Mathematical models for passive imaging I: general background

Passive imaging is a new technics which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields between different points is strongly related to the Green function of the wave propagation. The aim of this paper is to provide a mathematical context for this approach and to show, in particular, how the methods of semi-classical analysis can be be used in order to find the asymptotic behaviour of the correlations.

[1]  L. Hörmander,et al.  The spectral function of an elliptic operator , 1968 .

[2]  Richard L. Weaver,et al.  Information from Seismic Noise , 2005, Science.

[3]  J. D. Knowles RADON MEASURES ON ARBITRARY TOPOLOGICAL SPACES AND CYLINDRICAL MEASURES , 1977 .

[4]  Richard L. Weaver,et al.  Diffuse fields in open systems and the emergence of the Green’s function (L) , 2004 .

[5]  François Treves,et al.  Introduction to Pseudodifferential and Fourier Integral Operators , 1980 .

[6]  Mickael Tanter,et al.  Recovering the Green's function from field-field correlations in an open scattering medium. , 2003, The Journal of the Acoustical Society of America.

[7]  M. Fink,et al.  How to estimate the Green’s function of a heterogeneous medium between two passive sensors? Application to acoustic waves , 2003 .

[8]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[9]  Didier Robert,et al.  Uniform semiclassical estimates for the propagation of quantum observables , 2002 .

[10]  L. Hörmander Fourier integral operators. I , 1995 .

[11]  W.A. Kuperman,et al.  Using ocean ambient noise for array self-localization and self-synchronization , 2005, IEEE Journal of Oceanic Engineering.

[12]  L. Hörmander,et al.  Fourier integral operators. II , 1972 .

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

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

[15]  Francisco J. Sánchez-Sesma,et al.  Elastodynamic 2D Green function retrieval from cross‐correlation: Canonical inclusion problem , 2006 .

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

[17]  Michel Campillo,et al.  Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise , 2004 .

[18]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[19]  Yves Colin de Verdiere Mathematical models for passive imaging II: Effective Hamiltonians associated to surface waves , 2006 .

[20]  R. Weaver,et al.  On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons. , 2001, Ultrasonics.

[21]  Richard L. Weaver,et al.  On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons. , 2001, Ultrasonics.

[22]  M. Dimassi,et al.  Spectral Asymptotics in the Semi-Classical Limit: Improvement when the periodic trajectories form a set of measure 0 , 1999 .