1. Migration and Attenuation of Surface-Related and Interbed Multiple Reflections
Zhiyong Jiang
University of Utah
April 21, 2006

2. Outline Overview Surface Multiple Migration
Interbed Multiple Migration
Multiple Attenuation in
Multiple Imaging
Conclusions
Let’s first review the POIC approach.

3. Primary g s x
Surface Multiple s g x g s x
Interbed Multiple g s
High-order Multiple

4. Technical Contributions
For the first time, I examine the imaging and computational properties of three different surface multiple imaging methods, and apply them to both synthetic and field data
I develop two novel methods for imaging interbed multiples, and apply them to field and synthetic data
I attenuate high-order multiples to solve a major problem in multiple imaging: the interference from other multiples. This strategy makes multiple imaging a more practical tool

5. Outline Overview Surface Multiple Migration
Interbed Multiple Migration
Multiple Attenuation in
Multiple Imaging
Conclusions
Let’s first review the POIC approach.

6. Outline Overview Surface Multiple Migration Motivation Methodology
Numerical Results
Summary
Let’s first review the POIC approach.

7. Why Migrate Surface Multiples?
Better Vert. Res.
Advantages of migrating multiples.
Better Fold
Wider Coverage

8. 3D VSP Survey
Shot radius Z

9. Outline Overview Surface Multiple Migration Motivation Methodology
Numerical Results
Summary
Let’s first review the POIC approach.

10. exp[iω (τsx +τx g +τg g)]
Modeling Equation
d(s,g)mult. = m(x0 , ω) W(ω)
exp[iω (τsx +τx g +τg g)] . ~ x0 g0 s B0 g

11. Method 1: Model-based Multiple Imaging
m(x, ω) = ∫∫ d(s, g)mult. .
exp[-iω (τsx +τxg’ +τg’g)] dsdg
τxg’ +τg’g = min (τxg’ +τg’g) g’ B0 B0 s g’
g’0
τg’g
g’ : diffraction point
g0’: specular point X : trial image point
τsx
τxg’ x g

12. τxg’ +τg’g = min (τxg’ +τg’g)
Method 2: Mig. with Semi-natural Green’s functions
m(x, ω) = ∫∫ d(s, g)mult. . ~
exp[-iω (τsx +τxg’ +τg’g)] dsdg ~ ~
τxg’ +τg’g = min (τxg’ +τg’g) g’ B0 B0 s g’
g’0 ~
τg’g
g’ : diffraction point
g0’: specular point X : trial image point
τsx
τxg’ x g

13. exp[-iω (τsx +τxg’ +τg’g)] dsdgdg’
Method 3: Interferometric Imaging
m(x, ω) = ∫∫∫ d(s, g)mult. . ~
exp[-iω (τsx +τxg’ +τg’g)] dsdgdg’ g’ s B0
g’ : diffraction point
X : trial image point
τsx x g

14. Imaging Properties of Migration Methods
Sensitivity to velocity errors
Receiver Statics in VSP case eliminated?
Receiver geometry needs to be known in VSP case?
Coverage in VSP case
Applicablbe to IVSPWD?
Model-based multiple Migration
High No
Yes
Wide
Semi-natural Green’s functions
Low
Interferomet-ric Imaging
Primary Migration
Narrow

15. Outline Overview Surface Multiple Migration Motivation Methodology
Numerical Results
Summary
Let’s first review the POIC approach.

16. Numerical Results 2-D Dipping Layer Model 3-D Real Data
3-D Synthetic Data

17. Shots: 92; Receivers: 91 (50m -950 m)
Velocity Model
Well
X (m)
925
V (m/s)
4000
Depth (m)
1900
1300
Shots: 92; Receivers: 91 (50m -950 m)

18. CSG 51
Ghost Component
Time (s) A S
Well G X 3 50
950m 50
950m

19. CSG 51
Primary Component
Time (s) A S
Well G X 3 50
950m 50
950m

20. 8 Receivers Primary 1st-order multiple 1300 X (m) 925 X (m) 925
Depth (m)
Less receivers and the image is still good. A cheaper VSP.
1300
X (m)
925
X (m)
925

21. Numerical Results 2-D Dipping Layer Model 3-D Real Data
3-D Synthetic Data

22. Multiple can image above the receivers.

23. Numerical Results 2-D Dipping Layer Model 3-D Real Data
3-D Synthetic Data

24. Sources/Wells Locations
Y (m)
2000
Well
X (m)
2km*2km*2km for x by y by z.
1089 shots
111 receivers
2000

25. CSG10 CSG540 X 3.5 1 111 1 111 Time (s) Receiver Number
Time (s)
Different shots received in the same well. X
3.5 1
Receiver Number
111 1
Receiver Number
111

26. X=1000m Primary Velocity Model 100 1100 100 1100 Y (m) 2000 Depth (m)
Y (m)
2000

27. X=1000m 1st order ghost Velocity Model 100 1100 100 1100 Y (m) 2000
Depth (m)
1100
Velocity Model
100
Better image of the salt boundary with multiple.
Depth (m)
1100
Y (m)
2000

28. Y=1000m Primary Velocity Model 100 1100 100 1100 X (m) 2000 Depth (m)
Another slice.
Depth (m)
1100
X (m)
2000

29. Y=1000m 1st order ghost Velocity Model 100 1100 100 1100 X (m) 2000
Depth (m)
1100
Velocity Model
100
Depth (m)
1100
X (m)
2000

30. Outline Overview Surface Multiple Migration Motivation Methodology
Numerical Results
Summary
Let’s first review the POIC approach.

31. Summary Advantages Wider subsurface coverage can be achieved
by migrating multiples
Multiples illuminate areas invisible to primaries

32. Summary Limitation Multiple is weak
Interferences from primary and other events,
such as high-order multiples

33. Outline Overview Surface Multiple Migration
Interbed Multiple Migration
Multiple Attenuation in
Multiple Imaging
Conclusions
Let’s first review the POIC approach.

34. Outline Overview Interbed Multiple Migration Motivation Methods
Numerical Tests
Summary
Let’s first review the POIC approach.

35. What is below the salt? ?

36. Challenge with VSP Surface Multiples: Long raypath, strong attenuation, triple passage through salt

37. Challenge with CDP primary reflections: strong attenuation, double passage through salt

38. Can we try interbed multiples
Can we try interbed multiples? Advantages: short raypth, less attenuation, single passage through salt s g

39. Outline Overview Interbed Multiple Migration Motivation Methods
Numerical Tests
Summary
Let’s first review the POIC approach.

40. d(s,g)inter. = m(x0 , ω) W(ω)
Modeling Equation
d(s,g)inter. = m(x0 , ω) W(ω)
exp[iω (τsx +τx g +τg g)] . ~ B0 s x0 g0 B1 g

41. Method 1: Fermat’s principle
m(x, ω) = ∫∫ d(s, g)inter. .
exp[-iω (τsx +τxg’ +τg’g)] dsdg
τxg’ +τg’g = min (τxg’ +τg’g) g’ B1 B0 s g’
g’0 B1
τg’g
τsx
τxg’ x g

42. exp[-iω (τsx +τxg’ +τg’g)] dsdgdg’
Method 2: Summation of all the diffraction energy
m(x, ω) = ∫∫∫ d(s, g)inter. .
exp[-iω (τsx +τxg’ +τg’g)] dsdgdg’ B0 s g’ B1
τsx x g

43. Outline Overview Interbed Multiple Migration Motivation Methods
Numerical Tests
Summary
Let’s first review the POIC approach.

44. Numerical Tests SEG/EAGE Model Large Salt Model Field Data Test
Let’s first review the POIC approach.

45. Shots: 301; Receivers: 61 (1000m - 1600m)
Velocity Model
X (m)
3000
Depth (m)
2000
Shots: 301; Receivers: 61 (1000m m)

46. Upper-salt-boundary Interbed Multiples
g’0
Depth (m) g x
2000
3000
X (m)

47. Interbed Multiple Migration Image
Velocity Model
Interbed Multiple Migration Image
800
Depth (m)
2000
1200
1200
X (m)
X (m)

48. Lower-salt-boundary Interbed Multiples
Depth (m)
g’0 g x
2000
3000
X (m)

49. Interbed Multiple Migration Image
Velocity Model
Interbed Multiple Migration Image
800
Depth (m)
2000
1200
1200
X (m)
X (m)

50. Numerical Tests SEG/EAGE Model Large Salt Model Field Data Test
Let’s first review the POIC approach.

51. Velocity Model
X (m)
16000
Depth (m)
11000
Shots: 319; Receivers: 21

52. Lower-salt-boundary Interbed Multiples
Depth (m)
g’0 x g
11000
16000
X (m)

53. Interbed Multiple Migration Image
Velocity Model
6250
Depth (m)
7250
1200
X (m)
Interbed Multiple Migration Image
6250
Depth (m)
7250
1200
X (m)

54. Numerical Tests SEG/EAGE Model Large Salt Model Field Data Test
Let’s first review the POIC approach.

55. Velocity Model
16000m
Depth (m)
10668
Shots: 102; Receivers: 12

56. Sea-bed Interbed Multiple
16000m s
g’0 x
Depth (m) g
10668

57. Interbed Multiple Migration Image
Velocity Model
2000
Depth (m)
4000
Interbed Multiple Migration Image
2000
Depth (m)
4000
4000
X (m)

58. Outline Overview Interbed Multiple Migration Motivation Methods
Numerical Tests
Summary
Let’s first review the POIC approach.

59. Summary Interbed multiples are used to image salt
boundaries and subsalt structures
Challenge: Accuracy of the multiple
generating interface
Challenge: Interference from other multiples

60. Outline Overview Surface Multiple Migration
Interbed Multiple Migration
Multiple Attenuation in
Multiple Imaging
Conclusions
Let’s first review the POIC approach.

61. Outline Overview Multiple Attenuation in Multiple Imaging Motivation
Methodology
Numerical Examples
Summary
Let’s first review the POIC approach.

62. A major problem with multiple imaging:
interference from high-order multiple
high-order multiple
Incorrectly positioned as low-order multiple

63. Outline Overview Multiple Attenuation in Multiple Imaging Motivation
Methodology
Numerical Examples
Summary
Let’s first review the POIC approach.

64. Step1: Prediction S g’ g
second-order multiple

65. Physics Behind Prediction
D(g | s) =∫ G(g | g’) D(g’ | s) dg’ S g’ g
D(g’|s): Downgoing component
G(g|g’): Green’s function for propagating the wavefield
D(g|s): Predicted high-order multiples

66. p(t) = y(t) -  fj(t)mj(t)
Step2: Subtraction
p(t) = y(t)  fj(t)mj(t)
To attenuate the multiple from the data using a matching filter.
High-order multiple- free data
Original data
Predicted high-order multiple

67. Outline Overview Multiple Attenuation in Multiple Imaging Motivation
Methodology
Numerical Examples
Summary
Let’s first review the POIC approach.

68. Numerical Examples Synthetic Data Test Field Data Test
Let’s first review the POIC approach.

69. Density Model 276 shots, 50m spacing 20 receivers Depth (m)
20 receivers
6.25m spacing
Depth (m)
6,000
14,000
X (m)

70. CRG1: Different Order Multiples
direct wave
1st order
2nd order
3rd order

71. Before Attenuation
0.4
Time (sec)
2.5
X (m)
14,000

72. Prediction
0.4
Time (sec)
2.5
X (m)
14,000

73. After Attenuation
0.4
Time (sec)
2.5
X (m)
14,000

74. Before Attenuation
0.4
Time (sec)
2.5
X (m)
14,000

75. Migration Image: Before Attenuation
500
Interference from high- order multiple
Depth (m)
6000
1500
12500
X (m)

76. Migration Image: After Attenuation
500
Depth (m)
6000
1500
12500
X (m)

77. Numerical Examples Synthetic Data Test Field Data Test
Let’s first review the POIC approach.

78. Velocity Model V (ft/s) Depth (ft) X (ft) 652 shots 12 receivers 4910
V (ft/s)
12 receivers
4910
Depth (ft)
14300
43000
X (ft)
60000

79. Different Order Multiples
direct wave
1st order
2nd order

80. Before Attenuation 1.25 1st-order multiple Time (sec)
2nd-order multiple
5.00
X (ft)
60000

81. Predicted Multiple
1.25
Time (sec)
5.00
X (ft)
60000

82. After Attenuation
1.25
Time (sec)
5.00
X (ft)
60000

83. Before Attenuation 1.25 1st-order multiple Time (sec)
2nd-order multiple
5.00
X (ft)
60000

84. Multiple Migration Image: Before Attenuation10
interference from high- order multiple
Depth (kft) 26 16
X (kft) 32

85. Multiple Migration Image: After Attenuation10
Depth (kft) 26 16
X (kft) 32

86. Multiple Migration Images: Comparison10
Depth (kft) 26 16
X (kft) 32

87. Outline Overview Multiple Attenuation in Multiple Imaging Motivation
Methodology
Numerical Examples
Summary
Let’s first review the POIC approach.

88. Summary Attenuate high-order multiples to better image
low-order multiples, making multiple imaging a
more practical and useful tool
Obtained cleaner and more accurate subsurface
images to help avoid misinterpretation and thus
reduce risk in subsequent processes

89. Outline Overview Surface Multiple Migration
Interbed Multiple Migration
Multiple Attenuation in
Multiple Imaging
Conclusions
Let’s first review the POIC approach.

90. Conclusions As shown in the numerical examples,
surface multiple imaging and interbed
multiple imaging can be important imaging
methods
The multiple attenuation process is effective
in mitigating the interference in multiple
imaging

91. Future Work Apply interbed multiple imaging to more field data sets
Apply data-based multiple prediction method
in multiple filtering
Attenuate surface multiples prior to imaging
interbed multiples

92. Acknowledgements My advisor: Gerard T. Schuster
My supervisory committee: Ronanld L. Bruhn,
Brian E. Hornby, Richard D. Jarrard, and Robert
B. Smith
My wife Weining and my daughter Julia
My UTAM colleagues and my other friends