1. 1 OBS->OBS Extrapolation Interferometry Shuqian Dong and Sherif Hanafy Coarse OBS Virtual SWP

2. 2 3x3 Classification Matrix SSPVSPSWP VSP SSP SWP SSPSSPSSPSSPVSPSWP VSPVSPVSP SWPSWPSWP VSP SWP SWP VSP SSP SSP

3. 3 Seabed Reflectors OBS B A x Natural Green’s Function Seabed Reflectors SWP B A x Model based Green’s Function Seabed Reflectors OBS B A x Extrapolated Data OBS Extrapolation

4. 4 SIGSBEE 2B velocity model X (km) Z (km) 0 4.5 0 6.0 OBS Extrapolation 200 shots dx = 30 m 400 receivers aperture: 3 km dx = 7.62 m

5. 5 OBS Extrapolation Time (s) 0.8 4.0 X (km) 0 6.0 Original CSG Time (s) 0.8 4.0 X (km) 0 6.0 Extrapolated CSG Time (s) 0.8 4.0 X (km) 0 6.0 Real CSG We can improve the results by a matching filter but we do not have enough time

6. 6 Migration of narrow aperture OBS data Z (km) 04.5 X (km) 06.0 OBS Extrapolation 200 shots dx = 30 m 400 receivers aperture: 3 km dx = 7.62 m

7. 7 Migration of extrapolated OBS data Z (km) 04.5 X (km) 06.0 OBS Extrapolation Shows that you only recover part of the Green’s function Shows that you recover all of the Green’s function here

8. 8 Migration of extrapolated OBS data Z (km) 04.5 X (km) 06.0 OBS Extrapolation Shows that you only recover part of the Green’s function Shows that you recover all of the Green’s function here

9. 9 Velocity model Velocity model Z (km) 04.5 X (km) 06.0 OBS Extrapolation

10. 10 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests OBS interpolation OBS interpolation OBS extrapolation OBS extrapolation SSP extrapolation SSP extrapolation

11. 11 Seabed Reflectors SSP BA x Seabed Reflectors BA x Natural Green’s Function Seabed Reflectors SSP BA x Extrapolated Data Model based Green’s Function Natural, SSP Extrapolation

12. 12 A x SSP->SSP Reciprocity Correlation Equation B S Free surface G(A|x)=G(B|x)=0 Water-layer Green’s function = G(B|x) * G(A|x) S+S 0 OBS { G(B|A) – G(A|B) OBS { 0 SWP data 0 2ik Sea-floor

13. 13 SIGSBEE 2B velocity model Z (km) 04.5 X (km) 06.0 SSP Extrapolation 200 shots dx = 30 m 300 receivers aperture: 2.4 km dx = 7.62 m

14. 14 Time (s) 0.8 4.0 X (km) 0 6.0 Original CSG Time (s) 0.8 4.0 X (km) 0 6.0 Extrapolated CSG Time (s) 0.8 4.0 X (km) 0 6.0 Real CSG SSP Extrapolation We can improve the results by a matching filter but we do not have enough time

15. 15 Migration of extrapolated SSP data Z (km) 04.5 X (km) 06.0 SSP Extrapolation 200 shots dx = 30 m 300 receivers aperture: 2.4 km dx = 7.62 m

16. 16 Migration of extrapolated SSP data Z (km) 04.5 X (km) 06.0 SSP Extrapolation

17. 17 Velocity model Velocity model Z (km) 04.5 X (km) 06.0 SSP Extrapolation

18. 18 Field Data Test Mahogony OBS Data 800 Shots beneath free surface 180 receivers on sea floor Sea floor depth: about 120m Shots and receivers interval: 25 m Time sample interval: 4ms Z (m) 0 120 X (m) 0 20000 Acquisition geometry demenstration 180 receivers dx =25 m 800 shots dx = 25 m Sea floor

19. 19 OBS Extrapolation Time (s) 03.0 Original CSG X (m) 0 1200250 Time (s) 03.0 Virtual CSG X (m) 0 1200250 virtual tracesreal traces

20. 20 OBS Extrapolation Time (s) 03.0 Virtual CSG by 1 iteration X (m) 0 1200250 Time (s) 03.0 Virtual CSG by 5 iterations X (m) 0 1200250

21. 21 Time (s) 03.0 Original CSG X (m) 0 1200500 Time (s) 03.0 Virtual CSG X (m) 0 1200500 virtual traces real traces OBS Extrapolation

22. 22 OBS Extrapolation Virtual CSG by 1 iteration Virtual CSG by 5 iterations X (m) 0 1200500 Time (s) 03.0 X (m) 0 1200500 Time (s) 03.0

23. 23 3D Extrapolation Input: sparse OBS data Recording spread Recording spread x: 500 m to 3,000 m x: 500 m to 3,000 m y: 0 to 3,000 m Goal: Fill the near-offset gap 500 m 3000 m 0 X 0 Y

24. 24 3D Extrapolation Extrapolated Data for a 2D Line at X =400 m 0 3.0 Time (s) 0 2400 Y (m)

25. 25 3D Extrapolation Real Data for the 2D Line X = 400 m 0 3.0 Time (s) 0 2400 Y (m)

26. 26 3D Extrapolation Extrapolated Data for the 2D Line X = 300 m 0 3.0 Time (s) 0 2400 Y (m)

27. 27 3D Extrapolation Real Data for the 2D Line X = 300 m 0 3.0 Time (s) 0 2400 Y (m)

28. 28 3D Extrapolation Extrapolation Result for the 2D Line Y=1000 m 0 3.0 Time (s) 0 1400 Y (m) Extra p. Actual data 200

29. 29 3D Extrapolation Real Data for the 2D Line Y = 1000 m 0 3.0 Time (s) 0 1400 Y (m) 200

30. 30 Future Work Field data test 3D test Conclusions Helpful for OBS and SSP survey design Sparse OBS Dense OBS Narrow aperture Wide aperture Helpful for survey design in environmentally sensitive areas: receivers in town, sources out of town, e.g., Dhahran, Saudi Arabia Problems: attenuation ?