1. Seismic interferometry: Who needs a seismic source? Roel Snieder Center for Wave Phenomena Colorado School of Mines email rsnieder@mines.edursnieder@mines.edu http://www.mines.edu/~rsnieder download publications from: http://www.mines.edu/~rsnieder/Publications.html

2. Fluctuation-dissipation theorem F (Einstein, 1905) (Kubo, Rep. Prog. Phys., 29, 255-284, 1966)

3. Very Long Baseline Interferometry http://www.lupus.gsfc.nasa.gov/brochure/bintro.html

4. Distance between USA and Germany http://www.lupus.gsfc.nasa.gov/brochure/btoday2.html

5. Pseudo-random source Piezo-electric vibrator from CGG

6. 45°C 50°C Coda wave interferometry (Snieder et al., Science, 295, 2253-2255, 2002)

7. 1D example

8. Cross-correlation sum of causal and acausal response uncorrelated left- and rightgoing waves

9. Right-going wave only

11. DC-component must vanish

12. Need to extend this to include: - heterogeneous media - more space dimensions

13. Derivation based on normal-modes (Lobkis and Weaver, JASA, 110, 3011-3017, 2001)

14. Displacement response Heaviside function

15. Velocity response

16. Uncorrelated excitation

17. Correlation

18. Correlation as sum over modes

19. For uncorrelated modes

21. Correlation Green’s function

22. Correlation Green’s function

23. Correlation Green’s function

24. Correlation and Green’s function - sum of causal and acausal Green’s function - holds for arbitrary heterogeneity

25. Dealing with with acausal Green’s function - truncate correlation for t<0 - average correlation for t 0

26. Displacement instead of velocity Conclusion: time derivative may appear

27. (Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)

29. Representation theorem

30. Acoustic waves Green’s function:

31. Time reversal = complex conjugation Time-reversed solution

32. Time-reversal When is a solution. then is a solution as well N.B. this does not hold in the presence of attenuation

33. Representation theorem replace:

34. Left hand side reciprocity

35. Right hand side

36. For spherical surface far away Radiation condition:

37. Virtual-sources (Wapenaar, Fokkema, and Snieder, JASA, 118, 2783-2786 2005 heuristic derivation: Derode et al., JASA, 113, 2973-2976, 2003)

38. Computing synthetic seismograms (Van Manen et al., Phys. Rev. Lett., 94, 164301,2005)

41. Field example of virtual sources (Bakulin and Calvert, SEG expanded abstracts, 2477-2480, 2004) reservoir complicated overburden

42. Peace River 4D VSP Component used, along-the-well (45 0 )

43. Image from virtual sources top bottom

44. Virtual sourceSurface

45. Virtual-sources (Wapenaar, Fokkema, and Snieder, JASA, 118, 2783-2786 2005 heuristic derivation: Derode et al., JASA, 113, 2973-2976, 2003)

46. Excitation by uncorrelated sources on surface Uncorrelated sources can be: - sequential shots - uncorrelated noise

47. Response to uncorrelated noise

48. Green’s function from uncorrelated sources (For elastic waves: Wapenaar, Phys. Rev. Lett, 93, 254301, 2004)

49. Raindrop model Sources can be: - real sources - secondary sources (scatterers)

50. Response to random sources

51. Correlation:

52. Double sum over sources diagonal termscross-terms

53. Cross-terms - vanish on average - in a single realization: (Snieder, Phys. Rev. E, 69, 046610, 2004)

54. For dense scatterers n = scatterer density

55. Correlation as volume integral

56. Stationary phase contribution x y z

57. Stationary phase regions “anti-Fresnel zones”

58. Stationary phase integration (Snieder, Phys. Rev. E, 69, 046610, 2004, for reflected waves see: Snieder, Wapenaar, and Larner, Geophysics, in press, 2005)

61. Yet another type of illumination (Weaver and Lobkis, JASA, 116, 2731-2734)

62. Four types of averaging

63. Ultrasound experiment source receivers 54 mm 135 mm (Malcolm et al., Phys. Rev. E, 70, 015601, 2004)

67. Surface waves (Campillo and Paul, Science, 299, 547-549, 2003)

68. correlation Green’s tensor Z/Z Z/R Z/T

69. correlation Green’s tensor Z/Z Z/T R/Z R/R R/T T/Z T/R T/T Z/R

70. Surface wave Green’s function (Snieder, Phys. Rev. E, 69, 046610, 2004)

71. Surface wave dispersion from noise (Shapiro and Campillo, Geophys. Res. Lett., 31, L07614, 2004)

72. Seismic interferometry in Millikan Library

73. Deconvolution with top floor

74. Deconvolution with bottom floor

75. traveling waves normal modes

79. Deconvolution with bottom floor

80. + +

81. Sheiman-interpretation + - + -

82. Fundamental mode: - +

95. Borehole data from Treasure Island

96. T – Deconvolved (4.5 to 15 sec) time (sec) depth (m)

97. T – Deconvolved (4.5 to 15 sec) time (sec) depth (m) β β β β β =100 m/s =150 m/s =200 m/s =250 m/s =550 m/s

98. Z – Deconvolved (1 to 15 sec) time (sec) depth (m)

99. Z – Deconvolved (1 to 15 sec) time (sec) depth (m) α α α α α =1500 m/s =1250 m/s =1600 m/s =1350 m/s =2200 m/s

100. R – Deconvolved (4.5 to 15 sec) time (sec) depth (m)

101. time (sec) depth (m) β β β β β =100 m/s =150 m/s =200 m/s =250 m/s =550 m/s R – Deconvolved (4.5 to 15 sec)

102. Borehole data from Treasure Island

103. R – Deconvolved (1 to 4.5 sec) time (sec) depth (m)

104. R – Deconvolved (1 to 4.5 sec) time (sec) depth (m) β β β β β =100 m/s =150 m/s =200 m/s =250 m/s =550 m/s

105. Receiver Function time (sec) depth (m)

106. Receiver Function time (sec) depth (m)

107. Advantage (1), virtual sources at new locations reservoir salt

108. Advantage (1), virtual sources at new locations

109. Advantage (2), virtual sources at “all” times

110. Seismic interferometry in Millikan Library (Snieder and Safak, Bull. Seismol. Soc. Am., in press, 2005)

111. Deconvolution with top floor

112. Advantage (3), get better illumination

114. Use surface bounce

116. “Schuster trick”

117. Advantage (4), use other type of data (Shapiro et al., Science, 307, 1615-1618, 2005) earthquake correlation (1 year) correlation (1 month)

118. 10 10.1 0.01 Frequency (Hz)

119. 5-10 sec. 10 10.1 0.01 Frequency (Hz)