sparsity decon in the log domain with variable gain jon claerbout, qiang fu, and antoine guitton seg...
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Sparsity decon in the log domainwith variable gain
Jon Claerbout, Qiang Fu, and Antoine Guitton
SEGLas Vegas
November 2012
Ricker compliant decon; andSparsity decon in the log domain
with variable gain
Jon Claerbout, Qiang Fu, and Antoine Guitton
SEGLas Vegas
November 2012
Polarity revealing decon isRicker compliant decon; and
Sparsity decon in the log domainwith variable gain
Jon Claerbout, Qiang Fu, and Antoine Guitton
SEGLas Vegas
November 2012
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srhs0rhsr0h
s0r0h
Surface reflectioncoefficient is minus one.
Ricker wavelet ray paths
shot=sreflector=r
hydrophone=hsurface=0
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bubble
Rickerblack-white-black
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topsalt
saltbot
black
black
white
white
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Given the spectrum of 1001 GoM traces,average their spectra, compute a decon filter;its inverse should be the shot waveform,but it is not.zeros
NotRicker! We have been making this bad
assumption (minimum phase PEF) for 55 years.
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0
Ricker waveletFirst bubble
2 3 4
Same amplitude spectrum,different phase spectrum
I will tell how to get this “Ricker compliant” source
waveform,and the wonderful
consequences.
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Shot waveform from causal deconbased on spectrum of 1001 GoM traces
zeros
NotRicker!
Same amplitude spectrum,different phase spectrum
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Anticausality = 4 millisec
Same amplitude spectrum,different phase spectrum
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Anticausality = 8 millisec
Same amplitude spectrum,different phase spectrum
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Anticausality = 16 millisec
Same amplitude spectrum,different phase spectrum
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Anticausality = 32 millisec
Same amplitude spectrum,different phase spectrum
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Anticausality = 64 millisec
Jon’s favorite
Same amplitude spectrum,different phase spectrum
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Anticausality = 128 millisec
Same amplitude spectrum,different phase spectrum
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Anticausality = 256 millisec
bad!
0 120
midpoint is 60ms
Wavelet is becoming symmetrical.
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AfterBefore Notice polarity alternation.
Yilmaz & Cumro shot profile #33
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{{{{{{{{{{
{{{{{{{{{{
{{{{{{{{{{
{{{{{{{{{{CCVV
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Before
{{{{{{{{{{
{{{{{{{{{{
{{{{{{{{{{
{{{{{{{{{{CCVV
No parameter tuning(allow 60ms precursor)
I simply did
one filter,all traces.
Complications
After
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Why is polarity revealed?
Deconvolve with the right wavelet, thenseismogram polarity is revealed.
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Generally equivalent terms and conceptsBlind deconPredictive deconCausal deconAutoregression, Yule&Walker 1927Minimum-phase decon, MIT GAG 1954Wiener-Levinson, ToeplitzBurg, Robinson, and TreitelKolmogoroff decon (1939) (in my textbook FGDP 1974) (the code is in my book PVI 1992)
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Generally equivalent terms and conceptsBlind deconPredictive deconCausal deconAutoregression, Yule&Walker 1927Minimum-phase decon, MIT GAG 1954Wiener-Levinson, ToeplitzBurg, Robinson, and TreitelKolmogoroff decon (1939) (in my textbook FGDP 1974) (the code is in my book PVI 1992)Here we adapt Kolmogoroff to “Ricker
compliant,”and then the others too.
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Two ways to parameterize a filter’s logarithm
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How to force Ricker-like wavelets
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To make any decon filter reveal polarity
by respecting Ricker:
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To make any decon filter reveal polarity
by respecting Ricker:
“Grab its phase spectrum.Bring it into the time domain.
Near zero lag, dampen it down.”
(only 16 words)
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Now that polarity means something,shall we agree that,
White means hard, and
black means soft?
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Why did we not figure this out 40 years ago?
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Why did we not figure this out 40 years ago?
Because everyone got interested in migration.
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Two uses for this “Ricker trick”(1) Use “as is” to modify conventional decon
(2) Use as regularization for “fancy decons”
(Ricker trick was missing in our SEG abstract so there was a uniqueness problem.)
Sparsity decon in the log domainwith variable gain
Jon Claerbout, Qiang Fu, and Antoine Guitton
SEGLas Vegas
November 2012
Sparsity decon in the log domainwith variable gain
Jon Claerbout, Qiang Fu, and Antoine Guitton
SEGLas Vegas
November 2012
Sparsity decon in the log domainwith variable gain
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We seek sparse deconvolutionsby imposing a hyperbolic penalty function.
Sparsity decon in the log domainwith variable gain
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We seek sparse deconvolutionsby imposing a hyperbolic penalty function.
Sparsity decon in the log domainwith variable gain
Use the u(t) lag-log (quefrency) parameterization.
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We seek sparse deconvolutionsby imposing a hyperbolic penalty function.
Gain(t) and mute(t,x) should be done after decon,
not before.
Sparsity decon in the log domainwith variable gain
Use the u(t) lag-log (quefrency) parameterization.
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We seek sparse deconvolutionsby imposing a hyperbolic penalty function.
Gain(t) and mute(t,x) should be done after decon,
not before.Results will show that “gain after decon” benefits
(1) low frequencies, (2) noise
Sparsity decon in the log domainwith variable gain
Use the u(t) lag-log (quefrency) parameterization.
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Wantspike here.
Might getspike here.
Two years of frustration,always great results, but........
Might getspike here.
Polarity clear,but random!andunexpectedtime shifts.
3 students quit!
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Wantspike here.
Might getspike here.
Might getspike here.
Polarity clear,but random!andunexpectedtime shifts.
3 students quit!
All is resolved byRicker regularization.
Hooray!
Two years of frustration,always great results, but........
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Logarithmic parameterization
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Gain and sparsity
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softly clipped residual
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Physical output gradientw.r.t. lag-log variable
Statistical gradient
amazing result coming
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the step
A crosscorrelation: Compute it in the Fourier domain;
Jon’s favorite theory slide
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the step
A crosscorrelation: Compute it in the Fourier domain;
it’s the gradient, vanishes at convergence;it’s a delta function.
Jon’s favorite theory slide
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the step
A crosscorrelation: Compute it in the Fourier domain.
Special case: stationary L2 then r(t) is white.Generalized three ways,
(1) non-causal, (2) gain, and (3) sparsity!Jon’s favorite theory slide
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RESULTSCompare gain before with gain after.
data t-squared gain decon
data new decon t-squared gain
Want to get the low frequencies correct.
OLD:
NEW:
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Low frequencyprecursor
Clean
bubbleGain before Gain after
OLD: NEW:
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Compare
Gain after decon.
Gain before decon.
Scale up by 10x
Estimated shot
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CONCLUSIONS
Seismogram polarity is revealedby Ricker compliant deconvolution
which is simple to code.
Gain does not commute with decon and should be done after
(but not many examples yet).
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Fu YangAntoine Elita
Yi
I’d like to thank the team.
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We thank Western Geophysical for the Gulf of Mexico data and Lizzaralde et al for the Baja data.
Jon Claerbout and Qiang Fu thank the sponsors of the Stanford Exploration Project.
Antoine Guitton thanks Repsol Sinopec Brasil SA and Geo Imaging Solucoes Tecnologicas em Geociencias
Ltda.We'd like to thank Yang Zhang for continued interest.
ACKNOWLEDGEMENT
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If you liked this talk,my last practice talk
can be found at youtube.com
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Can you explain why traditional decon fails?
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Can you explain why traditional decon fails?
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Can you explain why traditional decon fails?