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Data modeling using Cagniard-de Hoop method

Explore the theory and application of data modeling using the innovative Cagniard-de Hoop method. Discover its benefits in deghosting, velocity imaging, and nonlinear inversion techniques for high-quality data generation and processing. This presentation covers theory, numerical tests, and conclusions from the M-OSRP annual meeting at the University of Houston in 2006.

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Data modeling using Cagniard-de Hoop method

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  1. Data modeling using Cagniard-de Hoop method Jingfeng Zhang and Arthur B. Weglein M-OSRP annual meeting University of Houston May 10th–12th, 2006

  2. Outline • Background and Motivation • Theory: • Data generation using Cagniard-de Hoop method • Numerical tests • Conclusions

  3. Background and Motivation • Data modeling is important for: • Evaluation of new algorithms • Forward model matching methods • Conventional data processing techniques: • Arrival time; Amplitude

  4. Background and Motivation • (Recently) developed new algorithms: • Deghosting • ISS free surface multiple removal method • ISS internal multiple attenuation and elimination • Imaging without the velocity • Nonlinear inversion

  5. Background and Motivation • Reasons to choose Cagniard-de Hoop method for deghosting: • 1.5D medium data will suffice for initial tests • “Perfect” data: regular integrand on a finite integral range • Quality control each processing step: deghosting performed in two steps

  6. Background and Motivation Primary and S-G Primary and S-G Receiver deghosting + Source deghosting Primary R-G and S-R-G

  7. Theory The 2D acoustic constant densitywave equation: The corresponding Green’s function equation: Relationship:

  8. Theory Fourier Transform over and (layered medium): where Just need to solving 1D wave equation and matching boundaries for layered medium.

  9. Theory Even for the direct wave in homogeneous medium:

  10. Caniard-de Hoop Fourier Transform over and Laplace transform over :

  11. Strategy: Manipulate the integral ( ) Aki & Richards (2nd Edition)

  12. Theory Direct wave: Primary: Pre-critical Pos-critical

  13. Theory (1) Evaluation of the integration (direct wave):

  14. Theory (2) Sign of :

  15. Numerical Tests

  16. Numerical Tests

  17. Numerical Tests Correct data

  18. Incorrect data

  19. Deghosting result using correct data

  20. Deghosting result using incorrect data

  21. Deghosting results Red Solid: Exact results; Blue Dash: Calculated results

  22. FSMR results Red Solid: Before FSMR; Blue Dash: After FSMR

  23. Conclusions and Acknowledgments • Very high quality of data can be generated using Cagniard-de Hoop method. • It is demonstrated that using the generated data deghosting and FSMR algorithms produce very good results. • We appreciate the help from Adrian de Hoop. • The support of M-OSRP sponsors is much appreciated.

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