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COMPARISON OF WAVE EQUATION MIGRATION METHODS WITH PHASE ENCODING

COMPARISON OF WAVE EQUATION MIGRATION METHODS WITH PHASE ENCODING. Jianhua Yu. University of Utah. CONTENTS. . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work. CONTENTS.

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COMPARISON OF WAVE EQUATION MIGRATION METHODS WITH PHASE ENCODING

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  1. COMPARISON OF WAVE EQUATION MIGRATION METHODS WITH PHASE ENCODING Jianhua Yu University of Utah

  2. CONTENTS . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work

  3. CONTENTS . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work

  4. INTRODUCTION Migration methods includes two classes: . Ray-based migration method Features: a. Computational efficiency b. Capability of irregular acquisition geometry and target-processing

  5. INTRODUCTION c. Depend on ray-tracing algorithm d. Less accurate image for complex area

  6. INTRODUCTION Wave equation methods: Solution for two-way or one-way equations Features: a. Accurate wavefield extrapolation b. High quality image for complex area c. Expensive computational cost

  7. OBJECTIVE Compare various wave-equation methods Compare phase encoding algorithms The final purpose is to develop an efficient wave equation method for 3D migration image in complex area

  8. CONTENTS . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work

  9. METHODOLOGY Phase-shift based wave equation methods: a. SSF b. PSPI c. FFD (SSF+FD)

  10. Less memory requirement Compressed data in frequency domain Why use phase-shift based method?

  11. Phase shift Method Basic equation for wavefield extrapolation is This equation can not handle velocity lateral variation !!

  12. SSF METHOD Basic steps include: Split velocity field: Vi=V0+dVi Wavefiled extrapolation with V0 in frequency-wavenumber domain Phase correction with dVi in frequency-space domain

  13. PSPI METHOD Basic steps of PSPI consist of: Introduce several reference velocities: Vi Wavefiled extrapolation with each Vi in frequency-wavenumber domain Interpolating reference wavefield in frequency- space domain

  14. SSF+FD(FFD) METHOD Basic equation for FFD migration is: SSF FD FFD = SSF+FD

  15. CONTENTS . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work

  16. PHASE ENCODING ALGORITHM Where Sn is source term; Dn is nth shot gather; Ss and Ds are the encoded source term and super shot gather; n is the index of shot gather

  17. can be obtained by following ways: Generate random coefficients with valuem of 1 or -1 Generate random coefficients with range [0,2 ] Generate random coefficients with Gaussian sampling HOW TO GET ?

  18. Phase encoding Phase encoding HOW TO PHASE ENCODE ? Strategy I: G1 Gn Gm-n Gm K<M G’k G’1 Migrating Output

  19. HOW TO PHASE ENCODE? Strategy II: G1 G2 Gi Gm Phase Encoding Gsuper Output Migrating

  20. CONTENTS . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work

  21. NUMERICAL RESULTS FOR SEG/EAGE SALT MODEL DATA X (km) 0 15 0 Depth (km) 3

  22. TEST1: Comparison of Four Migration Methods X (km) X (km) 0 0 15 15 0 Depth (km) 3 Kirchhoff SSF Without Multiples

  23. TEST1: Comparison of Four Migration Methods X (km) X (km) 0 0 15 15 0 Depth (km) 3 PSPI SSF+FD Without Multiples

  24. TEST1: Comparison of Four Migration Methods X (km) X (km) 0 0 15 15 0 Depth (km) 3 Kirchhoff SSF With Multiples

  25. TEST1: Comparison of Four Migration Methods X (km) X (km) 0 0 15 15 0 Depth (km) 3 PSPI SSF+FD With Multiples

  26. TEST1: CPU Time of Four Mig. Methods

  27. TEST2: Comparison of Three Phase Encoding Methods X (km) X (km) 0 0 15 15 0 Depth (km) 3 (a) (c) 0 15 0 a. Random distribution b. Linear encoding c. Gaussian distribution Depth (km) 3 (b)

  28. TEST3: Comparison of SSF Migration with Phase Encoding Strategy I X (km) X (km) 0 15 0 15 0 Depth (km) 3 (a). encode=2 (c). encode=10 0 Depth (km) 3 (b). encode=4 (d). no encoding(320)

  29. TEST3: CPU Time of SSF Migration with Phase Encoding Strategy I

  30. TEST3: Comparison of SSF Migration with Phase Encoding Strategy II X (km) X (km) 0 15 0 15 0 Depth (km) 3 (a). nmig=100 (c). nmig=60 0 Depth (km) 3 (b). nmig=80 (d). no encoding(320)

  31. TEST3: CPU Time of SSF Migration with Phase Encoding Strategy II

  32. TEST4: Comparison of SSF+FD Migration with Phase Encoding Strategy I X (km) X (km) 0 15 0 15 0 Depth (km) 3 (a). encode=2 (c). encode=10 0 Depth (km) 3 (b). encode=4 (d). no encoding(320)

  33. TEST4: CPU Time of SSF+FD Migration with Phase Encoding Strategy I

  34. TEST4: Comparison of SSF+FD Migration with Phase Encoding Strategy II X (km) X (km) 0 15 0 15 0 Depth (km) 3 (a). nmig=100 (c). nmig=80 0 Depth (km) 3 (b). nmig=80 (d). no encoding(320)

  35. TEST4: CPU Time of SSF+FD Migration with Phase Encoding Strategy II

  36. TEST5: CPU Time of SSF+FD Migration with Phase Encoding Strategy II 1 node 10 nodes

  37. TEST6: Preliminary Result of 3D SSF Migration with Salt Model(zero offset data) X (km) X (km) 0 4 0 4 0 Depth (km) 10 Velocity slice (depth=1.6 km) Migration image (depth=1.6 km)

  38. TEST4: Preliminary Result of 3D SSF Migration with Salt Model(zero offset data) X (km) X (km) 0 4 0 4 0 Depth (km) (c). nmig=80 10 Velocity slice (depth=2 km) Migration image (depth=2 km)

  39. CONTENTS . Introduction . Brief Description of Wave Equation Methods: SSF, PSPI, FFD (SSF+FD) . Phase Encoding Algorithm . Numerical Results . Conclusion and future work

  40. CONCLUSION The test results show: Phase encoding can reduce computational effort of wave equation migration by factor three or more SSF+FD yields best image result.  

  41. Future Work  3D prestack migration method is being tested on SALT model data We will mainly focus on developing an efficient wave equation method with phase encoding and other type compression technique for 3D migration 

  42. ACKNOWLEDGEMENTS I greatly appreciate the sponsors of UTAM Consortium for their financial support I also thank all the people who give me suggestions and help for this work

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