1. Interpolating and Extrapolating Marine Data with Interferometry
Sherif M. Hanafy
January 2010

2. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

3. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

4. Problem
In marine surveys the receiver array could be irregular, sparsely distributed and contain gaps
Solution: Use interferometric interpolation and extrapolation

5. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

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

7. Generate GF for Water Multiples Interpolate/Extrapolate Missing Data
Workflow
G(x|B)
Input Data
Time (s)
3.0
X (km)
4.5
Water Layer Thickness
Input Field Data
G(x|A)
Sea bed
Ocean Surface
Generate GF for Water Multiples
Unfiltered Virtual
Time (s)
3.0
X (km)
4.5
Interpolate/Extrapolate Missing Data
Filtered Virtual
Get Virtual CSG
Time (s)
3.0
X (km)
4.5
G(B|A)
Matching Filter N
Max. Itr (MF) Y N
Max Iteration Y
Final CSG

8. Local Matching Filter dtrue dvirtual dtrue = dvirtual * f Time (s) 3.0
3.0
X (km)
4.5
Time (s)
3.0
X (km)
4.5
dtrue = dvirtual
* f

9. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

10. Numerical Results
3D velocity model is used to test the interpolation approach
3000 x 3000 x 1400 m3 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 depth of 750 m
3 km
1.4 km
Source

11. Velocity Model Sea bed Reflector # 1 Reflector # 2 Velocity (m/s) 1500
2400

12. 3D Example Input Goal 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
Dense geometry
Sparse geometry

13. Original CSG, 300 traces, dx = 10 m
SSP Data Line # 180
Line # 180
Original CSG, 300 traces, dx = 10 m
Sparse CSG, 100 traces, dx = 30 m
Time (s)
Time (s) 5 5
X (m)
X (m)
3000
3000

14. Iterations: 1 interpolation and 8 MF
SSP Virtual Data
Line # 180
Iterations: 1 interpolation and 8 MF 5
Time (s)
3000
X (m)
Sparse CSG, 100 traces, dx = 30 m 5
Time (s)
3000
X (m)
Virtual CSG, 300 trace, dx = 10 m

15. Iterations: 3 interpolation and 8 MF/interpolation
SSP Virtual Data
Line # 180
Iterations: 3 interpolation and 8 MF/interpolation 5
Time (s)
3000
X (m)
Sparse CSG, 100 traces, dx = 30 m
Original CSG, 300 trace, dx = 10 m
Time (s) 5
X (m)
3000

16. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

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

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

19. SEG/EAGE Model – Input Data
Streamer offset = 150 m
No. of receiver = 310 8
Time (s)
Streamer 2 1 2 1
Scale
2 km

20. SEG/EAGE Model – Virtual Data
Streamer offset = 50 m
No. of receiver = 619 8
Time (s)
Streamer 2 1 2’ 1’ 2 1 2’ 1’
Scale
2 km

21. SEG/EAGE Model – Real Data
Streamer offset = 50 m
No. of receiver = 619 8
Time (s)
Streamer 4 1 3 2
Scale
2 km

22. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

23. Problem
In marine surveys the interval between some shots and recording array is large.
Solution: Use interferometric extrapolation to fill this gap

24. Local Matching Filter dtrue dvirtual dtrue = dvirtual * f Time (s) 3.0
3.0
X (km)
4.5
Time (s)
3.0
X (km)
4.5
dtrue = dvirtual
* f

25. Matching Filter Apply matching filter Source Get matching filter
Ocean bottom cable
Geology
Geology

26. Velocity Model

27. 2D Extrapolation Example
Time (s) 12 11
X (km)
CSG with true near offset traces
Time (s) 12 11
X (km)
CSG with 2 km gap at the near offset
Time (s) 12 11
X (km)
CSG with virtual traces

28. Virtual CSG with 1 iteration of MF Virtual CSG with 5 iterations of MF
2D Extrapolation Example
Time (s) 12 11
X (km)
Virtual CSG with 1 iteration of MF
Time (s) 12 11
X (km)
Virtual CSG with 5 iterations of MF
Time (s) 12 11
X (km)
True CSG

29. Virtual CSG with 1 iteration of MF Virtual CSG with 5 iterations of MF
2D Extrapolation Example
Time (s) 6 11
X (km)
Virtual CSG with 1 iteration of MF
Time (s) 6 11
X (km)
Virtual CSG with 5 iterations of MF
Time (s) 6 11
X (km)
True CSG

30. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

31. RTM image of the input data
Reverse Time Migration
RTM image of the input data
Z (km) 3 11

32. RTM image of the extrapolated data RTM image of the true data
Reverse Time Migration
RTM image of the extrapolated data
Z (km) 3 11
X (km)
RTM image of the true data
Z (km) 3 11
X (km)

33. Waveform inversion of the extrapolated data
True velocity model
Z (km) 3 11
X (km)
Waveform inversion of the extrapolated data
Z (km) 3 11
X (km)

34. Outline Problem: Missing and sparse traces
Theory: Interferometric interpolation and extrapolation
Numerical results:
Interpolation
3D layered velocity model
3D SEG/EAGE model
Extrapolation
2D SEG/EAGE model
Reverse time migration and waveform inversion
Conclusions and future work

35. Conclusions Interpolation Extrapolation
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.
Extrapolation
2D OBS extrapolation shows a promising results.

36. Future Work More work on the extrapolation (2D and 3D)
Use down-going field and not total field
Test on field data

37. We would like to thank the UTAM 2009 sponsors for their support.
Acknowledgement
We would like to thank the UTAM 2009 sponsors for their support.
Thank You