On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

Geophysics

Volumn 75, Issue 3, 2010, Pages

  Wapenaar, Kees ^a   Slob, Evert ^a   Snieder, Roel ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Department of Geology and Geological Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BORN APPROXIMATION; INTERFEROMETRY; SEISMOLOGY;

CROSS CORRELATIONS; FAR FIELD APPROXIMATION; FUNCTION REPRESENTATIONS; NONLINEAR SCATTERING; RECIPROCITY THEORY; SCATTERING MATRICES; SCATTERING THEORY; SEISMIC INTERFEROMETRIES;

NONLINEAR OPTICS;

BORN APPROXIMATION; DATA INVERSION; GREEN FUNCTION; INTERFEROMETRY; NUMERICAL MODEL; OPTICAL THEORY; SEISMIC METHOD; WAVE SCATTERING; MODEL TEST; MODEL VALIDATION; NONLINEARITY; SEISMIC MIGRATION; THEORETICAL STUDY;

EID: 84864155484     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.3374359     Document Type: Article

References (38)

1. Bojarski, N.N., 1983, Generalized reaction principles and reciprocity theorems for the wave equations, and the relationship between the time-advanced and time-retarded fields: Journal of the Acoustical Society of America, 74, 281-285.jas, JASMAN, 0001-4966, 10.1121/1.389721
2. Born, M. Wolf, E., 1965, Principles of optics: Pergamon Press.
3. Butkov, E., 1968, Mathematical physics: Addison-Wesley.
4. Carney, P.S. Schotland, J.C. Wolf, E., 2004, Generalized optical theorem for reflection, transmission, and extinction of power for scalar fields: Physical Review E, 70, 036611-1-036611-7.pre, PLEEE8, 1063-651X, 10.1103/PhysRevE.70.036611
5. Curtis, A. Halliday, D., 2010, Directional balancing for seismic and general wavefield interferometry: Geophysics, 75, no. 1, SA1-SA14.gpy, GPYSA7, 0016-8033, 10.1190/1.3298736
6. de Hoop, A.T., 1988, Time-domain reciprocity theorems for acoustic wave fields in fluids with relaxation: Journal of the Acoustical Society of America, 84, 1877-1882.jas, JASMAN, 0001-4966, 10.1121/1.397152
7. Fokkema, J.T. van den Berg, P.M., 1993, Seismic applications of acoustic reciprocity: Elsevier Scientific Publ. Co., Inc.
8. Gelius, L.-J. Lecomte, I. Tabti, H., 2002, Analysis of the resolution function in seismic prestack depth imaging: Geophysical Prospecting, 50, 505-515.8uc, GPPRAR, 0016-8025, 10.1046/j.1365-2478.2002.00331.x
9. Glauber, R. Schomaker, V., 1953, The theory of electron diffraction: Physical Review, 89, 667-671.phr, PHRVAO, 0031-899X, 10.1103/PhysRev.89.667
10. Groenenboom, J. Snieder, R., 1995, Attenuation, dispersion, and anisotropy by multiple scattering of transmitted waves through distributions of scatterers: Journal of the Acoustical Society of America, 98, 3482-3492.jas, JASMAN, 0001-4966, 10.1121/1.413780
11. Halliday, D. Curtis, A., 2009a, Generalized optical theorem for surface waves and layered media: Physical Review E, 79, 056603.pre, PLEEE8, 1063-651X, 10.1103/PhysRevE.79.056603
12. 2009b, Seismic interferometry of scattered surface waves in attenuative media: Geophysical Journal International, 178, 419-446.gji, GJINEA, 0956-540X, 10.1111/j.1365-246X.2009.04153.x
13. Heisenberg, W., 1943, Die "beobachtbaren Größen" in der Theorie der Elementarteilchen: Zeitschrift für Physik, 120, 513-538., 10.1007/BF01329800
14. Hu, J. Schuster, G.T. Valasek, P., 2001, Poststack migration deconvolution: Geophysics, 66, 939-952.gpy, GPYSA7, 0016-8033, 10.1190/1.1444984
15. Larose, E. Margerin, L. Derode, A. van Tiggelen, B. Campillo, M. Shapiro, N. Paul, A. Stehly, L. Tanter, M., 2006, Correlation of random wavefields: An interdisciplinary review: Geophysics, 71, no. 4, SI11-SI21.gpy, GPYSA7, 0016-8033, 10.1190/1.2213356
16. Lecomte, I., 2008, Resolution and illumination analyses in PSDM: A ray-based approach: The Leading Edge, 27, 650-663.lee, LEEDFF, 1070-485X, 10.1190/1.2919584
17. Marston, P.L., 2001, Generalized optical theorem for scatterers having inversion symmetry: Applications to acoustic backscattering: Journal of the Acoustical Society of America, 109, 1291-1295.jas, JASMAN, 0001-4966, 10.1121/1.1352082
18. Miller, D. Oristaglio, M. Beylkin, G., 1987, A new slant on seismic imaging: Migration and integral geometry: Geophysics, 52, 943-964.gpy, GPYSA7, 0016-8033, 10.1190/1.1442364
19. Morse, P.M. Feshbach, H., 1953, Methods of theoretical physics I: McGraw-Hill Book Company, Inc.
20. Newton, R.G., 1976, Optical theorem and beyond: American Journal of Physics, 44, no. 7, 639-642.ajp, AJPIAS, 0002-9505, 10.1119/1.10324
21. Oristaglio, M.L., 1989, An inverse scattering formula that uses all the data: Inverse Problems, 5, 1097-1105.inp, INPEEY, 0266-5611, 10.1088/0266-5611/5/6/015
22. Porter, R.P., 1970, Diffraction-limited, scalar image formation with holograms of arbitrary shape: Journal of the Optical Society of America, 60, 1051-1059.jas, JASMAN, 0001-4966, 10.1364/JOSA.60.001051
23. Rodberg, L.S. Thaler, R.M., 1967, Introduction to the quantum theory of scattering: Academic Press, Inc.
24. Schuster, G.T., 2009, Seismic interferometry: Cambridge University Press.
25. Schuster, G.T. Hu, J., 2000, Green's function for migration: Continuous recording geometry: Geophysics, 65, 167-175.gpy, GPYSA7, 0016-8033, 10.1190/1.1444707
26. Snieder, R., 1999, Imaging and averaging in complex media, , in J. P. Fouque, ed., Diffuse waves in complex media: Kluwer Academic Publ., 405-454.
27. Snieder, R. Miyazawa, M. Slob, E. Vasconcelos, I. Wapenaar, K., 2009a, A comparison of strategies for seismic interferometry: Surveys in Geophysics, 30, 503-523.svg, SUGEEC, 0169-3298, 10.1007/s10712-009-9069-z
28. Snieder, R. Sánchez-Sesma, F.J. Wapenaar, K., 2009b, Field fluctuations, imaging with backscattered waves, a generalized energy theorem, and the optical theorem: SIAM Journal on Imaging Sciences, 2, 763-776.cya, SJISBI, 1936-4954, 10.1137/08072913X
29. Snieder, R. van Wijk, K. Haney, M. Calvert, R., 2008, Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem: Physical Review E, 78, 036606.pre, PLEEE8, 1063-651X, 10.1103/PhysRevE.78.036606
30. Thorbecke, J. Wapenaar, K., 2007, On the relation between seismic interferometry and the migration resolution function: Geophysics, 72, no. 6, T61-T66.gpy, GPYSA7, 0016-8033, 10.1190/1.2785850
31. van Manen, D.-J. Curtis, A. Robertsson, J.O.A., 2006, Interferometric modeling of wave propagation in inhomogeneous elastic media using time reversal and reciprocity: Geophysics, 71, no. 4, SI41-SI60.gpy, GPYSA7, 0016-8033
32. van Manen, D.-J. Robertsson, J.O.A. Curtis, A., 2005, Modeling of wave propagation in inhomogeneous media: Physical Review Letters, 94, 164301-1-164301-4.prl, PRLTAO, 0031-9007, 10.1103/PhysRevLett.94.164301
33. van Rossum, M.C.W. Nieuwenhuizen, Th.M., 1999, Multiple scattering of classical waves: Microscopy, mesoscopy, and diffusion: Reviews of Modern Physics, 71, 313-371.rmp, RMPHAT, 0034-6861, 10.1103/RevModPhys.71.313
34. Vasconcelos, I. Snieder, R. Douma, H., 2009, Representation theorems and Green's function retrieval for scattering in acoustic media: Physical Review E, 80, 036605.pre, PLEEE8, 1063-651X, 10.1103/PhysRevE.80.036605
35. Wapenaar, K. Fokkema, J., 2006, Green's function representations for seismic interferometry: Geophysics, 71, no. 4, SI33-SI46.gpy, GPYSA7, 0016-8033, 10.1190/1.2213955
36. Wapenaar, K. Fokkema, J. Snieder, R., 2005, Retrieving the Green's function in an open system by cross-correlation: A comparison of approaches (L): Journal of the Acoustical Society of America, 118, 2783-2786.jas, JASMAN, 0001-4966, 10.1121/1.2046847
37. Weglein, A.B. Araújo, F.V. Carvalho, P.M. Stolt, R.H. Matson, K.H. Coates, R.T. Corrigan, D. Foster, D.J. Shaw, S.A. Zhang, H., 2003, Inverse scattering series and seismic exploration: Inverse Problems, 19, R27-R83.inp, INPEEY, 0266-5611, 10.1088/0266-5611/19/6/R01
38. Yu, J. Hu, J. Schuster, G.T. Estill, R., 2006, Prestack migration deconvolution: Geophysics, 71, no. 2, S53-S62.gpy, GPYSA7, 0016-8033, 10.1190/1.2187783