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G. Partyka Oct 2006

Seismic Resolution of Zero-Phase Wavelets Designing Optimum Zero-Phase Wavelets R. S. Kallweit and L. C. Wood Amoco Houston Division DGTS January 12, 1977. G. Partyka Oct 2006. Questions. Can different types of zero-phase wavelets be compared in terms of temporal resolution.

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G. Partyka Oct 2006

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  1. Seismic Resolution of Zero-Phase WaveletsDesigning Optimum Zero-Phase WaveletsR. S. Kallweit and L. C. WoodAmoco Houston DivisionDGTS January 12, 1977 G. Partyka Oct 2006

  2. Questions • Can different types of zero-phase wavelets be compared in terms of temporal resolution. What wavelet shape is well suited for comparing against? • Can we separate the ability of zero-phase wavelets to resolve thin beds from variations in side-lobe tuning effects? What is an optimum wavelet shape? Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  3. What are the Limits of Temporal Resolution? • How thin can a bed become and still be resolvable? In other words, when is the measured interval time essentially the same as the true interval time? • What are the errors between the true interval times and the measured interval times through thick beds? Review: Rayleigh Ricker Widess Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  4. Why Focus on Zero-Phase? • Non zero-phase wavelets greatly complicate resolution. • Zero-phase wavelets simplify resolution: • traces containing zero-phase wavelets will have seismic interfaces located in general at the centers of the peaks and troughs of the trace (neglecting tuning effects and noise). Thick Bed Thin Bed Well Log Well Log Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  5. What is an Optimum Wavelet Shape to Compare Against? Low Pass Sinc Time Frequency amplitude time frequency Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  6. Temporal Resolution of the Low-Pass Sinc Wavelet amplitude TR T0 fm f4 frequency Tb Temporal resolution is established in terms of the maximum frequency temporal resolution: TR = 1 / (3.0)fm = 1 / (1.5)f4 wavelet breadth: Tb = 1 / (1.4)fm = 1 / (0.7)f4 peak-to-trough: Tb / 2 = 1 / (2.8) fm = 1 / (1.4)f4 1st zero crossings: T0 = 1 / 2fm = 1 / f4 relationship of Tb to TR TR = 0.47Tb = 0.93Tb / 2 Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  7. What effect does a low cut have on resolution? Negligible for wavelets with bandpasses of 2-octaves or greater ….but, must have signal in bandpass. Time Frequency amplitude time frequency Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  8. Temporal Resolution (TR) of the Bandpass Sinc Wavelet f4 sinc f1 sinc band-pass sinc amplitude fm = (f1 + f4) / 2 f4 TR T0 f1 frequency f1 fm f4 Tb The band-pass sinc wavelet is the difference between two (f1 and f4) sinc functions. Effects of the f1 sinc are negligible for wavelets with band-pass ratios 2-octaves and greater. temporal resolution: TR = 1 / (1.5)f4 ; 2 octaves (where f4 / f1 .ge. 4) wavelet breadth: Tb = 1 / (0.7)f4 ; 2 octaves(where f4 / f1 .ge. 4) peak-to-trough: Tb / 2 = 1 / (1.4)f4 ; 2 octaves (where f4 / f1 .ge. 4) 1st zero crossings: T0 = 1 / (2fm) ; all octaves relationship of Tb to TR: TR = 0.47Tb = 0.93Tb / 2 ; for sincs .ge. 2 octaves Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  9. Sinc Bandwidth and Temporal Resolution with Constant fmax 30 30 2–64 Hz Sinc (5 octaves) 16–64 Hz Sinc (2 octaves) 20 20 peak-to-trough separation (ms) peak-to-trough separation (ms) 10 10 TR TR 0 0 0 10 20 30 0 10 20 30 spike separation (ms) spike separation (ms) Temporal Resolution is the same for all sinc wavelets with 2 octaves or greater bandwidths having the same fmax TR = 1 / (1.5)fmax Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  10. Non-Binary Complexity 30 16-to-64 Hz (2-octave) sinc wavelet convolved with alternate polarity spike pairs of unequal amplitude 25 20 What is the effect on temporal resolution when the amplitude of the second spike of a set of alternate polarity spike pairs is varied? peak-to-trough separation (ms) 15 1.0 -1.0 1.0 10 -0.8 1.0 5 1.51 TR -0.6 0 0 5 10 15 20 25 30 spike separation (ms) Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  11. Questions • Can different types of zero-phase wavelets be compared in terms of temporal resolution. What wavelet shape is well suited for comparing against? • Can we separate the ability of zero-phase wavelets to resolve thin beds from variations in side-lobe tuning effects? What is an optimum wavelet shape? Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  12. Wavelet Shape and Sidelobe Interference • Wavelets designed with a vertical or near-vertical high end slope exhibit high frequency sidelobes that can cause significant distortions in reflection amplitudes and associated event character. • An alternate wavelet is proposed called the Texas Double in recognition of the primary characteristic being a 2-octave slope on the high frequency side. Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  13. Texas Double Wavelets Time Domain: • negligible high frequency sidelobe tuning effects. • maximum peak-to-sidelobe amplitude ratios. Frequency Domain: • vertical or near-vertical low-end slope. • 2-octave linear slope on the high-end. Amplitudes are measured using a linear rather than decibel scale. • end frequencies correspond to the highest and lowest recoverable signal frequency components of the recorded data. Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  14. Development of High Frequency Side-Lobes High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  15. Development of High Frequency Side-Lobes High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  16. Development of High Frequency Side-Lobes High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 3 octave slope 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  17. Development of High Frequency Side-Lobes High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 2 octave slope 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  18. Development of High Frequency Side-Lobes High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 1 octave slope 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  19. Development of High Frequency Side-Lobes High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  20. Development of Low Frequency Side-Lobes Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  21. Development of Low Frequency Side-Lobes Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  22. Development of Low Frequency Side-Lobes Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 4.0 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  23. Development of Low Frequency Side-Lobes Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 3.0 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  24. Development of Low Frequency Side-Lobes Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 2.4 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  25. Development of Low Frequency Side-Lobes Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 2.0 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  26. High Frequency Held Constant (Klauder Wavelets) REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  27. High Frequency Held Constant (Klauder Wavelets) amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 4.0 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  28. High Frequency Held Constant (Klauder Wavelets) amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 3.0 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  29. High Frequency Held Constant (Klauder Wavelets) amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 2.4 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  30. High Frequency Held Constant (Klauder Wavelets) amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 2.0 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  31. High Frequency Held Constant (Klauder Wavelets) amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 1.4 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  32. Decreasing the Low Frequency Slope REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  33. Decreasing the Low Frequency Slope amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 3 octaves 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  34. Decreasing the Low Frequency Slope amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 2 octave slope 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  35. Decreasing the Low Frequency Slope amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 3 octave slope 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  36. Decreasing the High and Low Frequency Slopes REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  37. Decreasing the High and Low Frequency Slopes amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 3 octave sinc 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  38. Decreasing the High and Low Frequency Slopes amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  39. Decreasing the High and Low Frequency Slopes amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  40. Decreasing the High and Low Frequency Slopes amplitude 50 60 40 20 30 0 10 frequency REFLECTIVITY IMPEDANCE 0 0 Texas Double 50 50 100 100 Travel Time (ms) 150 150 200 200 Wavelet 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka Oct 2006

  41. Proposed Standard Equi-Resolution Comparison • One of the difficulties involved in trying to compare traces containing different zero-phase wavelets designed over identical bandpasses is the question of what to compare and measure each trace against. • It is rather unsatisfactory to compare the traces against one another since there are too many unknowns. • A standard comparison is needed. • The standard trace proposed is one where the convolving wavelet has the same temporal resolution as the sinc wavelet over a given bandpass but has no sidelobes whatsoever. Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  42. Low-Pass Sinc vs Low-Pass Texas Double 30 30 TR = 1 / 1.5f4 TR = 1 / 1.2f4 20 20 peak-to-trough separation (ms) peak-to-trough separation (ms) 10 0–0-62-64 Hz Sinc 10 0–0-20-80 Hz Texas Double TR TR 0 0 0 10 20 30 0 10 20 30 spike separation (ms) spike separation (ms) Conclusion: Over a given low-pass, temporal resolution of the Texas Double wavelet equals 80% of the temporal resolution of the sinc wavelet. Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  43. Equivalent Temporal Resolution: Ormsby to Low-Pass Sinc 1.0 0.9 amplitude 0.8 f3 fs/f4 0.7 fs f4 frequency 0.6 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 f3 / f4 Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  44. Is it worth giving up the 20% loss in Temporal Resolution? • Can the benefits associated with attenuating high-frequency sidelobes outweigh the 20% loss in temporal resolution? • Well-log based comparisons, suggest that they can. …as long as that 20% is not critical to the required imaging. Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  45. Well-Log Comparison 00-00-20-80 00-00-62-64 08-09-20-80 08-09-62-64 08-09-16-64 00-00-20-80 00-00-62-64 08-09-20-80 08-09-62-64 08-09-16-64 Reflectivity raw rc raw High Frequency Tuning Effects Only Desired Standard Negligible Effect Texas Double Sinc Wavelet Raw Input G. Partyka Oct 2006

  46. Well-Log Comparison - 3 Octaves 00-00-20-80 00-00-62-64 08-09-20-80 08-09-62-64 08-09-16-64 00-00-20-80 00-00-62-64 08-09-20-80 08-09-62-64 08-09-16-64 Layering raw layering Reflectivity raw rc G. Partyka Oct 2006

  47. Well-Log Comparison - 2 Octaves 00-00-20-80 00-00-62-64 16-17-20-80 16-17-62-64 16-17-18-64 00-00-20-80 00-00-62-64 16-17-20-80 16-17-62-64 16-17-18-64 Layering raw layering Reflectivity raw rc G. Partyka Oct 2006

  48. Gradually Increasing Frequency Content to Examine Tuning Effects When filters change in a linear and gradual manner, we would hope that the traces would do likewise. Unfortunately, sidelobe interference gets in the way. Seismic Resolution of Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka Oct 2006

  49. Well-Log Example - Layering Sinc Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant 6-10-036-040 6-10-066-070 6-10-096-100 Raw Layering 6-10-036-040 6-10-066-070 6-10-096-100 Raw Layering

  50. Well-Log Example - Layering 10 Hz High-Cut Slope Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant 6-10-030-040 6-10-060-070 6-10-090-100 Raw Layering 6-10-030-040 6-10-060-070 6-10-090-100 Raw Layering

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