoop,et al.  Estimating a Green's Function from "Field-Field" Correlations in a Random Medium , 2009, SIAM J. Appl. Math..

[10]  Liliana Borcea,et al.  Adaptive interferometric imaging in clutter and optimal illumination , 2006 .

[11]  Liliana Borcea,et al.  Coherent interferometric imaging in clutter , 2006 .

[12]  G. Papanicolaou,et al.  Coherent interferometric imaging, time gating, and beamforming , 2011 .

[13]  George Papanicolaou,et al.  Statistical Stability in Time Reversal , 2004, SIAM J. Appl. Math..

[14]  Josselin Garnier,et al.  Time reversal super resolution in randomly layered media , 2006 .

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

[16]  Josselin Garnier,et al.  Correlation-based virtual source imaging in strongly scattering random media , 2012 .

[17]  Andrey Bakulin,et al.  The virtual source method: Theory and case study , 2006 .

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

[19]  Josselin Garnier,et al.  Coupled paraxial wave equations in random media in the white-noise regime , 2009, 0903.0449.

[20]  George Papanicolaou,et al.  Frequency Content of Randomly Scattered Signals , 1991, SIAM Rev..

[21]  Liliana Borcea,et al.  Filtering Deterministic Layer Effects in Imaging , 2009, SIAM Rev..

[22]  Josselin Garnier,et al.  Wave Transmission through Random Layering with Pressure Release Boundary Conditions , 2010, Multiscale Model. Simul..

[23]  Fred D. Tappert,et al.  The parabolic approximation method , 1977 .

[24]  Josselin Garnier,et al.  Time-reversal refocusing for point source in randomly layered media , 2005 .

[25]  G. Papanicolaou,et al.  Enhanced statistical stability in coherent interferometric imaging , 2011 .

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

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

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

[29]  Jack K. Cohen,et al.  Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion , 2001 .

[30]  Josselin Garnier,et al.  Signal-to-Noise Ratio Estimation in Passive Correlation-Based Imaging , 2013, SIAM J. Imaging Sci..

[31]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[32]  Josselin Garnier,et al.  Imaging in Randomly Layered Media by Cross-Correlating Noisy Signals , 2005, Multiscale Model. Simul..