Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG...

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


SEGLas Vegas

November 2012

Polarity revealing decon isRicker compliant decon; and



SEGLas Vegas

November 2012

5

srhs0rhsr0h

s0r0h

Surface reflectioncoefficient is minus one.

Ricker wavelet ray paths

shot=sreflector=r

hydrophone=hsurface=0

7

bubble

Rickerblack-white-black

8

topsalt

saltbot

black

black

white

white

16

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.

17

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.

18

Shot waveform from causal deconbased on spectrum of 1001 GoM traces

zeros

NotRicker!


19

Anticausality = 4 millisec


20



21



22



23


Jon’s favorite


24



25


bad!

0 120

midpoint is 60ms

Wavelet is becoming symmetrical.

26

AfterBefore Notice polarity alternation.

Yilmaz & Cumro shot profile #33

26

{{{{{{{{{{

{{{{{{{{{{

{{{{{{{{{{

{{{{{{{{{{CCVV

27

Before

{{{{{{{{{{

{{{{{{{{{{

{{{{{{{{{{

{{{{{{{{{{CCVV

No parameter tuning(allow 60ms precursor)

I simply did

one filter,all traces.

Complications

After

28

Why is polarity revealed?

Deconvolve with the right wavelet, thenseismogram polarity is revealed.

29

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)

30

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.

31

Two ways to parameterize a filter’s logarithm

32

How to force Ricker-like wavelets

33

To make any decon filter reveal polarity

by respecting Ricker:

34

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)

35

Now that polarity means something,shall we agree that,

White means hard, and

black means soft?

36

Why did we not figure this out 40 years ago?

37

Why did we not figure this out 40 years ago?

Because everyone got interested in migration.

38

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.)



SEGLas Vegas

November 2012

42

We seek sparse deconvolutionsby imposing a hyperbolic penalty function.


43



Use the u(t) lag-log (quefrency) parameterization.

44


Gain(t) and mute(t,x) should be done after decon,

not before.



45


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



46

Wantspike here.

Might getspike here.

Two years of frustration,always great results, but........


Polarity clear,but random!andunexpectedtime shifts.

3 students quit!

47

Wantspike here.



Polarity clear,but random!andunexpectedtime shifts.

3 students quit!

All is resolved byRicker regularization.

Hooray!

Two years of frustration,always great results, but........

48

Logarithmic parameterization

49

Gain and sparsity

50

softly clipped residual

52

Physical output gradientw.r.t. lag-log variable

Statistical gradient

amazing result coming

53

the step

A crosscorrelation: Compute it in the Fourier domain;

Jon’s favorite theory slide

54

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

55

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

56

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:

57

Low frequencyprecursor

Clean

bubbleGain before Gain after

OLD: NEW:

58

Compare

Gain after decon.

Gain before decon.

Scale up by 10x

Estimated shot

59

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).

60

Fu YangAntoine Elita

Yi

I’d like to thank the team.

60

61

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

62

If you liked this talk,my last practice talk

can be found at youtube.com

65

Can you explain why traditional decon fails?

66


67


Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG...

Documents

Transcript of Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG...