1. 2004 SEPM.P. Brown Least-squares Joint Imaging of Multiples and Primaries Morgan Brown 2004 SEP Meeting 19 May 2004

2. 2004 SEPM.P. Brown We all know…multiples are bad If ignored, inhibit: Geologic interpretation Velocity analysis Prestack amplitudes Poststack inversion Suppression techniques: Shallow water: predictive decon 2-D Deep water: Delft SRME 3-D: Radon

3. 2004 SEPM.P. Brown …but, are multiples all bad? Multiples = “noise”? Reach prospect zone Strong and coherent Highly correlated with signal Imaging multiples: main questions Are they usable? What do they add? How can we use them?

4. 2004 SEPM.P. Brown Primary image TS BS TSM Midpoint (m) signal crosstalk

5. 2004 SEPM.P. Brown WB pegleg image TS BS TSM Midpoint (m) signal crosstalk

6. 2004 SEPM.P. Brown Prestack image gathers Illumination _gaps Missing _traces Reflection angle Time PrimaryWB pegleg 1

7. 2004 SEPM.P. Brown Prestack image gathers Time PrimaryWB pegleg 1 Time consistent signal Reflection angle

8. 2004 SEPM.P. Brown Prestack image gathers Time PrimaryWB pegleg 1 Time Reflection angle consistent crosstalk*

9. 2004 SEPM.P. Brown Multiples = useful signal Are they usable? Yes What do they add? Structural/angular redundancy Finer angular sampling Near offsets/illumination gaps How can we use them? Prestack image domain averaging Greater signal fidelity Nullspace constraints Crosstalk noise

10. 2004 SEPM.P. Brown Joint Imaging: tantalizing prospect? New view: primaries + multiples = ……………two datasets, one data record Separation  prerequisite to integration “LSJIMP” – Least-Squares Joint Imaging - --------.of Multiples and Primaries Simultaneous separation/integration Integration/joint imaging  better ……………………………………separation

11. 2004 SEPM.P. Brown Talk Outline LSJIMP theory My LSJIMP implementation 2-D field data results Extension to 3-D 3-D field data results

12. 2004 SEPM.P. Brown Talk Outline LSJIMP theory My LSJIMP implementation 2-D field data results Extension to 3-D 3-D field data results

13. 2004 SEPM.P. Brown LSJIMP Forward Model offset midpoint time earth midpoint depth primaries data = primaries + pegleg multiples

14. 2004 SEPM.P. Brown LSJIMP Forward Model offset midpoint time earth midpoint depth Source and receiver multiples primaries 1 st order leg 1 data = primaries + pegleg multiples

15. 2004 SEPM.P. Brown leg 2 LSJIMP Forward Model offset midpoint time earth midpoint depth Source and receiver multiples primaries 1 st order leg 1 data = primaries + pegleg multiples

16. 2004 SEPM.P. Brown LSJIMP Forward Model data = primaries + pegleg multiples Higher order multiples offset midpoint time earth midpoint depth primaries 1 st order leg 1 leg 2 2 nd order leg 1

17. 2004 SEPM.P. Brown LSJIMP Forward Model data = primaries + pegleg multiples Higher order multiples offset midpoint time earth midpoint depth primaries 1 st order leg 1 leg 2 2 nd order leg 1 leg 2

18. 2004 SEPM.P. Brown leg 3 LSJIMP Forward Model data = primaries + pegleg multiples Higher order multiples offset midpoint time earth midpoint depth primaries 1 st order leg 1 leg 2 2 nd order leg 1 leg 2

19. 2004 SEPM.P. Brown LSJIMP Forward Model data = primaries + pegleg multiples Other multiple generators offset midpoint time earth midpoint depth primaries 1 st order2 nd order leg 1 leg 2 leg 3 leg 1 leg 2

20. 2004 SEPM.P. Brown LSJIMP Forward Model data = primaries + pegleg multiples Other multiple generators modeled data offset midpoint time earth midpoint depth sum offset midpoint time primaries 1 st order2 nd order leg 1 leg 2 leg 3 leg 1 leg 2

21. 2004 SEPM.P. Brown LSJIMP Forward Model data = primaries + pegleg multiples modeled data primariespeglegs from…

22. 2004 SEPM.P. Brown LSJIMP Forward Model data = primaries + pegleg multiples …recorded orders of multiple …split peglegs …multiple generators

23. 2004 SEPM.P. Brown LSJIMP Forward Model Linear least-squares inversion modeled data offset midpoint time Cast as a linear function of model parameters “fit” recorded data offset midpoint time

24. 2004 SEPM.P. Brown LSJIMP Forward Model Key questions: How to achieve separation? ………………….How to achieve integration? My answer: Map to prestack image domain How to define model space?

25. 2004 SEPM.P. Brown LSJIMP Forward Model How to define model space?

26. 2004 SEPM.P. Brown LSJIMP Forward Model prestack primary image prestack pegleg image How to define model space? signal events directly comparable

27. 2004 SEPM.P. Brown LSJIMP Forward Model prestack primary modeling prestack pegleg modeling How to define model space? “true relative amplitude”

28. 2004 SEPM.P. Brown LSJIMP Forward Model How to define model space? NMO Kirchhoff Wave equation “true relative amplitude”

29. 2004 SEPM.P. Brown LSJIMP Inversion Minimize least-squares modeling error

30. 2004 SEPM.P. Brown The crosstalk problem x/  midpoint  /z signal LSJIMP Inversion

31. 2004 SEPM.P. Brown x/  midpoint  /z crosstalk LSJIMP Inversion The crosstalk problem

32. 2004 SEPM.P. Brown LSJIMP Inversion x/  midpoint  /z residual multiple imaged multiple The crosstalk problem Infinitely many ways to model first-order multiple ?

33. 2004 SEPM.P. Brown LSJIMP Inversion x/  midpoint  /z residual multiple imaged multiple ? ….A big problem… 1.Underdetermined problem 2.Crosstalk indistinguishable from signal 3.Nonuniqueness The crosstalk problem Infinitely many ways to model first-order multiple

34. 2004 SEPM.P. Brown Overcoming Crosstalk penalize crosstalk maximize separation enhance signal combine multiples/primaries Model regularization

35. 2004 SEPM.P. Brown ….Image attributes 1.signal flat 2.signal comparable 3.crosstalk curved 4.crosstalk inconsistent* 5.crosstalk predictable x/  midpoint  /z Overcoming Crosstalk Model regularization

36. 2004 SEPM.P. Brown Multiplicity within images Regularization 1: x/  differencing ….Image attributes 1.signal flat 2.signal comparable 3.crosstalk curved 4.crosstalk inconsistent* 5.crosstalk predictable x/  midpoint  /z -1 1

37. 2004 SEPM.P. Brown ….Similar approaches Regularized LS migration Illumination gaps/missing data Multiplicity within images Regularization 1: x/  differencing x/  midpoint  /z -1 1

38. 2004 SEPM.P. Brown ….Image attributes 1.signal flat 2.signal comparable 3.crosstalk curved 4.crosstalk inconsistent* 5.crosstalk predictable x/  midpoint  /z 1 Regularization 2: image differencing

39. 2004 SEPM.P. Brown Multiplicity between images Separation by integration Regularization 2: image differencing ….Image attributes 1.signal flat 2.signal comparable 3.crosstalk curved 4.crosstalk inconsistent* 5.crosstalk predictable x/  midpoint  /z 1

40. 2004 SEPM.P. Brown ….Image attributes 1.signal flat 2.signal comparable 3.crosstalk curved 4.crosstalk inconsistent* 5.crosstalk predictable x/  midpoint  /z Regularization 3: crosstalk weights

41. 2004 SEPM.P. Brown x/  midpoint  /z If we had the true signal... offset midpoint time …we could model any multiple… x/  midpoint  /z …and simulate crosstalk on any other image Regularization 3: crosstalk weights

42. 2004 SEPM.P. Brown x/  midpoint  /z But we don’t have the true signal*... Mute below WBM 1 offset midpoint time …though we can still model some multiples… x/  midpoint  /z …and simulate crosstalk on any other image Regularization 3: crosstalk weights

43. 2004 SEPM.P. Brown x/  midpoint  /z …and simulate crosstalk on any other image x/  midpoint  /z create crosstalk weight absolute value 1.0 0.0 Regularization 3: crosstalk weights

44. 2004 SEPM.P. Brown Talk Outline LSJIMP theory My LSJIMP implementation 2-D field data results Extension to 3-D 3-D field data results

45. 2004 SEPM.P. Brown How to image split peglegs?

46. 2004 SEPM.P. Brown How to image split peglegs? flat in offset/angle “HEMNO” – Heterogeneous Earth Multiple NMO Operator “1.5-D” method (vertical stretch) no diffractions, reflector movement moderate structure (picking, event tracking) zero-offset apex

47. 2004 SEPM.P. Brown How to image split peglegs? flat in offset/angle “HEMNO” – Heterogeneous Earth Multiple NMO Operator Fast (iterative inversion) Sparse 3-D geometries Amplitude-preserving

48. 2004 SEPM.P. Brown How to image split peglegs? comparable in angle to primary Snell Resampling Compress offset axis V(z) AVO consistent

49. 2004 SEPM.P. Brown How to image split peglegs? corrected for multiple reflection Differential geometric spreading correction Space-variant reflection coefficient Minimize: (r*primary – multiple) No AVO

50. 2004 SEPM.P. Brown How to image split peglegs? Imaged multiples now comparable to TS primary

51. 2004 SEPM.P. Brown LSJIMP Forward Model NMO for primaries

52. 2004 SEPM.P. Brown LSJIMP Forward Model differential geometric spreading Snell Resampling HEMNOreflection coefficient

53. 2004 SEPM.P. Brown Talk Outline LSJIMP theory My LSJIMP implementation 2-D field data results Extension to 3-D 3-D field data results

54. 2004 SEPM.P. Brown Mississippi Canyon dataset 750 CMPs max offset: 3000m 9 second recording Deep water: 1.8-2.0 sec TWT sedimentary basin strong shallow reflectors tabular salt feature reflection coefficient ~ 0.2-0.3

55. 2004 SEPM.P. Brown Computational highlights Model space = one CMP location Vertical stretch Coarse-grained parallelization (MPI) In-core optimization 20 CG iterations  3 hours 4 multiple generators Only first-order multiples 16 x 1.3 GHz P3 ~PSDM

56. 2004 SEPM.P. Brown Raw data Stack 1 2 3 4

57. 2004 SEPM.P. Brown Raw data Stack ( 3.5-5.5 sec )

58. 2004 SEPM.P. Brown LSJIMP Primaries ( m 0 ) stack

59. 2004 SEPM.P. Brown LSJIMP Primaries ( m 0 ) stack What’s left? primaries, diffracted/steep-dip multiples

60. 2004 SEPM.P. Brown Difference Stack

61. 2004 SEPM.P. Brown LSJIMP image gather results sediments subsalt

62. 2004 SEPM.P. Brown LSJIMP sediment image gather d d0d0 d mod d- d mod modeled peglegs from 4 reflectors NMO applied for viewing

63. 2004 SEPM.P. Brown LSJIMP subsalt image gather d d0d0 d mod d- d mod modeled peglegs from 4 reflectors

64. 2004 SEPM.P. Brown Least-squares Radon Demultiple data LSRD*LSJIMP * thanks to A. Guitton primariesmultiples primariesmultiples

65. 2004 SEPM.P. Brown Talk Outline LSJIMP theory My LSJIMP implementation 2-D field data results Extension to 3-D 3-D field data results

66. 2004 SEPM.P. Brown CGG Green Canyon IV 3-D data s s s s

67. 2004 SEPM.P. Brown Wide-tow marine acquisition midpoint locations “flip” s “flop” s

68. 2004 SEPM.P. Brown Wide-tow marine acquisition Regular crossline sampling Cheap Crossline CMP fold =1 Sparsity hurts SRME

69. 2004 SEPM.P. Brown Wide-tow marine acquisition Remove crossline -offset axis AMO/Common -- -azimuth No feathering inline offset xline offset CMP gather (model space)

70. 2004 SEPM.P. Brown Wide-tow marine acquisition HEMNO: vertical -- -.------..stretch Crossline structure: -measured dip 3-D cost/2-D cost --= # xline CMPs inline offset xline offset

71. 2004 SEPM.P. Brown Talk Outline LSJIMP theory My LSJIMP implementation 2-D field data results Extension to 3-D 3-D field data results

72. 2004 SEPM.P. Brown CGG Green Canyon IV 3-D data raw data stack

73. 2004 SEPM.P. Brown GC 3-D stacked results raw stackprimariesdifference

74. 2004 SEPM.P. Brown raw data est. prim d mod est. mult. WBR1 resid. GC 3-D CMP results (x-line 4)

75. 2004 SEPM.P. Brown Least-squares Radon Demultiple data LSRD LSJIMP primariesmultiples primariesmultiples

76. 2004 SEPM.P. Brown LSJIMP Improves AVO Estimation

77. 2004 SEPM.P. Brown LSJIMP Improves AVO Estimation

78. 2004 SEPM.P. Brown Summary and Conclusions LSJIMP Multiples useful, but… Integration + Separation Image space regularized LS inversion My LSJIMP Implementation: HEMNO: vertical stretch Fast Robust “1.5-D”

79. 2004 SEPM.P. Brown Summary and Conclusions (2) Mississippi Canyon 2-D Salt Pegleg splitting Competitive Green Canyon 3-D: Sparse crossline LS Radon demultiple AVO

80. 2004 SEPM.P. Brown Future Imaging Operator: Angle-domain W.E. PSDM Autoconvolutional? Information content? PSP Conversions? Internal multiples? Multiple datasets? multicomponent repeat surveys Velocity?

81. 2004 SEPM.P. Brown Acknowledgements WesternGeco, CGG Colleagues: Bob Clapp Antoine Guitton

82. 2004 SEPM.P. Brown Synthetic image gathers Illumination _gaps Missing _traces Reflection angle Time Primary WB pegleg 1 WB pegleg 2

83. 2004 SEPM.P. Brown Synthetic image gathers Time Primary WB pegleg 1 WB pegleg 2 consistent signal Reflection angle

84. 2004 SEPM.P. Brown Synthetic image gathers Time Primary WB pegleg 1 WB pegleg 2 consistent crosstalk* Reflection angle

85. 2004 SEPM.P. Brown My LSJIMP Implementation Kinematics: “HEMNO” Amplitude normalization: Snell Resampling Differential geometric spreading Space-variant reflection coefficient LSJIMP forward model

86. 2004 SEPM.P. Brown My LSJIMP Implementation Kinematics: “HEMNO” Amplitude normalization: Snell Resampling Differential geometric spreading Space-variant reflection coefficient LSJIMP forward model

87. 2004 SEPM.P. Brown Kinematic pegleg imaging Requirements: Fast (iterative inversion) 3-D Prestack on sparse geometries Amplitude-preserving Modified NMO operator 2-D: Levin & Shah (1977) 3-D: Ross et al. (1999) Limitations: Constant velocity Locally-planar reflectors

88. 2004 SEPM.P. Brown HEMNO for Kinematics HEMNO = Hetergeneous Earth ---- ------…..Multiple NMO Operator Plane reflector/small dip  Levin & Shah Strengths: Non-planar reflectors Intuitive interpretation 3-D marine geometries Limitations: Small dip/incidence angle Event tracking

89. 2004 SEPM.P. Brown HEMNO Derivation 1-D earth raypath  midpoint x offset y0y0 event midpoint

90. 2004 SEPM.P. Brown HEMNO Derivation 1-D earth raypath  y 0  y0y0 “pseudo-primary” yy

91. 2004 SEPM.P. Brown HEMNO Derivation 1-D earth raypath  y 0  y0y0 “pseudo-primary” “1-D” NMO equation for multiple 1

92. 2004 SEPM.P. Brown HEMNO Derivation Problem: Approximate true raypath 2-D earth raypath

93. 2004 SEPM.P. Brown HEMNO Derivation 1-D reflection points known Problem: Approximate true raypath 2-D earth raypath ymym ypyp

94. 2004 SEPM.P. Brown HEMNO Derivation measured  Problem: Approximate true raypath 2-D earth raypath ypyp ymym ignore lateral movement

95. 2004 SEPM.P. Brown HEMNO Derivation pseudo-primary 2-D earth raypath ypyp ymym ignore lateral movement

96. 2004 SEPM.P. Brown HEMNO Derivation pseudo-primary 2-D earth raypath ypyp ymym HEMNO equation

97. 2004 SEPM.P. Brown HEMNO Derivation HEMNO equation “1-D” NMO equation

98. 2004 SEPM.P. Brown HEMNO Derivation “1.5-D” method (vertical stretch) no diffractions no reflector movement zero-offset apex  ( y m ),  ( y p )? Sparse 3-D geometries

99. 2004 SEPM.P. Brown My LSJIMP Implementation Kinematics: “HEMNO” Amplitude normalization: Snell Resampling Differential geometric spreading Space-variant reflection coefficient LSJIMP forward model

100. 2004 SEPM.P. Brown Snell Resampling y x different reflection angles Inconsistent AVO behavior

101. 2004 SEPM.P. Brown Snell Resampling y x Compare these two events instead xpxp what is x p ?

102. 2004 SEPM.P. Brown Snell Resampling y x Stepout ( dt/dx ) same at x, x p [ V(z) ] xpxp Resample multiple from x to x p

103. 2004 SEPM.P. Brown Time Primary WB pegleg 1 WB pegleg 2 offset Snell Resampling

104. 2004 SEPM.P. Brown Differential Geometric Spreading Lu et al. (1999) give g prim, g mult Forward modeling: scale model by ----- g prim /g mult Function of time, offset

105. 2004 SEPM.P. Brown Reflection coefficient estimation midpoint ( y ) time ( t ) p(t,x,y) m(t,x,y) offset ( x ) After Snell Resampling, 1/differential GS

106. 2004 SEPM.P. Brown Reflection coefficient estimation p(t,x,y) m(t,x,y) r(y)r(y) space-variant RC spatial smoothness

107. 2004 SEPM.P. Brown Reflection coefficient estimation Assumptions: no AVO “smooth” target r ( y )

108. 2004 SEPM.P. Brown LSJIMP Multiple Model prior signal estimate, e.g.,--- modeled multiples

109. 2004 SEPM.P. Brown LSJIMP versus SRME (mid-offset) Midpoint Data LSJIMPSRME

110. 2004 SEPM.P. Brown LSJIMP versus SRME (CMP) Offset (m) Data LSJIMP SRME

111. 2004 SEPM.P. Brown CGG Green Canyon IV 3-D data

112. 2004 SEPM.P. Brown Wide-tow marine acquisition s s

113. 2004 SEPM.P. Brown CGG Green Canyon IV 3-D data s s s s

114. 2004 SEPM.P. Brown LSJIMP Nonlinear Iterations d d0d0 d mod d- d mod correlated residual energy change reflection coefficient

115. 2004 SEPM.P. Brown LSJIMP Nonlinear Iterations d d i,k,m d mod d- d mod subtract from weighting function

116. 2004 SEPM.P. Brown Data Residual

117. 2004 SEPM.P. Brown Least-squares Radon Demultiple raw stackprimariesdifference

118. 2004 SEPM.P. Brown LSJIMP Estimated Primaries raw stackprimariesdifference