June  2014, 19(4): 979-998. doi: 10.3934/dcdsb.2014.19.979

High frequency analysis of imaging with noise blending

1. 

Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Received  October 2012 Revised  January 2014 Published  April 2014

We consider sensor array imaging for simultaneous noise blended sources. We study a migration imaging functional and we analyze its sensitivity to singular perturbations of the speed of propagation of the medium. We consider two kinds of random sources: randomly delayed pulses and stationary random processes, and three possible kinds of perturbations. Using high frequency analysis we prove the statistical stability (with respect to the realization of the noise blending) of the scheme and obtain quantitative results on the image contrast provided by the imaging functional, which strongly depends on the type of perturbations.
Citation: Ennio Fedrizzi. High frequency analysis of imaging with noise blending. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 979-998. doi: 10.3934/dcdsb.2014.19.979
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).  doi: 10.1088/0266-5611/24/1/015011.  Google Scholar

[2]

A. J. Berkhout, Changing the mindset in seismic data acquisition,, The Leading Edge, 27 (2008), 924.  doi: 10.1190/1.2954035.  Google Scholar

[3]

N. Bleistein, J. K. Cohen and J. W. Stockwell Jr, Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion,, Springer-Verlag, (2001).   Google Scholar

[4]

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.  doi: 10.1038/ngeo104.  Google Scholar

[5]

F. Brenguier, N. M. Shapiro, M. Campillo, A. Nercessian and V. Ferrazzini, 3-D surface wave tomography of the Piton de la Fournaise volcano using seismic noise correlations,, Geophysical Research Letters, 34 (2007).  doi: 10.1029/2006GL028586.  Google Scholar

[6]

A. Curtis, P. Gerstoft, H. Sato, R. Snieder and K. Wapenaar, Seismic interferometry - turning noise into signal,, The Leading Edge, 25 (2006), 1082.  doi: 10.1190/1.2349814.  Google Scholar

[7]

M. De Hoop, E. Fedrizzi, J. Garnier and K. Sølna, Imaging with noise blending,, Contemporary Mathematics, 577 (2012), 105.  doi: 10.1090/conm/577/11466.  Google Scholar

[8]

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas and F. Wu, Time-reversed acoustics,, Reports on Progress in Physics, 63 (2000), 1933.  doi: 10.1088/0034-4885/63/12/202.  Google Scholar

[9]

J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media,, Springer, (2007).   Google Scholar

[10]

J. Garnier and G. Papanicolaou, Passive sensor imaging using cross correlations of noisy signals in a scattering medium,, SIAM Journal on Imaging Sciences, 2 (2009), 396.  doi: 10.1137/080723454.  Google Scholar

[11]

J. Garnier and G. Papanicolaou, Resolution analysis for imaging with noise,, Inverse Problems, 26 (2010).  doi: 10.1088/0266-5611/26/7/074001.  Google Scholar

[12]

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.  doi: 10.1111/j.1365-2478.2007.00684.x.  Google Scholar

[13]

G. Hampson, J. Stefani and F. Herkenhoff, Acquisition using simultaneous sources,, The Leading Edge, 27 (2008), 918.  doi: 10.1190/1.2954034.  Google Scholar

[14]

E. Larose, L. Margerin, A. Derode, B. Van Tiggelen, M. Campillo, N. Shapiro, A. Paul, L. Stehly and M. Tanter, Correlation of random wave fields: an interdisciplinary review,, Geophysics, 71 (2006).  doi: 10.1190/1.2213356.  Google Scholar

[15]

A. Mahdad, P. Doulgeris and G. Blacquiere, Separation of blended data by iterative estimation and subtraction of blending interference noise,, Geophysics, 76 (2011).  doi: 10.1190/1.3556597.  Google Scholar

[16]

K. G. Sabra, P. Roux, P. Gerstoft, W. A. Kuperman and M. C . Fehler, Extracting coherent coda arrivals from cross correlations of long period seismic waves during the Mount St. Helens 2004 eruption,, Geophysical Research Letters, 33 (2006).  doi: 10.1029/2005GL025563.  Google Scholar

[17]

G. T. Schuster, X. Wang, Y. Huang, W. Dai and C. Boonyasiriwat, Theory of multisource crosstalk reduction by phase-encoded statics,, Geophysical Journal International, 184 (2011), 1289.  doi: 10.1111/j.1365-246X.2010.04906.x.  Google Scholar

[18]

N. M. Shapiro, M. Campillo, L. Stehly and M. H. Ritzwoller, High-resolution surface-wave tomography from ambient seismic noise,, Science, 307 (2005), 1615.  doi: 10.1126/science.1108339.  Google Scholar

[19]

L. Stehly, M. Campillo and N. M. Shapiro, A study of the seismic noise from its long-range correlation properties,, Journal of Geophysical Research, 111 (2006).  doi: 10.1029/2005JB004237.  Google Scholar

[20]

D. J. E. Verschuur and A. J. G. Berkhout, Seismic migration of blended shot records with surface-related multiple scattering,, Geophysics, 76 (2011).  doi: 10.1190/1.3521658.  Google Scholar

[21]

K. Wapenaar, J. van der Neut and J. Thorbecke, On the relation between seismic interferometry and the simultaneous-source method,, Geophysical Prospecting, 60 (2012), 802.  doi: 10.1111/j.1365-2478.2012.01056.x.  Google Scholar

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).  doi: 10.1088/0266-5611/24/1/015011.  Google Scholar

[2]

A. J. Berkhout, Changing the mindset in seismic data acquisition,, The Leading Edge, 27 (2008), 924.  doi: 10.1190/1.2954035.  Google Scholar

[3]

N. Bleistein, J. K. Cohen and J. W. Stockwell Jr, Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion,, Springer-Verlag, (2001).   Google Scholar

[4]

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.  doi: 10.1038/ngeo104.  Google Scholar

[5]

F. Brenguier, N. M. Shapiro, M. Campillo, A. Nercessian and V. Ferrazzini, 3-D surface wave tomography of the Piton de la Fournaise volcano using seismic noise correlations,, Geophysical Research Letters, 34 (2007).  doi: 10.1029/2006GL028586.  Google Scholar

[6]

A. Curtis, P. Gerstoft, H. Sato, R. Snieder and K. Wapenaar, Seismic interferometry - turning noise into signal,, The Leading Edge, 25 (2006), 1082.  doi: 10.1190/1.2349814.  Google Scholar

[7]

M. De Hoop, E. Fedrizzi, J. Garnier and K. Sølna, Imaging with noise blending,, Contemporary Mathematics, 577 (2012), 105.  doi: 10.1090/conm/577/11466.  Google Scholar

[8]

M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas and F. Wu, Time-reversed acoustics,, Reports on Progress in Physics, 63 (2000), 1933.  doi: 10.1088/0034-4885/63/12/202.  Google Scholar

[9]

J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media,, Springer, (2007).   Google Scholar

[10]

J. Garnier and G. Papanicolaou, Passive sensor imaging using cross correlations of noisy signals in a scattering medium,, SIAM Journal on Imaging Sciences, 2 (2009), 396.  doi: 10.1137/080723454.  Google Scholar

[11]

J. Garnier and G. Papanicolaou, Resolution analysis for imaging with noise,, Inverse Problems, 26 (2010).  doi: 10.1088/0266-5611/26/7/074001.  Google Scholar

[12]

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.  doi: 10.1111/j.1365-2478.2007.00684.x.  Google Scholar

[13]

G. Hampson, J. Stefani and F. Herkenhoff, Acquisition using simultaneous sources,, The Leading Edge, 27 (2008), 918.  doi: 10.1190/1.2954034.  Google Scholar

[14]

E. Larose, L. Margerin, A. Derode, B. Van Tiggelen, M. Campillo, N. Shapiro, A. Paul, L. Stehly and M. Tanter, Correlation of random wave fields: an interdisciplinary review,, Geophysics, 71 (2006).  doi: 10.1190/1.2213356.  Google Scholar

[15]

A. Mahdad, P. Doulgeris and G. Blacquiere, Separation of blended data by iterative estimation and subtraction of blending interference noise,, Geophysics, 76 (2011).  doi: 10.1190/1.3556597.  Google Scholar

[16]

K. G. Sabra, P. Roux, P. Gerstoft, W. A. Kuperman and M. C . Fehler, Extracting coherent coda arrivals from cross correlations of long period seismic waves during the Mount St. Helens 2004 eruption,, Geophysical Research Letters, 33 (2006).  doi: 10.1029/2005GL025563.  Google Scholar

[17]

G. T. Schuster, X. Wang, Y. Huang, W. Dai and C. Boonyasiriwat, Theory of multisource crosstalk reduction by phase-encoded statics,, Geophysical Journal International, 184 (2011), 1289.  doi: 10.1111/j.1365-246X.2010.04906.x.  Google Scholar

[18]

N. M. Shapiro, M. Campillo, L. Stehly and M. H. Ritzwoller, High-resolution surface-wave tomography from ambient seismic noise,, Science, 307 (2005), 1615.  doi: 10.1126/science.1108339.  Google Scholar

[19]

L. Stehly, M. Campillo and N. M. Shapiro, A study of the seismic noise from its long-range correlation properties,, Journal of Geophysical Research, 111 (2006).  doi: 10.1029/2005JB004237.  Google Scholar

[20]

D. J. E. Verschuur and A. J. G. Berkhout, Seismic migration of blended shot records with surface-related multiple scattering,, Geophysics, 76 (2011).  doi: 10.1190/1.3521658.  Google Scholar

[21]

K. Wapenaar, J. van der Neut and J. Thorbecke, On the relation between seismic interferometry and the simultaneous-source method,, Geophysical Prospecting, 60 (2012), 802.  doi: 10.1111/j.1365-2478.2012.01056.x.  Google Scholar

[1]

Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020379

[2]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[3]

Wenmeng Geng, Kai Tao. Large deviation theorems for dirichlet determinants of analytic quasi-periodic jacobi operators with Brjuno-Rüssmann frequency. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5305-5335. doi: 10.3934/cpaa.2020240

[4]

Yongge Tian, Pengyang Xie. Simultaneous optimal predictions under two seemingly unrelated linear random-effects models. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020168

[5]

Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020345

[6]

Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020049

[7]

Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347

[8]

Shiqiu Fu, Kanishka Perera. On a class of semipositone problems with singular Trudinger-Moser nonlinearities. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020452

[9]

Bo Chen, Youde Wang. Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020268

[10]

Yu Zhou, Xinfeng Dong, Yongzhuang Wei, Fengrong Zhang. A note on the Signal-to-noise ratio of $ (n, m) $-functions. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020117

[11]

Jie Zhang, Yuping Duan, Yue Lu, Michael K. Ng, Huibin Chang. Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020071

[12]

Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020032

[13]

Anna Canale, Francesco Pappalardo, Ciro Tarantino. Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020274

[14]

Susmita Sadhu. Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020342

[15]

Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020442

[16]

Hoang The Tuan. On the asymptotic behavior of solutions to time-fractional elliptic equations driven by a multiplicative white noise. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020318

[17]

Serge Dumont, Olivier Goubet, Youcef Mammeri. Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020456

[18]

Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020383

[19]

Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5367-5386. doi: 10.3934/cpaa.2020242

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]