1. Time-frequency analysis of thin bed using a modified matching pursuit algorithm Bo Zhang Graduated from AASP consortium of OU in 2014 currently with The university of Alabama 1 - 20

2. Outline Motivation Basis pursuit matching pursuit Dipole-based matching pursuit Synthetic test Conclusions 2 - 20

3. Motivation Analyzing the time-frequency features of seismic traces plays an important role in seismic stratigraphy analysis and hydrocarbons detection. The current popular time- spectrum analysis methods include Short time Fourier transform (STFT) Continuous wavelet transform (CWT) S-transform (ST) Matching pursuit (PM) 3 - 20

4. Motivation The matching pursuit algorithm can be categorized into two types: The figure on the right is a widely used workflow of matching pursuit decomposition for time-frequency analysis of seismic traces (Liu and Marfurt, 2007). The “greedy” MP Instantaneous attributes based MP 4 - 20

5. Motivation The following figure is a simple wedge model and corresponding synthetic seismic. The wavelet used for synthetic is a 40 Hz Ricker Wavelet with zero phase. 1020304050 1 0 Trace Number 1020304050 0 0.1 0.2 Time (s) 1 0 Trace Number 5 - 20

6. The following two figures are the instantaneous envelop and frequency of the wedge model. 1 0 1.5 0.5 1020304050 0 0.1 0.2 Time (s) Trace Number 80 0 120 40 1020304050 Trace Number Motivation 6 - 20

7. Comparison of instantaneous frequency of the wedge model and single reflection. Motivation 80 0 120 40 1020304050 Trace Number 7 - 20

8. Comparison of instantaneous frequency of the wedge model and single reflection at the time index of the first reflection. Motivation 8 - 20

9. Motivation Suppose that seismic wavelet is stationary in the certain short time window, we propose to decompose the seismic trace waveform by waveform, instead of decomposing the wavelet by wavelet. Reflectivity Convolution Wavelet Synthetic Envelope MP Modeled wavelet Modified MP ReflectivityWavelet 9 - 20

10. Basis pursuit matching pursuit Original reflection coefficient pair a *Even pairb*Odd pair =+ 10 - 20 The exacted seismic data in the short time window Any seismic trace can be considered as a summation of wedge model seismic responses which slide along the time axis

11. Basis pursuit matching pursuit The exacted seismic data in the short time window Any seismic trace can be considered as a summation of wedge model seismic responses which slide along the time axis 11 - 20

12. Basis pursuit matching pursuit A flowchart for a wavelet-based spectral-decomposition algorithm using a modified matching pursuit technique named basis pursuit matching pursuit (BPMP). BPMP decompose the seismic traces waveform by waveform. The inverted reflectivity model can be directly used for the thickness estimation of thin bed and channels. 12 - 20

13. Dipole-based matching pursuit The second solution of considering the interfering is to build a dipole wavelet library. The dipole wavelet library is convolution result of dipole pair and wavelets. Original reflection coefficient pair a *Even pairb*Odd pair =+ 13 - 20

14. Dipole-based matching pursuit The even and odd wedge model and their seismic responses for a wavelet. The size of the new wave library is much larger than that of conventional MP 14 - 20

15. A flowchart for a wavelet-based spectral-decomposition algorithm using a modified matching pursuit technique named dipole based (DBMP). DBMP decomposes the seismic traces waveform by waveform. The inverted reflectivity model can be directly used for the thickness estimation of thin bed and channels. Dipole-based matching pursuit 15 - 20

16. Synthetic test We first test the algorithm on the synthetic generated using the same wavelet. The time intervals of the second, third, and fourth reflection pair are 10ms, 20ms, and 40ms. The source wavelet is 40 Hz Ricker wavelet with zero phase and 200 ms length. 0 0.4 0.8 Time (s) Magnitude -2 0 2 Convolution 16 - 20

17. Synthetic test The time-frequency decomposed results of synthetic trace using MP, BPMP, and DBMP are MP DBMPBPMP 0 0. 4 0. 8 Time (s) Magnitu de -2 0 2 Synthetic 17 - 20

18. Synthetic test The inverted scalar/reflectivity corresponding to time-frequency decomposed results are MP DBMPBPMP Original RC 18 - 20

19. Synthetic test We second the algorithm on the synthetic generated using the multiple wavelet. The time intervals is the same as that of the first model. The source wavelet is Ricker wavelet with zero phase. The center frequency pair are 40 Hz, (40, 38) Hz, (40,38) Hz, and (35, 30) Hz. Convolution 40 Hz 35 Hz 38 Hz 30 Hz 19 - 20

20. Synthetic test The time-frequency decomposed results of synthetic trace using MP, BPMP, and DBMP are MP DBMPBPMP Synthetic 20 - 20

21. Synthetic test The inverted scalar/reflectivity corresponding to time-frequency decomposed results are MP DBMPBPMP Original RC 21 - 20

22. Conclusions The proposed modified matching pursuit algorithms own the following the advantages when compared to matching pursuit The inverted reflectivity has higher correlation with the original model The time-frequency features has higher correlation with the amplitude spectrum of original wavelets. The computation cost of proposed algorithms is much higher than the instantaneous frequency based MP but is comparable to the greedy MP. 22 - 20