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 Data

After 1017 iterations

50 msBed Thickness < 5 ms

Inverted Impedance

TRUE IMPEDANCE

Input Data

True Reflectivity

Reflectivity from Inversion

Reconstructed Seismic trace by

Recursive Wavelet Summation

Difference

Bed Thickness < 5 ms

50ms

Input Data

True Reflectivity

Reflectivity from Inversion

Reconstructed Seismic trace by

Recursive Wavelet SummationDifference

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

the MULTISPECTRAL solution

* 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 of the seismic data between 18 and 190 HZ!

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 BLUE curve is the reflectivity

from the Multispectral RWS inversion convolved with the same BP wavelet.

-0.050

0.000

0.050

-0.500

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0.500

100 150 200 250 300 350 400 450 500 550 600

RINV1 RINV2

Note the different scale for CONV2 and RINV2

FF

T A

mp

litu

de

Frequency

FF

T A

mp

litu

de

Note how the character of the Multispectral RWS inversion follows the

true reflectivity at the very low end. However, the amplitude is higher

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MAIN W

FFT 70Hz Ricker

Hz

0

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MAIN

W

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ALPHA (4Hz

Window)

PEARSON (4Hz

Window)

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AUTO CORRELATION

MAIN W

FFT 70Hz Ricker

DOUBLE FFT

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AUTO CORRELATION

MAIN W

DOUBLE FFT

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AUTO CORRELATION

MAIN W

DOUBLE FFT

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FFT(R2) Rc Smooth

Raw and Smoothed spectra of calibrated inverted reflectivity

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70Hz Ricker

W

W/Rc Smooth

Rc Smooth

Note that W2

will

need to be tapered

between 0 and 15Hz