Surveys in Geophysics

, Volume 30, Issue 4–5, pp 503–523 | Cite as

A Comparison of Strategies for Seismic Interferometry

  • Roel Snieder
  • Masatoshi Miyazawa
  • Evert Slob
  • Ivan Vasconcelos
  • Kees Wapenaar


The extraction of the response from field fluctuations excited by random sources has received considerable attention in a variety of different fields. We present three methods for the extraction of the systems response that are based on cross-correlation, deconvolution, and the solution of an integral equation, respectively. For systems that are invariant for time-reversal the correlation method requires random sources on a bounding surface only, but when time-reversal invariance is broken, for example by attenuation, a volume distribution of sources is needed. For this reason the correlation method is not useful for diffusive or strongly attenuating systems. We provide examples of the three methods and compare their merits and drawbacks. We show that the extracted field may satisfy different boundary conditions than does the physical field. This can be used, for example, to suppress surface-related multiples in exploration seismology, to study the coupling of buildings to the subsurface, and to remove the airwave in controlled source electromagnetics (CSEM).


Deconvolution Geophone Seismic Noise Field Fluctuation Correlation Approach 



We thank two anonymous reviewers for their useful corrections and suggestions. This work was supported by the NSF (Grant EAS-0609595), by ExxonMobil Upstream Research Co., and by the GameChanger program of Shell.


  1. Aki K (1957) Space and time spectra of stationary stochastic waves with special reference to microtremors. Bull Earthq Res Inst 35:415–456Google Scholar
  2. Amundsen L (2001) Elimination of free-surface related multiples without the need of the source wavelet. Geophysics 66:327–341CrossRefGoogle Scholar
  3. Amundsen L, Løseth L, Mittet R, Ellingsrud S, Ursin B (2006) Decomposition of electromagnetic fields into upgoing and downgoing components. Geophysics 71:G211–G223CrossRefGoogle Scholar
  4. Bakulin A, Calvert R (2004) Virtual source: new method for imaging and 4D below complex overburden. Expanded abstracts of the 2004 SEG-meeting, pp 2477–2480Google Scholar
  5. Bakulin A, Calvert R (2006) The virtual source method: theory and case study. Geophysics 71:SI139–SI150CrossRefGoogle Scholar
  6. Bakulin A, Mateeva A, Mehta K, Jorgensen P, Ferrandis J, Sinha Herhold I, Lopez J (2007) Virtual source applications to imaging and reservoir monitoring. The Leading Edge 26:732–740CrossRefGoogle Scholar
  7. Bensen GD, Ritzwoller MH, Barmin MP, Levshin AL, Lin F, Moschetti MP, Shapiro NM, Yang Y (2007) Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements. Geophys J Int 169:1239–1260CrossRefGoogle Scholar
  8. Brenguier F, Campillo M, Hadziioannou C, Shapiro N, Larose E (2008) Postseismic relaxation along the San Andreas Fault at Parkfield from continuous seismological observations. Science 321:1478–1481CrossRefGoogle Scholar
  9. Callen HB, Welton TA (1951) Irreversibility and generalized noise. Phys Rev 83:34–40CrossRefGoogle Scholar
  10. Campillo M, Paul A (2003) Long-range correlations in the diffuse seismic coda. Science 299:547–549CrossRefGoogle Scholar
  11. Chaput JA, Bostock MG (2007) Seismic interferometry using non-volcanic tremor in Cascadia. Geophys Res Lett 34:L07304. doi: 10.1029/2007/GL028987 CrossRefGoogle Scholar
  12. Chávez-Garcia FJ, Luzón F (2005) On the correlation of seismic microtremors. J Geophys Res 110:B11313. doi: 10.1029/2005JB003686 CrossRefGoogle Scholar
  13. Curtis A, Gerstoft P, Sato H, Snieder R, Wapenaar K (2006) Seismic interferometry—turning noise into signal. The Leading Edge 25:1082–1092CrossRefGoogle Scholar
  14. Derode A, Larose E, Tanter M, de Rosny J, Tourin A, Campillo M, Fink M (2003a) Recovering the Green’s function from far-field correlations in an open scattering medium. J Acoust Soc Am 113:2973–2976CrossRefGoogle Scholar
  15. Derode A, Larose E, Campillo M, Fink M (2003b) How to estimate the Green’s function for a heterogeneous medium between two passive sensors? Application to acoustic waves. Appl Phys Lett 83:3054–3056CrossRefGoogle Scholar
  16. Draganov D, Wapenaar K, Mulder W, Singer J, Verdel A (2007) Retrieval of reflections from seismic background-noise measurements. Geophys Res Lett 34:L04305CrossRefGoogle Scholar
  17. Gerstoft P, Fehler MC, Sabra KG (2006) When Katrina hit California. Geophys Res Lett 33:L17308CrossRefGoogle Scholar
  18. Griffiths DJ (1999) Introduction to electrodynamics, 3 edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  19. Gutenberg B (1947) Microseisms and weather forecasting. J Meteorol 4:21–28Google Scholar
  20. Hill D, Combee L, Bacon J (2006) Over/under acquisition and data processing: the next quantum leap in seismic technology? First Break 24:81–96Google Scholar
  21. Hornby BE, Yu J (2007) Interferometric imaging of a salt flank using walkaway VSP data. The Leading Edge 26:760–763CrossRefGoogle Scholar
  22. Kennett BLN (1979) The suppression of surface multiples on seismic records. Geophys Prosp 27:584–600CrossRefGoogle Scholar
  23. Kohler MD, Heaton TH, Bradford SC (2007) Propagating waves in the steel, moment-frame Factor building recorded during earthquakes. Bull Seismol Soc Am 97:1334–1345CrossRefGoogle Scholar
  24. Kubo R (1966) The fluctuation–dissipation theorem. Rep Prog Phys 29:255–284CrossRefGoogle Scholar
  25. Larose E, Derode A, Campillo M, Fink M (2004) Imaging from one-bit correlations of wideband diffuse wave fields. J Appl Phys 95:8393–8399CrossRefGoogle Scholar
  26. Larose E, Montaldo G, Derode A, Campillo M (2006a) Passive imaging of localized reflectors and interfaces in open media. Appl Phys Lett 88:104103CrossRefGoogle Scholar
  27. Larose E, Margerin L, Derode A, van Tiggelen B, Campillo M, Shapiro N, Paul A, Stehly L, Tanter M (2006b) Correlation of random wavefields: an interdisciplinary review. Geophysics 71:SI11–SI21CrossRefGoogle Scholar
  28. Le Bellac M, Mortessagne F, Batrouni GG (2004) Equilibrium and non-equilibrium statistical thermodynamics. Cambridge University Press, CambridgeGoogle Scholar
  29. Lobkis OI, Weaver RL (2001) On the emergence of the Green’s function in the correlations of a diffuse field. J Acoust Soc Am 110:3011–3017CrossRefGoogle Scholar
  30. Longuet-Higgins MS (1950) A theory for the generation of microseisms. Phil Trans R Soc Lond A 243:1–35CrossRefGoogle Scholar
  31. Louie JN (2001) Faster, better: shear-wave velocity to 100 meters depth from refraction microtremor analysis. Bull Seismol Soc Am 91:347–364CrossRefGoogle Scholar
  32. Malcolm A, Scales J, van Tiggelen BA (2004) Extracting the Green’s function from diffuse, equipartitioned waves. Phys Rev E 70:015601CrossRefGoogle Scholar
  33. Mehta K, Snieder R, Graizer V (2007a) Downhole receiver function: a case study. Bull Seismol Soc Am 97:1396–1403CrossRefGoogle Scholar
  34. Mehta K, Bakulin A, Sheiman J, Calvert R, Snieder R (2007b) Improving the virtual source method by wavefield separation. Geophysics 72:V79–V86CrossRefGoogle Scholar
  35. Mehta K, Snieder R, Calvert R, Sheiman J (2008a) Acquisition geometry requirements for generating virtual-source data. The Leading Edge 27:620–629CrossRefGoogle Scholar
  36. Mehta K, Sheiman JL, Snieder R, Calvert R (2008b) Strengthening the virtual-source method for time-lapse monitoring. Geophysics 73:S73–S80CrossRefGoogle Scholar
  37. Miyazawa M, Snieder R, Venkataraman A (2008) Application of seismic interferometry to extract P and S wave propagation and observation of shear wave splitting from noise data at Cold Lake, Canada. Geophysics 73:D35–D40CrossRefGoogle Scholar
  38. Moldoveanu N, Combee L, Egan M, Hamson G, Sydora L, Abriel W (2007) Over/under towed-streamer acquisition: a method to extend seismic bandwidth to both higher and lower frequencies. The Leading Edge 26:41–58CrossRefGoogle Scholar
  39. Morse PM, Ingard KU (1968) Theorerical acoustics. McGraw-Hill, New YorkGoogle Scholar
  40. Paul A, Campillo M, Margerin L, Larose E, Derode A (2005) Empirical synthesis of time-asymmetrical Green functions from the correlation of coda waves. J Geophys Res 110:B08302. doi: 10.1029/2004JB003521 CrossRefGoogle Scholar
  41. Pharez S, Hendrick N, Tenghemn R (2008) First look at seismic data from a towed dual-sensor streamer. The Leading Edge 27:904–913CrossRefGoogle Scholar
  42. Poletto F, Miranda F (2004) Seismic while drilling, fundamentals fo drill-bit seismic for exploration. In: Helbig K, Treitel S (eds) Handbook of geophysical exploration, vol 35. Elsevier, AmsterdamGoogle Scholar
  43. Poletto F, Malusa M, Miranda F, Tinivella U (2004) Seismic-while-drilling by using dual sensors in drill strings. Geophysics 69:1261–1271CrossRefGoogle Scholar
  44. Prieto G, Lawrence JF, Beroza GC (2009) Anelastic earth structure from the coherency of the ambient seismic field. J Geophys Res (submitted)Google Scholar
  45. Rector JW, Marion BP (1991) The use of drill-bit energy as a downhole seismic source. Geophysics 56:628–634CrossRefGoogle Scholar
  46. Rickett JE, Claerbout JF (1999) Acoustic daylight imaging via spectral factorization: helioseismology and reservoir monitoring. The Leading Edge 18:957–960CrossRefGoogle Scholar
  47. Rickett JE, Claerbout JF (2000) Calculation of the sun’s acoustic impulse response by multidimensional spectral factorization. Sol Phys 192:203–210CrossRefGoogle Scholar
  48. Riley DC, Claerbout JF (1976) 2-D multiple reflections. Geophysics 41:592–620CrossRefGoogle Scholar
  49. Ritzwoller MH (2009) Ambient noise seismic imaging. In: McGraw Hill yearbook of science and technology 2009. McGraw-Hill, New YorkGoogle Scholar
  50. Robinson EA (1999) Seismic inversion and deconvolution. In: Helbig K, Treitel S (eds) Handbook of geophysical exploration, vol 4B. Pergamon, AmsterdamGoogle Scholar
  51. Roux P, Fink M (2003) Green’s function estimation using secondary sources in a shallow water environment. J Acoust Soc Am 113:1406–1416CrossRefGoogle Scholar
  52. Roux P, Kuperman WA, NPAL Group (2004) Extracting coherent wave fronts from acoustic ambient noise in the ocean. J Acoust Soc Am 116:1995–2003CrossRefGoogle Scholar
  53. Roux P, Sabra KG, Gerstoft P, Kuperman WA (2005) P-waves from cross correlation of seismic noise. Geophys Res Lett 32:L19303. doi: 10.1029/2005GL023803 CrossRefGoogle Scholar
  54. Rytov SM, Kravtsov YuA, Tatarskii VI (1989) Principles of statistical radiophysics, vol 3, elements of random fields. Springer, BerlinGoogle Scholar
  55. Sabra KG, Roux P, Thode AM, D’Spain GL, Hodgkiss WS (2005a) Using ocean ambient noise for array self-localization and self-synchronization. IEEE J Ocean Eng 30:338–347CrossRefGoogle Scholar
  56. Sabra KG, Gerstoft P, Roux P, Kuperman WA, Fehler MC (2005b) Surface wave tomography from microseisms in Southern California. Geophys Res Lett 32:L14311. doi: 10.1029/2005GL023155 CrossRefGoogle Scholar
  57. Sabra KG, Roux P, Gerstoft P, Kuperman WA, Fehler MC (2006) Extracting coherent coda arrivals from cross-correlations of long period seismic waves during the Mount St. Helens 2004 eruption. J Geophys Res 33:L06313. doi: 1029.2005GL025563 Google Scholar
  58. Sabra KG, Conti S, Roux P, Kuperman WA (2007) Passive in-vivo elastography from skeletal muscle noise. Appl Phys Lett 90:194101CrossRefGoogle Scholar
  59. Sabra KG, Srivastava A, di Scalea FL, Bartoli I, Rizzo P, Conti S (2008) Structural health monitoring by extraction of coherent guided waves from diffuse fields. J Acoust Soc Am 123:EL8Google Scholar
  60. Sawazaki K, Sato H, Nakahara H, Nishimura T (2009) Time-lapse changes of seismic velocity in the shallow ground caused by strong ground motion shock of the 2000 Western-Tottori earthquake, Japan, as revealed from coda deconvolution analysis. Bull Seismol Soc Am 99:352–366CrossRefGoogle Scholar
  61. Schuster GT, Yu J, Sheng J, Rickett J (2004) Interferometric/daylight seismic imaging. Geophys J Int 157:838–852CrossRefGoogle Scholar
  62. Sens-Schönfelder C, Wegler U (2006) Passive image interferometry and seasonal variations at Merapi volcano, Indonesia. Geophys Res Lett 33:L21302. doi: 10.1029/2006GL027797 CrossRefGoogle Scholar
  63. Shapiro NM, Campillo M (2004) Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise. Geophys Res Lett 31:L07614. doi: 10.1029/2004GL019491 CrossRefGoogle Scholar
  64. Shapiro NM, Campillo M, Stehly L, Ritzwoller MH (2005) High-resolution surface-wave tomography from ambient seismic noise. Science 307:1615–1618CrossRefGoogle Scholar
  65. Slob E, Draganov D, Wapenaar K (2007) Interferometric electromagnetic Green’s functions representations using propagation invariants. Geophys J Int 169:60–80CrossRefGoogle Scholar
  66. Snieder R (2004) Extracting the Green’s function from the correlation of coda waves: a derivation based on stationary phase. Phys Rev E 69:046610CrossRefGoogle Scholar
  67. Snieder R (2006) Retrieving the Green’s function of the diffusion equation from the response to a random forcing. Phys Rev E 74:046620CrossRefGoogle Scholar
  68. Snieder R (2007) Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves. J Acoust Soc Am 121:2637–2643CrossRefGoogle Scholar
  69. Snieder R, Şafak E (2006) Extracting the building response using seismic interferometry: theory and application to the Millikan library in Pasadena, California. Bull Seismol Soc Am 96:586–598CrossRefGoogle Scholar
  70. Snieder R, Sheiman J, Calvert R (2006a) Equivalence of the virtual source method and wavefield deconvolution in seismic interferometry. Phys Rev E 73:066620CrossRefGoogle Scholar
  71. Snieder R, Wapenaar K, Larner K (2006b) Spurious multiples in seismic interferometry of primaries. Geophysics 71:SI111–SI124CrossRefGoogle Scholar
  72. Snieder R, Wapenaar K, Wegler U (2007a) Unified Green’s function retrieval by cross-correlation: connection with energy principles. Phys Rev E 75:036103CrossRefGoogle Scholar
  73. Snieder R, Hubbard S, Haney M, Bawden G, Hatchell P, Revil A, Calvert R, Curtis A, Fehler M, Gerstoft P, Hornby B, Landrø M, Lesmes D, Mehta K, Mooney M, Pacheco C, Prejean S, Sato H, Schuster J, Wapenaar K, Wilt M (2007b) Advanced non-invasive geophysical monitoring techniques. Ann Rev Earth Planet Sci 35:653–683CrossRefGoogle Scholar
  74. Snieder R, van Wijk K, Haney M, and Calvert R (2008) The cancellation of spurious arrivals in Green’s function extraction and the generalized optical theorem. Phys Rev E 78:036606CrossRefGoogle Scholar
  75. Stehly L, Campillo M, Shapiro NM (2006) A study of seismic noise from long-range correlation properties. J Geophys Res 111. doi: 10.1029/2005JB004237
  76. Stehly L, Campillo M, Froment B, Weaver RL (2008) Reconstructing Green’s function by correlation of the coda of the correlation (C3) of ambient seismic noise. J Geophys Res 113:B11306CrossRefGoogle Scholar
  77. Tatarskii VP (1987) Example of the description of dissipative processes in terms of reversible dynamic equations and some comments on the fluctuation dissipation theorem. Sov Phys Usp 30:134–152CrossRefGoogle Scholar
  78. Thompson D, Snieder R (2006) Seismic anisotropy of a building. The Leading Edge 25:1093CrossRefGoogle Scholar
  79. Trampert J, Cara M, Frogneux M (1993) \(SH\) propagator matrix and \({Q}_s\) estimates from borehole- and surface-recorded earthquake data. Geophys J Int 112:290–299CrossRefGoogle Scholar
  80. Um ES, Alumbaugh DL (2007) On the physics of the marine controlled-source electromagnetic method. Geophysics 72:WA13–WA26CrossRefGoogle Scholar
  81. Vasconcelos I, Snieder R (2008a) Interferometry by deconvolution, Part 1—theory for acoustic waves and numerical examples. Geophysics 73:S115–S128CrossRefGoogle Scholar
  82. Vasconcelos I, Snieder R (2008b) Interferometry by deconvolution: Part 2—theory for elastic waves and application to drill-bit seismic imaging. Geophysics 73:S129–S141CrossRefGoogle Scholar
  83. Vasconcelos I, Snieder R, Hornby B (2008a) Imaging internal multiples from subsalt VSP data—examples of target-oriented interferometry. Geophysics 73:S157–S168CrossRefGoogle Scholar
  84. Vasconcelos I, Snieder R, Sava P, Taylor T, Malin P, Chavarria A (2008b) Drill bit noise illuminates the san andreas fault. EOS Trans Am Geophys Union 89(38):349CrossRefGoogle Scholar
  85. Verschuur DJ, Berkhout AJ, Wapenaar CPA (1992) Adaptive surface-related multiple elimination. Geophysics 57:1166–1177CrossRefGoogle Scholar
  86. Wapenaar K (2004) Retrieving the elastodynamic Green’s function of an arbitrary inhomogeneous medium by cross correlation. Phys Rev Lett 93:254301CrossRefGoogle Scholar
  87. Wapenaar K, Fokkema J (2006) Green’s function representations for seismic interferometry. Geophysics 71(4):SI33–SI46CrossRefGoogle Scholar
  88. Wapenaar K, Fokkema J, Dillen M, Scherpenhuijsen P (2000) One-way acoustic reciprocity and its applications in multiple elimination and time-lapse seismics. In: 70th annual SEG meeting, Calgray, expanded abstracts, pp 2377–2380Google Scholar
  89. Wapenaar K, Fokkema J, Snieder R (2005) Retrieving the Green’s function by cross-correlation: a comparison of approaches. J Acoust Soc Am 118:2783–2786CrossRefGoogle Scholar
  90. Wapenaar K, Slob E, Snieder R (2006) Unified Green’s function retrieval by cross-correlation. Phys Rev Lett 97:234301CrossRefGoogle Scholar
  91. Wapenaar K, Slob E, Snieder R (2008) Seismic and electromagnetic controlled-source interferometry in dissipative media. Geophys Prosp 56:419–434CrossRefGoogle Scholar
  92. Weaver RL (2008) Ward identities and the retrieval of Green’s functions in the correlations of a diffuse field. Wave Motion 45:596–604CrossRefGoogle Scholar
  93. Weaver RL, Lobkis OI (2001) Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies. Phys Rev Lett 87:134301CrossRefGoogle Scholar
  94. Weaver R, Lobkis O (2003) On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons. Ultrasonics 40:435–439CrossRefGoogle Scholar
  95. Weaver RL, Lobkis OI (2005) Fluctuations in diffuse field-field correlations and the emergence of the Green’s function in open systems. J Acoust Soc Am 117:3432–3439CrossRefGoogle Scholar
  96. Webb SC (1998) Broadband seismology and noise under the ocean. Rev Geophys 36:105–142CrossRefGoogle Scholar
  97. Weber J (1956) Fluctuation–dissipation theorem. Phys Rev 101:1620–1626CrossRefGoogle Scholar
  98. Webster GM (ed.) (1978) Deconvolution, vol 1 of geophysics reprint series. SEG, TulsaGoogle Scholar
  99. Weglein AB, Gasparotto FA, Carvalho PM, Stolt RH (1998) An inverse scattering series method for attenuating multiples in seismic reflection data. Geophysics 62:1975–1989CrossRefGoogle Scholar
  100. Wegler U, Sens-Schönfelder C (2007) Fault zone monitoring with passive image interferometry. Geophys J Int 168:1029–1033CrossRefGoogle Scholar
  101. van Borselen RG, Fokkema JT, van den Berg PM (1996) Removal of surface-related wave phenomena—the marine case. Geophysics 61:202–210CrossRefGoogle Scholar
  102. van Wijk K (2006) On estimating the impulse response between receivers in a controlled ultrasonic experiment. Geophysics 71:SI79–SI84CrossRefGoogle Scholar
  103. Yang Y, Ritzwoller MH (2008) Teleseismic surface wave tomography in the western US using the transportable array component of USArray. Geophys Res Lett 5:L04308CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Roel Snieder
    • 1
  • Masatoshi Miyazawa
    • 1
    • 2
  • Evert Slob
    • 3
  • Ivan Vasconcelos
    • 1
    • 4
  • Kees Wapenaar
    • 3
  1. 1.Center for Wave Phenomena and Department of GeophysicsColorado School of MinesGoldenUSA
  2. 2.Earthquake Research InstituteUniversity of TokyoTokyoJapan
  3. 3.Department of GeotechnologyDelft University of TechnologyDelftThe Netherlands
  4. 4.ION Geophysical, GXT Imaging SolutionsEghamUK

Personalised recommendations