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

Transcription

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

2 Outline! Introduction! Theory! Numerical modeling methodology and results! NORSARD anisotropy ray mapping! Discussion and conclusions! Future work! Acknowledgement

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

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

5 Source θ φ Elliptical wavefront Ray Spherical wavefront The definitions of the phase angle and ray angle

6 [ ] ) ( D θ εsin 1 α ) ( v * P θ θ + + = + = ) ( D β α θ εsin β α 1 β ) ( v * SV θ θ [ ] θ sin 1 β (θ) v SH γ + = = 1 θ sin ) α β (1 ε)ε α β 4(1 θ θcos sin ) α β (1 4δ 1 β α 1 1 ) ( D 1 4 * * θ [ ] ) dθ dv v tan θ (1 ) dθ dv v 1 (tan θ φ(θ) tan + = Thomsen s exact equations

7 v p v sv v sh () ( 4 θ = α 1 + δ sin θ cos θ + ε θ ) sin α cos β () θ = β 1 + ( ε δ ) sin θ θ () ( θ = β 1 + γ θ) sin tanφ = tanθ sinθ cosθ 1 dv v() θ dθ Thomsen s linear approximations

8 v ε = P ( π ) α α δ V = P (π 4) V P (π ) V P () V P () γ v = SH ( π ) β β Thomsen s definition of the anisotropy parameters

9 Angles and offsets included in the algorithm

10 Calculate the P- wave ray parameter for θ P Find the corresponding by Snell s law θ S VTI Calculate the and φ P V P Calculate the and φ S V S Isotropic Calculate XP Calculate XS XP + XS = offset X P (VTI) - X P (Isotropic) = displacement

11 δ=. δ=.1 δ=.5 ε=.1, exact equations

12 δ=. δ=. δ=.1 δ=.1 δ=.5 δ=.5 ε=.1, Thomsen s linear approximation

13 Source Receiver -1 - MP -3-4 Isotropic raypath m VTI raypath m ε=., δ=.5, offset/depth=1

14 Source Receiver MP Isotropic raypath VTI raypath ε=., δ=.1, offset/depth=1

15 Source Receiver MP VTI raypath Isotropic raypath ε=., δ=., offset/depth=1

16 Source Receiver MP Isotropic raypath VTI raypath ε=., δ=.15, offset/depth=1

17 Source Receiver VTI raypath MP Isotropic raypath ε=., δ=.5, offset/depth=1

18 δ=.5ε

19 δ=.5ε

20 δ=.75ε

21 δ= 1.ε

22 δ= 1.5ε

23 offset/depth δ= 1.5ε

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

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

26 For ε=.1 Displacement from NORSARD (m) Displacement from linear equations (m) Displacement from exact equations (m) δ= δ= δ= δ= δ= δ= Table 1, NORSAR D experiments in VTI media, with ε=.1

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 ε and δ.! When ε is greater than δ, the conversion point is displaced towards the source relative to its location in the isotropic case.

28 Discussion and Conclusions! When ε is less than δ, 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.

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 γ effective

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