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- 1. Rapid variation of impedance. Sparse Spike Inversion. Smooth variation of impedance. Other methods preferred.
- 2. * The inversion is a 8.5 million cells spreadsheet!!!! REFLECTIVITY SEISMIC Trace IMPEDANCE
- 3. Reconstructed Seismic trace by Recursive Wavelet Summation Reflectivity from Inversion True Reflectivity Difference Input Data After 1017 iterations
- 4. 50 msBed Thickness < 5 ms Inverted Impedance TRUE IMPEDANCE
- 5. Input Data True Reflectivity Reflectivity from Inversion Reconstructed Seismic trace by Recursive Wavelet Summation Difference
- 6. Bed Thickness < 5 ms 50ms
- 7. Input Data True Reflectivity Reflectivity from Inversion Reconstructed Seismic trace by Recursive Wavelet SummationDifference
- 8. 50ms
- 9. Smoothed spectrum of the seismic trace used as the main wavelet Low Residual
- 10. The reconstructed waveform is almost PERFECTLY identical to the original seismic trace. v v v Note the improvements from the MULTISPECTRAL solution
- 11. * We may have been too aggressive in computing the high frequency normalizing filter
- 12. Between 18Hz and 190Hz the Pearson Coefficient are > 0.8 The multispectral RWS inversion has recovered the FULL BANDWIDTH of the seismic data between 18 and 190 HZ!
- 13. Note the gain in the high frequencies
- 14. The RED curve is the original seismic trace. The BLACK curve is the TRUE reflectivity convolved with the BP wavelet. The BLUE curve is the reflectivity from the Multispectral RWS inversion convolved with the same BP wavelet.
- 15. -0.050 0.000 0.050 -0.500 0.000 0.500 100 150 200 250 300 350 400 450 500 550 600 RINV1 RINV2 Note the different scale for CONV2 and RINV2
- 16. FFTAmplitude Frequency FFTAmplitude
- 17. Note how the character of the Multispectral RWS inversion follows the true reflectivity at the very low end. However, the amplitude is higher
- 18. 0 2 4 6 8 10 12 10 20 30 40 50 60 70 80 90 100 MAIN W FFT 70Hz Ricker Hz
- 19. 0 1 2 10 30 50 70 90 MAIN W 0 1 2 10 20 30 40 50 60 70 80 90 100 ALPHA (4Hz Window) PEARSON (4Hz Window)
- 20. 0 2 4 6 8 10 12 10 20 30 40 50 60 70 80 90 100 AUTO CORRELATION MAIN W FFT 70Hz Ricker DOUBLE FFT
- 21. 0 1 2 10 30 50 70 90 AUTO CORRELATION MAIN W DOUBLE FFT
- 22. 0 1 2 100 120 140 160 180 200 AUTO CORRELATION MAIN W DOUBLE FFT
- 23. 0 1 2 3 4 5 6 7 8 9 0 50 100 150 200 250 FFT(R2) Rc Smooth Raw and Smoothed spectra of calibrated inverted reflectivity
- 24. 0 2 4 0 2 4 6 8 10 12 0 20 40 60 80 100 120 140 160 180 200 70Hz Ricker W W/Rc Smooth Rc Smooth Note that W2 will need to be tapered between 0 and 15Hz

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