1. Seismic Thickness Estimation: Three Approaches, Pros and Cons Gregory A. Partyka bp

2. Outline IntroductionIntroduction Three Approaches Examples Pros and Cons

3. Outline IntroductionIntroduction Three Approaches Examples Pros and Cons

4. Blocky Wedge Model 366 400 Travel Time (ms) 432 466 REFLECTIVITY Temporal Thickness (ms) 050 40 302010

5. Blocky Wedge Model 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) REFLECTIVITY BANDLIMITED REFLECTIVITY (8-10-40-50hz) +0.025 -0.025 Amplitude 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) 050 40 302010050 40 302010

6. Blocky Wedge Model 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) REFLECTIVITY BANDLIMITED REFLECTIVITY (8-10-40-50hz) +0.025 -0.025 Amplitude 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) 050 40 302010050 40 302010

7. Outline Introduction Three ApproachesThree Approaches Examples Pros and Cons

8. Three Approaches to Thickness Estimation 1.Conventional peak-trough time separation amplitude 2.Spectral Decomposition 1 st dominant frequency and amplitude 3.Spectral Decomposition discrete frequency components

9. Three Approaches to Thickness Estimation 1.Conventional peak-trough time separationpeak-trough time separation amplitudeamplitude 2.Spectral Decomposition 1 st dominant frequency and amplitude 3.Spectral Decomposition discrete frequency components

10. Conventional Thickness Estimation 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) REFLECTIVITY BANDLIMITED REFLECTIVITY (8-10-40-50hz) +0.025 -0.025 Amplitude 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) 050 40 302010050 40 302010

11. Conventional Thickness Estimation 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) REFLECTIVITY BANDLIMITED REFLECTIVITY (8-10-40-50hz) +0.025 -0.025 Amplitude 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) 050 40 302010050 40 302010 tuning thickness Widess, M.B., 1973, How Thin is a Thin Bed?, Geophysics, vol. 38, pg 1176-1180. Kallweitt, R.S. and Wood, L.C, 1982, The Limits of Resolution of Zero-Phase Wavelets, Geophysics, vol.47, pg 1035-1046.

12. -0.0250 Conventional Thickness Estimation 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) REFLECTIVITY BANDLIMITED REFLECTIVITY (8-10-40-50hz) +0.025 -0.025 Amplitude 366 400 Travel Time (ms) 432 466 Temporal Thickness (ms) 050 40 302010050 40 302010 Temporal Thickness (ms) 050 40 302010 50 40 Peak-Trough Time Separation (ms) 30 20 10 0 -0.0000 Largest Negative Amplitude -0.0050 -0.0100 -0.0150 45 35 25 15 5 -0.0200 tuning thickness tuning thickness = 1 1.4 * frequency upper tuning thickness Widess, M.B., 1973, How Thin is a Thin Bed?, Geophysics, vol. 38, pg 1176-1180. Kallweitt, R.S. and Wood, L.C, 1982, The Limits of Resolution of Zero-Phase Wavelets, Geophysics, vol.47, pg 1035-1046.

13. Three Approaches to Thickness Estimation 1.Conventional peak-trough time separation amplitude 2.Spectral Decomposition 1 st dominant frequency and amplitude1 st dominant frequency and amplitude 3.Spectral Decomposition discrete frequency components

14. Spectral Decomposition uses the discrete Fourier transform to: –quantify thin-bed interference, and –detect subtle discontinuities.

15. Spectral Interference Source Wavelet Amplitude Spectrum Thin Bed Reflection Amplitude Spectrum Thin Bed Reflection Reflected Wavelets Source Wavelet Thin Bed Reflectivity Acoustic Impedance Temporal Thickness Fourier Transform Fourier Transform Amplitude Frequency Temporal Thickness 1 The spectral interference pattern is imposed by the distribution of acoustic properties within the short analysis window. Paryka, Gridley and Lopez, The Leading Edge, vol 18, no 3, 1999

16. Blocky Wedge Model 366 400 Travel Time (ms) 432 466 REFLECTIVITY Temporal Thickness (ms) 050 40 302010

17. 050 40 302010050 40 302010 Spectral Interference 366 400 Travel Time (ms) 432 466 5050 150 Frequency (Hz) 100 200 0 250 Temporal Thickness (ms) REFLECTIVITY SPECTRAL AMPLITUDE 0.0014 0 Amplitude Temporal Thickness (ms)

18. 050 40 302010050 40 302010 Spectral Interference and Frequency 366 400 Travel Time (ms) 432 466 5050 150 Frequency (Hz) 100 200 0 250 Temporal Thickness (ms) REFLECTIVITY SPECTRAL AMPLITUDE 0.0014 0 Amplitude Temporal Thickness (ms) The temporal thickness of the wedge (t), determines the period of notching in the amplitude spectrum (P f ) with respect to frequency. Temporal Thickness 1 P f = 1 / t

19. 050 40 302010050 40 302010 Spectral Interference and Thickness 366 400 Travel Time (ms) 432 466 5050 150 Frequency (Hz) 100 200 0 250 Temporal Thickness (ms) REFLECTIVITY SPECTRAL AMPLITUDE 0.0014 0 Amplitude Temporal Thickness (ms) The value of the frequency component (f), determines the period of notching in the amplitude spectrum (P t ) with respect to bed thickness. Frequency 1 P t = 1 / f

20. 050 40 302010050 40 302010 Spectral Interference 366 400 Travel Time (ms) 432 466 5050 150 Frequency (Hz) 100 200 0 250 Temporal Thickness (ms) REFLECTIVITY SPECTRAL AMPLITUDE 0.0014 0 Amplitude Temporal Thickness (ms) 050 40 302010050 40 302010 Bandwidth 8-10-40-50 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 5050 150 Frequency (Hz) 100 200 0 250 Temporal Thickness (ms) +0.025 -0.025 Amplitude

21. Spectral Interference Bandwidth 8-10-40-50 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) +0.025 -0.025 Amplitude

22. Thickness via 1 st Dominant Frequency and Amplitude Bandwidth 8-10-40-50 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) +0.025 -0.025 Amplitude 1 st Dominant Frequency

23. Frequency upper and Frequency 1st-dominant = tuning thickness = 1 1.4 * frequency upper 1 2 * frequency 1st-dominant

24. Thickness via 1 st Dominant Frequency and Amplitude 1 st Dominant Frequency Bandwidth 8-10-40-50 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 1 st Dominant Amplitude 0.0008 0.0006 0.0002 0.0000 40 35 1 st Dominant Frequency 30 25 20 10 5 0 15 +0.025 -0.025 Amplitude tuning thickness tuning thickness = 1 2 * frequency 0.014sec = 1 2 * 36hz 1st-dominant

25. Three Approaches to Thickness Estimation 1.Conventional peak-trough time separation amplitude 2.Spectral Decomposition 1 st dominant frequency and amplitude 3.Spectral Decomposition discrete frequency componentsdiscrete frequency components

26. Spectral Interference Bandwidth 8-10-40-50 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) +0.025 -0.025 Amplitude

27. Thickness via Discrete Frequency Components 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 10hz Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 Amplitude 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 +0.025 -0.025 Amplitude 10hz tuning thickness 10hz amp 10hz tuning thickness tuning thickness = 1 2 * frequency 0.050sec = 1 2 * 10hz 1st-dominant

28. Thickness via Discrete Frequency Components 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 20hz Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 Amplitude 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 +0.025 -0.025 Amplitude 20hz tuning thickness 20hz amp 20hz tuning thickness tuning thickness = 1 2 * frequency 0.025sec = 1 2 * 20hz 1st-dominant

29. Thickness via Discrete Frequency Components 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 30hz Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 Amplitude 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 +0.025 -0.025 Amplitude 30hz tuning thickness 30hz amp 30hz tuning thickness tuning thickness = 1 2 * frequency 0.017sec = 1 2 * 30hz 1st-dominant

30. Thickness via Discrete Frequency Components 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 20hz 30hz 10hz Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 Amplitude 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 +0.025 -0.025 Amplitude 20hz tuning thickness10hz tuning thickness 20hz amp 30hz amp 10hz amp 30hz tuning thickness20hz tuning thickness 10hz tuning thickness tuning thickness = 1 2 * frequency 1st-dominant 30hz tuning thickness

31. Thickness via Discrete Frequency Components 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 20hz 30hz 10hz Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 Amplitude 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 +0.025 -0.025 Amplitude 20hz tuning thickness10hz tuning thickness 20hz amp 30hz amp 10hz amp 30hz tuning thickness20hz tuning thickness 10hz tuning thickness By choosing an appropriately-low frequency component, the entire range of possible thickness is forced below the tuning thickness, and therefore can be quantified using amplitude variability alone. 30hz tuning thickness

32. Thickness via 1 st Dominant Frequency and Amplitude 1 st Dominant Frequency Bandwidth 8-10-40-50 050 40 302010050 40 302010 366 400 Travel Time (ms) 432 466 BANDLIMITED REFLECTIVITY (8-10-40-50hz) BANDLIMITED SPECTRAL AMPLITUDE 0.0014 0 Amplitude 25 75 Frequency (Hz) 50 100 0 125 Temporal Thickness (ms) 050 40 302010 0.0014 0.0012 1 st Dominant Amplitude 0.0008 0.0006 0.0002 0.0000 40 35 1 st Dominant Frequency 30 25 20 10 5 0 15 +0.025 -0.025 Amplitude 20hz tuning thickness10hz tuning thickness 30hz tuning thickness20hz tuning thickness 10hz tuning thickness tuning thickness = 1 2 * frequency 1st-dominant 30hz tuning thickness

33. Outline Introduction Three Approaches ExamplesExamples Pros and Cons

34. Example Using discrete frequency components to determine relative thickening/thinning.

36. Simple Channel Cross-Section Animating from low to high frequency, causes amplitude contours to move from thick to thin. REFLECTIVITY SPECTRAL AMPLITUDE travel time (ms) frequency (Hz) 0 250

37. Example Using discrete frequency components to calibrate reservoir thickness.

38. Deep-Water Gulf of Mexico 8hz Spectral Amplitude Map WELL #1 Zone 1 1 mile Partyka, Thomas, Turco and Hartmann, SEG 2000

39. Thickness Modeling Thickness (ft) 040208060100 Frequency (hz) 0 40 60 20 10 30 50 70 amplitude 1 0 Spectral Signatures Well-Log Interpretation (Zone 1) shale Seismic Modeling (Zone 1) Two-Way Traveltime (ms) 0 200 100 150 50 amplitude 1 0 depth (feet) 01 sandoil Temporal Wedge Model 6hz 8hz Partyka, Thomas, Turco and Hartmann, SEG 2000

40. Thickness Calibration 6hz amplitude 8hz amplitude Amplitude 08hz Spectral Amplitude Zone 1 Thickness from 6hz and 8hz energy WELL #1 06hz Spectral Amplitude Zone 1 Modeled Spectral Signatures vs Thickness Zone 1 Frequency (hz) 0.008 0.007 0.006 0.005 0.004 0.003 WELL #1 0 100 50 WELL #1 1 0 1 mile 0 40 20 10 30 102030405060708090100 Thickness (ft) 6hz 8hz Partyka, Thomas, Turco and Hartmann, SEG 2000

41. Outline Introduction Three Approaches Examples Pros and ConsPros and Cons

42. Conventional Thickness Estimation Pros: –user and time intensiveness mandates careful QC. Cons: –two attributes are required to quantify thickness: peak-trough time-separation for thickness greater-than the tuning thickness, and amplitude for thickness less-than the tuning thickness. –user and time intensiveness mandates careful QC.

43. 1 st Dominant Frequency and Amplitude Pros: –collapses the Tuning Cube into two maps. –does not require careful seismic event picking when the zone of interest is relatively bright. Cons: –as in the conventional approach, two attributes are required to quantify thickness: 1 st -dominant frequency for thickness greater-than the tuning thickness, and 1 st -dominant amplitude for thickness less-than the tuning thickness.

44. Discrete Frequency Components Pros: –can be used qualitatively to determine relative thickening/thinning. –can be used quantitatively to calibrate reservoir thickness. –usually exhibit substantially more fidelity than full-bandwidth, conventional amplitude/attributes. Can therefore selectively analyse frequencies exhibitting highest signal fidelity. –usually provide superior rock mass (stratigraphic and structural) and fault definition. –can be integrated with other appropriate information to yield a more comprehensive understanding of the reservoir. –does not require careful seismic event picking when the zone of interest is relatively bright.

45. Discrete Frequency Components Cons: –complex layer distributions require seismic modeling analysis to determine relationship between spectral response and thickness.