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Interpretational Applications of Spectral Decomposition

Interpretational Applications of Spectral Decomposition. Greg Partyka, James Gridley, and John Lopez. Spectral Decomposition. uses the discrete Fourier transform to: quantify thin-bed interference, and detect subtle discontinuities. Outline. Convolutional Model Implications

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Interpretational Applications of Spectral Decomposition

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  1. Interpretational Applications of Spectral Decomposition Greg Partyka, James Gridley, and John Lopez

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

  3. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  4. Long Window Analysis • The geology is unpredictable. • Its reflectivity spectrum is therefore white/blue.

  5. Reflectivity r(t) Wavelet w(t) Noise n(t) Seismic Trace s(t) Travel Time TIME DOMAIN Fourier Transform Amplitude Amplitude Amplitude Amplitude FREQUENCY DOMAIN Frequency Frequency Frequency Frequency Long Window Analysis

  6. Short Window Analysis • The non-random geology locally filters the reflecting wavelet. • Its non-white reflectivity spectrum represents the interference pattern within the short analysis window.

  7. Reflectivity r(t) Wavelet w(t) Noise n(t) Seismic Trace s(t) Travel Time TIME DOMAIN Fourier Transform Amplitude Amplitude Amplitude Amplitude FREQUENCY DOMAIN Frequency Frequency Frequency Frequency Wavelet Overprint Short Window Analysis

  8. Spectral Interference • The spectral interference pattern is imposed by the distribution of acoustic properties within the short analysis window.

  9. Source Wavelet Amplitude Spectrum Source Wavelet Reflected Wavelets Thin Bed Reflection Thin Bed Reflection Amplitude Spectrum 1 Amplitude Amplitude Temporal Thickness Frequency Frequency Fourier Transform Fourier Transform Acoustic Impedance Reflectivity Thin Bed Temporal Thickness Spectral Interference

  10. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  11. Temporal Thickness (ms) 0 0 0 REFLECTIVITY Travel Time (ms) 100 100 100 Temporal Thickness 200 200 200 Temporal Thickness (ms) 0 0 10 10 20 20 30 30 40 40 50 50 0 10 20 30 40 50 FILTERED REFLECTIVITY (Ormsby 8-10-40-50 Hz) 1 Temporal Thickness Travel Time (ms) Temporal Thickness (ms) Amplitude 0.0015 SPECTRAL AMPLITUDES Frequency (Hz) 0 Amplitude spectrum of 10ms blocky bed Amplitude spectrum of 50ms blocky bed 10Hz spectral amplitude 50Hz spectral amplitude Wedge Model Response

  12. 0 20 40 60 80 100 120 140 160 180 200 220 240 0.0014 Amplitude spectrum of 10ms blocky bed. 0.0012 Amplitude spectrum of 50ms blocky bed. 0.0010 0.0008 Pf = 1/t where: Pf = Period of amplitude spectrum notching with respect to frequency. t = Thin bed thickness. Amplitude 0.0006 0.0004 0.0002 0 Frequency (Hz) Individual Amplitude Spectra • The temporal thickness of the wedge (t) determines the period of notching in the amplitude spectrum (Pf) with respect to frequency

  13. Temporal Thickness (ms) 0 0 0 REFLECTIVITY Travel Time (ms) 100 100 100 Temporal Thickness 200 200 200 Temporal Thickness (ms) 0 0 10 10 20 20 30 30 40 40 50 50 0 10 20 30 40 50 FILTERED REFLECTIVITY (Ormsby 8-10-40-50 Hz) 1 Temporal Thickness Travel Time (ms) Temporal Thickness (ms) Amplitude 0.0015 SPECTRAL AMPLITUDES Frequency (Hz) 0 Amplitude spectrum of 10ms blocky bed Amplitude spectrum of 50ms blocky bed 10Hz spectral amplitude 50Hz spectral amplitude Wedge Model Response

  14. 0.0014 10Hz spectral amplitude. 0.0012 50Hz spectral amplitude. 0.0010 0.0008 Amplitude Pt = 1/f where: Pt= Period of amplitude spectrum notching with respect to bed thickness. f = Discrete Fourier frequency. 0.0006 0.0004 0.0002 0 0 10 20 30 40 50 Temporal Thickness (ms) Discrete Frequency Components • The value of the frequency component (f) determines the period of notching in the amplitude spectrum (Pt) with respect to bed thickness.

  15. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  16. y x z 3-D Seismic Volume Interpret y x z Interpreted 3-D Seismic Volume Subset y x Zone-of-Interest Subvolume z Compute y x Zone-of-Interest Tuning Cube (cross-section view) freq Animate y x Frequency Slices through Tuning Cube (plan view) freq The Tuning Cube

  17. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  18. Tuning Cube y y y y x x x x freq freq freq freq Multiply Add + + Thin Bed Interference Seismic Wavelet Noise Prior to Spectral Balancing • The Tuning Cube contains three main components: • thin bed interference, • the seismic wavelet, and • random noise

  19. Reflectivity r(t) Wavelet w(t) Noise n(t) Seismic Trace s(t) Travel Time TIME DOMAIN Fourier Transform Amplitude Amplitude Amplitude Amplitude FREQUENCY DOMAIN Frequency Frequency Frequency Frequency Wavelet Overprint Short Window Analysis

  20. y y y y y y y y y y x x x x x x x x x x Tuning Cube Split Spectral Tuning Cube into Discrete Frequencies Frequency 1 Frequency 2 Frequency 3 Frequency 4 Frequency n Frequency Slices through Tuning Cube (plan view) Independently Normalize Each Frequency Map Spectrally Balanced Frequency Slices through Tuning Cube (plan view) Frequency 1 Frequency 2 Frequency 3 Frequency 4 Frequency n y y Gather Discrete Frequencies into Tuning Cube x x freq freq Spectrally Balanced Tuning Cube Spectral Balancing

  21. Tuning Cube y y y x x x freq freq freq Add + Thin Bed Interference Noise After Spectral Balancing • The Tuning Cube contains two main components: • thin bed interference, and • random noise

  22. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  23. Real Data Example • Gulf-of-Mexico, Pleistocene-age equivalent of the modern-day Mississippi River Delta.

  24. Channel “A” Fault-Controlled Channel Point Bar Amplitude 1 0 N Channel “B” 10,000 ft Gulf of Mexico Example analysis window length = 100ms Response Amplitude

  25. Channel “A” North-South Extent of Channel “A” Delineation Fault-Controlled Channel Point Bar Amplitude 1 0 N Channel “B” 10,000 ft Gulf of Mexico Example analysis window length = 100ms Tuning Cube, Amplitude at Frequency = 16 hz

  26. Channel “A” North-South Extent of Channel “A” Delineation Fault-Controlled Channel Point Bar Amplitude 1 0 N Channel “B” 10,000 ft Gulf of Mexico Example analysis window length = 100ms Tuning Cube, Amplitude at Frequency = 26 hz

  27. Amplitude Spectrum Phase Spectrum Phase Amplitude Thin BedReflection Frequency Frequency Fourier Transform Hey…what about the phase? • Amplitude spectra delineate thin bed variability via spectral notching. • Phase spectra delineate lateral discontinuities via phase instability.

  28. Faults Phase 180 -180 N 10,000 ft Gulf of Mexico Example Response Phase

  29. Faults Phase 180 -180 N 10,000 ft Gulf of Mexico Example analysis window length = 100ms Tuning Cube, Phase at Frequency = 16 hz

  30. Faults Phase 180 -180 N 10,000 ft Gulf of Mexico Example analysis window length = 100ms Tuning Cube, Phase at Frequency = 26 hz

  31. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  32. y z = 1 x z 3-D Seismic Volume z = n Compute y y y y y y y z = 1 x x x x x x x freq freq freq freq freq freq freq z = 2 z = 3 z = 4 Time-Frequency 4-D Cube z = 5 z = 6 z = n Subset y y y y y z = 1 z = 1 z = 1 z = 1 z = 1 x x x x x z z z z z Discrete Frequency Energy Cubes z = n z = n z = n z = n z = n Frequency 1 Frequency 2 Frequency 3 Frequency 4 Frequency m Discrete Frequency Energy Cubes

  33. Outline • Convolutional Model Implications • Wedge Model Response • The Tuning Cube • Spectral Balancing • Real Data Examples • Alternatives to the Tuning Cube • Summary

  34. Summary • Spectral decomposition uses the discrete Fourier transform to quantify thin-bed interference and detect subtle discontinuities. • For reservoir characterization, our most common approach to viewing and analyzing spectral decompositions is via the “Zone-of-Interest Tuning Cube”. • Spectral balancing removes the wavelet overprint. • The amplitude component excels at quantifying thickness variability and detecting lateral discontinuities. • The phase component detects lateral discontinuities.

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