1. AASPI
Attribute-Assisted Seismic Processing and Interpretation
Brazilian carbonate reservoir study using the Wavelet Transform Teager-Kaiser Energy
Marcílio Castro de Matos or
Kurt J. Marfurt
Oklahoma University
Paulo Roberto Schroeder Johann
João Adolfo Rosseto
Petrobras

2. Now, carbonates are very important to Brazil !!!
Motivation
Now, carbonates are very important to Brazil !!!
Seismic attributes applied to carbonate reservoirs examples:
Masaferro et al. (2004) state that the combined effects of variation in depositional facies and diagenetic alteration play a key role in controlling variations in sonic velocities and thus is acoustic impedance in carbonate systems.
Pearson and Hart (2004) showed that spectral components can be used in carbonate reservoir characterization. Specifically, they predicted the porosity of a carbonate reservoir from a linear combination of the slope from peak to maximum spectral frequency and the ratio of the number of positive samples over the number of negative samples within a time interval.
Chopra and Marfurt (2007) show how the shape or geomorphology of reflection patterns, coupled with appropriate models deposition and diagenesis, further aid the mapping of carbonate facies. Thus, both geometric (measuring lateral changes) and trace shape (measuring vertical seismic waveform) seismic attributes can be a great aid in the characterization of carbonate reservoirs.

3. Objectives
To show how the seismic density energy can be related to the Wavelet Transform Teager-Kaiser Energy
To show that this nonlinear energy-tracking algorithm allows us to differentiate high amplitude reservoir from other high amplitude reflections
To show how we applied this technique to a Brazilian carbonate reservoir

4. Summary Introduction: Seismic x Teager-Kaiser Wave Energy
The Wavelet Transform TK Energy - WaveTeKE
WaveTeKE applied to a Brazilian carbonate reservoir
Conclusions

5. Seismic Wave Energy Density (Sheriff and Geldart, 1995)
Simple Harmonic Motion Energy (Kaiser, 1990)
Animation courtesy of Dr. Dan Russell, Kettering University
Newton’s law of motion of a mass m suspended by a spring of force constant k:
Total Energy E of the system:
Total energy is equal to the maximum value of the kinetic energy

6. Teager-Kaiser Energy (Kaiser, 1990)
A/D conversion
Oscillatory Phenomena
Teager-Kaiser Energy
TK energy estimation error < 11 %
sampling period: ts
sampling frequency: fs
4 ms
250 Hz
31.25 Hz
2 ms
500 Hz
62.5 Hz

7. Teager-Kaiser Energy: examples and drawbacks
Ex: Signal consisting on two sinusoids
drawback
sin(pi/6*n) sin(pi/4*n)
sin(pi/6*n)+sin(pi/4*n)
TK Energy crossterms
It is essential to separate the components of the signal by some form of band-pass filtering before applying the algorithm.

8. Summary Introduction: Seismic x Teager-Kaiser Wave Energy
The Wavelet Transform TK Energy - WaveTeKE
WaveTeKE applied to a Brazilian carbonate reservoir
Conclusions

9. Continuous Wavelet Transform
(x)  L2() is called a wavelet

10. Continuous Wavelet Transform (CWT)
The CWT can be interpreted as a band pass filter response at each scale s
Amplitude
Scales
time
Time (ms)
Time (ms)

11. ... ... WaveTeKE Description WaveTeKE Reservoir Wavelet Transform
Band pass filter 1
Band pass filter 2
Band pass filter n
...
Teager-Kaiser Energy
Teager-Kaiser Energy
Teager-Kaiser Energy
Case 01: Carbonate Oil Well
Reservoir

12. Time-frequency attributes
Amplitude
Difference between PA and HFPA
Peak Amplitude over mean
Highest Frequency Peak Amplitude over mean
Mean
Peak Amplitude
Highest Frequency Peak Amplitude
Difference between PF and HFP
Frequency
Peak Frequency
Highest Frequency Peak

13. WaveTeKE Applied to wedge model
The same dominant frequency and instant time
Thin bed model
Seismic trace
CWT with real Morlet
WaveTeKE with real Morlet
CWT with complex Morlet
WaveTeKE with complex Morlet
Maximum instantaneous frequency
Amplitude of the maximum instantaneous frequency
Instantaneous seismic attributes generated from the time-frequency analysis
Time interval seismic attributes generated from the time-frequency analysis

14. Highest Frequency Peak Amplitude Highest Frequency Peak Amplitude
Time
Freq
Time
Amplitude
High
Low
20 ms
Freq
Time
Freq
Time
Peak Amplitude
Highest Frequency Peak Amplitude
30 ms
Freq
Time
Freq
Time
Peak Amplitude
Highest Frequency Peak Amplitude
35 ms

15. Summary Introduction: Seismic x Teager-Kaiser Wave Energy
The Wavelet Transform TK Energy - WaveTeKE
WaveTeKE applied to a Brazilian carbonate reservoir
Conclusions

16. 80 ms below the negative peak horizon
BB’ A’
Reservoir Base Map Amplitude Seismic Sections (dip/strike) of a Carbonate Oil Field - Campos Basin
400 ms
80 ms below the negative peak horizon
producer B’
Negative
Positive
Amplitude B
AA’ B’ A’
400 ms A
Figure 3: a) Amplitude extraction along the top of the reservoir; b) Seismic amplitude; c) Seismic amplitude. B
2 km
producer
dry hole
1.2 km 16

17. Reservoir Base Maps (a) Reservoir top Structural Time Semblance
1.4
1.5
1.6
1.7
Reservoir top
Structural Time
Low
High
Semblance
Semblance

18. Most negative curvature
Reservoir Base Maps
Most Neg Curv
Pos
Neg B B’
Most negative curvature A’ A
(b)
Sobel Filter
Low
High
Sobel filter
(d)

19. Peak amplitude Carbonate Oil Field - Campos Basin
BB’ A’
WaveTeKE
Peak amplitude Carbonate Oil Field - Campos Basin
Zero
Positive
400 ms
producer
2 km B B’ A’ A B
AA’ B’
400 ms
Figure 3: a) TE energy extraction along the top Horizon; b) TE energy absolute sum value between the top Horizon and 80 ms bellow it; c) The WaveTeKE instantaneous amplitude attribute; d) The WaveTeKE instantaneous amplitude attribute.
TE energy absolute sum value between the top Horizon and 80 ms bellow it
producer
dry hole
1.2 km 19

20. 80 ms Time interval seismic attributes
Peak WaveTeKE frequency and its associated amplitude plotted together using a 2D color bar bellow the reservoir top
Minimum amplitude bellow the reservoir top + +
low
high
Peak energy 50 10
Peak frequency (Hz)
Minimum amplitude
Max
Min

21. RGB display of spectrum attributes
Peak Amplitude over mean
Red
Difference between PF and HFP
Green
Mean
Blue
Frequency
Peak Frequency

22. RGB display of spectrum attributes
Highest Frequency Peak Amplitude over mean
Red
Difference between PF and HFP
Green
Mean
Blue
Frequency
Highest Frequency Peak

23. RGB display of spectrum attributes
Difference between PF and HFP
Green
Mean
Red
Blue
Frequency
Peak Frequency
Highest Frequency Peak

24. RGB display of spectrum attributes
Peak Amplitude over mean
Highest Frequency Peak Amplitude over mean
Red
Blue
Green
Mean
Difference between PF and HFP
Frequency

25. Summary Introduction: Seismic x Teager-Kaiser Wave Energy
The Wavelet Transform TK Energy - WaveTeKE
WaveTeKE applied to a Brazilian carbonate reservoir
Conclusions

26. Conclusions
We show that the Teager-Kaiser energy can be computed for seismic data through the joint time-frequency representation.
The TK energy appears to be quite effective in delineating strong amplitude, high frequency events associated with a producing areas of a carbonate reservoir.
The results obtained with real seismic data show the WaveTeKE potential use as an exploratory tool to detect energy associated with important geological marks and potential exploratory leads.

27. Acknowledgements
The first two authors would like to thank the support from the University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation Consortium and its sponsors.
Attribute-Assisted Seismic Processing and Interpretation
We also would like to thank PETROBRAS for their cooperation in providing the data, support and the authorization to publish this work.