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Interferometric Interpolation of 3D OBS Data

Interferometric Interpolation of 3D OBS Data. Weiping Cao, University of Utah Oct. 29 2009. Outline. Problems: Missing and sparse traces Methodology: Interferometric interpolation Numerical results: 3D layered model Anti-aliasing condition for interferometric redatuming Conclusions.

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Interferometric Interpolation of 3D OBS Data

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  1. Interferometric Interpolation of 3D OBS Data Weiping Cao, University of Utah Oct. 29 2009

  2. Outline • Problems: Missing and sparse traces • Methodology: Interferometric interpolation • Numerical results: • 3D layered model • Anti-aliasing condition for interferometric redatuming • Conclusions

  3. Outline • Problems: Missing and sparse traces • Methodology : Interferometric interpolation • Numerical results: • 3D layered model • Anti-aliasing condition for interferometric redatuming • Conclusions

  4. Water Water Motivations Problem: Receiver interval of OBS data is (sometimes) too large Solution: Interferometric interpolation • Benefits of Interferometric Interpolation: • Accuracy (wave-equation based scheme) • No sedimentary velocity needed

  5. Outline • Problems: Missing and sparse traces • Methodology: Interferometric interpolation • Numerical results: • 3D layered velocity model • Anti-aliasing condition for interferometric redatuming • Conclusions

  6. Ocean Surface Ocean Surface Ocean Surface A A A Seabed Seabed Seabed x x B x Reflectors Reflectors Interferometric Interpolation of OBS Data B G(x|A) Natural OBS Green’s Function Go(x|B)* Model based Green’s Function G(B|A) Interpolated OBS Data Dong S. and G. T. Schuster, 2008, Interferometric interpolation and extrapolation of sparse OBS and SSP data: UTAM 2007 annual meeting, 39 – 48.

  7. Interferometric Interpolation of OBS Data 2-state reciprocity equation: Up-down separation, far-field approximation Water-layer reflection OBS reflection Artifacts? (up-down separation, far-field approx., limited aperture, wavelet, sampling… Matching filter!

  8. 0 Ocean Surface 0 Seabed Time (s) x 0 Time (s) 3.0 0 X (km) 4.5 Time (s) 3.0 0 X (km) 4.5 3.0 0 X (km) 4.5 Workflow Input Data Input Field Data Water Layer Model Generate GF for Water Multiples Unfiltered Virtual Interpolate Missing Data Filtered Virtual Get Virtual CSG Matching Filter N Max. Itr (MF) Y N Max Itr Intr/Extr Y Final CSG

  9. Outline • Problems: Missing and sparse traces • Methodology: Interferometric interpolation • Numerical results: • 3D layered velocity model • Anti-aliasing condition for interferometric redatuming • Conclusions

  10. 3 km Source 3 km 1.4 km Numerical Results • 3D velocity model size: 3000 x 3000 x 1400 m3 • Source located at (10 m,10 m, 30 m) • 300 by 300 receivers dx = dy = 10 m • Sea bed is flat at a depth of 750 m

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

  12. Synthetic Data 0 0 CSG in the x direction: y=1000 m, dx = 10 m CSG in the y direction: x=1000 m, dx = 10 m Time (s) Time (s) 5 5 X (m) Y (m) 0 3000 0 3000 Line y=1000m

  13. Input: sparse OBS data • Recording interval • 50 m × 50 m ( =104 m ) • Total number of receivers: • 60 ×60 = 3, 600 3D Interpolation • Goal: dense OBS data • Recording interval: • 10 m × 10 m • Total number of receivers: • 300 × 300 = 90, 000

  14. Sparse Data 0 Decimated CSG in the Y direction: X = 1000 m, dx = 50 m Time (s) 5 Y (m) 0 3000 Line y=1000m 0 Decimated CSG in the X direction: Y = 1000 m , dx = 50 m Time (s) 5 X (m) 0 3000

  15. Interpolation Results: X direction 0 Virtual dense data, dx = 10 m Time (s) 5 Y (m) 0 3000 Line y=1000m 0 Decimated CSG in the X direction: Y =1000 m , dx = 50 m Time (s) 5 X (m) 0 3000

  16. 0 0 Time (s) Time (s) 3.0 3.0 0 X (km) 4.5 0 X (km) 4.5 Local Matching Filter

  17. Interpolation Results: X direction Line y=1000m 0 0 Decimated CSG in the X direction: Y =1000 m , dx = 50 m Filtered virtual data, dx = 10 m Time (s) Time (s) 5 5 X (m) X (m) 0 3000 0 3000

  18. Interpolation Results: X direction Line y=1000m 0 0 Decimated CSG in the X direction: Y =1000 m , dx = 50 m Real dense data, dx = 10 m Time (s) Time (s) 5 5 X (m) X (m) 0 3000 0 3000

  19. Interpolation Results: Y direction 0 Virtual dense data, dx = 10 m Time (s) 5 Y (m) 0 3000 Line y=1000m 0 Decimated CSG in the Y direction: X =1000 m , dx = 50 m Time (s) 5 Y (m) 0 3000

  20. Interpolation Results: Y direction Line y=1000m 0 0 Decimated CSG in the Y direction: X =1000 m , dx = 50 m Decimated CSG in the Y direction: X =1000 m , dx = 50 m Virtual data after filtering, dx = 10 m Time (s) Time (s) 5 5 Y (m) Y (m) 0 3000 0 3000

  21. Interpolation Results: Y direction Line y=1000m 0 0 Decimated CSG in the Y direction: X =1000 m , dx = 50 m Real dense data, dx = 10 m Time (s) Time (s) 5 5 Y (m) Y (m) 0 3000 0 3000

  22. Interpolation Results: Trace Comparison True vs. Virtual traces before Filtering 1.0 True Virtual Time (s) 3.5 X offset (m) 10 2710

  23. Interpolation Results: Trace Comparison True vs. the Virtual Traces after Filtering 1.0 True Virtual Time (s) 3.5 X offset (m) 10 2710

  24. Interpolation Results: Trace Comparison True vs. the Virtual Traces after Filtering 1.0 Time (s) 3.5 X offset 10 2710

  25. Different Recording Spacings Interpolation error vs. recording spacing 0.5 Normalized error 0.05 1.2 0.2 Recording spacing of input data (λxmin) The normalized error =

  26. Outline • Problems: Missing and sparse traces • Methodology: Interferometric interpolation • Numerical results: • 3D layered velocity model • Anti-aliasing condition for interferometric redatuming • Conclusions

  27. less than Phase difference between and Anti-aliasing condition Anti-aliasing Condition for Interferometric Redatuming Interferometric redatuming equation: G(B|x) G(A|x)

  28. Remove Interf. Artifacts with the Anti-aliasing Condition Regular Interf. Result Anti-aliased Interf. Result 0 0 Time (s) Time (s) 3 3 X (km) X (km) 4 4 0.6 0.6 Recording interval 0.49 λ

  29. Remove Interf. Artifacts with the Anti-aliasing Condition Regular Interf. Result with Up-down Separation Anti-aliased Interf. Result with Up-down Separation 0 0 Time (s) Time (s) 3 3 X (km) X (km) 4 4 0.6 0.6 Recording interval 0.97 λ

  30. Outline • Problems: Missing and sparse traces • Methodology: Interferometric interpolation • Numerical results: • 3D layered velocity model • Anti-aliasing condition for interferometric redatuming • Conclusions

  31. Conclusions Encouraging results obtained for interpolating sparse OBS data (recording spacing: ) Degraded interpolation results when the recording spacing of the input sparse data increases Remaining artifacts: up-down separation, anti-aliasing condition

  32. Acknowledgments • Thank UTAM 2008 sponsors for the support of the research. • Thank you all for your attention.

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