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M-OSRP: objectives, strategy and game-changing delivery Recent advances to on-shore, ocean bottom and towed streamer preprocessing for deghosting and ground roll removal Jing Wu and Arthur B. Weglein University of Houston February 7, 2017

  1. General theory of Green’s theorem wave separation S’ 𝝇 𝟐 𝑄 = 𝑄 $ + 𝑄 ) 𝑠 ⃑ ' + 𝜍 ) 𝐻 & ' = 𝜍 $ 𝐻 & P 2 𝝇 πŸ‘ ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ 𝑄 ) 𝑠 ⃑, πœ• = 2 𝑄𝛼′𝐻 & 8𝑒𝑇′ ; < ' : Causal Green’s function in the homogeneous whole world 𝐻 & 30

  2. Marine experiment Air F.S. Water M.S.(Cable) O.B. Earth F.S. free surface, or air/water boundary O.B. ocean bottom M.S. measurement surface 31

  3. Homogeneous whole-space of water Water 32

  4. 𝝇 𝟐 : Air gun Water 𝝇 𝟐 33

  5. 𝝇 πŸ‘ : Air perturbation 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 34

  6. 𝝇 πŸ’ : Earth perturbation 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 O.B. 𝝇 πŸ’ Earth 35

  7. Predict a portion of total wave at 𝑠 ⃑ contributed by 𝝇 πŸ’ S’ 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 𝑠 ⃑ O.B. 𝝇 πŸ’ Earth 36

  8. Predict a portion of total wave at 𝑠 ⃑ contributed by 𝝇 πŸ’ S’ 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 𝑠 ⃑ Up O.B. 𝝇 πŸ’ Earth 37

  9. Predict a portion of total wave at 𝑠 ⃑ contributed by 𝝇 πŸ’ S’ 𝝇 πŸ‘ Air F.S. Down Water 𝝇 𝟐 𝑠 ⃑ Down Up O.B. 𝝇 πŸ’ Earth 38

  10. Predict deghosted data at 𝑠 ⃑ contributed by 𝝇 πŸ’ S’ 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 𝑠 ⃑ Deghosted O.B. 𝝇 πŸ’ Earth 39

  11. Predict deghosted data at 𝑠 ⃑ contributed by 𝝇 πŸ’ 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 𝑠 ⃑ S’ Deghosted O.B. 𝝇 πŸ’ Earth 40

  12. Predict deghosted data at 𝑠 ⃑ contributed by 𝝇 πŸ’ 𝝇 πŸ‘ Air F.S. Water 𝝇 𝟐 𝑠 ⃑ S’ M.S.(Cable) Deghosted O.B. 𝝇 πŸ’ Earth 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 41

  13. Advantage 1 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 πŸ‘ Air β€’ Can accommodate cable with an arbitrary shape F.S. 𝝇 𝟐 ( Z. Zhang & Weglein, 2016 ) Water 𝑠 ⃑ M.S.(Cable) Deghosted O.B. Earth 𝝇 πŸ’ 42

  14. Advantage 1 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 πŸ‘ Air β€’ Can accommodate cable with an arbitrary shape F.S. 𝝇 𝟐 ( Z. Zhang & Weglein, 2016 ) Water 𝑠 ⃑ M.S.(Cable) Deghosted O.B. Earth 𝝇 πŸ’ 43

  15. Advantage 1 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 πŸ‘ Air β€’ Can accommodate cable with an arbitrary shape F.S. 𝝇 𝟐 ( Z. Zhang & Weglein, 2016 ) Water 𝑠 ⃑ M.S.(Cable) Deghosted O.B. Earth 𝝇 πŸ’ 44

  16. Advantage 1 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 πŸ‘ Air β€’ Can accommodate cable with an arbitrary shape F.S. 𝝇 𝟐 ( Z. Zhang & Weglein, 2016 ) Water 𝑠 ⃑ M.S.(Cable) Deghosted β€’ Supersedes 𝑄 βˆ’ π‘Š E method that assumes cable O.B. Earth 𝝇 πŸ’ being horizontal 45

  17. Advantage 2 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 πŸ‘ Air β€’ Needs no information about the β€œsources”: F.S. 𝝇 𝟐 ΓΌ wavelet, radiation pattern Water ΓΌ air property (shape and reflection at sea surface) 𝑠 ⃑ ΓΌ earth property M.S.(Cable) Deghosted O.B. Earth 𝝇 πŸ’ 46

  18. Advantage 2 𝑄 >? 𝑠 ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 πŸ‘ Air β€’ Needs no information about the β€œsources”: F.S. 𝝇 𝟐 ΓΌ wavelet, radiation pattern Water ΓΌ air property (shape and reflection at sea surface) 𝑠 ⃑ ΓΌ earth property M.S.(Cable) Deghosted O.B. Earth 𝝇 πŸ’ 47

  19. Progress v Deghosting data on a depth variable cable v Wave separation onshore for the removal of ground roll and ghosts v Deghosting data at the ocean bottom 48

  20. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data Issue of current Green’s theorem deghosting method 𝝇 πŸ‘ Air F.S. 𝝇 𝟐 Water 𝑠 ⃑ M.S.(Cable) O.B. Earth 𝝇 πŸ’ 49

  21. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data Issue of current Green’s theorem deghosting method 𝝇 πŸ‘ Air F.S. 𝝇 𝟐 Water 𝑠 ⃑ M.S.(Cable) O.B. Earth 𝝇 πŸ’ 50

  22. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data Issue of current Green’s theorem deghosting method 𝝇 πŸ‘ Air β€’ Can only output deghosted data at a depth F.S. 𝝇 𝟐 above cable ( Weglein et al., 2013 ) Water 𝑠 ⃑ 𝑄 >? 𝑠 ' βˆ’ 𝐻 & M.S.(Cable) ' 𝛼′𝑄 6 π‘œ ⃑, πœ• = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ O.B. A.C. Earth 𝝇 πŸ’ 51

  23. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data How to deghost the actual acquired data? 𝝇 πŸ‘ Air β€’ 𝑄 βˆ’ π‘Š E if cable being horizontal F.S. 𝝇 𝟐 Water 𝑠 ⃑ M.S.(Cable) O.B. Earth 𝝇 πŸ’ 52

  24. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data How to deghost the actual acquired data? 𝝇 πŸ‘ Air β€’ 𝑄 βˆ’ π‘Š E if cable being horizontal F.S. 𝝇 𝟐 Water β€’ A new method without assuming cable being 𝑠 ⃑ horizontal ( J. Wu & Weglein, 2016 ) M.S.(Cable) O.B. Earth 𝝇 πŸ’ 53

  25. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data The new method 𝝇 πŸ‘ Air Step 1: F.S. 𝝇 𝟐 Water Deghost data at a depth (at E.S.) above cable 𝑸 𝒗𝒒 (output) E.S. Use current Green’s theorem deghosting 𝑸 , 𝑸 𝒐 (input) M.S.(Cable) ( Weglein 2002, J. Zhang & Weglein 2007 ) O.B. Earth 𝝇 πŸ’ E.S. evaluation surface, shallower than cable 54

  26. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data The new method 𝝇 πŸ‘ Air Step 2: F.S. 𝝇 𝟐 Water Predict deghosted data right on the cable 𝑸 𝒗𝒒 (input) E.S. Use Green’s theorem one-way wave prediction 𝑸 𝒗𝒒 (output) M.S.(Cable) ( Weglein et al., 2011a,b, 2016 ) O.B. Earth 𝝇 πŸ’ 55

  27. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data Numerical test: Model 0m F.S. 10m 40m M.S. Water 300m O.B. Earth Layer Velocity (m/s) Density (kg/m 3 ) Water 1500 1000 Earth 2500 1000 56

  28. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data Numerical test: Model 0m F.S. 10m E.S. 25m 40m M.S. Water 300m O.B. Earth Layer Velocity (m/s) Density (kg/m 3 ) Water 1500 1000 Earth 2500 1000 57

  29. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Input total 𝑄 at cable cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 58

  30. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Input total 𝑄 at cable cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 59

  31. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Input total 𝑄 at cable cable Offset/m -1000 -500 0 500 1000 0 Direct 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 Receiver-ghost x105 0.8 60

  32. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Deghosted 𝑄 at E.S. (Step 1) cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 61

  33. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Input total 𝑄 at cable cable Offset/m -1000 -500 0 500 1000 0 Direct 0.2 1.0 0.5 Time/s 0.4 0 -0.5 -1.0 0.6 Receiver-ghost x105 0.8 62

  34. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Deghosted 𝑄 at E.S. (Step 1) cable Offset/m -1000 -500 0 500 1000 0 Direct 0.2 1.0 0.5 Time/s 0.4 0 -0.5 -1.0 0.6 Receiver-ghost x105 0.8 63

  35. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Input total 𝑄 at cable cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 64

  36. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Deghosted 𝑄 at E.S. (Step 1) cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 65

  37. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Deghosted 𝑄 at cable (Step 2) cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 66

  38. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Input total 𝑄 on cable cable Offset/m -1000 -500 0 500 1000 0 Direct 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 Receiver-ghost x105 0.8 67

  39. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data E.S. Deghosted 𝑄 at cable (Step 2) cable Offset/m -1000 -500 0 500 1000 0 0.2 1.0 0.5 Primary Time/s 0.4 0 -0.5 -1.0 0.6 x105 0.8 68

  40. ΓΌ Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data Summary Step 1 Step 2 One-way wave prediction Current deghosting method output deghosted data on cable output deghosted data above cable v Provide a two-step new method to deghost actual data on the cable, and without limitation of cable’s shape. 69

  41. Progress v Deghosting data on a depth variable cable v Wave separation onshore for the removal of ground roll and ghosts v Deghosting data at the ocean bottom 70

  42. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Ground roll (Rayleigh wave) ( Boustani et al., Journal of Geophysics and Engineering, 2013 ) 71

  43. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Deliverable ( J. Wu & A. Weglein, SEG 2016 ) v A new and simplified Green’s theorem wave separation algorithm ΓΌ for onshore ground roll and ghost removal ΓΌ with a reduced data requirement ΓΌ retains effectiveness of original algorithm ( J. Wu & A. Weglein, SEG 2015 ) 72

  44. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Wave separation ' βˆ’ 𝐻 & ' πœ– K 𝑄 𝑒𝑇′ 𝑄 & = @ π‘„πœ– K 𝐻 & A.C. ( Weglein & Secrest 1990 ) Air Water 𝑄 & : Reference wave Earth 73

  45. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Data requirement ' βˆ’ 𝐻 & ' πœ– K 𝑄 𝑒𝑇′ 𝑄 & = @ π‘„πœ– K 𝐻 & A.C. ( Weglein & Secrest 1990 ) Air Water 𝑄 & : Reference wave Earth 74

  46. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Data requirement ' βˆ’ 𝐻 & ' πœ– K 𝑄 𝑒𝑇′ 𝑄 & = @ π‘„πœ– K 𝐻 & A.C. ( Weglein & Secrest 1990 ) β€’ πœ– K 𝑄 was rarely measured in 1990s 75

  47. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Reduce data requirement ' βˆ’ 𝐻 & ' πœ– K 𝑄 𝑒𝑇′ 𝑄 & = @ π‘„πœ– K 𝐻 & A.C. ( Weglein & Secrest 1990 ) β€’ πœ– K 𝑄 was rarely measured in 1990s ' = 0 along the cable β€’ Reduce requirement of πœ– K 𝑄 with 𝐻 & ( Osen et al. 1998, Tan 1999 ) 76

  48. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) 𝑣 >? Reflection without ground roll & receiver ghost 𝑯 & Green’s tensor in homogenous whole-space elastic reference 𝜯 & Stress tensor of Green’s function 𝑣 Displacement ⃑ 𝑒 Traction 77

  49. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation ' βˆ’ 𝐻 & ' 𝛼′𝑄 6 π‘œ @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) 𝑣 >? Reflection without ground roll & receiver ghost 𝑯 & Green’s tensor in homogenous whole-space elastic reference 𝜯 & Stress tensor of Green’s function 𝑣 Displacement ⃑ 𝑒 Traction 78

  50. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) Not a filtering method of ground roll removal, but a wave theory based wave prediction and no damage on 𝑣 >? 79

  51. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) 𝑣 >? Reflection without ground roll & receiver ghost 𝑯 & Green’s tensor in homogenous whole-space elastic reference 𝜯 & Stress tensor of Green’s function 𝑣 Displacement ⃑ 𝑒 Traction 80

  52. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Data requirement 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) 𝑣 >? Reflection without ground roll & receiver ghost 𝑯 & Green’s tensor in homogenous whole-space elastic reference 𝜯 & Stress tensor of Green’s function 𝑣 Displacement ⃑ 𝑒 Traction 81

  53. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Data requirement 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) πœ‡πœ„ + 2πœˆπœ– U 𝑣 U 𝜈(πœ– U 𝑣 W + πœ– W 𝑣 U ) 𝜈(πœ– U 𝑣 E + πœ– E 𝑣 U ) π‘œ U 𝑣 >? Reflection without ground roll & receiver ghost π‘œ W ⃑ = 𝜈(πœ– U 𝑣 W + πœ– W 𝑣 U ) πœ‡πœ„ + 2πœˆπœ– W 𝑣 W 𝜈(πœ– W 𝑣 E + πœ– E 𝑣 W ) 𝑒 π‘œ E 𝑯 & Green’s tensor in homogenous whole-space elastic reference 𝜈(πœ– U 𝑣 E + πœ– E 𝑣 U ) 𝜈(πœ– W 𝑣 E + πœ– E 𝑣 W ) πœ‡πœ„ + 2πœˆπœ– E 𝑣 E 𝜯 & Stress tensor of Green’s function πœ„=πœ– U 𝑣 U + πœ– W 𝑣 W + πœ– E 𝑣 E 𝑣 Displacement ⃑ 𝑒 Traction 82

  54. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data The data requirement is satisfied ( J. Wu and A. Weglein, SEG 2015 ) ⃑ β€’ Measure both 𝒗 and 𝒖 83

  55. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data ⃑ ) from air/earth Model -- Generate data ( 𝒗 & 𝒖 Air A/E boundary M.S. 100m (𝑣 U , 𝑣 E ) , (𝑒 U , 𝑒 E ) Earth 400m Layer P Velocity (m/s) S Velocity (m/s) Density (kg/m 3 ) 1(Air) 340 0 3 2(Top earth) 1800 1200 1500 3(Bottom earth) 4000 2500 1800 84

  56. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Total 𝑣 U input to the separation algorithm Offset/m -3000 -2000 -1000 0 1000 2000 3000 0 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 85

  57. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Total 𝑣 U input to the separation algorithm Offset/m -3000 -2000 -1000 0 1000 2000 3000 Direct Direct 0 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 86

  58. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Total 𝑣 U input to the separation algorithm Offset/m -3000 -2000 -1000 0 1000 2000 3000 0 Rayleigh Rayleigh 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 87

  59. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Total 𝑣 U input to the separation algorithm Offset/m -3000 -2000 -1000 0 1000 2000 3000 0 Primary Primary 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 88

  60. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Total 𝑣 U input to the separation algorithm Offset/m -3000 -2000 -1000 0 1000 2000 3000 0 Ghost Ghost 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 89

  61. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Total 𝑣 U input to the separation algorithm Offset/m -3000 -2000 -1000 0 1000 Direct 2000 3000 0 Rayleigh Primary Ghost 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 90

  62. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Deghosted 𝑣 U from the separation algorithm Offset/m -3000 -2000 -1000 0 1000 2000 3000 0 Primary 0.5 5 4 3 2 1.0 1 Time/s 0 -1 -2 -3 1.5 -4 -5 x10-12 2.0 91

  63. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data The data requirement is satisfied ( J. Wu and A. Weglein, SEG 2015 ) ⃑ β€’ Measure both 𝒗 and 𝒖 β€’ Effectively separate ground roll and ghosts out, without damaging reflection data 92

  64. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data The data requirement is satisfied ( J. Wu and A. Weglein, SEG 2015 ) ⃑ β€’ Measure both 𝒗 and 𝒖 β€’ Effectively separate ground roll and ghosts out, without damaging reflection data The data requirement is not satisfied ( J. Wu and A. Weglein, SEG 2016 ) ⃑ β€’ Measure only 𝒗 , but not 𝒖 93

  65. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data 2D onshore experiment Air (𝐺 U , 𝐺 E ) A/E boundary (𝑣 U , 𝑣 E ) Earth 94

  66. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data 2D onshore experiment -- approximation ΓΌ Vacuum/earth boundary Vacuum (𝐺 U , 𝐺 E ) V/E boundary (𝑣 U , 𝑣 E ) Earth 95

  67. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data 2D onshore experiment -- approximation ΓΌ Vacuum/earth boundary ⃑(𝑒)πœ€(𝑦 βˆ’ 𝑦 C ) , 𝐺 ⃑ 𝑒 : source wavelet ΓΌ A localized force on surface 𝐺 Vacuum (𝐺 U , 𝐺 E ) V/E boundary (𝑣 U , 𝑣 E ) Earth 96

  68. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Boundary condition ⃑(πœ•) : source wavelet ⃑ πœ• πœ€ 𝑦 βˆ’ 𝑦 C ⃑ 𝑦, 𝑨 = 0, πœ• = βˆ’πΊ 𝐺 𝑒 Vacuum (𝐺 U , 𝐺 E ) V/E boundary (𝑣 U , 𝑣 E ) Earth 97

  69. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Formula simplification ⃑(πœ•) : source wavelet ⃑ πœ• πœ€ 𝑦 βˆ’ 𝑦 C ⃑ 𝑦, 𝑨 = 0, πœ• = βˆ’πΊ 𝐺 𝑒 Original 𝑣 >? (𝑠 ⃑(𝑠 ⃑, 𝑠 C , πœ•) = @ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 ⃑′, 𝑠 C , πœ•) 6 𝑯 & (𝑠 ⃑′, 𝑠 ⃑, πœ•) 𝑒𝑇′ A.C. 98

  70. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Formula simplification ⃑(πœ•) : source wavelet ⃑ πœ• πœ€ 𝑦 βˆ’ 𝑦 C ⃑ 𝑦, 𝑨 = 0, πœ• = βˆ’πΊ 𝐺 𝑒 Original 𝑣 >? (𝑠 ⃑(𝑠 ⃑, 𝑠 C , πœ•) = @ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 ⃑′, 𝑠 C , πœ•) 6 𝑯 & (𝑠 ⃑′, 𝑠 ⃑, πœ•) 𝑒𝑇′ A.C. Simplified ⃑(πœ•) 6 𝑯 𝟏 (𝑠 𝑣 >? (𝑠 8 6 𝜯 & 𝑒𝑇 ^ ⃑, 𝑠 C , πœ•) = @ 𝑣 6 π‘œ + 𝐺 C , 𝑠 ⃑, πœ•) A.C. 99

  71. Deghosting on a depth variable cable ΓΌ Removal of ground roll & ghost onshore Deghosting ocean bottom data Formula simplification ⃑(πœ•) : source wavelet ⃑ πœ• πœ€ 𝑦 βˆ’ 𝑦 C ⃑ 𝑦, 𝑨 = 0, πœ• = βˆ’πΊ 𝐺 𝑒 Original 𝑣 >? (𝑠 ⃑(𝑠 ⃑, 𝑠 C , πœ•) = @ 𝑣 6 π‘œ 8 6 𝜯 & βˆ’ 𝑒 ⃑′, 𝑠 C , πœ•) 6 𝑯 & (𝑠 ⃑′, 𝑠 ⃑, πœ•) 𝑒𝑇′ A.C. Require traction everywhere along acquisition surface Simplified ⃑(πœ•) 6 𝑯 𝟏 (𝑠 𝑣 >? (𝑠 8 6 𝜯 & 𝑒𝑇 ^ ⃑, 𝑠 C , πœ•) = @ 𝑣 6 π‘œ + 𝐺 C , 𝑠 ⃑, πœ•) A.C. Require source wavelet 100

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