AASPI Attribute-Assisted Seismic Processing and Interpretation http://geology.ou.edu/aaspi/ Brazilian carbonate reservoir study using the Wavelet Transform Teager-Kaiser Energy Marcílio Castro de Matos marcilio@ou.edu or www.matos.eng.br Kurt J. Marfurt kmarfurt@ou.edu Oklahoma University Paulo Roberto Schroeder Johann johann@petrobras.com.br João Adolfo Rosseto jrosseto@petrobras.com.br Petrobras

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.

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

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

Seismic Wave Energy Density (Sheriff and Geldart, 1995) Simple Harmonic Motion Energy (Kaiser, 1990) http://www.kettering.edu/~drussell/demos.html 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: http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm Total energy is equal to the maximum value of the kinetic energy

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

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.

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

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

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)

... ... 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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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.

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 http://geology.ou.edu/aaspi/ We also would like to thank PETROBRAS for their cooperation in providing the data, support and the authorization to publish this work.