Chao Ma!! San Antonio, TX! 2013 M-OSRP Annual Meeting! May 2, 2013!
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1 One-dimensional analytic analysis of the effects of! treating s in the data as subevents! in the leading-order ISS multiple-removal algorithms:! comparison between free-surface and cases Chao Ma!! San Antonio, TX! 2013 M-OSRP Annual Meeting! May 2, 2013! 1
2 Key points! ISS leading-order attenuation:!! Strengths (data driven):! Predicts all first-order s at all depths at once;! The prediction has correct time and an approximate, wellunderstood amplitude of first-order s;! A limitation & Solution:! A new higher-order attenuation algorithm is developed, retaining the strengths of the current algorithm and addressing one of its limitations.!! 2
3 Key points & Outline! ISS Leading-order attenuation algorithm! A limitation and solution (higherorder modification)! 3
4 Key points & Outline! ISS Leading-order attenuation algorithm! A limitation and solution (higherorder modification)! Two examples to help understanding! 4
5 Key points & Outline! ISS Leading-order attenuation algorithm! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Two examples to help understanding! 5
6 Key points & Outline! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification and When this limitation can be serious and needs higher-order modification! 6
7 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification and When this limitation can be serious and needs higher-order modification! Summary! 7
8 Introduction! M-OSRP is concerned with the seismic data processing.! Green s Theorem! 1. Wavefield separation! 2. Wavelet estimation! 3. Deghosting! Inverse Scattering Series! (ISS)! 4. Free-surface multiple removal! 5. Internal-multiple removal! 6. Imaging! 7. Inversion! 8
9 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion! attenuation ISS leading-order attenuation subseries for firstorder! 9
10 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion! attenuation ISS leading-order attenuation subseries for firstorder! 10
11 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion! attenuation b IM = b 1 + b 3 + b 5 +. ISS leading-order attenuation subseries for firstorder! 11
12 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion! attenuation Stolt migration! of input data! (P+IM)! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of secondorder s! ISS leading-order attenuation subseries for firstorder! D(t) D(ω ) D( 2ω ) c 0 b 1 (k) b 1 (z) Leading-order prediction of first-order s! k = 2ω ; z c 0t c
13 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion attenuates internal multiples of all orders! ISS! leading-order! attenuation Stolt migration! of input data! (P+IM)! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of secondorder s! ISS leading-order attenuation subseries for firstorder! Leading-order prediction of first-order s! 13
14 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion attenuates internal multiples of all orders! ISS! leading-order! attenuation Stolt migration! of input data! (P+IM)! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of secondorder s! attenuates internal multiples of first-order! ISS leading-order attenuation subseries for firstorder! Leading-order prediction of first-order s! b 1 + b 3 14
15 Introduction! Green s Theorem! Data without reference and ghosts! Inverse scattering series(iss)! ISS free surface multiple removal ISS internal multiple removal ISS imaging ISS inversion attenuates internal multiples of all orders! ISS! leading-order! attenuation Stolt migration! of input data! (P+IM)! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of secondorder s! attenuates internal multiples of first-order! ISS leading-order attenuation subseries for firstorder! Leading-order prediction of first-order s! b 1 + b 3 15
16 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and its higher-order modification! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification and When this limitation can be serious and needs higher-order modification! Summary! 16
17 The ISS leading-order attenuation! The leading-order prediction of the first-order s, in 1D, is! (Araújo et al, 1994; Weglein et al., 1997): b 3 (k) = dz 1 e ikz 1 b (z ) dz e ikz 2 b (z ) dz e ikz 3 b (z ) 1 3 z 1 ε z 2 +ε 17
18 The ISS leading-order attenuation! The leading-order prediction of the first-order s, in 1D, is! (Araújo et al, 1994; Weglein et al., 1997): b 3 (k) = dz 1 e ikz 1 b (z ) dz e ikz 2 b (z ) dz e ikz 3 b (z ) 1 3 z 1 ε z 2 +ε Data after the removal of reference wave, wavelet, ghosts, free-surface multiples.! D(t) D(ω ) D( 2ω c 0 ) b 1 (k) b 1 (z) k = 2ω ; z c t 0 c
19 The ISS leading-order attenuation! The leading-order prediction of the first-order s, in 1D, is! (Araújo et al, 1994; Weglein et al., 1997): Primaries + Internal multiples! Primaries + Internal multiples! b 3 (k) = dz 1 e ikz 1 b (z ) dz e ikz 2 b (z ) dz e ikz 3 b (z ) 1 3 z 1 ε z 2 +ε Primaries + Internal multiples! Data after the removal of reference wave, wavelet, ghosts, free-surface multiples.! D(t) D(ω ) D( 2ω c 0 ) b 1 (k) b 1 (z) k = 2ω ; z c t 0 c
20 The ISS leading-order attenuation! The leading-order prediction of the first-order s, in 1D, is! (Araújo et al, 1994; Weglein et al., 1997): Primaries + Internal multiples! Primaries + Internal multiples! b 3 (k) = dz 1 e ikz 1 b (z ) dz e ikz 2 b (z ) dz e ikz 3 b (z ) 1 3 Air-water/! Primaries + Internal multiples! Air-land! A! D! C! G! z 1 ε z 2 +ε E! F! ABC (+)! DEC (-)! DFG (+)! B! First-order prediction through three primary subevents 20
21 The ISS leading-order attenuation! The leading-order prediction of the first-order s, in 1D, is! (Araújo et al, 1994; Weglein et al., 1997): Primaries + Internal multiples! Primaries + Internal multiples! b 3 (k) = dz 1 e ikz 1 b (z ) dz e ikz 2 b (z ) dz e ikz 3 b (z ) 1 3 Air-water/! Primaries + Internal multiples! Air-land! A! D! C! G! z 1 ε z 2 +ε E! F! ABC (+)! DEC (-)! DFG (+)! B! First-order prediction through three primary subevents 21
22 What leading-order term can achieve (among others)! ISS leading-order attenuation subseries for firstorder.! b 1 (k) + b 3 (k) 1. Predicts all first-order s at all depths at once;! 2. The correct time and an approximate, well-understood amplitude of first-order s;! Data driven; avoids assumptions that many other methods make, e.g., subsurface information.! 22
23 The ISS leading-order attenuation! The leading-order prediction of the first-order s, in 1D, is! (Araújo et al, 1994; Weglein et al., 1997): Primaries + Internal multiples! Primaries + Internal multiples! b 3 (k) = dz 1 e ikz 1 b (z ) dz e ikz 2 b (z ) dz e ikz 3 b (z ) 1 3 Air-water/! Primaries + Internal multiples! Air-land! A! D! C! G! z 1 ε z 2 +ε E! F! ABC (+)! DEC (-)! DFG (+)! B! First-order prediction through three primary subevents 23
24 Possible subevents combinations! b1 = P + I b 3 = (P + I)(P + I)(P + I) = PPP + PPI + IPP + IPI + III + PIP + PII + IIP Where P stands for primaries,! I stands for s. First-order s! 24
25 Possible subevents combinations! b1 = P + I (Two reflector example)! Higher-order s! e.g., second-order, third-order *! b 3 = (P + I)(P + I)(P + I) = PPP + PPI + IPP + IPI + III + PIP + PII + IIP Where P stands for primaries,! I stands for s. First-order s! * Zhang and Shaw (2010)! 25
26 Prediction of a second-order! (an first-order acts as one subevent)! 1! 2! Pimary_2! Pimary_1! A first-order! A second-order internal multiple! 26
27 ISS attenuation! attenuates internal multiples of all orders! attenuates internal multiples of first-order! ISS internal multiple removal ISS leading-order attenuation ISS leading-order attenuation subseries for firstorder! Stolt migration! of input data! (P+IM)! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of first-order internal multiples! 27
28 ISS attenuation! attenuates internal multiples of all orders! attenuates internal multiples of first-order! ISS internal multiple removal ISS leading-order attenuation ISS leading-order attenuation subseries for firstorder! Stolt migration! of input data! (P+IM)! Leading-order prediction of second-order internal multiples! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of first-order internal multiples! + Higher-order internal multiples! 28
29 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! 1. Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! Free-surface multiple removal! Summary! 29
30 1-D free-surface multiple elimination! Green s Theorem! Data without reference and ghosts! ISS free surface multiple removal Data without reference and ghosts! Prediction of second-order free-surface multiple! R(ω ) = R FS (ω ) + R 2 FS(ω ) + R 3 FS(ω ) + R 4 FS(ω ) + Prediction of first-order free-surface multiple! (-1)! (-1)! (-1)! Air-water! 1! R 1! R 1! R 1! R 1! R 1! R 1! Water bottom! Pimary_1! A first-order free-surface multiple! A second-order free-surface multiple! 30
31 1-D free-surface multiple elimination! Green s Theorem!! term! Data without reference and ghosts! data! ISS free surface multiple removal Primary! Data without reference and ghosts! R(ω ) = R FS (ω ) + R 2 FS(ω ) + R 3 FS(ω ) + R 4 FS(ω ) + First-order! Free-surface multiples! Prediction of first-order free-surface multiple! Prediction of second-order free-surface multiple! Second-order! Free-surface multiples! R FS! 1! 1! 1! R 2 FS! 0! -1! -2! R 3 FS! 0! 0! 1! 31
32 1-D free-surface multiple elimination! 1! R 1! Air-water! Water bottom! Pimary_1! Primary_1! Actual amplitude: (R 1 )(-1)(R 1 )! Predicted amplitude: [R 1 ][R 1 ]! A first-order free-surface multiple! 1! R 1! Actual amplitude: (R 1 )(-1)(R 1 )(-1)(R 1 )! Predicted amplitude: [R 1 (-1)(R 1 )][R 1 ]! Air-water! Water bottom! 32
33 1-D free-surface multiple elimination! Green s Theorem!! term! Data without reference and ghosts! data! ISS free surface multiple removal Primary! Data without reference and ghosts! R(ω ) = R FS (ω ) + R 2 FS(ω ) + R 3 FS(ω ) + R 4 FS(ω ) + First-order! Free-surface multiples! Prediction of first-order free-surface multiple! Prediction of second-order free-surface multiple! Second-order! Free-surface multiples! R FS! 1! 1! 1! R 2 FS! 0! -1! -2! R 3 FS! 0! 0! 1! 33
34 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! Free-surface multiple removal! To remove second-order free-surface multiples, more than one terms are needed (collective works are needed).! Summary! 34
35 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! Free-surface multiple removal! Internal multiple attenuation (two reflector example)! Summary! 35
36 ISS attenuation! attenuates internal multiples of all orders! attenuates internal multiples of first-order! ISS internal multiple removal ISS leading-order attenuation ISS leading-order attenuation subseries for firstorder! Stolt migration! Leading-order prediction of second-order internal multiples! b IM = b 1 + b 3 + b 5 +. Leading-order prediction of first-order internal multiples! + Higher-order internal multiples! 36
37 1-D internal-multiple attenuation (two-reflector case)! 1! 2! R 1! T 01! R 2! T 10! Pimary_1! Pimary_2! A first-order! A second-order! 37
38 1-D internal-multiple attenuation (two-reflector case)! Data without reference, ghosts and free-surface multiples! ISS free surface multiple removal ISS leading-order attenuation Stolt migration! Leading-order prediction of secondorder s! b IM (k) = b 1 (k) + b 3 (k) + b 5 (k) +. Leading-order prediction of first-order s!! term! data! Primary! First-order! internalmultiples! Second-order! Internal multiples! b 1! 1! 1! 1! b 3! 0! -1(T 01 T 10 )! -2(T 01 T 10 )+ (T 01 T 10 R 1 ) 2! b 5! 0! 0! 1(T 01 T 10 ) 2! 38
39 1-D internal-multiple attenuation (two-reflector case)! T 01! 1! R 2! 2! T 10! R 1! Pimary_2! Pimary_1! Pimary_2! A first-order! Actual amplitude: T 01 R 2 (-R 1 )R 2 T 12! Predicted amplitude: [T 01 R 2 T 10 ][R 1 ][T 01 R 2 T 10 ]=(-1T 01 T 10 )[T 01 R 2 (-R 1 )R 2 T 12 ]! 39
40 1-D internal-multiple attenuation (two-reflector case)! 1! 2! A second-order! Pimary_1! Pimary_2! A second-order! Actual amplitude: T 01 R 2 (-R 1 )R 2 (-R 1 )R 2 T 10! Predicted amplitude: [T 01 R 2 (-R 1 )R 2 T 10 ][R 1 ][T 01 R 2 T 10 ]! =(-1T 01 T 10 )[T 01 R 2 (-R 1 )R 2 (-R 1 )R 2 T 10 ]! 40
41 1-D internal-multiple attenuation (two-reflector case)! 1! 2! Pimary_2! Pimary_1! Pimary_2! Pimary_1! Pimary_2! A second-order! Actual amplitude: T 01 R 2 (-R 1 )R 2 (-R 1 )R 2 T 10! Predicted amplitude: [T 01 R 2 T 10 ][R 1 ][T 01 R 2 T 10 ] [R 1 ][T 01 R 2 T 10 ]! =(T 01 T 10 ) 2 [T 01 R 2 (-R 1 )R 2 (-R 1 )R 2 T 10 ]! 41
42 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! To attenuate second-order s, more than one terms are needed (collective works are needed).! Internal multiple attenuation (two reflector example)! Summary! 42
43 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! Terms within each subseries work collectively to achieve the corresponding task! (e.g., free-surface multiple removal and attenuation)! Summary! 43
44 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! Summary! 44
45 A limitation of the leading-order algorithm! b1 = P + I (Two reflector example)! Higher-order s! e.g., second-order, third-order *! b 3 = (P + I)(P + I)(P + I) = PPP + PPI + IPP + IPI + III + PIP + PII + IIP Where P stands for primaries,! I stands for s. First-order s! * Zhang and Shaw (2010)! 45
46 A limitation of the leading-order algorithm! b1 = P + I (Two reflector example)! Higher-order s! e.g., second-order, third-order! b 3 = (P + I)(P + I)(P + I) = PPP + PPI + IPP + IPI + III + PIP + PII + IIP Where P stands for primaries,! I stands for s. First-order s! (three reflector example)! Higher-order s! + Spurious events! 46
47 A three reflector model! 1! 2! R 1! T 01! R 2! T 10! T 12! T 21! 3! Pimary_1! Pimary_2! A first-order! R 3! Pimary_3! 47
48 A limitation of the leading-order algorithm! P + I! P + I! P + I! z ikz ε ikz ikz 3 = 1 1 z + ε 1 b ( k ) dze b ( z ) dze b ( z ) dz e b ( z ) 48
49 A limitation of the leading-order algorithm! P I! P z ikz ε ikz ikz 3 = 1 1 z + ε 1 b ( k ) dze b ( z ) dze b ( z ) dz e b ( z ) P I P Primary-Internal multiple-primary! 49
50 A limitation of the leading-order algorithm! 1! 2! 3! Pirmary_3! An internal mutiple_212! Pirmary_3! A spurious event! Assumption: t 3 >(2t 2 -t 1 )! 50
51 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification When this limitation can be serious and needs higher-order modification! Terms within each subseries work collectively to achieve the corresponding task! (e.g., free-surface multiple removal and attenuation)! Summary! 51
52 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification and when this limitation can be serious and needs higher-order modification! Summary! 52
53 Higher-order terms introduced to deal with spurious prediction! P I! P z ikz ε ikz ikz 3 = 1 1 z + ε 1 b ( k ) dze b ( z ) dze b ( z ) dz e b ( z ) P I P 53
54 Higher-order terms introduced to deal with spurious prediction! P I! P z ikz ε ikz ikz 3 = 1 1 z + ε 1 b ( k ) dze b ( z ) dze b ( z ) dz e b ( z ) b 5 PIP (k) = dze ikz b 1 (z) d z e ik z b ( z ) ik d z e z b 3 1 ( z ) z ε z +ε P I pred P 54
55 Higher-order terms introduced to deal with spurious prediction! P I! P z ikz ε ikz ikz 3 = 1 1 z + ε 1 b ( k ) dze b ( z ) dze b ( z ) dz e b ( z ) b 5 PIP (k) = dze ikz b 1 (z) d z e ik z b ( z ) ik d z e z b 3 1 ( z ) z ε z +ε PIP b 5 is derived from!(g d 0V 1 G d 0V 3 G d 0V 1 G d 0) m.s. P I pred P 55
56 When the limitation is significant! When is this spurious prediction important?!! If N=2,!! No spurious prediction;! If N>=3 & Amplitude of primary Amplitude of s,! e.g., Off-shore Brazil, Middle East, Western Canada,!! Higher-order modification should be included.! 56
57 Higher-order terms introduced to deal with spurious prediction! Model parameters! V 1 = 1500m / s; ρ 1 = 1.0g / cm 3 V 2 = 1700m / s; ρ 2 = 1.8g / cm 3 Z 1 = 500m Z 2 = 900m V 3 = 1750m / s; ρ 3 = 1.0g / cm 3 Z 3 = 1530m V 4 = 5000m / s; ρ 4 = 4.0g / cm 3 57
58 Higher-order terms introduced to deal with spurious prediction! Traces P 1! P 1! P 2! P 3! 1 1! Z 1 = 500m Time (s) 2 P 2! I 212! 2! Z 2 = 900m x P 3! 3! Z 3 = 1530m 4 Input data! 58
59 Higher-order terms introduced to deal with spurious prediction! Traces P 1! I 212! 1 1! Z 1 = 500m Time (s) 2 P 2! I 212! 2! Z 2 = 900m x P 3! 3! Z 3 = 1530m 4 Input data! 59
60 Higher-order terms introduced to deal with spurious prediction! Traces Trace P 1! P 2! Time (s) 2 I 212! Time(s) 2 I 2-1-2! x P 3! I ! 4 4 Spurious event! (P 3 -I 212 -P 3 )! Input data! Leading-order prediction b 3! 60
61 Higher-order terms introduced to deal with spurious prediction! Trace Trace Time(s) 2 3 I 212! I 212! Time(s) Spurious event! (P 3 -I 212 -P 3 )! I 21212! I 312! 4 Higher-order modification! Leading-order prediction b 3! Higher-order modification b 5 PIP! 61
62 Key points & Outline! Introduction! ISS Leading-order attenuation algorithm! Two examples to help understanding! A limitation and solution (higherorder modification)! Simplest circumstance (a three reflector example) the limitation can occur! Higher-order modification and when this limitation can be serious and needs higher-order modification! Free-surface multiple removal! Internal multiple attenuation (two reflector example)! Summary! 62
63 Summary! 1. We analyze the effects of treating s as subevents in the ISS leading-order attenuation algorithm;! 2. When the current algorithm can produce spurious prediction;! 3. Higher-order modifications are identified within the ISS framework to accommodate the limitation of the current leading-order algorithm.! Number of reflectors! (N)! ISS attenuation algorithm! N=2! b 1 +b 3! N=3! b 1 +b 3 +b 5 PIP! N>=4 (Hong Liang s talk)! 63
64 Key points! ISS leading-order attenuation:!! Strengths (data driven):! Predicts all first-order s at all depths at once;! The prediction has correct time and an approximate, wellunderstood amplitude of first-order s;! A limitation & Solution:! A new higher-order attenuation algorithm is developed, retaining the strengths of the current algorithm and addressing one of its limitations.!! 64
65 65
66 Reference!! Araujo, F. V., A. B. Weglein, P. M. Carvalho, and R. H. Stolt, 1994, Inverse scattering series for multiple attenuation: An example with surface and s: SEG Technical Program Expanded Abstracts, !! Weglein, A. B., F. A. Gasparotto, P. M. Carvalho, and R. H. Stolt, 1997, An inversescattering series method for attenuating multiples in seismic reflection data:! Geophysics, 62, !! Zhang, H., and S. Shaw, 2010, 1-d analytical analysis of higher order internal multiples predicted via the inverse scattering series based algorithm: SEG Expanded Abstracts, 29, !!! 66
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