1 Interferometric Interpolation and Extrapolation of Sparse OBS and SSP Data Shuqian Dong and G.T.Schuster

2 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests OBS interpolation OBS interpolation OBS extrapolation OBS extrapolation SSP extrapolation SSP extrapolation

3 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests OBS interpolation OBS interpolation OBS extrapolation OBS extrapolation SSP extrapolation SSP extrapolation

4 MotivationAnswer: Interfer. predict. + matching filter Questions: We have: Sparse OBS ? Narrow aperture OBS ? Wide aperture OBS Narrow aperture SSP ? Wide aperture SSP SSP: Interferometric transform VSP Narrow aperture wide aperture

5 Seabed Reflectors Seabed Reflectors Seabed Reflectors OBS SWP OBS B A x B A x B A x Theory Sparse OBS interferometric interpolation Sparse OBS interferometric interpolation Natural Green’s Function Model based Green’s Function Interpolated data

6 Z (km) 03.0 X (km) Density model Z (km) 03.0 X (km) Velocity model km/s kg/m3 Sparse OBS Interpolation

7 Z (km) 03.0 X (km) Density model Z (km) 03.0 X (km) Velocity model km/s kg/m3 Sparse OBS Interpolation 300 shots dx = 16 m 600 receivers dx = 8 m

8 X (km) Time (s) 03.0 Original CSG Sparse OBS Interpolation Time (s) X (km) Virtual CSG dx = 80 m Total traces: 60 dx = 8 m

9 X (km) Time (s) 03.0 Original CSG Sparse OBS Interpolation Time (s) X (km) Virtual CSG dx = 80 m Total traces: 60 dx = 8 m * f (t,x ) d real d virtual0 0 0 x0 x0 * f d (t,x’ ) real d (t,x’)virtual0

10 Sparse OBS Interpolation Time (s) X (km) Virtual CSG Time (s) X (km) Real CSG Time (s) X (km) Filtered virtual CSG

11 X (km) Time (s) 03.0 Original CSG X (km) Time (s) 03.0 Virtual CSG X (km) Time (s) 03.0 Real CSG X (km) 04.5 Time (s) 03.0 Filtered virtual CSG dx = 160 m Total traces: 30 dx = 8 m Total traces: 600 dx = 8 m Total traces: 600 dx = 8 m Total traces: 600 Sparse OBS Interpolation

12 X (km) Time (s) 03.0 Original CSG X (km) Time (s) 03.0 Virtual CSG X (km) Time (s) 03.0 Real CSG X (km) 04.5 Time (s) 03.0 Filtered virtual CSG dx = 320 m Total traces: 30 dx = 8 m Total traces: 600 dx = 8 m Total traces: 600 dx = 8 m Total traces: 600 Sparse OBS Interpolation

13 Migration of interpolated OBS data Z (km) Migration of sparse OBS data X (km) Z (km) X (km) shots dx = 16 m 6 receivers dx = 800 m Sparse OBS Interpolation

14 SIGSBEE 2B velocity model X (km) Z (km) Sparse OBS Interpolation

15 Velocity model Z (km) 04.5 X (km) shots dx = 30 m 800 receivers dx = 7.62 m Sparse OBS Interpolation

16 X (km) 06.0 Time (s) 03.0 Original CSG X (km) 06.0 Time (s) 03.0 Virtual CSG X (km) 06.0 Time (s) 03.0 Real CSG X (km) 06.0 Time (s) 03.0 Filtered virtual CSG dx = 76.2 m traces: 80 dx = 7.62 m traces: 800 dx = 7.62 m traces: 800 dx = 7.62 m traces: 800 Sparse OBS Interpolation

17 X (km) 06.0 Time (s) 03.0 Original CSG X (km) 06.0 Time (s) 03.0 Virtual CSG X (km) 06.0 Time (s) 03.0 Real CSG X (km) 06.0 Time (s) 03.0 Filtered virtual CSG dx = 300 m traces: 20 dx = 7.62 m traces: 800 dx = 7.62 m traces: 800 dx = 7.62 m traces: 800 Sparse OBS Interpolation

18 Z (km) 04.5 X (km) 06.0 Migration of sparse OBS data 20 receivers dx =300 m 200 shots dx = 30 m Sparse OBS Interpolation

19 Migration of interpolated OBS data Z (km) 04.5 X (km) 06.0

20 Z (km) 04.5 X (km) 06.0 Velocity model Velocity model

21 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests OBS interpolation OBS interpolation OBS extrapolation OBS extrapolation SSP extrapolation SSP extrapolation

22 Seabed Reflectors Seabed Reflectors Seabed Reflectors OBS SWP OBS B A x B A x B A x Natural Green’s Function Model based Green’s Function Etrapolated data OBS Extrapolation

23 SIGSBEE 2B velocity model X (km) Z (km) OBS Extrapolation 200 shots dx = 30 m 400 receivers apertue: 3 km dx = 7.62 m

24 OBS Extrapolation Time (s) X (km) 06.0 Original CSG Time (s) X (km) 06.0 Extrapolated CSG Time (s) X (km) 06.0 Real CSG

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

26 Migration of extrapolated OBS data Z (km) 04.5 X (km) 06.0 OBS Extrapolation

27 Velocity model Velocity model Z (km) 04.5 X (km) 06.0 OBS Extrapolation

28 Outline Motivation Motivation Theory Theory Conclusions Conclusions Numerical Tests Numerical Tests OBS interpolation OBS interpolation OBS extrapolation OBS extrapolation SSP extrapolation SSP extrapolation

29 Seabed Reflectors SSP BA x Seabed Reflectors BA x Seabed Reflectors BA x Natural Green’s Function Model based Green’s Function Etrapolated data Natural or SSP Extrapolation

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

31 Time (s) X (km) 06.0 Original CSG Time (s) X (km) 06.0 Extrapolated CSG Time (s) X (km) 06.0 Real CSG SSP Extrapolation

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

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

34 Velocity model Velocity model Z (km) 04.5 X (km) 06.0 SSP Extrapolation

35 Future Work Field data test. 3D test Conclusion Helpful for OBS and SSP survey design Sparse OBS Narrow aperture Wide aperture

36 We thank Utah Tomography and Modeling/Migration Consortium sponsors for their financial support Acknowledgements

37 Thanks