M-OSRP: objectives, strategy and game-changing delivery Recent - PowerPoint PPT Presentation

General theory of Green’s theorem wave separation S’ 𝝇 𝟐 𝑄 = 𝑄 $ + 𝑄 ) 𝑠 ⃑ ' + 𝜍 ) 𝐻 & ' = 𝜍 $ 𝐻 & P 2 𝝇 𝟑 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 𝑄 ) 𝑠 ⃑, 𝜕 = 2 𝑄𝛼′𝐻 & 8𝑒𝑇′ ; < ' : Causal Green’s function in the homogeneous whole world 𝐻 & 30

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

Homogeneous whole-space of water Water 32

𝝇 𝟐 : Air gun Water 𝝇 𝟐 33

𝝇 𝟑 : Air perturbation 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 34

𝝇 𝟒 : Earth perturbation 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 O.B. 𝝇 𝟒 Earth 35

Predict a portion of total wave at 𝑠 ⃑ contributed by 𝝇 𝟒 S’ 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 𝑠 ⃑ O.B. 𝝇 𝟒 Earth 36

Predict a portion of total wave at 𝑠 ⃑ contributed by 𝝇 𝟒 S’ 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 𝑠 ⃑ Up O.B. 𝝇 𝟒 Earth 37

Predict a portion of total wave at 𝑠 ⃑ contributed by 𝝇 𝟒 S’ 𝝇 𝟑 Air F.S. Down Water 𝝇 𝟐 𝑠 ⃑ Down Up O.B. 𝝇 𝟒 Earth 38

Predict deghosted data at 𝑠 ⃑ contributed by 𝝇 𝟒 S’ 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 𝑠 ⃑ Deghosted O.B. 𝝇 𝟒 Earth 39

Predict deghosted data at 𝑠 ⃑ contributed by 𝝇 𝟒 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 𝑠 ⃑ S’ Deghosted O.B. 𝝇 𝟒 Earth 40

Predict deghosted data at 𝑠 ⃑ contributed by 𝝇 𝟒 𝝇 𝟑 Air F.S. Water 𝝇 𝟐 𝑠 ⃑ S’ M.S.(Cable) Deghosted O.B. 𝝇 𝟒 Earth 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 41

Advantage 1 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 𝟑 Air • 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 𝟒 42

Advantage 1 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 𝟑 Air • 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 𝟒 43

Advantage 1 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 𝟑 Air • 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 𝟒 44

Advantage 1 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 𝟑 Air • Can accommodate cable with an arbitrary shape F.S. 𝝇 𝟐 ( Z. Zhang & Weglein, 2016 ) Water 𝑠 ⃑ M.S.(Cable) Deghosted • Supersedes 𝑄 − 𝑊 E method that assumes cable O.B. Earth 𝝇 𝟒 being horizontal 45

Advantage 2 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 𝟑 Air • Needs no information about the “sources”: F.S. 𝝇 𝟐 ü wavelet, radiation pattern Water ü air property (shape and reflection at sea surface) 𝑠 ⃑ ü earth property M.S.(Cable) Deghosted O.B. Earth 𝝇 𝟒 46

Advantage 2 𝑄 >? 𝑠 ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝝇 𝟑 Air • Needs no information about the “sources”: F.S. 𝝇 𝟐 ü wavelet, radiation pattern Water ü air property (shape and reflection at sea surface) 𝑠 ⃑ ü earth property M.S.(Cable) Deghosted O.B. Earth 𝝇 𝟒 47

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

ü 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 𝟑 Air F.S. 𝝇 𝟐 Water 𝑠 ⃑ M.S.(Cable) O.B. Earth 𝝇 𝟒 49

ü 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 𝟑 Air F.S. 𝝇 𝟐 Water 𝑠 ⃑ M.S.(Cable) O.B. Earth 𝝇 𝟒 50

ü 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 𝟑 Air • Can only output deghosted data at a depth F.S. 𝝇 𝟐 above cable ( Weglein et al., 2013 ) Water 𝑠 ⃑ 𝑄 >? 𝑠 ' − 𝐻 & M.S.(Cable) ' 𝛼′𝑄 6 𝑜 ⃑, 𝜕 = @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ O.B. A.C. Earth 𝝇 𝟒 51

ü Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data How to deghost the actual acquired data? 𝝇 𝟑 Air • 𝑄 − 𝑊 E if cable being horizontal F.S. 𝝇 𝟐 Water 𝑠 ⃑ M.S.(Cable) O.B. Earth 𝝇 𝟒 52

ü Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data How to deghost the actual acquired data? 𝝇 𝟑 Air • 𝑄 − 𝑊 E if cable being horizontal F.S. 𝝇 𝟐 Water • A new method without assuming cable being 𝑠 ⃑ horizontal ( J. Wu & Weglein, 2016 ) M.S.(Cable) O.B. Earth 𝝇 𝟒 53

ü Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data The new method 𝝇 𝟑 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 𝟒 E.S. evaluation surface, shallower than cable 54

ü Deghosting on a depth variable cable Removal of ground roll & ghost onshore Deghosting ocean bottom data The new method 𝝇 𝟑 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 𝟒 55

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

ü 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

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

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

Deghosting on a depth variable cable ü 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 ü for onshore ground roll and ghost removal ü with a reduced data requirement ü retains effectiveness of original algorithm ( J. Wu & A. Weglein, SEG 2015 ) 72

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Wave separation ' − 𝐻 & ' 𝜖 K 𝑄 𝑒𝑇′ 𝑄 & = @ 𝑄𝜖 K 𝐻 & A.C. ( Weglein & Secrest 1990 ) Air Water 𝑄 & : Reference wave Earth 73

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Data requirement ' − 𝐻 & ' 𝜖 K 𝑄 𝑒𝑇′ 𝑄 & = @ 𝑄𝜖 K 𝐻 & A.C. ( Weglein & Secrest 1990 ) Air Water 𝑄 & : Reference wave Earth 74

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Data requirement ' − 𝐻 & ' 𝜖 K 𝑄 𝑒𝑇′ 𝑄 & = @ 𝑄𝜖 K 𝐻 & A.C. ( Weglein & Secrest 1990 ) • 𝜖 K 𝑄 was rarely measured in 1990s 75

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Marine -- Reduce data requirement ' − 𝐻 & ' 𝜖 K 𝑄 𝑒𝑇′ 𝑄 & = @ 𝑄𝜖 K 𝐻 & A.C. ( Weglein & Secrest 1990 ) • 𝜖 K 𝑄 was rarely measured in 1990s ' = 0 along the cable • Reduce requirement of 𝜖 K 𝑄 with 𝐻 & ( Osen et al. 1998, Tan 1999 ) 76

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 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 ⃑ 𝑢 Traction 77

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation ' − 𝐻 & ' 𝛼′𝑄 6 𝑜 @ 𝑄𝛼′𝐻 & 8𝑒𝑇′ A.C. 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 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 ⃑ 𝑢 Traction 78

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 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

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Wave separation 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 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 ⃑ 𝑢 Traction 80

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Data requirement 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 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 ⃑ 𝑢 Traction 81

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Onshore -- Data requirement 𝑣 >? = @ ⃑ 6 𝑯 & 𝑒𝑇′ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 A.C. ( Weglein & Secrest 1990, J. Wu & Weglein, SEG, 2015 ) 𝜇𝜄 + 2𝜈𝜖 U 𝑣 U 𝜈(𝜖 U 𝑣 W + 𝜖 W 𝑣 U ) 𝜈(𝜖 U 𝑣 E + 𝜖 E 𝑣 U ) 𝑜 U 𝑣 >? Reflection without ground roll & receiver ghost 𝑜 W ⃑ = 𝜈(𝜖 U 𝑣 W + 𝜖 W 𝑣 U ) 𝜇𝜄 + 2𝜈𝜖 W 𝑣 W 𝜈(𝜖 W 𝑣 E + 𝜖 E 𝑣 W ) 𝑢 𝑜 E 𝑯 & Green’s tensor in homogenous whole-space elastic reference 𝜈(𝜖 U 𝑣 E + 𝜖 E 𝑣 U ) 𝜈(𝜖 W 𝑣 E + 𝜖 E 𝑣 W ) 𝜇𝜄 + 2𝜈𝜖 E 𝑣 E 𝜯 & Stress tensor of Green’s function 𝜄=𝜖 U 𝑣 U + 𝜖 W 𝑣 W + 𝜖 E 𝑣 E 𝑣 Displacement ⃑ 𝑢 Traction 82

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

Deghosting on a depth variable cable ü 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 ) , (𝑢 U , 𝑢 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

Deghosting on a depth variable cable ü 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

Deghosting on a depth variable cable ü 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

Deghosting on a depth variable cable ü 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

Deghosting on a depth variable cable ü 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

Deghosting on a depth variable cable ü 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

Deghosting on a depth variable cable ü 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

Deghosting on a depth variable cable ü 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

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

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

Deghosting on a depth variable cable ü 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

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

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data 2D onshore experiment -- approximation ü Vacuum/earth boundary ⃑(𝑢)𝜀(𝑦 − 𝑦 C ) , 𝐺 ⃑ 𝑢 : source wavelet ü A localized force on surface 𝐺 Vacuum (𝐺 U , 𝐺 E ) V/E boundary (𝑣 U , 𝑣 E ) Earth 96

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Boundary condition ⃑(𝜕) : source wavelet ⃑ 𝜕 𝜀 𝑦 − 𝑦 C ⃑ 𝑦, 𝑨 = 0, 𝜕 = −𝐺 𝐺 𝑢 Vacuum (𝐺 U , 𝐺 E ) V/E boundary (𝑣 U , 𝑣 E ) Earth 97

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Formula simplification ⃑(𝜕) : source wavelet ⃑ 𝜕 𝜀 𝑦 − 𝑦 C ⃑ 𝑦, 𝑨 = 0, 𝜕 = −𝐺 𝐺 𝑢 Original 𝑣 >? (𝑠 ⃑(𝑠 ⃑, 𝑠 C , 𝜕) = @ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 ⃑′, 𝑠 C , 𝜕) 6 𝑯 & (𝑠 ⃑′, 𝑠 ⃑, 𝜕) 𝑒𝑇′ A.C. 98

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Formula simplification ⃑(𝜕) : source wavelet ⃑ 𝜕 𝜀 𝑦 − 𝑦 C ⃑ 𝑦, 𝑨 = 0, 𝜕 = −𝐺 𝐺 𝑢 Original 𝑣 >? (𝑠 ⃑(𝑠 ⃑, 𝑠 C , 𝜕) = @ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 ⃑′, 𝑠 C , 𝜕) 6 𝑯 & (𝑠 ⃑′, 𝑠 ⃑, 𝜕) 𝑒𝑇′ A.C. Simplified ⃑(𝜕) 6 𝑯 𝟏 (𝑠 𝑣 >? (𝑠 8 6 𝜯 & 𝑒𝑇 ^ ⃑, 𝑠 C , 𝜕) = @ 𝑣 6 𝑜 + 𝐺 C , 𝑠 ⃑, 𝜕) A.C. 99

Deghosting on a depth variable cable ü Removal of ground roll & ghost onshore Deghosting ocean bottom data Formula simplification ⃑(𝜕) : source wavelet ⃑ 𝜕 𝜀 𝑦 − 𝑦 C ⃑ 𝑦, 𝑨 = 0, 𝜕 = −𝐺 𝐺 𝑢 Original 𝑣 >? (𝑠 ⃑(𝑠 ⃑, 𝑠 C , 𝜕) = @ 𝑣 6 𝑜 8 6 𝜯 & − 𝑢 ⃑′, 𝑠 C , 𝜕) 6 𝑯 & (𝑠 ⃑′, 𝑠 ⃑, 𝜕) 𝑒𝑇′ A.C. Require traction everywhere along acquisition surface Simplified ⃑(𝜕) 6 𝑯 𝟏 (𝑠 𝑣 >? (𝑠 8 6 𝜯 & 𝑒𝑇 ^ ⃑, 𝑠 C , 𝜕) = @ 𝑣 6 𝑜 + 𝐺 C , 𝑠 ⃑, 𝜕) A.C. Require source wavelet 100