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

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

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

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

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

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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.

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

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

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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

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

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Wedge Model Response Temporal Thickness (ms) REFLECTIVITY FILTERED REFLECTIVITY (Ormsby 8-10-40-50 Hz) SPECTRAL AMPLITUDES Temporal Thickness (ms) 01020304050 01020304050 01020304050 0 100 200 0 100 200 0 100 200 Travel Time (ms) Frequency (Hz) Temporal Thickness 1 0.0015 0 Amplitude Amplitude spectrum of 10ms blocky bed Amplitude spectrum of 50ms blocky bed 10Hz spectral amplitude 50Hz spectral amplitude

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Individual Amplitude Spectra Amplitude spectrum of 10ms blocky bed. Amplitude spectrum of 50ms blocky bed. P f = 1/t where: P f = Period of amplitude spectrum notching with respect to frequency. t = Thin bed thickness. 020406080100120140160180200220240 0 0.0002 0.0004 0.0006 0.0008 0.0010 0.0014 0.0012 Frequency (Hz) Amplitude The temporal thickness of the wedge (t) determines the period of notching in the amplitude spectrum (P f ) with respect to frequency

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Wedge Model Response Temporal Thickness (ms) REFLECTIVITY FILTERED REFLECTIVITY (Ormsby 8-10-40-50 Hz) SPECTRAL AMPLITUDES Temporal Thickness (ms) 01020304050 01020304050 01020304050 0 100 200 0 100 200 0 100 200 Travel Time (ms) Frequency (Hz) Temporal Thickness 1 0.0015 0 Amplitude Amplitude spectrum of 10ms blocky bed Amplitude spectrum of 50ms blocky bed 10Hz spectral amplitude 50Hz spectral amplitude

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Discrete Frequency Components 10Hz spectral amplitude. 50Hz spectral amplitude. 01020304050 0 0.0002 0.0004 0.0006 0.0008 0.0010 0.0014 0.0012 Amplitude Temporal Thickness (ms) P t = 1/f where: P t = Period of amplitude spectrum notching with respect to bed thickness. f = Discrete Fourier frequency. The value of the frequency component (f) determines the period of notching in the amplitude spectrum (P t ) with respect to bed thickness.

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

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

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

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Prior to Spectral Balancing The Tuning Cube contains three main components: –thin bed interference, –the seismic wavelet, and –random noise Multiply Tuning Cube x y freq x y x y x y Seismic WaveletNoiseThin Bed Interference + + Add

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

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

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After Spectral Balancing The Tuning Cube contains two main components: –thin bed interference, and –random noise Tuning Cube x y freq x y x y NoiseThin Bed Interference + Add

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

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

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

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

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

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

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

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

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

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

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Discrete Frequency Energy Cubes

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

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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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