1. Interferometric Interpolation of 3D SSP Data Sherif M. Hanafy Weiping Cao Gerard T. Schuster October 2009

2. Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

3. Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

4. Problem In marine surveys, receiver interval could be large (especially in cross line direction) Solution: Use interferometric interpolation Sparse geometry Dense geometry

5. Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

7. Sea bed Ocean Surface Reflectors Sea bed Ocean Surface Theory G(x|A) Natural Green’s function G(x|B) Model based data x A x B A Virtual source G(B|A) Interpolated data Sea bed Reflectors Ocean Surface x A B Virtual receiver SSP Data h h Water Velocity (V) SSP Data

8. Workflow Input Field DataWater Layer Thickness Generate GF for Water Multiples Interpolate/Extrapolate M issing D ata Max. Itr (MF ) Get Virtual CSG Max Iteration Final CSG N Matching Filter N Y Y Time (s) 03.0 X (km) 04.5 Sea bed Ocean Surface Time (s) 03.0 X (km) 04.5 Time (s) 03.0 X (km) 04.5 Input Data Unfiltered Virtual Filtered Virtual G(x|B) G(B|A) G(x|A)

9. Time (s) 03.0 X (km) 04.5 Time (s) 03.0 X (km) 04.5 Local Matching Filter f (t,x 0 )d Virt (t,x 0 )d Real (t,x 0 )≈*

10. Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Future work

11. Numerical Results 3D velocity model is used to test the interpolation approach 3000 x 3000 x 1400 m 3 in x, y, and z directions Source is at (10,10,30) (x,y,z) 300 by 300 receiver points are used with dx=dy=10 m Sea bottom is flat @ depth of 750 m 3 km 1.4 km Source

12. Velocity Model Sea bed Reflector # 1 Reflector # 2 Velocity (m/s)15002400

13. 2D Example Line # 1 Source Input 60 Traces Trace interval = 50 m Goal 300 Traces Trace interval = 10 m Sparse geometryDense geometry

14. 2D Test 0 5 Time (s) 03000 X (m) Original CSG, 300 trace, dx = 10 m Keep every 4 th trace Line # 1 Source 0 5 Time (s) 0 3000 X (m) Sparse CSG, 60 trace, dx = 50 m

15. 2D Test 0 5 Time (s) 03000 X (m) Virtual CSG before matching filter, 300 trace, dx = 10 m Virtual CSG after matching filter, 300 trace, dx = 10 m 0 5 Time (s) 03000 X (m) Line # 1 Source 0 5 Time (s) 03000 X (m) Original CSG, 300 trace, dx = 10 m

16. 3D Example Input 60 crossline Crossline interval = 50 m 100 traces/line Trace interval = 30 m Total number of traces = 6000 Goal 300 crossline Crossline interval = 10m 300 traces/line Trace interval = 10 m Total number of traces = 90,000 Sparse geometry Dense geometry

17. SSP Data Line # 180 0 5 Time (s) 03000 X (m) Original CSG, 300 trace, dx = 10 m 0 5 Time (s) 03000 X (m) Sparse CSG, 60 trace, dx = 50 m Line # 180

18. SSP Virtual Data 0 5 Time (s) 03000 X (m) Virtual CSG, 300 trace, dx = 10 m 0 5 Time (s) 03000 X (m) Original CSG, 300 trace, dx = 10 m Iterations: 1 interpolation and 8 MF Line # 180

19. SSP Virtual Data 0 5 Time (s) 03000 X (m) 0 5 Time (s) 03000 X (m) Original CSG, 300 trace, dx = 10 m Iterations: 3 interpolation and 8 MF/interpolation Original CSG, 300 trace, dx = 10 m Line # 180

20. Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

21. SEG/EAGE Velocity Model Velocity (m/s)1500 4500

22. Acquisition Parameters Input –12 Streamers –Crossline offset is 150 m –Inline offset is 25 m –310 receivers/streamer –Total number of receivers 3720 Goal –34 Streamers –Crossline offset is 50 m –Inline offset is 12.5 m –619 receivers/streamer –Total number of receivers 21046 Sparse geometry Dense geometry

23. Scale 2 km 0 21 0 8 Time (s) Streamer 21 SEG/EAGE Model – Input Data

24. Scale 2 km 0 21 2’1’ 0 8 Time (s) Streamer 212’1’ SEG/EAGE Model – Virtual Data

25. Scale 2 km 0 SEG/EAGE Model – Real Data 0 8 Time (s) Streamer 4132

26. True-Virtual Traces Comparison

27. Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

28. Conclusions 3D marine SSP data can be interpolated with interferometry. Proposed approach is successfully tested on two synthetic models. Number of receivers can be increased 8 to 10 times by interferometry.

29. Limitation and Advantage Limitation Non-aliased data are required for better interpolation Advantage Irregular geometry can be used to generate more dense and regular geometry

30. Future Work Extrapolation of the data Test on field data

31. Acknowledgement We would like to thank the UTAM 2008 sponsors for their support. Thank You

32. Input Field DataWater Layer Thickness Generate GF for Water Multiples Interpolate/Extrapolate M issing D ata Max. Itr (MF ) Get Virtual CSG Max Iteration Final CSG N Matching Filter N Y Y