1. Multiple Removal with Local Plane Waves
Dmitri Lokshtanov

2. Content Motivation WE multiple suppression operator
Fast 2D/3D WE approach for simple sea-floor
2D/3D WE approach for irregular sea-floor
Conclusions

3. Motivation Seismic processing and imaging - main challenges:
Velocity model building for sub-salt and sub-basalt imaging
Removal of multiples from strong irregular boundaries

5. Near offset section (no AGC)

6. Depth migration with water velocity

7. Input shot gathers (no AGC)

8. Multiple suppression
For multiples from complex boundaries the methods based on periodicity or kinematic discrimination usually don’t work or are not sufficient.
In such cases the main demultiple tools are based on the Surface Related Multiple Elimination (SRME) or Wave-Equation (WE) techniques.

9. SRME (Berkhout, 1982; Verschuur, 1991) – advantages and limitations
Does not require any structural information. Predicts all free-surface multiples
As a rule becomes less efficient with increased level of interference of multiples of different orders
Requires the same dense sampling between sources as between receivers
Noise in data and poor sampling significantly degrade the prediction quality
Missing traces required by 3D SRME are reconstructed with least-square Fourier or Radon interpolation; residual NMO correction; DMO/inverse DMO; migration/demigration

10. WE approach versus SRME
SRME is the method of preference for data from areas with deep sea-floor, especially when a thick package of strong reflectors is present below the sea-floor
WE approach is especially efficient when the main free-surface multiples are just ‘pure’ water-layer multiples and peg-legs. Gives usually better results than SRME when several orders of multiples are involved
3D WE approach has less sampling problems than 3D SRME and it gives a flexiblility in methods for wavefield extrapolation depending on complexity of structure

11. The operator Pg transforms the primary reflection event recorded at receiver 1 into the multiple event recorded at receiver 2 (Wiggins, 1988; Berryhill & Kim, 1986).
The operator Pg transforms the primary reflection event recorded at receiver 1 into the multiple event recorded at receiver 2 (Wiggins, 1988; Berryhill & Kim, 1986).

12. Principles of WE approach

13. Adaptive subtraction of predicted multiples

14. Wave-equation approach – main features
All predicted multiples are split into 3 terms, where each term requires the same amplitude correction
All source-side and receiver-side multiples of all orders are suppressed simultaneously in one consistent step
The prediction and the adaptive subtraction of multiples are performed in the same domain
Fast version (WEREM) for a simple sea-floor. Slower version for irregular sea-floor

15. Why in the tau-p domain Easier to apply antialiasing protection
No problems with muting of direct arrival
Easier to define ‘multiple’ zone of tau-p domain and mute it away
Estimated reflection coefficients are explicitly angle dependent

16. 2D WEREM – prediction of multiples - 1

17. 2D WEREM – prediction of multiples - 2

18. Velocity model used to generate synthetic FD data

19. Constant P sections (angle at the surface is about 3º)
Input After Werem After Remul

20. Constant P sections (angle at the surface is about 15º)
Input After Werem After Remul

21. Velocity model 2 used to generate synthetic FD data

22. Constant P sections (angle at the surface is about 3º)
 m. residual
Input After Werem

23. Stack before multiple suppression Stack after Werem
T. Shetland
 T. Draupne
 T. Brent
Stack before multiple suppression Stack after Werem

24. Constant P sections (angle at the surface is about 10º
Input After Werem

25. Stack before multiple suppression (left) and after Werem multiple suppression (right).
The pink line shows the expected position of the first-order water-layer peg-leg from the
Top Cretaceous (black line). The multiple period is about 140 msec.

26. Constant P sections (angle at the surface is about 8º
Input After Werem multiple suppression Difference

27. raw stack

28. stack after WEREM

29. 500 m input WEREM

30. 4000 m input WEREM

31. Improving the results - local prediction / subtraction of multiples
Within the same prediction term, for the same CMP and the same p we have events reflected at different positions along the water bottom
Inconsistency between prediction and subtraction in case of rapid variation of sea-floor reflectivity
The problem is partly solved by applying adaptive subtraction in different time windows
Or by making prediction dependent on both p and offset (window)

32. 3D WEREM – basic features
3D data can be represented as a sum of plane waves with different vertical angles and azimuths from the source-side and receiver-side.
Current quasi 3D marine acquisition does not allow full 4D decomposition
Decomposition uniquely defines the direction of propagation from the receiver-side and is an integral over crossline slownesses from the source-side
The result of decomposition are used for exact prediction of multiples from the receiver-side and approximate prediction from the source-side
The approximation is that the crossline slowness from the source-side is the same as from the receiver-side (the same azimuth for 1D structures). The approximation allows us to mix data for flip flop shooting

39. Input constant P section (small angles)

40. Predicted multiples – R-side (small angles)

41. Input constant P section (small angles)

42. Constant P section – after prediction / subtraction (small angles)

43. Difference (Input – 3D WEREM), small angles

44. Input constant P section (larger angles)

45. Constant P section – after 3D WEREM (larger angles)

46. Werem - conclusions
Very efficient when the main assumptions are met: strongest multiples are water-layer multiples and peg-legs and the sea-floor is simple
Very fast - each predicted p trace is simply obtained as a sum of time-delayed input traces with the same p from the neighbour CMPs

47. WE for irregular sea-floor
Kinematic prediction of multiples (extrapolation through the water layer) takes into account coupling between incident and reflected / scattered plane waves with different slownesses
Both multiple reflections and diffractions are predicted
The procedure starts from the Radon transformed CS gathers (no interleaving is required)
In 3D exact prediction from the receiver side; approximate prediction from the source side

48. 2D prediction of multiples from the receiver side for irregular sea-floor

49. 2D prediction of multiples from the source side for irregular sea-floor

50. Velocity model for FD modelling

51. Input P-section (zero angle) Receiver-side prediction

52. Input P-section (zero angle) Receiver-side prediction

53. Input P-section (20 degrees) Receiver-side prediction Source-side prediction

54. Input CS gather After prediction + subtraction

55. Input CS gather After prediction + subtraction

56. Raw stack with final velocity / mute libraries

57. Stack after WE + VF

58. Raw CMP (no AGC) CMP after WE + VF (no AGC)

59. Input Constant P section R-side prediction

60. Input Constant P section R-side prediction

61. Input Constant P section After adaptive subtraction

64. Model for 3D ray tracing of primaries and sea-floor multiples

65. primary
peg-legs
Modelled CS gathers

66. Radon transformed CS gathers

67. Constant P sections (small angle) for line with crossline offset 250m.
Input D prediction D prediction

68. Constant P sections (larger angle) for line with crossline offset 250m.
Input D prediction D prediction

69. Constant P sections (small angle) for line with crossline offset 250m.
Input quasi 3D prediction D prediction

70. Constant P sections (larger angle) for line with crossline offset 250m.
Input quasi 3D prediction D prediction

71. WE for irregular sea-floor
Both multiple reflections and diffractions are predicted
Exact 3D prediction of pure water-layer multiples and peg-legs from the receiver-side
Quasi 3D prediction of peg-legs from the the source side
3-5 times slower than WEREM

72. Conclusions
SRME is the method of preference for data from areas with deep sea-floor, especially when a thick package of strong reflectors is present below the sea-floor
As a rule the method becomes less efficient when several orders of multiples are involved
For such data we use the wave-equation schemes, especially when the main free-surface multiples are just water-layer multiples and peg-legs
The 3D WE approach has fewer sampling problems than 3D SRME and it allows us to use different WE extrapolation schemes for different complexities of sea-floor and structure below it

73. Thank you