1. SISMO www.sismo.srv.br Can we use the spectral ridges to estimate Q ? Marcílio Castro de Matos marcilio@matos.eng.brmarcilio@matos.eng.br www.matos.eng.brwww.matos.eng.br 1 Attribute-Assisted Seismic Processing and Interpretation http://geology.ou.edu/aaspi/ Signal Processing Research, Training & Consulting www.sismo.srv.br

2. Summary Spectral ridges Q estimation Examples Conclusions SyntheticReflectivityCWT Magnitude CWT magnitude 0 pos CWT MML

3. Spectral ridges Introduction Continuous Wavelet Transform (very brief review) ICWTdec Examples Conclusions 3

4. Time Frequency Reflectivity r(t) Source wavelet s(t) Noise n(t) Seismic data u(t) * + Bandlimited white spectrum Modified from Kurt Marfurt course(Partyka et al, 1999) Long window spectral decomposition and the convolutional model White spectrum

5. Colored spectrum Time Frequency Reflectivity r(t) Source wavelet s(t) Noise n(t) Seismic data u(t) * + Bandlimited colored spectrum Short window spectral decomposition and the convolutional model Modified from Kurt Marfurt course(Partyka et al, 1999)

6. 1822 Fourier book From: http://books.google.com/ Animated plot of the first five successive partial Fourier series. From wikipedia.org

7. (Yilmaz, 2001) Seismic zero phase wavelet Summation of co-sinusoids with zero phase

8. 8 Short Time Fourier Transform – STFT The simplest time-frequency representation

9. 9 Short Time Fourier Transform – STFT Amplitude and Phase spectrum

10. Time-frequency pattern???

11. Spectral ridges Introduction Continuous Wavelet Transform (very brief review) ICWTdec Examples Conclusions 11

12. Continuous Wavelet Transform  (x)  L 2 (  ) is called a wavelet

13. Continuous Wavelet Transform (CWT) time Amplitude The CWT can be interpreted as a band pass filter response at each scale s Scales Time (ms)

14. Grossmann and Morlet introduced CWT formally in 1984

15. Inverse CWT SyntheticReflectivityCWT MagnitudeVoicesICWT CWT magnitude 0 pos Σ

16. Summary Introduction Continuous Wavelet Transform (very brief review) Pseudo deconvolution (icwtdec) Examples Conclusions 16

17. Math behind…

18. Singularities detection and characterization through Continuous Wavelet Transform (CWT): Lipschitz (Hölder) Coefficients

20. CWT modulus maxima line SyntheticReflectivityCWT Magnitude CWT magnitude 0 pos CWT MML

21. WTMMLA seismic applications

22. ICWT “deconvolution” workflow SyntheticReflectivityCWT Magnitude CWT magnitude 0 pos CWT MML CWT Morlet CWT MML ICWT Shrunken Morlet CWT MML voices Σ

23. Relative acoustic impedance from ICWTDEC WORKFLOW - Re-scale seismic trace: |s(t)|<<1 - Integration filter (Peacock, 1979) - High-pass filter

24. Summary Introduction Continuous Wavelet Transform (very brief review) ICWTdec Examples Conclusions 24

25. Case 1: Synthetic seismic channel 10 ms thickness trace

26. Case 1: Synthetic seismic channel 30 ms thickness trace

27. Synthetic channel and its ICWTdec ICWTDECRAI

28. Adding random noise

29. Case 2: Barnet Shale Original Seismic

30. ICWTdec

31. THINMAN™

32. Marble Falls Upper Barnett Lm Upper Barnett Sh Forestburg Lower Barnett Sh Viola ICWTdec 60 Amplitude 60 0

33. Marble Falls Upper Barnett Lm Upper Barnett Sh Forestburg Lower Barnett Sh Viola THINMAN™ 10 Amplitude 10 0

34. Case 3: Pre-stack (Hampson&Russel 2D demo data set) Twt (s) 0 0.7 Offset

35. ICWTdec Twt (s) 0 0.7 Offset

36. RAI Twt (s) 0 0.7 Offset

37. Spectral ridges Conclusions CWT spectral decomposition filtering process described dear generates high resolution events that correlate to major acoustic impedance changes. Since this broadening is a trace-by- trace independent process, laterally- consistent thin bed terminations and other truncations can be interpreted with confidence.

38. Q estimation Anelasticity and wave propagation “very brief” review Q estimation and spectral ridges Conclusions

39. Anelasticity Berea Sandstone Wyllie, et al, 1958 From Carl Sondergeld Rock Physics Course Notes, 2009

40. Anelasticity review From Carl Sondergeld Rock Physics Course Notes, 2009

41. Wave equation From Carl Sondergeld Rock Physics Course Notes, 2009

42. Attenuation per wavelength From Carl Sondergeld Rock Physics Course Notes, 2009

43. Normal incidence anelastic reflections From Carl Sondergeld Rock Physics Course Notes, 2009

44. Seismic wave behavior in absorptive media defined by v, ρ and Q. Figure 2.4 of Seismic Absorption Estimation and Compensation by Changjun Zhang M.Sc., The University of British Columbia, 2009 Q is inversely proportional to attenuation. The greater the Q value, the smaller the loss or attenuation! The phase lag Ψ is a direct measure of attenuation. The greater the phase lag, the greater the attenuation. Q for rock lies in the range of 10 to 200. If Q = Q( ω ) then M must also be a function of frequency! Moduli must depend upon frequency!

45. Q estimation Anelasticity and wave propagation “very brief” review Q estimation and spectral ridges Conclusions

46. Q estimation from spectral ratio freq Adrinal Ilyas, 2010, Estimation of q factor from seismic reflection data, MsC Curtin University Chopra, Alexeev, and Sudhakar, TLE 2003, High-frequency restoration of surface seismic data

47. Q estimation from spectral ratio SyntheticReflectivityCWT Magnitude CWT magnitude 0 pos CWT MML Spectral ridges can guide Q estimation from spectral ratio In Q computation, we need to compute the amplitude spectra of two adjacent events (Taner, 2000)

48. Q estimation from Peak Frequency variation Ricker wavelet Zhang & Ulrych, 2002, Geophysics, Estimation of Quality factors from CMP records

49. Q estimation from Peak Frequency variation Zhang & Ulrych, 2002, Geophysics, Estimation of Quality factors from CMP records

50. Q estimation from Peak Frequency variation Zhang_Ulrych_2007_Geophysics_Seismic absorption compensation A least squares inverse scheme

51. Frequency decay caused by thin-bed tuning and absorption Figure 4.2 of Seismic Absorption Estimation and Compensation by Changjun Zhang M.Sc., The University of British Columbia, 2009

52. Absorption and specdecomp phase components SyntheticReflectivityCWT Magnitude CWT magnitude 0 pos CWT MML 180 -180 CWT phase 1070 Frequency (Hz)

53. CWT Magnitude and Phase overlaid by spectral ridges The phase spectra will provide information for dispersion estimation. Attributes picked at the peak of the envelope represent the average of the wavelet attribute. That is why we pick the amplitude spectrum at the time of envelop peak for Q computation. Phase spectra is picked the same way. If we look at the phase spectra, we observe that most of the spectra of the events are horizontal, which means that these wavelets are zero phase, and their rotation angle is the phase corresponding to the envelop peak. Therefore, computation of dispersion consists of determining the phase differences at each sub-band trace and compute an average phase delay per cycle per second. Since dispersion is related to absorption, higher levels of dispersion will point to higher levels of absorption, which may indicate fracture in carbonates or unconsolidated snads in clastic environment. (Taner, 2000).

54. Conclusions CWT spectral decomposition filtering process described dear generates high resolution events that correlate to major acoustic impedance changes. It seems we can correlate spectral ridges with Q estimation

55. Acknowledgements Attribute-Assisted Seismic Processing and Interpretation http://geology.ou.edu/aaspi/ marcilio@matos.eng.brwww.matos.eng.br marcilio@matos.eng.brwww.matos.eng.br Thank you for your attention!!! Thanks to DEVON for providing a license to one of the seismic data volume used herein. Thanks to Carl Sondergeld Thanks to Roderick Perez from OU for his Barnet shale interpretation. Thanks also to PETROBRAS Reservoir Geophysics Management friends for their comments. Signal Processing Research, Training & Consulting www.sismo.srv.br