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

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

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

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

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

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

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

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

14. 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.
10Hz spectral amplitude.
50Hz spectral amplitude. 10 20 30 40 50
0.0002
0.0004
0.0006
0.0008
0.0010
0.0014
0.0012
Amplitude
Temporal Thickness (ms)
Pt = 1/f
where: Pt= Period of amplitude spectrum notching
with respect to bed thickness.
f = Discrete Fourier frequency.

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

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

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

18. 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
Seismic Wavelet
Noise
Thin Bed Interference +
Add

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

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

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

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

25. N Tuning Cube, Amplitude at Frequency = 16 hz Channel “A”
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
Amplitude
analysis window length = 100ms

26. N Tuning Cube, Amplitude at Frequency = 26 hz Channel “A”
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
Amplitude
analysis window length = 100ms

27. 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
Thin Bed Reflection
Fourier
Transform

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

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

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

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

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

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.