1. Wavelet estimation from towed-streamer pressure measurement and its application to free surface multiple attenuation
Zhiqiang Guo (UH, PGS)
Arthur Weglein (UH)
And
T. H. Tan (Shell)

2. Outline
Introduction
Theory
Numerical examples
Conclusions

3. Introduction
Theory
Numerical examples
Conclusions

4. Why do we need the wavelet? De-ghosting
Air
Water
The recorded data will be a combination of reflection and ghost.

5. De-multiple Wave equation based method needs the wavelet
Multiple includes the two wavelets
Energy minimization criterion (indirect)
it is too blunt when multiples and primaries are weak, near each other or experience destructive interference.
this motivates the search for a direct wavelet, allows the multiple attenuation method to reach their full potential.

6. Scattering inversion & imaging= G - G =
D/A 1

7. Review of the current wavelet estimation methods
Statistical method: Wiener deconvolution
Assumption: white reflectivity, minimum phase
Problem: no phase property
Deterministic method: matching surface seismic to well-log data
Direct measurement in marine case
Deep water
No interference between the direct wave and reflections

8. Outline
Introduction
Theory
Numerical examples
Conclusions

9. Total wavefield at cable Normal derivative of wavefield
Outline of new wavelet estimation FS
Total wavefield at cable MS
water
Normal derivative of wavefield
Or Velocity a
Wavelet
: source
: cable a
: earth

10. Wavelet estimation (Weglein and Secrest, 1990 )FS FS MS MS ?
Require: wavefield and its normal derivative/velocity

11. Derivative of the Wavefield (Osen, Tan)
F.S
M.S
Require: wavefield and an extra receiver

12. Derivative of the Wavefield (cont.)FS MS

13. New method of the wavelet estimation
Is it perfect to take the derivative when and then substitute it into wavelet formula ?
No. Wavelet eq. is the same as prediction eq. at M.S., they are linearly dependent.
I deliberately introduce some perturbation, and it is valid for all x by altering the two equations so that they are independent.

14. New method of the wavelet estimation (cont.)FS MS
where

15. Outline
Introduction
Theory
Numerical examples
Conclusions

16. Model 1: the total wavefield
dx=2 m, f=40 Hz, Ricker wavelet, time sample=1 ms, three scatteres in half space.
F.S 2m 6m
P.S.
M.S
C0=1500m/s
Three scatters: (-50,40), (0,0), (50,40)

17. Estimated wavelets
z=0.3m
Input &
z=0.7m
z=2.5m

18. Error analyses

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

20. Model 2: 40m reflector & 10% random noise (H. Tan)
dx=2 m, f=30 Hz, Blackman wavelet, time sample=1 ms, one reflector in half space, the reflector is at 40 m, 60m and 80 m below F.S., the water velocity is 1500 m/s, below water layer is 2000 m/s. Model all the wavefield.

21. Wavelet estimation for model 40m, 60m, 80m

22. Final estimated wavelet
A: weight by 1 for all depths; B: 100% zero offset, 20% far offset; C: 100% at 100m, 60% at 1500 m.

23. Wavelet application: de-multiple examples
Take the 80 m model
Primary interfere with multiple
Predict 1st order multiple with and without the estimated wavelet
Comparison of adaptive subtraction with and without the wavelet

24. 80 m model: shot gather-- primary and multiple
1st M

25. Predicted 1st order multiple by P*P
1st M

26. Predicted 1st order multiple by P*P/A
1st M

27. De-multiple without the wavelet
Residual 1st M

28. De-multiple with the wavelet

29. Model 3: two primaries and 1 multiple
H1=235 m
V1= 1500 m/s
H2=480 m
V2= 3000 m/s P2
V3=4000 m/s
P1: primary one
P2: primary two, M1: 1st order multiple

30. Second primary interfering with 1st order multiple
P1: primary one
P2: primary two, M1: 1st order multiple

31. De-multiple without the wavelet
Energy minimization criterion failed, because it produces the signal that has minimum energy when the multiple is attenuated. However the energy of P2 should be increased after de-multiple.

32. De-multiple with the estimated wavelet
Adaptive subtraction, P2 is preserved.

33. Outline
Introduction
Theory
Numerical examples
Conclusions

34. Conclusions
This is a new method to estimate the wavelet, it requires no information below the earth, no assumption about the wavelet itself, only pressure wavefield on the cable.
Numerical results for different prediction depths and noise show that the method is stable
Wave-theoretic demultiple gets benefit when the wavelet was used.