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Wavelet Estimation Below Towed Streamers

Wavelet Estimation Below Towed Streamers. Zhiqiang Guo University of Houston and PGS. M-OSRP Annual Meeting University of Houston March 31 – April 1, 2004. Why Do We Need the Wavelet?. De-multiple, de-ghosting Wave equation based method needs wavelet. Why Do We Need the Wavelet? (cont.).

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Wavelet Estimation Below Towed Streamers

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  1. Wavelet Estimation Below Towed Streamers Zhiqiang Guo University of Houston and PGS M-OSRP Annual Meeting University of Houston March 31 – April 1, 2004

  2. Why Do We Need the Wavelet? De-multiple, de-ghosting Wave equation based method needs wavelet

  3. Why Do We Need the Wavelet? (cont.) Inverse scattering & sub-series image All events are assumed to be primaries

  4. Wavelet Estimation (Weglein and Secrest, 1990 ) FS FS MS MS (1) ? Require: wavefield and its normal derivative

  5. Wavefield prediction (H. Tan & A. Osen) F.S M.S (2) Require: wavefield and an extra receiver

  6. Observation (H. Tan) when f<125Hz, z=6m

  7. Amplitude of Predicted Wavefield Predicted Exact

  8. Phase of Predicted Wavefield Predicted Exact

  9. Amplitude of Predicted Derivative Predicted Exact

  10. Phase of Predicted Derivative Predicted Exact

  11. Problem FS MS We do need normal derivative under the source, in order to use Weglein&Secrest’s formula to obtain wavelet

  12. New Method of Wavelet Estimation To avoid the singularity under the source, we include AG Is it perfect to take the derivative when and then substitute it into Weglein & Secrest formula ?

  13. Alteration: add some perturbation on purpose No. Equation (1) is the same as equation (2) at M.S. (Weglein and Amundsen 2003) , in order to use both of them, we deliberately introduce some error, and it is valid for all x by altering the two equations so that they are independent. • Is it ok to take the derivative above M.S. instead of at M.S. ?

  14. New Method of Wavelet Estimation (cont.) Weglein & Secrest

  15. New Method of Wavelet Estimation (cont.) • How big is the error ? • Stable ? As • Take account of the effect of Green’s • Function under source

  16. Model with three scatters Scatters: (-50,40), (0,40), (50,40) Free surface 2m 6m Measurement surface C0=1500m/s

  17. Estimated wavelets

  18. Error analyses

  19. Dx(1,2,5m) change effect on wavelet estimation

  20. Cable depth error (15 % of cable depth=6m)

  21. Model: 40m Reflector & 10% random noise (H. Tan)

  22. Weighting F.S. Reflector =40m zb=100m Zb=500m Zb=1000m Zb=1500m

  23. Weighting (cont.) W= 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2 Zb=100m Zb=500m Zb=1000m Zb=1500m Zero offset: 100% Far offset(200m): 20% For all four estimation depths B W=0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2 Zero offset: 100% Far offset(200m): 20% For 1st depth 2ns: 80% of 1st 3rd : 70% of 1st 4th: 60 % of 1st C 80% 70% 60%

  24. Weighting (cont.)

  25. Conclusion & future work • Tests for different prediction depths and noise stability on synthetic data are encouraging • Further tests are planned for the impact on wave-theoretic demultiple methods based on energy minimization method for wavelet

  26. Acknowledgements Dr. Weglein Dr. Tan M-OSRP

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