1. Weighted Stacking of 3-D Converted-wave Data for Birefringent Media Richard Bale

2. Introduction Shear-wave splitting (birefringence) is a “litmus test” for azimuthal anisotropy Used to characterize fractured media Can degrade image if uncorrected  Causes acquisition footprint for 3-D 

3. Radial and Transverse DMO Stacks Transverse @ 2200 msRadial @ 2172 ms 1040106010801110102010401060108011101020 960 940 920 900 880 860 960 940 920 900 880 860 In-lines Cross Lines Cross Lines

4. Background Estimation of principal axes –e.g. using transverse polarity from 3-D data Layer stripping to remove anisotropy –needs estimates of S1-S2 transmission 2-D: rotation after stack 3-D: must rotate before stack –…but is that all?

5. Converted Wave Splitting Legend: P SV S1 S2 Azimuthally Anisotropic Layer Fracture Direction Radial Direction X Y Shot Receiver Conversion Point

6. Surface Geometry X Y S1 S2 Radial   U PS Receiver Shot

7. The 3-D Splitting Equation where:is a rotation matrix, Radial converted wave Projection onto S1 & S2 S1 & S2 propagation Recording on X and Y and:

8. Multi-azimuth CCP Binning X CCP Bin Receivers Shots 11 22 33 NN …. Þ Acquisition- dependent amplitudes

9. Least Squares Stacking for S1 and S2 We have two (decoupled) least squares problems, for U PS1 and U PS2 Weighted stacking equations: S1 Effective Fold S2 Effective Fold

10. Orthogonal Acquisition 1200 1000 800 Y (meters) 600 400 200 0 0200 400 600 800 1000 1200 X (meters) Shot Lines Receiver Lines

11. Isotropic ACCP Fold Cross-line Number In-line Number

12. S1 Effective ACCP Fold:  =0° Cross-line Number In-line Number

13. S1 Effective ACCP Fold:  =45° Cross-line Number In-line Number

14. Gryphon: Acquisition Geometry 1013 1050 1100 In-lines 950 Cross lines 900 860 30 20 10 0 CCP Stacking Fold Cables Shot Lines 400m

15. Effective Fold Maps 1013 1050 1100 In-lines 950 Cross lines 900 860 S1 Norm:  cos 2 (  i -  ) S2 Norm:  sin 2 (  i -  ) 1013 1050 1100 In-lines 950 Cross lines 900 860

16. TransverseRadial Radial and Transverse DMO Stacks 10401060108011101020 2.0 2.1 2.2 2.3 2.4 2.0 2.1 2.2 2.3 2.4 Cross line 895 Cross line 922 10401060108011101020 2.0 2.1 2.2 2.3 2.4 2.0 2.1 2.2 2.3 2.4

17. S2S1 Least-squares S1 and S2 DMO Stacks 10401060108011101020 2.0 2.1 2.2 2.3 2.4 2.0 2.1 2.2 2.3 2.4 Cross line 895 Cross line 922 10401060108011101020 2.0 2.1 2.2 2.3 2.4 2.0 2.1 2.2 2.3 2.4

18. Least-squares S1 and S2 DMO Stacks S2 @ 2200 msS1 @ 2172 ms 1040106010801110102010401060108011101020 960 940 920 900 880 860 960 940 920 900 880 860 In-lines Cross Lines Cross Lines

19. Radial and Transverse DMO Stacks Transverse @ 2200 msRadial @ 2172 ms 1040106010801110102010401060108011101020 960 940 920 900 880 860 960 940 920 900 880 860 In-lines Cross Lines Cross Lines

20. Offset Dependence Converted wave amplitudes strongly depend on angle of incidence For small angles (<20°): for ray-parameter p, local compressional velocity V P, angle of incidence , and local shear velocity V S (Stewart, Zhang, and Guthoff; 1995)

21. Angle Gathers: Alba Radial Component -60 -40 -20 0 20 40 60 Maximum Amplitude in Window Linear Sampling Sin(  ) Sampling Time (sec.)

22. Offset Dependent Least Squares Stacking for S1 and S2 Updated weighted stacking equations: S2 Effective Fold S1 Effective Fold t 0 = 2-way zero-offset time r i = offset t(r i ) = 2-way time

23. S1 Effective ACCP Fold:  =45° Cross-line Number In-line Number

24. Offset weighted S1 Eff. ACCP Fold:  =45° Cross-line Number In-line Number

25. Conclusions Preliminary work done on a method for 3-D S1 and S2 imaging Offset dependence can be included Effective fold maps include azimuth and offset effects for S1 and S2 Initial results show increased resolution, and less acquisition footprint

26. Future Work Test method on synthetic and field data Fractured reservoir imaging: consider conversions within birefringent medium Long offset issues: –Orthogonality –2-term AVO fit: I S, (I S1, I S2 ?),  parameterization Multiple birefringent layers PS1-PS2 Migration?

27. Acknowledgements Kerr-McGee North Sea (UK) Ltd., and the Gryphon partners Chevron and the Alba partners WesternGeco –In particular Tony Probert and Gabriela Dumitru The CREWES sponsors