1 Fast 3D Target-Oriented Reverse Time Datuming Shuqian Dong University of Utah 2 Oct. 2008

2 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

3 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

4 Motivation Theory Numerical Tests Conclusions z (km) KM image x (km) Time (s) Common shot gather x (km) Motivation z (km) Velocity model x (km) km/s Defocusing: lower resolution, distorted image Multiples: image artifacts. Problem: KM: high frequency approximation. Reason: Solutions?

5 Solutions: Motivation Reverse time migration: solving two-way wave equation Reverse time migration: solving two-way wave equation Velocity model KM image RTM image Target-oriented reverse time datuming: Target-oriented reverse time datuming: solving two-way wave equation to bypass overburden solving two-way wave equation to bypass overburden Luo, 2002: target-oriented RTD Luo and Schuster, 2004: bottom-up strategy Motivation Theory Numerical Tests Conclusions

6 Motivation Motivation Theory Numerical Tests Conclusions RTD + Kirchhoff = accurate + cheap RTD + Kirchhoff = accurate + cheap RTD can reduce defocusing effects RTD can reduce defocusing effects RTD Complex structures cause defocusing effects Complex structures cause defocusing effects RTM is computationally expensive RTM is computationally expensive

7 Bottom-up strategy: computational efficiency Bottom-up strategy: computational efficiency Redatumed data can be used for least squares Redatumed data can be used for least squares migration and migration velocity analysis (MVA) migration and migration velocity analysis (MVA) Reduce defocusing effects for subsalt imaging Reduce defocusing effects for subsalt imaging Closer to the target: better resolution Closer to the target: better resolution Motivation Theory Numerical Tests Conclusions Motivation

8 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

9 d(s|r) R S x’ x’’ Reverse time datuming Theory Motivation Theory Numerical Tests Conclusions

10 S x’ x’’ d(s|x”)=g*(r|x”)d(s|r) d(s|x’’) Reverse time datuming R Theory Motivation Theory Numerical Tests Conclusions

11 x’ x’’ d(s|x”)=g*(r|x”)d(s|r) d(x’|x’’) d(x’|x”)=g*(s|x’) d(s|x”) Reverse time datuming R S Theory Motivation Theory Numerical Tests Conclusions

12 Theory Motivation Theory Numerical Tests Conclusions Calculate Green ’ s functions Real source number on surface: 10 Virtual source number on datum: 3 VSP (source on surface) Green ’ s functions: 10

13 Calculate Green ’ s functions Theory Motivation Theory Numerical Tests Conclusions Real source number on surface: 10 Virtual source number on datum: 3 VSP (source on surface) Green ’ s functions: 10 RVSP (source on datum) Green ’ s functions: 3 Reciprocity: RVSP=VSP

14 FD: Compute RVSP Green’s functions Original data: FFT: time domain =>frequency domain Crosscorrelation: Green’s functions with original data Workflow Motivation Theory Numerical Tests Conclusions Reciprocity: RVSP =>VSP Green’s functions: FFT: time domain => frequency domain IFFT: frequency domain => time domain Redatumed data

15 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

16 Motivation Theory Numerical Tests Conclusions z (km) Velocity model x (km) km/s Time (s) 04.0 RVSP Green’s function x (km) D SEG/EAGE Test Time (s) 04.0 True CSG at datum x (km) Time (s) 04.0 Redatumed CSG x (km) 0 8.0

17 z (km) Velocity model x (km) km/s z (km) KM image x (km) z (km) RTM image x (km) z (km) 02.0 KM of redatumed data x (km) Motivation Theory Numerical Tests Conclusions 2D SEG/EAGE Test

18 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

19 3D SEG/EAGE test Z (km) 02.0 y (km) 20 x (km) km/s Velocity model SSP geometry: 1700 shots 1700 receivers Datum depth: 1.5 km RVSP Green’s functions: 850 shots 1700 receivers Motivation Theory Numerical Tests Conclusions

20 3D SEG/EAGE test y (km) Time (s) Original CSG Motivation Theory Numerical Tests Conclusions y (km) Time (s) RVSP Green’s function y (km) Time (s) True CSG at datum y (km) Time (s) Redatumed CSG

21 Z (km) y (km) 2 0 x (km) KM of original data 3D SEG/EAGE test Z (km) y (km) 2 0 x (km) KM of RTD data Motivation Theory Numerical Tests Conclusions

22 x (km) z (km) Velocity model x (km) z (km) KM of original data x (km) z (km) KM of redatumed data ( Inline No. 41 ) Motivation Theory Numerical Tests Conclusions 3D SEG/EAGE test

23 x (km) 03.5 z (km) 02.0 Velocity model x (km) 03.5 z (km) 02.0 KM of original data x (km) 03.5 z (km) 02.0 KM of redatumed data ( Inline No. 101 ) Motivation Theory Numerical Tests Conclusions 3D SEG/EAGE test

24 y (km) 02.0 z (km) 02.0 Velocity model y (km) 02.0 z (km) 02.0 KM of original data y (km) 02.0 z (km) 02.0 KM of redatumed data ( Crossline No. 161 ) Motivation Theory Numerical Tests Conclusions 3D SEG/EAGE test

25 y (km) 02.0 z (km) 02.0 Velocity model y (km) 02.0 z (km) 02.0 KM of original data y (km) 02.0 z (km) 02.0 KM of redatumed data ( Crossline No. 201 ) Motivation Theory Numerical Tests Conclusions 3D SEG/EAGE test

26 x (km) 03.5 y (km) 02.0 Velocity model x (km) 03.5 y (km) 02.0 KM of original data x (km) 03.5 y (km) 02.0 KM of redatumed data ( depth: z=1.4 km ) Motivation Theory Numerical Tests Conclusions 3D SEG/EAGE test

27 x (km) 03.5 y (km) 02.0 Velocity model x (km) 03.5 y (km) 02.0 KM of original data x (km) 03.5 y (km) 02.0 KM of redatumed data ( depth: z=1.5 km ) Motivation Theory Numerical Tests Conclusions 3D SEG/EAGE test

28 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

29 Z (km) y (km) x (km) 12 0 Interval velocity model 3D Field Data Test OBC geometry: 50,000 shots 180 receivers per shot Datum depth: 1.5 km RVSP Green’s functions: 5,000 shots 180 receivers per shot km/s Motivation Theory Numerical Tests Conclusions

30 3D Field Data Test y (km) Time (s) Original CSG y (km) Time (s) Redatumed CSG Motivation Theory Numerical Tests Conclusions

31 KM of RTD data Z (km) 0 8 y (km) 5 0 x (km) 12 0 KM of original data Z (km) 0 8 y (km) 5 0 x (km) 12 0 KM of redatumed data Motivation Theory Numerical Tests Conclusions 3D Field Data Test

32 X (km) 0 12 Z (km) 08.0 KM of original data KM of RTD data ( Inline No. 21 ) X (km) 0 12 Z (km) 08.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test

33 ( Inline No. 41 ) X (km) 0 12 Z (km) 08.0 KM of RTD data X (km) 0 12 Z (km) 08.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

34 ( Inline No. 61 ) X (km) 0 12 Z (km) 08.0 KM of RTD data X (km) 0 12 Z (km) 08.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

35 ( Crossline No. 41 ) Y (km) Z (km) 08.0 KM of RTD data Y (km) Z (km) 08.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

36 ( Crossline No. 61 ) Y (km) Z (km) 08.0 KM of RTD data Y (km) Z (km) 08.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

37 ( Crossline No. 81 ) Y (km) Z (km) 08.0 KM of RTD data Y (km) Z (km) 08.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

38 ( Depth 2.0 km ) X (km) 0 12 Y (km) 05.0 KM of RTD data X (km) 0 12 Y (km) 05.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

39 ( Depth 2.5 km ) X (km) 0 12 Y (km) 05.0 KM of RTD data X (km) 0 12 Y (km) 05.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

40 ( Depth 4.0 km ) X (km) 0 12 Y (km) 05.0 KM of RTD data X (km) 0 12 Y (km) 05.0 Motivation Theory Numerical Tests Conclusions 3D Field Data Test KM of original data

41 RTM (CPU-hours) RTD (CPU-hours) Speed up 2D SEG/EAGE test D SEG/EAGE test 16,000 (estimated) 1,8669 3D filed data test5,000,000 (estimated)52, Computational Costs Motivation Theory Numerical Tests Conclusions

42 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests 2-D SEG/EAGE salt model 2-D SEG/EAGE salt model 3-D SEG/EAGE salt model 3-D field data Motivation Theory Numerical Tests Conclusions

43 KM of RTD achieved image quality comparable to RTM at much lower cost. Motivation Theory Numerical Tests Conclusions 2-D numerical test 2-D numerical test 3-D RTD is implemented for synthetic and GOM data at acceptable computational cost; 3-D numerical test 3-D numerical test Apparent improvements in mage quality are achieved compared to KM image of original data. Future application Future application Subsalt least suqares migration and migration velocity analysis Conclusions

44 Acknowledgements Dr. Gerard Schuster and my committee members: Dr. Michael Zhdanov, Dr. Richard D. Jarrard for their advice and constructive criticism; UTAM friends: –Dr. Xiang Xiao, Weiping Cao, and Chaiwoot Boonyasiriwat for their help on my thesis research; –Ge Zhang for his experiences on field data processing; –Dr. Sherif Hanafy, Shengdong Liu, Naoshi Aoki and all other UTAM members for their support in my life and work; CHPC for the computation support.

45 Thanks!

46 Motivation Theory Numerical Tests Conclusions z (km) Velocity model x (km) km/s z (km) KM image x (km) Time (s) Common shot gather x (km) Motivation z (km) RTM image x (km) 0 8.0

47 d(s|r) R S x’ x’’ Traditional reverse time datuming Theory Motivation Theory Numerical Tests Conclusions

48 S x’ x’’ d(s|x”)=g*(r|x”)d(s|r) d(s|x’’) Reverse time Datuming R Theory Motivation Theory Numerical Tests Conclusions

49 x’ x’’ d(s|x”)=g*(r|x”)d(s|r) d(x’|x’’) d(x’|x”)=g*(s|x’) d(s|x”) Reverse time Datuming R S Theory Motivation Theory Numerical Tests Conclusions

50 Target-oriented RTD (Luo, 2006) Theory Motivation Theory Numerical Tests Conclusions

51 Target-oriented RTD (Luo, 2006) g(s|x’)g(r|x”)* d(s|r) = d(x’|x’’) Theory Motivation Theory Numerical Tests Conclusions

52 Target-oriented RTD (Luo, 2006) Theory Motivation Theory Numerical Tests Conclusions g(s|x’)g(r|x")* d(s|r) = d(x’|x’’)

53 Compute VSP Green’s functions in time domain Original data: time domain to frequency domain Green’s functions: Time domain to frequency domain Reverse time datum for different frequency Workflow Sum over frequency Redatumed data: frequency domain to time domain Motivation Theory Numerical Tests Conclusions

54 FD: Compute RVSP Green’s functions Original data: FFT: time domain =>frequency domain Crosscorrelation: Green’s functions with original data Workflow Motivation Theory Numerical Tests Conclusions Reciprocity: RVSP =>VSP Green’s functions: FFT: time domain => frequency domain Sum over frequency IFFT: frequency domain => time domain Redatumed data

55 Conclusions Bottom-up strategy: computational efficiency Bottom-up strategy: computational efficiency Redatumed data can be used by LSM & MVA Redatumed data can be used by LSM & MVA Reduce defocusing effects for subsalt imaging Reduce defocusing effects for subsalt imaging Closer to the target: better resolution Closer to the target: better resolution Benefits: Limitations: Extra I/O for accessing Green’s functionsExtra I/O for accessing Green’s functions Motivation Theory Numerical Tests Conclusions