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This PowerPoint version of the material, was compiled by Greg Partyka (October 2006)

Designing Optimum Zero-Phase Wavelets R. S. Kallweit and L. C. Wood Amoco Houston Division DGTS January 12, 1977. This PowerPoint version of the material, was compiled by Greg Partyka (October 2006). G. Partyka (Oct 06). Wavelet Shape and Sidelobe Interference.

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This PowerPoint version of the material, was compiled by Greg Partyka (October 2006)

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  1. Designing Optimum Zero-Phase WaveletsR. S. Kallweit and L. C. WoodAmoco Houston DivisionDGTS January 12, 1977 This PowerPoint version of the material, was compiled by Greg Partyka (October 2006) G. Partyka (Oct 06)

  2. 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. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  3. Texas Double Wavelets • Time Domain Characteristics: • negligible high frequency sidelobe tuning effects. • maximum peak-to-sidelobe amplitude ratios. • Frequency Domain Characteristics: • 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. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  4. 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 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  5. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  6. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  7. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  8. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  9. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  10. 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 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  11. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  12. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  13. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  14. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  15. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  16. 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 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  17. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  18. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  19. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  20. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  21. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  22. 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 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  23. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  24. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  25. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  26. 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 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  27. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  28. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  29. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  30. 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) 150 150 200 200 250 250 300 300 0 10 20 30 40 50 0 10 20 30 40 50 Temporal Thickness (ms) Temporal Thickness (ms) G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  31. Texas Double in Practice • One may implement the Texas Double on real data by first running an amplitude whitening program followed by a 2-octave slope Ormsby filter. • The Texas Double design criteria should not be a goal of data acquisition. • It is of utmost importance that the signal-to-noise ratio of the high-frequency components be as large as possible, and therefore filtering process such as the Texas Double should occur in data processing and not in data acquisition. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  32. Example Amplitude Response of Dynamite Data 1.0 0.8 Raw Whitened Texas Double 0.6 amplitude 0.4 0.2 0 0 10 20 30 40 50 60 70 80 90 100 Frequency (Hz) The Texas Double in effect does not attenuate the high frequency components of the recorded data, but rather amplifies them less than the conventional whitened output obtained using program DAFD. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  33. 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. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  34. Temporal Resolution – 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 10 TR TR 0–0-62-64 Hz Sinc 0–0-20-80 Hz Texas Double 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. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  35. 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 G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  36. 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? • The following well-log based comparisons, suggest that they can. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  37. Well-Log Comparison • Any observed differences are due to sidelobe tuning or temporal resolution. • To determine differences associated with sidelobes as opposed to those associated with temporal resolution, compare each trace to the 8-9-20-80 track. • 2-octave and 3-octave bandpass wavelets: • have identical terminal frequencies. • have the same high frequency sidelobes and temporal resolution. • allow low frequency sidelobes to be compared. • Traces containing different wavelets but with the same temporal resolution can be compared in order to observe differences due to sidelobe tuning effects. 00-00-20-80 00-00-62-64 08-09-20-80 08-09-62-64 08-09-16-64 raw Desired Standard No Sidelobes (resolution of a 64 Hz sinc) Negligible Effect Low Frequency Sidelobes (resolution of a 64 Hz sinc) Texas Double Low Frequency Sidelobes (80% resolution of of a 64 Hz sinc) Sinc Wavelet High and Low Frequency Sidelobes (resolution of a 64 Hz sinc) High Frequency Tuning Effects Only High Frequency Sidelobes (resolution of a 64 Hz sinc) Raw Input Layering or Reflectivity G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  38. 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 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  39. 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 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  40. 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 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  41. 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 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  42. 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 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  43. 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 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  44. Well-Log Examples • The following figures illustrate the sensitivity of the side-lobe tuning effects of the sinc and Texas Double wavelets to small changes in high frequency components. • The layered log and corresponding reflectivity were filtered holding the low side constant for each filter and varying the high side in 1 Hz increments. • Since the filters change in a linear and gradual manner, we would hope that the traces would do likewise. Unfortunately, significant trace-to-trace variations are apparent. • Two sets of Texas Double filters are also applied, and compared with the sinc wavelet results. One Texas Double set exhibits the same temporal resolution as the bandpass sinc set. The other Texas Double set mirrors the f1 and f4 filter positions of the sinc wavelets. • The Texas Double design reduces tuning effects to a negligible level, and trace-to-trace variations are gradual and consistent. G. Partyka (Oct 06) Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

  45. Well-Log Example - Layering G. Partyka (Oct 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 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

  46. Well-Log Example - Layering G. Partyka (Oct 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 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

  47. Well-Log Example - Layering G. Partyka (Oct 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 Texas Double Wavelets – high frequency side varies 52 to 112 Hz; low frequency held constant 6-10-013-052 6-10-021-082 6-10-028-112 Raw Layering 6-10-013-052 6-10-021-082 6-10-028-112 Raw Layering

  48. Well-Log Example - Layering G. Partyka (Oct 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 Texas Double Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant 6-10-011-040 6-10-020-070 6-10-025-100 Raw Layering 6-10-011-040 6-10-020-070 6-10-025-100 Raw Layering

  49. Well-Log Example - Reflectivity G. Partyka (Oct 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 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 RC 6-10-036-040 6-10-066-070 6-10-096-100 Raw RC

  50. Well-Log Example - Reflectivity G. Partyka (Oct 06) After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 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 RC 6-10-030-040 6-10-060-070 6-10-090-100 Raw RC

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