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,

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

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

Development of High Frequency Side-Lobes REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 3 octave slope High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 High frequency sidelobes can be attenuated to an insignificant level via a 2-octave or greater high side slope. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 4.0 octaves Low frequency sidelobes are a function of the wavelet’s bandpass. They cannot be reduced beyond what is shown here. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets) REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets) frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 4.0 octaves Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 3 octaves Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 2 octave slope Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 3 octave slope Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 3 octave sinc Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes frequency 100 amplitude 2030 40 5060 REFLECTIVITYIMPEDANCE 0 100 Travel Time (ms) 200 300 50 150 250 0 100 200 300 50 150 250 Temporal Thickness (ms) 05040302010 Temporal Thickness (ms) 50403020100 Texas Double Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

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

Example Amplitude Response of Dynamite Data 0.4 0.6 0.8 1.0 amplitude Frequency (Hz) 0 0.2 0 402060709010 Raw Whitened Texas Double 305080100 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. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

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

Temporal Resolution – Low-Pass Sinc vs Low-Pass Texas Double 0 10 20 30 peak-to-trough separation (ms) 0102030 spike separation (ms) 0–0-62-64 Hz Sinc TRTR 0 10 20 30 peak-to-trough separation (ms) 0102030 spike separation (ms) TRTR Conclusion:Over a given low-pass, temporal resolution of the Texas Double wavelet equals 80% of the temporal resolution of the sinc wavelet. T R = 1 / 1.5f 4 0–0-20-80 Hz Texas Double T R = 1 / 1.2f 4 Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Equivalent Temporal Resolution: Ormsby to Low-Pass Sinc fsfs frequency amplitude f4f4 f3f3 0.5 0.6 0.7 f s /f 4 0.8 0.9 1.0 00.10.20.30.40.50.60.70.80.91.0 f 3 / f 4 Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

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

Well-Log Comparison raw 00-00-20-8000-00-62-6408-09-62-6408-09-16-6408-09-20-80 Raw Input Layering or Reflectivity Desired Standard No Sidelobes (resolution of a 64 Hz sinc) High Frequency Tuning Effects Only High Frequency Sidelobes (resolution of a 64 Hz sinc) Negligible Effect Low Frequency Sidelobes (resolution of a 64 Hz sinc) Sinc Wavelet High and Low Frequency Sidelobes (resolution of a 64 Hz sinc) Texas Double Low Frequency Sidelobes (80% resolution of of a 64 Hz sinc) 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. Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 3 Octaves raw rc 00-00-20-8000-00-62-6408-09-62-6408-09-16-6408-09-20-80 raw layering 00-00-20-8000-00-62-6408-09-62-6408-09-16-6408-09-20-80 LayeringReflectivity After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

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

Well-Log Example - Layering Sinc Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant Raw Layering 6-10-096-100 6-10-066-070 6-10-036-040 Raw Layering 6-10-096-100 6-10-066-070 6-10-036-040 After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Example - Layering 10 Hz High-Cut Slope Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant Raw Layering 6-10-090-100 6-10-060-070 6-10-030-040 Raw Layering 6-10-090-100 6-10-060-070 6-10-030-040 After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

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

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

Well-Log Example - Reflectivity Sinc Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant Raw RC 6-10-096-100 6-10-066-070 6-10-036-040 Raw RC 6-10-096-100 6-10-066-070 6-10-036-040 After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Example - Reflectivity 10 Hz High-Cut Slope Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant 6-10-090-100 6-10-060-070 6-10-030-040 6-10-090-100 6-10-060-070 6-10-030-040 Raw RC After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

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

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

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,

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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,

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Presentation on theme: "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,"— Presentation transcript:

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