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Rapid variation of impedance.
Sparse Spike Inversion.
Smooth variation of impedance.
Other methods preferred.
* The inversion is a 8.5 million cells spreadsheet!!!!
REFLECTIVITY
SEISMIC Trace
IMPEDANCE
Reconstructed Seismic trace by
Recursive Wavelet Summation
Reflectivity from Inversion True Reflectivity
Difference
Input ...
50 msBed Thickness < 5 ms
Inverted Impedance
TRUE IMPEDANCE
Input Data
True Reflectivity
Reflectivity from Inversion
Reconstructed Seismic trace by
Recursive Wavelet Summation
Differ...
Bed Thickness < 5 ms
50ms
Input Data
True Reflectivity
Reflectivity from Inversion
Reconstructed Seismic trace by
Recursive Wavelet SummationDiffere...
50ms
Smoothed spectrum of the
seismic trace used as the
main wavelet
Low Residual
The reconstructed waveform is almost PERFECTLY identical to the original seismic trace.
v
v
v
Note the improvements from
t...
* We may have been too aggressive in computing the high frequency normalizing filter
Between 18Hz and 190Hz the Pearson Coefficient are > 0.8
The multispectral RWS inversion has recovered the FULL
BANDWIDTH ...
Note the gain in the high frequencies
The RED curve is the original seismic trace. The BLACK curve is the TRUE reflectivity convolved with the BP wavelet. The B...
-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...
FFTAmplitude
Frequency
FFTAmplitude
Note how the character of the Multispectral RWS inversion follows the
true reflectivity at the very low end. However, the ...
0
2
4
6
8
10
12
10 20 30 40 50 60 70 80 90 100
MAIN W
FFT 70Hz Ricker
Hz
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)
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
0
1
2
10 30 50 70 90
AUTO CORRELATION
MAIN W
DOUBLE FFT
0
1
2
100 120 140 160 180 200
AUTO CORRELATION
MAIN W
DOUBLE FFT
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
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 ...
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
Seismic Inversion by Multispectral Recursive Wavelet Summation
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Seismic Inversion by Multispectral Recursive Wavelet Summation

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Seismic Inversion by Multispectral Recursive Wavelet Summation. The Multispectral RWS inversion is a novel poststack hybrid sparse spike inversion. The inversion is capable of retrieving all the information contained within the frequency range of the seismic trace. It is a very effective mean of seismic bandwidth extension with gains of over 20dB at the high end.

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Seismic Inversion by Multispectral Recursive Wavelet Summation

  1. 1. Rapid variation of impedance. Sparse Spike Inversion. Smooth variation of impedance. Other methods preferred.
  2. 2. * The inversion is a 8.5 million cells spreadsheet!!!! REFLECTIVITY SEISMIC Trace IMPEDANCE
  3. 3. Reconstructed Seismic trace by Recursive Wavelet Summation Reflectivity from Inversion True Reflectivity Difference Input Data After 1017 iterations
  4. 4. 50 msBed Thickness < 5 ms Inverted Impedance TRUE IMPEDANCE
  5. 5. Input Data True Reflectivity Reflectivity from Inversion Reconstructed Seismic trace by Recursive Wavelet Summation Difference
  6. 6. Bed Thickness < 5 ms 50ms
  7. 7. Input Data True Reflectivity Reflectivity from Inversion Reconstructed Seismic trace by Recursive Wavelet SummationDifference
  8. 8. 50ms
  9. 9. Smoothed spectrum of the seismic trace used as the main wavelet Low Residual
  10. 10. The reconstructed waveform is almost PERFECTLY identical to the original seismic trace. v v v Note the improvements from the MULTISPECTRAL solution
  11. 11. * We may have been too aggressive in computing the high frequency normalizing filter
  12. 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. 13. Note the gain in the high frequencies
  14. 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. 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. 16. FFTAmplitude Frequency FFTAmplitude
  17. 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. 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. 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. 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. 21. 0 1 2 10 30 50 70 90 AUTO CORRELATION MAIN W DOUBLE FFT
  22. 22. 0 1 2 100 120 140 160 180 200 AUTO CORRELATION MAIN W DOUBLE FFT
  23. 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. 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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