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