1. High Resolution Velocity Analysis for Resource Plays
Bo Zhang and J. T. Kwiatkowski

2. Outline Factors that affect the fidelity of velocity analysis
High resolution velocity spectrum
The engine for automatic velocity optimization
Automatic interval velocity analysis based on DE (workflow)
Synthetic and Real data examples
Conclusion
Road-ahead

3. Factors that affect the fidelity of velocity analysis
The resolution of velocity spectrum.
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Semblance
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SN based on PFA
Vs.

4. Factors that affect the fidelity of velocity analysis
Manually picking velocity at CDP location?
Manually picking velocity for each reflection events?
Conventional velocity analysis
Dense velocity analysis (

5. Outline Factors that affect the fidelity of velocity analysis
High resolution velocity spectrum
The engine for automatic velocity optimization
Automatic interval velocity analysis based on DE (workflow)
Synthetic and Real data examples
Conclusion
Road-ahead

6. High resolution velocity spectrum
The seismic trace d(t) can be written as
where d(t) is the seismic traces, s(t) is the reflection signal, and n(t) is the noise. Suppose we have M traces in one CDP gather, then
Construction the correlation matrix between each traces
d_corr

7. High resolution velocity spectrum
Assume the noise and reflected signals are uncorrelated, then the eigenstructure of d_corr has the following properties:
d_corr is not sensitive to amplitude variation (AVO)
In the ideal case, d_corr is a rank 1 matrix.
The maximum eigenvalue of d_corr is corresponding major underline factors which is regards as the reflected signals.
Those two properties suggest giving an estimated signal-to-noise ratio (S/N) to the corrected gather

8. High resolution velocity spectrum
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Synthetic gather with random noise added

9. High resolution velocity spectrum
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semblance

10. High resolution velocity spectrum
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SN based on PCA

11. Outline Factors that affect the fidelity of velocity analysis
High resolution velocity spectrum
The engine for automatic velocity optimization
Automatic interval velocity analysis based on DE (workflow)
Synthetic and Real data examples
Conclusion
Road-ahead

12. The engine for automatic velocity optimization
Differential evolutionary (DE) algorithm is an efficient and simple global optimization scheme. The basic features can be summarized as follows:
Mutation
Initialization
Crossover
Selection
DE workflow

13. The engine for automatic velocity optimization
Problem statement and notation
Suppose we want to optimize a function with D real parameters
We must select the size of the population N (it must be at least 4)
The parameter vectors have the form:
where G is the generation number.

14. The engine for automatic velocity optimization
Define upper and lower bounds for each parameter:
Mutation
Initialization
Crossover
Selection
Randomly select initial parameter values uniformly between the upper and lower bounds.

15. The engine for automatic velocity optimization
Each of the N parameter vectors undergoes mutation, recombination and selection
Mutation expands the search space
For a given parameter vector xi,G randomly select the three different vectors:
Mutation
Initialization
Crossover
Selection

16. The engine for automatic velocity optimization
Add the weighted difference of two of the vectors to the third to form the donor vector:
Mutation
Initialization
Crossover
Selection
The mutation factor F is a user defined constant from [0, 2]

17. The engine for automatic velocity optimization
Crossover incorporates successful solutions from the previous generation
The trial vector ui,G+1 is developed from the elements of the target vector, xi,G, and the elements of the donor vector, vi,G+1
Elements of the donor vector enter the trial vector with probability CR
Mutation
Initialization
Crossover
Selection

18. The engine for automatic velocity optimization
if or
Mutation
Initialization
Crossover
Selection
if or
, Irandom is a random integer from [1,2,…D]

19. The engine for automatic velocity optimizationif
Mutation
Initialization
Crossover
Selection
otherwise
, Irandom is a random integer from [1,2,…D]
Mutation, crossover and selection continue until some stopping criterion is reached

20. Outline Factors that affect the fidelity of velocity analysis
High resolution velocity spectrum
The engine for automatic velocity optimization
Automatic interval velocity analysis based on DE (workflow)
Synthetic and Real data examples
Conclusion
Road-ahead

21. Automatic interval velocity analysis
Conventional migration velocity analysis on the coarse grid
Initialize the population set based on the conventional velocity model
Get the trail interval velocity set by DE operation
Define the analysis time grids along t0 axis for each CDP
Prestack time migrated gather after reverse NMO
Output the best member
Compare the semblance value of trail and target interval model. The one with greater semblance value survives into next generation
More generations
Yes No

22. Outline Factors that affect the fidelity of velocity analysis
High resolution velocity spectrum
The engine for automatic velocity optimization
Automatic interval velocity analysis based on DE (workflow)
Synthetic and Real data examples
Conclusion
Road-ahead

23. Synthetic data examples
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24. Synthetic data examples
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Synthetic gather

25. Synthetic data examples
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26. Synthetic data examples
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SN based PCA

27. Synthetic data examples

28. Synthetic and Real data examples

29. Synthetic data examples
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NMO correction based velocity model from DE

30. Synthetic data examples
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NMO correction based manual picking velocity model

31. Synthetic data examples
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Synthetic gather with random noise added

32. Synthetic data examples
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33. Synthetic data examples
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SN based PCA

34. Synthetic data examples

35. Synthetic data examples

36. Synthetic data examples
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NMO correction based velocity model from DE

37. Synthetic data examples
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NMO correction based manual picking velocity model

38. Real data examples
Location map of the Chicontepec foredeep in East-Central Mexico(Sarkar, 2011)

39. Real data examples
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Interval velocity from Dix inversion based on RMS velocity

40. Real data examples Interval velocity based on de search 0.0 0.5 1.0
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Interval velocity based on de search

41. Real data examples Manually picking RMS velocity 0.0 0.5 1.0 1.5 2.0 1
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Manually picking RMS velocity

42. Real data examples RMS velocity from DE optimization 0.0 0.5 1.0 1.5
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RMS velocity from DE optimization

43. Real data examples
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stacked section based on the RMS velocity from manual picking

44. Real data examples
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stacked section based on the RMS velocity from DE optimization

45. Real data examples Model based Impedance inversion 0.0 0.5 1.0 1.5 2.0
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Model based Impedance inversion

46. Outline Factors that affect the fidelity of velocity analysis
High resolution velocity spectrum
The engine for automatic velocity optimization
Automatic interval velocity analysis based on DE (workflow)
Synthetic and Real data examples
Conclusion
Road-ahead

47. Conclusion
Interval velocity from RMS velocity strongly suffers the errors contained in the RMS velocity model
From the synthetic testing, interval velocity model from DE optimization is superior to that generated from RMS velocity.
In the real case study, the optimized interval velocity model has more detail than that inverted from RMS velocity
By employing Gardner’s equation, high resolution interval velocity model can be used for model based impedance inversion
Multiples will strongly damage the the optimized interval velocity

48. Road-ahead
Consider the analysis time location on the section instead of each CDP alone.
Integrate the interpreted horizons into the analysis.
Testing on other surveys.

49. Acknowledgements PEMEX for permission to use and show their data
The industry sponsors of the University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation (AASPI) Consortium.