1. Mapping the P-S Conversion Point in VTI Media * Jianli Yang Don C. Lawton

2. Outline  Introduction  Theory  Numerical modeling methodology and results  NORSAR2D anisotropy ray mapping  Discussion and conclusions  Future work  Acknowledgement

3. P- wave S-wave Source Receiver The geometry of converted wave obeying Snell’s law MP

4. MD P-wave Source Receiver S-wave P-S trajectory The conversion point traces a trajectory in the multi- layered model

5. Elliptical wavefront Ray   The definitions of the phase angle and ray angle Spherical wavefront Source

6. Thomsen’s exact equations

7. Thomsen’s linear approximations

8. Thomsen’s definition of the anisotropy parameters

9. Angles and offsets included in the algorithm

10. Calculate the P- wave ray parameter for Find the corresponding by Snell’s law Calculate the and Isotropic Calculate + = offset VTI - = displacement

11.  =0.10, exact equations  =0.20  =0.10  =0.05

12.  =0.10, Thomsen’s linear approximation  =0.20  =0.10  =0.05  =0.20  =0.10  =0.05

13. 02004006008001000 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 m m MP Isotropic raypath VTI raypath  =0.20,  =0.05, offset/depth=1 SourceReceiver

14.  =0.20,  =0.10, offset/depth=1 SourceReceiver Isotropic raypath VTI raypath MP SourceReceiver

15. VTI raypath Isotropic raypath  =0.20,  =0.20, offset/depth=1 SourceReceiver MP

16. VTI raypath Isotropic raypath  =0.20,  =0.15, offset/depth=1 SourceReceiver MP

17. VTI raypath Isotropic raypath  =0.20,  =0.25, offset/depth=1 SourceReceiver MP

18.  = 0.25 

19.  = 0.50 

20.  = 0.75 

21.  = 1.0 

22.  = 1.25 

23.  = 1.5  offset/depth

24. Isotropic VTI Isotropic The VTI model designed for NORSAR2D experiment P wave S wave Isotropic case

25. An example of the synthetic seismogram obtained from NORSAR2D anisotropy ray tracing on the model and displayed by PROMAX

26. For  =0.10 Displacement from NORSAR2D (m) Displacement from linear equations (m) Displacement from exact equations (m)  =0.20 236.1244.18316.42  =0.15 142.3139.16163.58  =0.10 4741.5649.53  =0.05 -50-56.50-49.39  =0.00 -146-151.26-140.15  = -0.05 -244-237-218.68 Table 1, NORSAR 2D experiments in VTI media, with  =0.10

27. Discussion and Conclusions  The location of the conversion point in VTI media is different to that in the isotropic case.  The displacement of the conversion point is dependent on the offset/depth, velocity ratio, anisotropic parameters  and .  When  is greater than , the conversion point is displaced towards the source relative to its location in the isotropic case.

28.  When  is less than , the conversion point moves towards the receiver compared to its location in isotropic case.  Results using linear approximations are similar to those obtained from NORSAR code.  Accurate placement of the conversion point is necessary for P-S survey design and data processing. Discussion and Conclusions

29. Future work  Further investigation of the relation between the displacement of the conversion point and Vp/Vs  Apply results of this work in the 3-C seismic survey design  Compare results using Thomsen’s  effective

30. Acknowledgements  We thank Dr. Larry Lines and Dr. Jim Brown for valuable suggestions  CREWES Sponsors’ financial support is also greatly appreciated