1. Enhancing Migration Image Quality by 3-D Prestack Migration Deconvolution Gerard Schuster Jianhua Yu, Jianxing Hu University of Utah andGXT 1 2 2 1 1 2

2. Blurring Problems in Migration Outline Migration Deconvolution Examples Conclusions

3. Outline Migration Deconvolution Examples Conclusions Blurring Problems in Migration

4. Migration noise and artifacts Migration Noise Problems 0 3.5 Depth (km) Weak illumination Footprint

5. m = L d T Migration = Blurred r but d = L  Migrated Section DataModeling

6. m = L T but d = L  Migrated Section L L L L  Migration Image m = True Reflectivity Model  Migration = Blurred r

7. Outline Migration Deconvolution Examples Conclusions Blurring Problems in Migration

8. Migration Deconvolution m  LLT Migration imageReflectivity  Migration Green’s function

9. m  LLT  LL T][ LL T][ 1 1 Migration Deconvolution

10. m   LL T][ 1

11. Assume Local v(z) Approximation m   LL T][ 1 Migration Deconvolution

12. m   LL T ][ r r 0  r,r  0 0 r ith column=ith pt scatterer Response to migration r 0 Migration Deconvolution r r 0 Pt. scatterer location Trial image pt. sgsoogsg rdrdrrGrrGrrGrrG)()()()( **  ][ Migration Green’s function (Schuster and Hu, 2000)

13. m   LL T ][ sgsoogsg rdrdrrGrrGrrGrrG)()()()( **  ][ Migration Green’s function (Schuster and Hu, 2000)  r,r  0 0 r r 0 Migration Deconvolution r r 0 r r 0 Special Case: r=r o e  gx e  sx e  gx e  sx |g-x| 2 |s-x| 2  |g-x| 2 |s-x| 2 xx = LL T ][ Preconditioner for LSM Pt. scatterer location Trial image pt.

14. MD Implementation Steps: Step 1: Prepare traveltime table Velocity cube Acquisition geometry information or Use migration timetable

15. Calculate the migration Green’s function MD Implementation Steps: Step 2: Y (km) Depth (km) m  r L L T ][ * N ithdepth L  r,r  0 r r r0

16. N Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) L M  R ][ithdepth  r,r  0 r r r0

17. Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) Depth (km) M  R ][ithdepth  r,r  0 r r 0

18. Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) M  R ][ithdepth  r,r  0 r r 0

19. Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) M  R ][ithdepth  r,r  0 r r 0

20. Step 3: FFT in x and y   ),0,0|,,( 0 zzyyxx oomig oooooo dzdzdydydxdxzyx R( ),,( Model Space ooomig rdrRrrrm)()()(   Model Space x-y shift invariance

21. Step 3: FFT in x and y   ),0,0|,,( 0 zzyyxx oomig oooooo dzdzdydydxdxzyx R ),,( Model Space FFT in x and y FFT in x and y ooomig rdrRrrrm)()()(   Model Space   ),0,0|,,( ~ ),,( ~ 0 zzkkzkk m yxyx ooyx dzdzzkkR),,( ~

22. Discrete MD Equation FFT of Migrateddata True Reflectivity Invert Blocks of 15x15 matrices for each k

23. Step 4: Invert MD image at the depth Z i by solving linear equations MD Implementation Steps: Step 5: Repeat Steps 2-4 until the maximum depth is finished M  R ][  (k, k, z  xy

24. Outline Migration Deconvolution Examples : Synthetic data Conclusions Blurring Problems in Migration

25. 0 3 km 0 3-D Point Scatterer Model 3 km 11 X 11 Receivers 11 X 11 Receivers dxg=dyg=0.3 km Imaging: dx=dy=50 m dz=100 m 3X3 Sources; dxshot=dyshot=1.5 km 10 km

26. 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) MIG MD Z=1 km Z=3 km Z=5 km Depth Slices

27. 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) MIG MD Z=7 km Z=9 km Z=10 km Depth Slices

28. 0 2.5 km 0 Meandering Stream Model 2.5 km 5 X 1 Sources; 11 X 7 Receivers 3.5 km

29. Mig MD Model 0 Y (km) X (km) 2.5 0 Z=3.5 KM

30. Meandering River Model 01000 X (m) 0 1000 Y (m)

31. Kirchhoff Migration Image 01000 X (m) 0 1000 Y (m)

32. MD Image 01000 X (m) 0 1000 Y (m)

33. 0 12.2 km 0 3-D SEG/EAGE Salt Model 12.2 km 9 X5 Sources; dxshot=dyshot=1 km 201 X 201 Receivers Imaging: dx=dy=20 m

34. 3-D SEG/EAGE Salt Model X (km)Y (km) Y=7.12 km

35. Mig and MD ( z=1.4 km, negative polarity) X (km) 3 10 Y (km) 59.85 X (km) MDMig

36. 3-D SEG/EAGE Salt Model X (km)Y (km) Y=7.12 km

37. MD (z=1.2 km)Mig (z=1.2 km) X (km) 3 10 Y (km) 59.85 X (km)

38. MD (z=1.2 km)Mig (z=1.2 km)

39. X (km) 020 3 10 Depth (km) SIGSBEE2B Model

40. X (km)020 3 10 Depth (km) Wave Equation Migration Before MD

41. X (km) 020 3 10 Depth (km) Wave Equation Migration after MD

42. Outline Migration Deconvolution Examples: 2-D field data Conclusions Blurring Problems in Migration

43. PSTM Image 0 6 X (km) 0 8 Time (s) MD PSTM Image

44. PSTM Image 0 6 X (km) 0 8 Time (s) MD PSTM Image

45. Outline Migration Deconvolution Examples: 3-D field data Conclusions Blurring Problems in Migration

46. 3-D Land Field Data : Receivers : Sources

47. Unocal Alaska 3D Data 8 km 0 km 5 km

48. Kirchhoff Migration MD

49. Unocal Alaska 3D Data 8 km 0 km 5 km

50. Inline Number 190 1.1 7.0 Depth (kft) 90Inline Number1 Kirchhoff MigrationMD (Crossline=50)

51. Unocal Alaska 3D Data 8 km 0 km 5 km

52. (crossline 200) 1901 1.1 8.0 Depth (kft) Kirchhoff MigrationMD

53. 2.0 s MDStandard MD 1.2 s

54. 1250 1.1 7.0 Depth (kft) Crossline Number 7.0 1.1 (Inline =50) Mig ( Unocal ) MD

55. Unocal Alaska 3D Data 8 km 0 km 5 km

56. Kirchhoff Migration MD Inline Number 1901 1 300 Crossline Number Inline Number 3 km

57. (3.08 kft) Inline Number 1901 1 265 Crossline Number Inline Number Mig (Courtesy of Unocal) MD

58. (3.6 kft) Inline Number 1901 1 265 Crossline Number Inline Number Mig (Courtesy of Unocal) MD

59. Outline Migration Deconvolution Examples Conclusions Blurring Problems in Migration

60. Conclusions MD = Least Squares Migration MD Improve resolution, suppresses mig. artifacts, balances illumination 20% @ 2 km; 10% @10 km Sensitive to choice of filter parameters MD $$ = 1 Migration MD Problems MD effectiveness diminishes with depth Local V(z) Approximation

61. Gaussian Beam MD, WE MD MD Future Conjugate Gradient MD

62. 10 Depth (km) After MD No AGC Before MD

63. 5 10 Depth (km) Before MD After MD

64. 0 6 X (km) 0 8 Time (s) MD

65. 0 6 X (km) 0 8 Time (s) MD PSTM(courtesy of Unocal) PSTMD

66. 0 6 X (km) 3 8 Time (s) MD

67. MD Time (s) Mig (courtesy of Aramco)

68. Time (s) Mig (Courtesy of Aramco)MD

69. Mig MD Mig MD

70. Fault

71. Purpose of MD Processing: Enhancing illumination Suppressing migration noise and artifacts Improving spatial resolution

72. Acknowledgements Aramco, Unocal, and Chevron- TexacoAramco, Unocal, and Chevron- Texaco UTAM sponsorsUTAM sponsors Bob Estill and George Yao (Unocal), Alan Leeds (ChevronTexaco)Bob Estill and George Yao (Unocal), Alan Leeds (ChevronTexaco) http://utam.gg.utah.eduhttp://utam.gg.utah.edu

73. Mig MD Model 0 Y (km) X (km) 2.5 0 Z=3.5 KM

75. 1.6 s Inline Crossline 3D PSTM (courtesy of Unocal) MD