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Wave-Equation Migration in Anisotropic Media

Wave-Equation Migration in Anisotropic Media. Jianhua Yu. University of Utah. Contents. Motivation. Anisotropic Wave-Equation Migration. Numerical Examples:. Cusp model. 2-D SEG/EAGE model. 3-D SEG/EAGE model. Conclusions. Contents. Motivation. Anisotropic Wave-Equation Migration.

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Wave-Equation Migration in Anisotropic Media

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  1. Wave-Equation Migration in Anisotropic Media Jianhua Yu University of Utah

  2. Contents Motivation Anisotropic Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  3. Contents Motivation Anisotropic Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  4. Irregular acquisition geometry Bandwidth source wavelet Velocity errors Higher order phenomenon: Anisotropy What Blurs Seismic Images?

  5. Anisotropic wave-equation migration: Anisotropic Imaging Ray-based anisotropic migration: Anisotropic velocity model ---Ristow et al, 1998 ---Han et al. 2003

  6. >78 wave propagator High efficiency Improve image accuracy o Develop 3-D anisotropic wave-equation migration method in orthorhombic model Objective:

  7. Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  8. General Wave Equation Wave equation in displacement Ui : displacement component Cijkl : 4th-order stiffness tensor

  9. Eigensystem Equation Polarization components of P-P, SV, and SH waves

  10. Orthorhombic Anisotropic

  11. Orthorhombic Anisotropic

  12. and Decoupled P plane Wave Motion Equations in (x,z) and (y,z) planes

  13. det and det Decoupled P plane Wave Motion Equations in (x,z) and (y,z) planes

  14. (y,z) plane Thomsen’s Parameters Dispersion Equations (x,z) plane

  15. Thomsen’s Parameters

  16. VTI: FFD algorithm

  17. FFD Anisotropy Migration

  18. Velocity: Anisotropy: How to Set Velocity and Anisotropy Parameters a& b : Optimization coefficients of Pade approximation for FD

  19. Pade Approximation Comparison 5 Error % 0 0 Angle 90

  20. Pade Approximation Comparison 0.05 Beyond 78 within 0.02 % Error % 0 0 Angle 78

  21. Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  22. Exact Exact Approximation Approximation ** ** Strong Anisotropy Weak Anisotropy 0.6 Kz 0 -0.3 0.3 -0.3 0.3 Kx Kx

  23. Dispersion Equation Approximation 0.3 Kz Strong anisotropy 0 -0.3 Kx 0.3

  24. 0 New V/V0=3 iso Depth (km) Standard V/V0=3 iso 2.0

  25. V/V0=3 V/V0=3 0 Strong Aniso Depth (km) Weak Aniso 2.0

  26. Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  27. Velocity (2.0-3.0 km/s) X (km) 0 1.5 0 Depth (km) 1

  28. Velocity (2.0-3.0 km/s) Isotropic data (SUSYNLY) Anisotropic data (SUSYNLVFTI) X (km) X (km) 0 1.5 0 1.5 0 0 Time (s) Time (s) 1.2 1

  29. 0 1.5 0 1.5 Anisotropic data Isotropic mig Anisotropic data Anisotropic mig X (km) 0 1.5 0 Depth (km) 1 Isotropic data Isotropic mig (su)

  30. Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  31. X (km) 0 5 0 Depth (km) Salt Model (VTI) 4

  32. X (km) 0 5 0 Depth (km) 4 Iso-mig

  33. X (km) 0 5 0 Depth (km) 4 VTI Aniso-mig

  34. 0 0 0 1.5 1.5 1.5 X (km) X (km) Anisotropy Error 20 % Anisotropy Error 40 % Inaccurate Thomsen’s Parameters (VTI) X (km) 0 Depth (km) 4 Anisotropy Error 10 %

  35. Inaccurate Thomsen’s Parameters 5 10 X (km) X (km) X (km) 5 10 5 10 3 Depth (km) 4 Anisotropy Error 10 % Anisotropy Error 20 % Anisotropy Error 40 %

  36. Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE VTI model 3-D SEG/EAGE VTI model Conclusions

  37. X (km) 0 5 Iso (y=1.5 km) X (km) 0 5 0 Depth (km) 4 VTI Aniso (y=1.5 km)

  38. Y (km) 0 5 Iso (x=1.5 km) Y (km) 0 5 0 Depth (km) VTI Aniso (x=1.5 km) 4

  39. Y (km) 0 5 Y (km) 0 5 0 Depth (km) Iso (x=3 km) VTI Aniso (x=3 km) 4

  40. Iso (z=0.5 km) X (km) X (km) 0 5 0 5 0 VTI Aniso (z=0.5 km) Y (km) 5

  41. Iso (z=2.5 km) X (km) X (km) 0 5 0 5 0 VTI Aniso (z=2.5 km) Y (km) 5

  42. Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model 2-D SEG/EAGE model 3-D SEG/EAGE model Conclusions

  43. Works for 2-D and 3-D media Valid for VTI and TI Improves spatial resolution o • 78 Propagator Cost = Cost of Standard 45^o propagator Conclusions o New > 78 Anisotropic wave propagator:

  44. Thanks To 2003 UTAM Sponsors CHPC

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