1. Volumetric aberrancy: a complement to coherence and curvature
Xuan Qi, Ph.D. candidate
2016 AASPI Consortium Meeting
11/23/2018
2016 AASPI Consortium Meeting

2. 2016 AASPI Consortium Meeting
Outline
Background
Introduction
Motivation
Method
Results
Conclusion
11/23/2018
2016 AASPI Consortium Meeting

3. Background: curvature
Anticline
Syncline
Dipping Plane
Flat Plane
k>0
k=0
k<0 R x z
Anticline: k > 0
Plane: k = 0
Syncline: k < 0
11/23/2018
2016 AASPI Consortium Meeting

4. Introduction: aberrancy – curvature gradient
Depth
Dip
Aberrancy measures the gradient change along curvature. For example, in a two-dimensional perfect circle, the curvature does not change at every single sample point, thus the aberrancy is zero at every single sample points. Using the perfect circle analogy, we would observe large aberrancy in terms of magnitude for an anticlinal geometry, which is a common geometry for folds or faults structure.
Curvature
11/23/2018
2016 AASPI Consortium Meeting

5. Introduction: aberrancy – curvature gradient
Depth
Depth
Curvature
Aberrancy measures the gradient change along curvature. For example, in a two-dimensional perfect circle, the curvature does not change at every single sample point, thus the aberrancy is zero at every single sample points. Using the perfect circle analogy, we would observe large aberrancy in terms of magnitude for an anticlinal geometry, which is a common geometry for folds or faults structure.
Aberrancy
11/23/2018
2016 AASPI Consortium Meeting

6. Motivation: Accurately map sub-seismic resolution faults
Coherence
Aberrancy
Aberrancy measures the gradient change along curvature. For example, in a two-dimensional perfect circle, the curvature does not change at every single sample point, thus the aberrancy is zero at every single sample points. Using the perfect circle analogy, we would observe large aberrancy in terms of magnitude for an anticlinal geometry, which is a common geometry for folds or faults structure.
11/23/2018
2016 AASPI Consortium Meeting

7. Internal Steps Step 1: Compute Derivatives Inline dip, p
crossline dip, q
Rotate to prime system (p’=0, q’=0)
Find extrema of third derivatives as function of azimuth, φ
Rotate back to original system
Azimuth and magnitude, amax
Azimuth and magnitude, amin
Internal Steps
Compute Derivatives
Step 1:
Due to the nature of aberrancy, it characterizes the third-order surface behavior. Computation of aberrancy involves two main challenges, high order equations and high dimensional calculation. The original aberrancy equation proposed by Di & Gao, (2014) is absolutely complicated, it is almost impossible to derive an analytical solution from it. That is why we have to rotate the coordinate system to simplify the equation (Di and Gao, 2016). After rotation the coordinate system, the super difficult equation simplified into a third order polynomial equation.
11/23/2018
2016 AASPI Consortium Meeting

8. Rotate Coordinate system
Inline dip, p
crossline dip, q
Rotate to prime system (p’=0, q’=0)
Find extrema of third derivatives as function of azimuth, φ
Rotate back to original system
Azimuth and magnitude, amax
Azimuth and magnitude, amin
Internal Steps
Compute Derivatives
Step 1:
Rotate Coordinate system
Step 2:
Due to the nature of aberrancy, it characterizes the third-order surface behavior. Computation of aberrancy involves two main challenges, high order equations and high dimensional calculation. The original aberrancy equation proposed by Di & Gao, (2014) is absolutely complicated, it is almost impossible to derive an analytical solution from it. That is why we have to rotate the coordinate system to simplify the equation (Di and Gao, 2016). After rotation the coordinate system, the super difficult equation simplified into a third order polynomial equation.
11/23/2018
2016 AASPI Consortium Meeting

9. Rotate Coordinate system Compute the extreme aberrancy
Inline dip, p
crossline dip, q
Rotate to prime system (p’=0, q’=0)
Find extrema of third derivatives as function of azimuth, φ
Rotate back to original system
Azimuth and magnitude, amax
Azimuth and magnitude, amin
Internal Steps
Compute Derivatives
Step 1:
Rotate Coordinate system
Step 2:
Due to the nature of aberrancy, it characterizes the third-order surface behavior. Computation of aberrancy involves two main challenges, high order equations and high dimensional calculation. The original aberrancy equation proposed by Di & Gao, (2014) is absolutely complicated, it is almost impossible to derive an analytical solution from it. That is why we have to rotate the coordinate system to simplify the equation (Di and Gao, 2016). After rotation the coordinate system, the super difficult equation simplified into a third order polynomial equation.
Compute the extreme aberrancy
Step 3:
11/23/2018
2016 AASPI Consortium Meeting

10. Rotate back to original coordinate system
Inline dip, p
crossline dip, q
Rotate to prime system (p’=0, q’=0)
Find extrema of third derivatives as function of azimuth, φ
Rotate back to original system
Azimuth and magnitude, amax
Azimuth and magnitude, amin
Internal Steps
Due to the nature of aberrancy, it characterizes the third-order surface behavior. Computation of aberrancy involves two main challenges, high order equations and high dimensional calculation. The original aberrancy equation proposed by Di & Gao, (2014) is absolutely complicated, it is almost impossible to derive an analytical solution from it. That is why we have to rotate the coordinate system to simplify the equation (Di and Gao, 2016). After rotation the coordinate system, the super difficult equation simplified into a third order polynomial equation.
Rotate back to original coordinate system
Step 4:
11/23/2018
2016 AASPI Consortium Meeting

11. Theory: Aberrancy before rotation
𝝋: azimuth [0,360)
11/23/2018
2016 AASPI Consortium Meeting

12. Theory: aberrancy after rotation (Di and Gao 2015)
𝜙 1 : azimuth [0,360)
11/23/2018
2016 AASPI Consortium Meeting

13. Fault-controlled karst – Fort Worth Basin, Texas
Results
Fault-controlled karst – Fort Worth Basin, Texas
11/23/2018
2016 AASPI Consortium Meeting

14. Case study : Fault-controlled karst – Fort Worth Basin, Texas
Genetic paleocave model for the Lower Ordovician of West Texas showing cave floor, cave roof, and collapsed breccia (modified after Kerans, 1988, 1989).
The Fort Worth Basin is one of several basins that formed during the late Paleozoic Ouachita Orogeny, generated by convergence of Laurasia and Gondwana (Bruner and Smosna, 2011). The Mississippian-age organic-rich Barnett Shale gas reservoir is a major resource play in the Fort Worth Basin. It extends more than 28;000 mi2 with most production coming from a limited area, in which the shale is relatively thick and isolated between effective hydraulic fracture barriers. Conformably overlying the Barnett Shale is the Marble Falls Formation. The lower Marble Falls consists of a lower member of interbedded dark limestone and gray-black shale. Underlying the Barnett Shale are the Ordovician Viola-Simpson Formations, which dominantly consist of dense limestone, and dolomitic Lower Ordovician Ellenburger Group. (Qi et al. 2014)
Qi et al,. 2014
11/23/2018
2016 AASPI Consortium Meeting

15. Results: variance on top of Marble Falls
Fault
Karst
Extract the coherence and project on the top Marble Falls surface.
11/23/2018
2016 AASPI Consortium Meeting

16. Results: Co-rendered curvature and variance on top of Marble Falls
Fault
Karst
How curvature
11/23/2018
2016 AASPI Consortium Meeting

17. 2016 AASPI Consortium Meeting
Results: Co-render aberrancy amax and amax azimuth on top of Marble Falls
Fault
Karst
11/23/2018
2016 AASPI Consortium Meeting

18. Results: Co-render variance and amax on top of Marble Falls
Fault
Karst
As you can see that, aberrancy provide more detailed information where coherence is not able to pick up.
11/23/2018
2016 AASPI Consortium Meeting

19. Results: top of Marble Falls time structure
11/23/2018
2016 AASPI Consortium Meeting

20. Results: top of Marble Falls time structure
11/23/2018
2016 AASPI Consortium Meeting

21. Results: top of Marble Falls time structure
11/23/2018
2016 AASPI Consortium Meeting

22. Results: vertical section of AA’
Aberrancy
Compare aberrancy with coherence. 1）some of the features we can observe from aberrancy are not able or poorly to be picked up from coherence.
Variance
11/23/2018
2016 AASPI Consortium Meeting

23. Results: vertical section of BB’
Aberrancy
Compare how aberrancy and coherence characterize faults differently. The faults were highlighted as vertical thin lines (higher resolution, continuous), while in coherence cross section, faults were observed as less continuous dots.
Variance
11/23/2018
2016 AASPI Consortium Meeting

24. Results: vertical section of CC’
Aberrancy
Compare how aberrancy and coherence characterize karst features differently. Similar to faults.
Variance
11/23/2018
2016 AASPI Consortium Meeting

25. 2016 AASPI Consortium Meeting
Conclusions
11/23/2018
2016 AASPI Consortium Meeting

26. AASPI volumetric attributes curvature 3d
11/23/2018
2016 AASPI Consortium Meeting

27. 2016 AASPI Consortium Meeting
THANK YOU
QUESTIONS?
11/23/2018
2016 AASPI Consortium Meeting

28. 2016 AASPI Consortium Meeting
Rotational matrix
Rotated along z axis clock wise with phi as the rotational andl
11/23/2018
2016 AASPI Consortium Meeting

29. 2016 AASPI Consortium Meeting
Theory: aberrancy
11/23/2018
2016 AASPI Consortium Meeting

30. Short wavelength vs long wavelength
11/23/2018
2016 AASPI Consortium Meeting

31. Figuring out the meaning of the cubic roots…
Three roots scenario
One root scenario
If the discriminator is less than 0, we will expect to have three distinct roots (a), if the discriminator is larger than 0, there will be 2 imaginary roots and one real root (b).
11/23/2018
2016 AASPI Consortium Meeting

32. Variance
As you can see that, aberrancy provide more detailed information where coherence is not able to pick up.