1. Image segmentation for velocity model construction and updating
Adam Halpert*
Robert G. Clapp
SEP-134,
13 May 2008

2. Why segmentation?
Velocity model building is a “bottleneck” for large iterative imaging projects
Manually picking salt boundaries is often tedious, ambiguous, and time-consuming
Image segmentation offers a consistent, efficient means of delineating salt bodies
Integration with velocity model building produces many benefits 1

3. Before 2

4. After 3

5. Agenda Segmentation review Migration algorithms
Effects on segmentation
Velocity model construction
Sediment flood, salt flood
Velocity model updating
Optimization of the boundary pick
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6. Segmentation defined
First applied to seismic data by Hale and Emanuel (2002, 2003): Atomic meshing
Lomask (2007): Divide a seismic image into two volumes - a salt body, and the surrounding sediments
Based on tracking one or more key attributes ( i.e. envelope amplitude) that can identify likely salt interfaces
Ultimate goal: Produce globally accurate salt boundaries with minimal human interaction
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7. Segmentation algorithm
Normalized cuts image segmentation (Shi and Malik, 2000)
Divide a migrated seismic image into pixels
For each pixel, compare values of envelope amplitude between it and a random selection of neighbors
For each pair of pixels, assign a weight inversely proportional to the likelihood of a salt boundary between them
From Lomask (2007)
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8. Segmentation algorithm
Normalized cuts image segmentation (Shi and Malik, 2000)
Divide a migrated seismic image into pixels
A path that minimizes the sum of weights across an image is the salt boundary
From Lomask (2007)
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9. Segmentation algorithm
The expression for a vector representing the minimized cut can be expressed as a Rayleigh quotient:
W: matrix containing all calculated weights
D: diagonal matrix formed from W’s columns
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10. Segmentation algorithm
This is an eigenvector/eigenvalue problem
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11. Segmentation algorithm
The eigenvector corresponding to the second- smallest eigenvalue is used to segment the image
When following the “zero contour,” positive eigenvector values are in one group (salt), negative values in the other (sediment)
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12. Example: Image
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13. Example: Eigenvector
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14. Migration Segmentation operates on migrated images
Higher quality images  higher quality segmentation
Plane wave migration in tilted coordinates (Shan, 2008) excels at imaging steeply- dipping structures
Ideal for salt-boundary delineation
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15. Image: Regular coordinates
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16. Image: Tilted coordinates
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17. Eigenvector: Regular coordinates
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18. Eigenvector: Tilted coordinates
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19. Quantitative comparison
Regular coordinates
Tilted coordinates
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20. Image: Regular coordinates
Uncertainties
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21. Image: Tilted coordinates
Uncertainties
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22. Eigenvector: Regular coordinates
Uncertainties
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23. Eigenvector: Tilted coordinates
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24. Quantitative comparison
Regular coordinates
Tilted coordinates
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25. Velocity model building
Common procedure:
Sediment flood migration resolves salt top
Flood with salt velocity below picked top boundary
Salt flood migration resolves salt base
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26. Stratigraphic velocity model
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27. Sediment flood velocity model
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28. Stratigraphic velocity model
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29. Sediment flood image
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30. Sediment flood eigenvector
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31. Zero-contour boundary
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32. Salt flood image
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33. Salt flood eigenvector
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34. Zero-contour boundary
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35. Updating velocity models
Segmentation can improve pre-existing velocity models
Now, the existing model acts as a priori information for choosing salt boundaries
In uncertain (grey) areas, follow (or stay away from) the boundary on the existing model
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36. Beyond the zero-contour
Lomask’s algorithm follows a single eigenvector contour value across the entire image
The “best” boundary likely follows different values of the second eigenvector in different parts of the image
Pose the boundary pick as an optimization problem
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37. Boundary optimization
This is a NONLINEAR problem
Primary goal: follow the zero-contour
Linearize the problem around the zero-contour boundary
Address the problem via a series of fitting goals
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38. Boundary optimization
Create a linear operator, G
G is the vertical gradient of the eigenvector across the zero-contour boundary
G is large when there is a sharp transition from postive to negative values, small when the transition is gradual
0  G ∆m
Deviation from zero-contour boundary
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39. Boundary optimization
Use the boundary from the existing model when the zero-contour is ambiguous
Weighting operator W is large when there is great uncertainty in the eigenvector:
0  W (m-mprior)
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40. Boundary optimization
Impose a smoothness constraint on the modeled boundary
0  A m,
where A is a roughening operator, in this case the gradient
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41. Boundary optimization
0  G ∆m
0  W (m-mprior)
0  A m
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42. Image after salt flood migration
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43. Image after salt flood migration
Bottom of canyon
placed too shallow
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44. Zero-contour boundary
Still too shallow…
move away from
zero contour
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45. Optimized boundary
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46. Remigrated image
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47. Original Image
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48. Remigrated image Canyon imaged better, but still placed too shallow
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49. One more iteration
Original zero contour
First optimization iteration
Second optimization iteration
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50. Final remigrated image
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51. Previous Iteration
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52. Final remigrated image
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53. Perfect velocity migration
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54. Real data example: Original image
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55. Original velocity model
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56. Optimized salt boundary
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57. Updated velocity model
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58. Original velocity model
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59. Remigrated image
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60. Original image
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61. Conclusions Image segmentation can accurately identify salt boundaries
Segmentation can greatly expedite the velocity model-building process by operating on sediment-flood and salt-flood images
When a velocity model already exists, optimizing the algorithm’s boundary picks produces improved velocity models and migrated images 53

62. Acknowledgments
We thank WesternGeco and SMAART JV for supplying the data used in these examples, and several SEP students for providing suggestions and technical guidance. 54