Semiclassical analysis and passive imaging

Nonlinearity

Volumn 22, Issue 6, 2009, Pages

  Colin De Verdière, Yves ^a  

^a INSTITUT FOURIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650763424     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/6/R01     Document Type: Article

References (36)

1. Bambusi D, Graffi S and Paul T 1999 Long time semiclassical approximation of quantum flows: a proof of Ehrenfest time Asymptotic Anal. 21 149-60 (Pubitemid 129565609)
2. Bardos C, Garnier J and Papanicolaou G 2008 Identification of Green's functions singularities Inverse Problems 24 015011
3. Bouzouina A and Robert D 2002 Uniform semiclassical estimates for the propagation of quantum observables Duke Math. J. 111 223-52
4. Brenguier F, Shapiro N, Campillo M, Ferrazzini V, Duputel Z, Coutant O and Nercessian A 2008 Towards forecasting volcanic eruptions using seismic noise Nature Geosci. doi:10.1038/ngeo104
5. Campillo M and Paul A 2003 Long range correlations of seismic codas Science 299 547-9
6. Colin de Verdière Y Méthodes semi-classiques et théorie spectrale Lecture Notes in preparation http://www-fourier.ujf- grenoble.fr/∼ycolver/
7. Colin de Verdière Y A semiclassical inverse problem II: reconstruction of the potential arXiv:math-ph/08021643
8. Derode A, Larose E, Tanter M, de Rosny J, Tourin A, Campillo M and Fink M 2004 Recovering the Green's function from field-field correlations in an open scattering medium J. Acoust. Soc. Am. 113 2973-6
9. Derode A, Larose E, Campillo M and Fink M 2003 How to estimate the Green's function of a heterogeneous medium between to passive sensors? Application to acoustic waves Appl. Phys. Lett. 83 3054-6
10. Dimassi M and Sjöstrand J 1999 Spectral Asymptotics in the Semi-Classical Limit (London Mathematical Society Lecture Notes Series vol 268) (Cambridge, UK: CUP)
11. Duistermaat J 1996 Fourier Integral Operators (Boston, MA: Birkhäuser)
12. Duvall T, Jefferies S, Harvey J and Pomerantz M 1993 Time-distance in helioseismology Nature 362 430-2 (Pubitemid 23961993)
13. Emmrich C and Weinstein A 1996 Geometry of the transport equation in multicomponent WKB approximation Commun. Math. Phys. 176 701-11 (Pubitemid 126324716)
14. Evans L and Zworski M Lectures on semiclassical analysis (Version 0.2) Available at http://math.berkeley.edu/∼zworski/
15. Gel'fand I M and Vilenkin N Y 1964 Generalised Functions, vol 4: Applications to Harmonic Analysis (New York: Academic)
16. Gouédard P et al 2008 Cross-correlation of random fields: mathematical approach and applications Geophys. Prospect. 56 375-93
17. Hörmander L 1968 The spectral function of an elliptic operator Acta Math. 12 193-218
18. Lobkis O I and Weaver R L 2001 On the emergence of Green's function in the correlations of a diffuse field J. Acoust. Soc. Am. 110 3011-7 (Pubitemid 33144300)
19. Rauch J and Taylor M 1975 Decay of solutions of non-dissipative hyperbolic systems on compact manifolds Commun. Pure Appl. Math. 28 501-23
20. Reed M and Simon B 1979 Methods of Modern Mathematical Physics: Scattering Theory vol III (New York: Academic)
21. Roux P, Sabra K and Kupperman W 2005 Ambient noise cross correlation in free space: theoretical approach J. Acoust. Soc. Am. 117 79-84 (Pubitemid 40130134)
22. Sabra K, Roux P, Thode A, D'Spain G, Hogliss W and Kuperman W 2005 Using ocean ambient noise for array self-localization and self-synchronization IEEE J. Ocean. Eng. 30 338-46
23. Sanchez-Sesma F, Pérez-Ruiz J, Campillo M and Luzón F 2006 The elastodynamic 2D Green's function retrieval from cross-correlation: the canonical inclusion problem Geophys. Res. Lett. 33 13305
24. Shapiro N and Campillo M 2004 Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise Geophys. Res. Lett. 31 L07614
25. Shapiro N, Campillo M, Stehly L and Ritzwoller M 2005 High resolution surface wave tomography from ambient seismic noise Science 307 1615
26. Schubert R 2005 Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times Commun. Math. Phys. 256 254
27. Schwartz L 1973 Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures (Oxford: Oxford University Press)
28. Sjöstrand J 1993 Projecteurs adiabatiques du point de vue pseudo-différentiel C. R. Acad. Sci. Paris 317 217-20 Série 1
29. Teufel S 2003 Adiabatic Perturbation Theory in Quantum Dynamics (Lecture Notes in Mathematics vol 1821) (New York: Springer)
30. Trèves F 1980 Introduction to Pseudo Differential and Fourier Integral Operators (New York: Plenum Press)
31. Weaver R L and Lobkis O I 2002 On the emergence of Green's function in the correlations of a diffuse field: pulse echo using thermal phonon's Ultrasonics 40 435-9
32. Weaver R L and Lobkis O I 2001 Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies Phys. Rev. Lett. 87 134301-4
33. Weaver R L and Lobkis O I 2004 Diffuse fields in open systems and the emergence of the Green's functions (L) J. Acoust. Soc. Am. 116 1-4
34. Weaver R L 2005 Information from seismic noise Science 307 1568-9 (Pubitemid 40354725)
35. Wiener N 1950 Extrapolation, Interpolation and Smoothing of Stationary Time Series (Cambridge, MA/New York: MIT Press/Wiley)
36. Yosida K 1965 Functional Analysis (Grundlheren der Mathematischen Wissenschaffen vol 123) (Berlin: Springer)