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Michelangelo, Seismic andSeeing Whats ThereJan Dewar, Jon Downton, Glen Larsen;Core Lab Reservoir Technologies Division, Calgary, Alberta

In oil painting restoration, masterpieces dirtied bycenturies of grime and smoke are cleaned to reveal theoriginal brilliant image. The recent cleaning and restora-tion of the frescoes in the Sistine Chapel are a familiarexample. Once the unwanted dirt had been removed, the

beauty and vibrant colors of the true image was stunning.The splendor of the true image had been there all the time,unseen and obscured by noise, for years. The restorationrenewed the vivid colors of Michelangelos work, and, infact, caused art historians to reconsider their under-standing of the masters use of color.

Interestingly, early restorers attempted to clean the Sistineceiling with materials ranging from bread to retsina wine.

It became apparent that to successfully uncover the orig-inal painting, proper cleaning methods would be needed.But just removing the noise would not be enough: heavy-handed approaches like scrubbing by brute force orcleaning with solvents could do this but would damage thepaint. A method had to be found which could lift the dirtwithout altering the original image.

How can art restoration inspire seismic dataprocessing?

Seismic data contains both desirable signal and undesir-able noise. One of the challenges of seismic data processingis to remove the noise, leaving just the good signal. There

are many approaches to doing this; most have shortcom-ings such as mathematical artifacts that alter or distort thesignal, or simply fail to address certain kinds of noise. Forexample, Radon de-multiple methods transform surfaceseismic data from time-offset coordinates to zero offsetintercept time slowness coordinates, where variouselements of the recorded data, such as signal and noise,may be more easily separated. Unwanted multiple eventsare isolated in the transform space and reconstructed in thedata space using an inverse Radon transform. The recon-structed multiples are then subtracted from the input,leaving, in theory, modeled primaries only.

Non-hyperbolic multiples are problematic for Radonmethods

Traditional Radon methods often work well but fail toaddress situations where the multiple reflection is non-hyperbolic. This happens frequently in marine data wherethe sea floor has rugged, rapidly changing topography: thetime-offset curve of the water bottom multiple reverbera-tion is not hyperbolic. A Radon transform typicallyassumes that a multiple exhibits a parabolic or hyperbolict-x curve, and, in addition, assumes that the apex of the

curve is at zero offset. Most standard Radon methodscannot handle situations where the multiple reflections donot honor these assumptions.

Limited aperture causes edge effects and near offset

leakage for Radon methods

Radon methods are aperture-limited. As noted by Wang(2003), the limited spatial aperture causes edge effects,impairing the separation of primary and multiple reflec-tions in the Radon transform domain (the events do nottransform as they should to points in tau-p space, rather,they transform to smeared interfering lines). The limitedsize of the spatial aperture of a seismic gather affects theability of Radon transform to separate multiple andprimary reflections. With Radon there is near offset leakageof multiple energy.

To accommodate this shortcoming of Radon, adaptivesurgical muting or inside mutes have often been used toremove the near offset data. To address spurious randomnoise, noise burst attenuation programs are also commonlyused. This approach - inside mute accompanied by de-

burst - yields a reasonable looking stack but does notpreserve amplitude integrity and, in fact, completely sacri-fices near offset information. This may be satisfactory ifstack is the required output, but is problematic if furtherpre-stack processing is desired.

High resolution Radon de-multiple methods attempt toovercome limitations of spatial aperture and spatialsampling by imposing sparseness constraints in the Radondomain. The sparcity constraints, a departure from theconventional least-squares solution, effectively move thetransformed energy to where it would be if there were nosampling or aperture limits. Think of it as focusing intau-p space: the smeared (aliased) lines become points. HRRadon de-multiple has been useful to deal with aliasing onfar offset data and to discriminate more precisely betweenclose curvatures.

SRME (Surface-Related Multiple Elimination) is another

multiple attenuation tool. We have seen this approachwork well, particularly in situations where the surfacegenerating the multiple reflections has moderate structuralcomplexity; complex enough that other de-multiplemethods like Radon, tau-p decon and time domain gappeddeconvolution fail. However, for multiples from a surfacewith rapidly changing 3D topography, we have found theSRME method is limited by the assumptions behind thetechnique, namely: 1) a source for every receiver and viceversa, usually requiring interpolation and extrapolation(potentially introducing aliasing issues which become even

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more problematic in 3D), and 2) it is difficult for SRME to getthe amplitudes correct (iterations of SRME do indeed convergeto the response without free-surface multiples when the correctweights are used at each iteration, but not when they aredefined from the minimum energy criterion). Picture a multiplefrom an irregular 3D water bottom. The multiple changes

shape, amplitude and position with offset. In fact, at mid andfar offsets, the WB multiple no longer aligns with the sea floortopography. It is difficult for SRME methods to accommodatethis. HR Radon methods are inefficient in addressing thesediffracted multiples with shifted apexes in the cmp gathers.

Spatial filters can be frustrating

For other kinds of coherent noise, such as air-blast, ground-rollnoise, or any coherent linear noise, spatial filters such as F-K(frequency-wave number) transforms are commonly used.Many of these techniques do attenuate coherent noise, but leavefrustrating mathematical artifacts that alter or distort the signalsomewhat.

To address random noise, other methods such as FXDeconvolution have traditionally been used. The F-X predic-tion filter makes a general signal model assumption: that signalis predictable by convolution filters. The seismic signals in thefrequency-offset domain are represented by complex sinusoidsin the X-direction, which are then predictable. In comparison,random noise is unpredictable and can be rejected. Care must

be taken, especially with dealing with edges, if the amplitudeintegrity of the signal is to be left intact; something which isimportant for any subsequent AVO analysis.

The LIFT Approach

LIFT is an amplitude-friendly technique to attenuate noise andmultiples. LIFT is a significantly different approach to theproblem of noise attenuation than what has been done tradi-tionally. The LIFT method was built to attenuate any kind ofnoise - including multiples - while preserving the AVO integrityof primaries. This is important if one is to carry out amplitude-preserving processing and meaningful AVO analysis, includingthe possibility of AVO analysis on pre-stack migrated gathers.

LIFT General Methodology

The general method is to simultaneously model signal andcoherent noise, and then in a nonlinear adaptive fashion, atten-uate noise. Signal and noise can be modeled in a variety ofways, depending on the nature of the problem.

LIFT is not a single module or algorithm, it is an umbrella namefor a sequence of a variety of steps. Some of the steps within theLIFT sequence will include traditional ways to describe signaland noise - like FX Decon (for random noise), FK (for linearnoise), simulated geophone arrays (for ground roll), Fatti et al.sAVO Equation (for primaries) or Radon transform (for multi-ples). The steps chosen will depend on the nature of the partic-ular noise we are addressing.

Data Example: LIFT to Attenuate Multiples

The methodology is first to perform Radon de-multiple asneeded, to identify coherent noise and to improve signal-tonoise ratio. Signal can then be modeled in a variety of ways, forexample, by an AVO equation. (In a sense, this approach tomodeling signal exploits the assumptions of Zoeppritzs equations: plane waves and reflection between two half-spaces. Dueto these assumptions, a Zoeppritz-based AVO inversion wilconsider multiples and converted waves to be noise and wilexclude them in its reconstruction. Voil, primary signal ismodeled.) Then the LIFT sequence estimates and suppressemultiple energy from the original data in an adaptive nonlineafashion (Figure 1).

The LIFT Technique for multiple attenuation has been found towork well in both land and marine data. Figure 2 shows anexample of multiple attenuation in offshore data.

From left to right are zoom displays of the stacks of the inputdata, the data after Radon de-multiple (to attenuate the wate

bottom multiple), and after LIFT. One can see that multiplenergy from the irregular sea floor is attenuated effectively. Thequestion sometimes arises whether this multiple attenuationscheme will preserve diffractions for pre-stack migration. Onecan clearly see that diffraction patterns are still present after the

LIFT process. In fact, originally noise was sitting on top of thediffraction energy, making it difficult to identify the diffractions.

The rightmost panel is the Difference display, (the differencebetween Radon and LIFT), showing what LIFT removed.

Article ContdMichelangelo, Seismic and Seeing Whats ThereContinued from Page 47


Figure 1: A LIFT scheme to attenuate multiples.


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Data Example: LIFT to Attenuate Source-gener-ated Noise

A very successful application of LIFT in land data has been toattenuate difficult source-related noise. A typical LIFT method-ology is to address ground-roll noise with array forming - acomputer simulation of geophone field arrays. Geophonearrays in the field, spanning dimensions comparable to thedominant wavelength of the noise, have traditionally been usedto discriminate against events on the basis of their moveout orapparent wavelength, but long geophone arrays can greatlyreduce the frequency content of recorded data. With arrayforming on the computer, the effective array length can be setdifferently for each frequency considered. Carrying on with theLIFT sequence, the source-related noise is then estimated andsuppressed (Figure 3).

Figure 4 shows a typical Alberta land shot record. Geometricdivergence correction is the only process that has been applied.Air blast and ground roll noise are evident. Figure 5 shows the

shot record after the LIFT sequence to attenuate source-relatednoise has been run.


Figure 3: A LIFT scheme to attenuate source noise.

Figure 4: Input shot record.

Figure 5: The shot record after LIFT to attenuate source-generated noise.

Figure 2: Zoom displays of stacks. LIFT was used to attenuate multiples; diffraction energy - desirable for subsequent pre-stack migration - is clearly preserved through theLIFT process.



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Figure 6: Synthetic data.

Figure 7: Left to right: Input gather (primaries + multiples); Radon De-multiple; Difference. The Difference displays show what Radon removed.


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Figure 8: Left to right: Radon De-multiple; LIFT output; Difference. The Difference displays shows what LIFT removed.

Figure 9: Comparison of ideal (primaries only), and the gather after LIFT multiple attenuation.Continued on Page 52


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We have also found this technique works well in the chal-lenging Mackenzie Delta area, where the seismic data collectedcan be affected by permafrost, sea ice, and the deposits of theMackenzie River itself. Groundroll noise travels fast throughthe frozen near-surface, and data recorded here often has a verypoor signal-to-noise ratio generally. The noise is typically in the

same bandwidth as the signal, making it difficult to deal with.Historical approaches like spatial filters perform reasonably butthe results suffer from some spatial smearing, and amplitudesof signal are not necessarily preserved. Again, the challenge isto reduce the noise without smearing, distorting, (or creating)signal. The results from the LIFT approach have beenwelcomed by the client. The approach can be iterative andparameters can be fine-tuned for particular datasets.

How can we know it preserves amplitudes?

Investigation of LIFTs AVO-friendliness in attenuating

multiples

To investigate LIFTs ability to attenuate multiples and topreserve legitimate amplitude variations of primaries,synthetic pre-stack data was generated from well log data. Thesynthetic data is a simple convolutional model.

The model is shown in Figure 6 (on page 50). The modelincludes Class I and Class II AVO reflectors (followingRutherfords classification, Class I is a gas sand which is higherimpedance than the overlying material. Class I AVO is a peakwhich dims with offset more rapidly than the regional seismicresponse. Class II is a near-zero impedance contrast gas sandwhose reflection amplitude brightens with offset.)

The first step is Radon de-multiple (Figure 7). The Difference

display shows that Radon alone does not capture the multipleenergy at near offsets, and does not preserve primary ampli-tudes (note primary energy leakage on the difference display).

The LIFT technique then effectively removes residual multipleenergy that Radon could not attenuate, most notably multipleenergy at near offsets. Further, there is very little primaryenergy leakage (Figure 8).

The ability of the LIFT technique to preserve primary ampli-tudes is illustrated more clearly on the summary display shownin Figure 9. This display assembles the primaries-only paneland the final LIFT output panel, and shows the difference

between the two. The primaries panel is the ideal of what oneshould be left with if multiples have been removed perfectly.

The difference display shows some leakage of primary energyat very far angles (the mute is 45 degrees). Looking back toFigure 7, most of this leakage occurred at the Radon step,suggesting that the Radon parameters be reviewed.

Investigation of LIFTs implications for quantitative

AVO analyses

To investigate the implications for quantitative AVO analyses,Rp and Rs were calculated from the same synthetic pre-stack

seismic gather by solving Fatti et al.s linear approximation ofZoeppritz equations for Rp and Rs (P- and S-impedance reflec-tivity). Rp and Rs were solved for four different inputs: theprimaries-only gather; primaries + multiples gather; the gatherafter Radon de-multiple, and the LIFT output gather.

Compare the results to those from the primaries-only or ideal(Figures 11 and 12). Please note that the Rp and Rs traces have

been duplicated ten times for ease of viewing.) Observe that theAVO attributes calculated from the LIFT gather are very closeto the values calculated from the primaries-only gather. Thereflectivities calculated from the Radon gather and from theraw gather are not very accurate, particularly in the 2.0-4.0 seczone in this example. Here the t-x curves of the multiples arerelatively flat: the multiples look a lot like primaries. The AVOequation was not able to distinguish multiple from primary inthis situation. The poor Rp and Rs results calculated from theprimaries + multiples gather tell us that something must bedone to address multiples prior to AVO analysis. The poorresult from the Radon de-multiple tell us that Radon is notsufficient. Application of the LIFT technique enables a moreaccurate AVO analysis.

Limitations and Weaknesses of the LIFTTechnique

Since we need some signal to model, the input to LIFT musthave reasonable signal-to-noise ratio. If the S/N is too poor, theLIFT approach will not give any benefit.

Warning: New Techniques May Necessitate aNew Look at Interpretations

While restoration of Michelangeloss frescoes has stirred

controversy among art historians (some saying that removingthe markings of the passage of time has impoverished theaesthetic experience; others calling it one of the great revela-tions of our time) it is undeniable that the restoration has trans-formed the painting into a state substantially different fromwhat was previously known and revered. The editor of TheArt Newspaper International, put it this way: some peopleliked things to look romantic and old, and cant cope with theclarity and brilliance of what the Sistine Chapel looks like nowit has been cleaned. The analogy between art and seismic dataends here. Seismic data is not art, and cleaning noise fromseismic data should be free of such controversies. Practicedseismic interpreters are not emotionally attached to theaesthetic value of their interpretation. If a multiple is obscuring

the real signal, they want to know about it, and they want it tobe dealt with properly so they can view the signal, not theprevious interpretation of signal that may have been knownand revered.

LIFT is one of those new techniques that may prompt inter-pretations to be re-evaluated. For example, one may need to(or been thankful to) re-interpret a sub-salt zone after LIFT hasattenuated multiples that other methods could not handle. (Weknow of one such situation, but, as is often the case, the successof the method ironically prevents it from becoming well-




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known - the interpreter views the techniqueas a competitive advantage and understand-ably will not grant permission to show theresults.)

We encourage you to give new approaches atry; you might end up seeing seismic in adifferent way.

A beautiful thing never gives so much painas does failing to hear and see it. ~

Michelangelo

Acknowledgements

The authors wish to thank Yongyi Li for hisassistance. R

References andSuggested ReadingFatti, J. L., Smith, G. C. , Vail, P. J., Strauss, P. J., and Levitt,P.R., 1994, Detection of gas in sandstone reservoirs using AVOanalysis: A 3-D seismic case history using the Geostack tech-nique, Geophysics, 59, 1362-1376.

Rutherford, S. R., and Williams, R. H., 1989, Amplitude-versus-offset variations in gas sands: Geophysics, 54, 680-688.

Wang, Y., 2003, EAGE, Geophysical Prospecting, vol. 51,pp 75-87


Jan Dewar is a geophysicist and technicalwriter at Core Lab RTD, and is the corre-sponding author for this article:

[email protected]

Jon Downton is a Director of Research and

Development at Core Lab RTD, and is alsocompleting graduate studies at theUniversity of Calgary.

Glen Larsen is a Seismic Processing TeamLeader at Core Lab RTD, specializing inland processing.

Figure 10: Various inputs to AVO analysis.

Figure 11: Rp computed from the various inputs.

Figure 12: Rs computed from the various inputs.

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