Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG Las Vegas November 2012

Ricker compliant decon; and Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG Las Vegas November 2012

Polarity revealing decon is Ricker compliant decon; and Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG Las Vegas November 2012

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5 srh s0rh sr0h s0r0h Surface reflection coefficient is minus one. Ricker wavelet ray paths shot=s reflector=r hydrophone=h surface=0

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7 bubble Ricker black-white-black

8 top salt bot black white

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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 Not Ricker! We have been making this bad assumption (minimum phase PEF) for 55 years.

17 0 Ricker wavelet First bubble 2 34 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 decon based on spectrum of 1001 GoM traces zeros Not Ricker! Same amplitude spectrum, different phase spectrum

19 Anticausality = 4 millisec Same amplitude spectrum, different phase spectrum

20 Anticausality = 8 millisec Same amplitude spectrum, different phase spectrum

21 Anticausality = 16 millisec Same amplitude spectrum, different phase spectrum

22 Anticausality = 32 millisec Same amplitude spectrum, different phase spectrum

23 Anticausality = 64 millisec Jon’s favorite Same amplitude spectrum, different phase spectrum

24 Anticausality = 128 millisec Same amplitude spectrum, different phase spectrum

25 Anticausality = 256 millisec bad! midpoint is 60ms Wavelet is becoming symmetrical.

26 After Before Notice polarity alternation. Yilmaz & Cumro shot profile #33 26 {{{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{{{{ CVCVCVCV

27 Before {{{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{{{{ {{{{{{{{{{{{{{{{{{{{ CVCVCVCV 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, then seismogram polarity is revealed.

29 Generally equivalent terms and concepts Blind decon Predictive decon Causal decon Autoregression, Yule&Walker 1927 Minimum-phase decon, MIT GAG 1954 Wiener-Levinson, Toeplitz Burg, Robinson, and Treitel Kolmogoroff decon (1939) (in my textbook FGDP 1974) (the code is in my book PVI 1992)

30 Generally equivalent terms and concepts Blind decon Predictive decon Causal decon Autoregression, Yule&Walker 1927 Minimum-phase decon, MIT GAG 1954 Wiener-Levinson, Toeplitz Burg, Robinson, and Treitel Kolmogoroff 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.)

Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG Las Vegas November 2012

Sparsity decon in the log domain with variable gain Jon Claerbout, Qiang Fu, and Antoine Guitton SEG Las Vegas November 2012

Sparsity decon in the log domain with variable gain

42 We seek sparse deconvolutions by imposing a hyperbolic penalty function. Sparsity decon in the log domain with variable gain

43 We seek sparse deconvolutions by imposing a hyperbolic penalty function. Sparsity decon in the log domain with variable gain Use the u(t) lag-log (quefrency) parameterization.

44 We seek sparse deconvolutions by imposing a hyperbolic penalty function. Gain(t) and mute(t,x) should be done after decon, not before. Sparsity decon in the log domain with variable gain Use the u(t) lag-log (quefrency) parameterization.

45 We seek sparse deconvolutions by 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 domain with variable gain Use the u(t) lag-log (quefrency) parameterization.

46 Want spike here. Might get spike here. Two years of frustration, always great results, but Might get spike here. Polarity clear, but random! and unexpected time shifts. 3 students quit!

47 Want spike here. Might get spike here. Might get spike here. Polarity clear, but random! and unexpected time shifts. 3 students quit! All is resolved by Ricker regularization. Hooray! Two years of frustration, always great results, but

48 Logarithmic parameterization

49 Gain and sparsity

50 softly clipped residual

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52 Physical output gradient w.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 RESULTS Compare 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 frequency precursor Clean bubble 57 Gain before Gain after OLD:NEW:

58 Compare Gain after decon. Gain before decon. Scale up by 10x Estimated shot

59 CONCLUSIONS Seismogram polarity is revealed by 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 Yang Antoine 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

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65 Can you explain why traditional decon fails?

66 Can you explain why traditional decon fails?

67 Can you explain why traditional decon fails?