Annual Meeting SelectionRedundant and useless seismic attributesArthur E. Barnes1ABSTRACTMany seismic attributes are redundant or useless and con-fuse seismic interpretation more than they help. They are eas-ily recognized given a few guidelines and tools. Discardingthemleaves an attribute list that is both more manageable andmore honest.INTRODUCTIONHundreds of seismic attributes have been invented and more ap-pear each year e.g., Brown, 1999. Their great number and varietyare daunting and make it difcult to choose which ones to use.Many seismic attributes duplicate each other, or are obscure, un-stable, or unreliable, or are purely mathematical quantities, or are notreally attributes at all. These unnecessary seismic attributes can beidentied through inspection aided by crossplots, histograms, andcorrelation. Discardingredundant anduselessattributesleavesamuch-reduced set of attributes that is easier to use.METHODTodistinguishusefulseismicattributesfromthoseofdoubtfulutility, review your attributes in the light of the following common-sense principles.Seismic attributes should be unique. You only need one attributeto measure a seismic property. Discard duplicate attributes. Wheremultiple attributes measure the same property, choose the one thatworks best. If you cant tell which one works best, then it doesntmatter which one you choose.Seismic attributes should have clear and useful meanings. If youdont knowwhat an attribute means, dont use it. If you knowwhat itmeans but it isnt useful, discard it. Prefer attributes with geologic orgeophysical meaning; avoidattributeswithpurelymathematicalmeaning.Seismic attributes represent subsets of the information in seismicdata. Quantities that are not subsets of the data are not attributes.Attributes that differ only in resolution are the same attribute; treatthemthat way.Seismic attributes should not vary greatly in response to smalldata changes. Avoid overly sensitive attributes.Not all seismic attributes are created equal. Details of implemen-tation can be important. Avoid poorly designed attributes.The utility of a seismic attribute is readily judged through visualinspection aided by crossplots, histograms, correlation, rank corre-lation, principal components analysis, and spectral analysis.Standardcorrelationidentieslinearrelationshipsbetweenat-tributes. Rank correlation is more robust as it can also identify non-linear relationships. Rank correlation is computed like standard cor-relation, except that the attribute values are rst sorted in order ofvalueandthentheirranksinthesort arecorrelatedIsaaksandSrivastava, 1989, p. 31.Like standard correlation, principal components analysis identi-es linear relationships between attributes Duda et al., 2001. Longappliedforcoherencyltering, principal componentsanalysisisalso used for reducing the number of attributes needed for analysis.In essence, it transforms a set of linearly related attributes into a newset of unrelated attributes. If some of the transformed attributes lackuseful information, then there is duplication of information withinthe original attributes.APPLICATIONDuplicateattributesarelegion.Manybasicseismicproperties,particularly amplitude, frequency, and discontinuity, are quantiedthrough a variety of similar seismic attributes.Consider the most important seismic property, amplitude. Thereare more than a dozen common amplitude attributes. Figure 1 com-pares four of them: average reection strength, rms amplitude, aver-Manuscript received by the Editor August 7, 2006; revised manuscript received October 10, 2006; published onlineApril 19, 2007.1ParadigmGeophysical, Kuala Lumpur, Malaysia. E-mail: artb@paradigmgeo.com.2007 Society of Exploration Geophysicists. All rights reserved.GEOPHYSICS, VOL. 72, NO. 3 MAY-JUNE2007; P. P33P38, 7 FIGS., 2TABLES.10.1190/1.2716717P33age absolute amplitude, and maximum peak amplitude AppendixA. They all look about the same. Correlations, crossplots, and prin-cipal components analysis of these maps indicate that they containnearly the same information Table 1; Figure 2. Similar analysis ofaverage peak amplitude, average trough amplitude, and other ampli-tude attributes conrms that most amplitude attributes are stronglycorrelated. Rarelyis anythinggainedbyusingmore thanone of theseas a general amplitude measure. Average reection strength nearlyalways sufces.You may prefer average energy because it exhibits more contrastthan reection strength. Use it, but recognize that average energy hasexactly the same information as rms amplitude and almost the sameas reection strength see Appendix A. Its greater contrast is due tohow it presents the information. Perhaps you want to use the maxi-mum peak amplitude because you really are interested only in thestrongest positive events in a window. Use it for this purpose but notas a general amplitude measure.Consider a more involved seismic property, discontinuity. Figure3 compares four common discontinuity attributes based on correla-tion,semblance,covariance,andweightedcorrelationAppendixB. Their correlation coefcients all exceed 0.92 and their rank cor-relation coefcients all exceed 0.95 Table 2. Despite signicantcomputational differences and enthusiastic claims, these four dis-continuity attributes are so nearly the same that it doesnt matterwhich one you use.Discontinuity attributes based on principal components derivedfrom principal components analysis of seismic data in an analysiswindow masquerade as independent measures, yet tend to be wellcorrelated. Attributesdenedasratiosof principal components,such as the Karhunen-Loeve signal complexity a confusing name,often show the same picture. The rst principal component normal-ized by the total energy is identical to covariance discontinuity. Ifyou dont already have a discontinuity attribute, then use the rstTable 1. Standard correlation coefcients between fouramplitude attributes. ARS is average reection strength, rmsis rms amplitude, AAA is average absolute amplitude, andMPA is maximum peak amplitude.ARS rms AAA MPAARS 1 0.977 0.991 0.792rms 0.977 1 0.978 0.857AAA 0.991 0.978 1 0.782MPA 0.792 0.857 0.782 15 miReflection strength5 mirms amplitudeHighLow5 miAverage absolute amplitude5 miMaximum peak amplitudeAmplitudeFigure 1. Maps of four amplitude attributes computed in the same100 ms window25 samples.015010050050 100 150 200 250100 200Reflection strengthrms amplitude015010050050 100 150 200 250100 200Reflection strengthAverage absolute amplitude04002000400200050 100 15050 100 150Reflection strengthMaximum peak amplitude50 100 150rms amplitudeMaximum peak amplitudeFigure 2. Crossplots between the amplitude attributes of Figure 1.5 miCorrelation5 miSemblance5 miCovariance5 miWeighted correlation Figure 3. Four discontinuity attributes based on correlation, sem-blance, covariance, and correlation weighted by trace magnitude,computed as maps in a 60 ms window15 samples. These attributesare nearly identical. Discontinuous data is shown as blue, continu-ous data as white.P34 Barnesprincipal component attribute but discard the others; otherwise, dis-card themall.Some attributes are not only similar, they are essentially identical.They contain exactly the same information and differ merely in howthey present it. As already noted, rms amplitude and average energyare identical. Other identical attributes include instantaneous phaseand cosine of the phase, and dip-azimuth reection dip combinedwith reection azimuth and shaded relief. Choose one and discardthe other.Cosine of the phase removes all amplitude information and re-sembles a strong amplitude gain Figure 4. Treat it more as a processthan as an attribute.Watchout forattributesthat havemultiplenames. Reectionstrength, trace envelope, and instantaneous amplitude are the sameattribute. Slope and dip are used interchangeably, as are continuity,coherence, discontinuity, and similarity. Eigen-structure discontinu-ity is the same as covariance discontinuity. Arc length is sometimescalled reection heterogeneity. Response attributes are called wave-let attributes. The quadrature trace and the imaginary trace are thesame but the quadrature trace is a 90 phase rotation and is not re-ally an attribute since it does not subset the information.Attributes such as arc length and Karhunen-Loeve signal com-plexity lack clear and useful meaning and are useless. Average in-stantaneous phase is also useless because the more instantaneousphaseisaveraged, themoreit tendstowardszero.Averageun-wrapped instantaneous phase is scarcely better. The slope of the in-stantaneous frequency may have clear mathematical meaning but itlacks useful geologic or geophysical meaning. Avoid it. The same istrue of dominant frequencies derived from maximum entropy spec-tral decomposition. Response phase and response frequency are use-less if you insist that they describe the seismic source wavelet as ad-vertised because they fail on real data White, 1991. Use them em-pirically, recognizingwhat theyreallyrecord. Response phaserecordstheapparent phaseofreectionsat envelopepeaks. Re-sponse frequency applies a nonlinear lter to smooth the instanta-neous frequency. Response frequency has utility, but weighted aver-age frequency is smoother and has simpler meaning.Resolution is an important parameter of most attributes. It is deter-mined by the size of the window in time and space in which the at-tribute is computed. Changing an attributes resolution does not cre-ate a newkind of attribute. This is obvious for attributes like rms am-plitude and energy half-time. Less obviously, it is also true of instan-taneous frequency and weighted average frequency. You might rea-sonablyusebothtoinvestigatetargetsofdifferentsize,buttheyremain the same attribute.Average frequency, rms frequency, bandwidth, and a few otherspectral attributes can be computed equally well in the time domainor in the frequency domain. It is pointless to compute them in bothdomains. Not all spectral attributes are so exible. Spectral skewandkurtosis must be computed in the frequency domain, but they havelittleinherentgeologicorgeophysicalmeaning,soyouprobablydont need them.Table 2. Rank correlation between the four discontinuitymaps of Figure 3.Correlation Semblance CovarianceWeightedcorrelationCorrelation 1 0.988 0.975 0.981Semblance 0.988 1 0.959 0.967Covariance 0.975 0.959 1 0.998WeightedCorrelation0.981 0.967 0.998 12 km2 kma) 0.0 1.5Time (s)b) 0.0 1.5Time (s)Figure 4. Aseismic line processed with a cosine of the phase, andb a strong amplitude gain28 ms or 7 sample operator length.They are almost indistinguishable. 0 400Time (ms)Synthetic data 0 400Time (ms)Apparent polarity 0 400Time (ms)Response phase Figure 5. Illustration of instability in apparent po-larity. The synthetic data has three reections and asmall amount of random noise. The top reectionhas positive polarity, the bottomreection has neg-ative polarity, and the middle reection is a com-posite of two reections 4 ms apart. The compositereection looks like a single reection with 90 ofphase for which the apparent polarity ips random-ly. The same problem occurs on real data. Everytwentieth trace is overlain in wiggle format. Red ispositive polarity, blue is negative.Redundant anduselessseismicattributes P35Attributes that are sensitive to small perturbations in the data areunstable. Apparent polarity is an example. It is dened as the sign ofthe seismic data at envelope peaks scaled by the envelope peak andheld constant in each interval around a peak. It works ne for cleanzero-phase data that is free of reection interference, but it is ambig-uousfor thin-bedreections, whichhaveanapparent phaseofaround 90 Figure 5. Discard apparent polarity and use responsephase instead. Attributes that count the integral events in an intervalare also unstable as they are sensitive to small changes in intervaldenition. Avoid them.Unsupervised waveformclassication is more sensitive to detailsof the analysis window than most other attribute methods. Differ-ences due to small changes in the window are often signicant. InFigure 6, a one-sample shift in the analysis window causes a largechange in the attribute maps produced by the Kohonen self-organiz-ing feature map KSOFM. Somewhat surprisingly, for this same ex-ample a competing algorithm, K-means clustering, nds the samepatterns as the KSOFM, but their maps appear markedly differentbecause they follow different rules in assigning class numbers towaveforms. Assigningthesamecolors tothesamewaveformsshows that the competing maps found nearly the same classes. Forbasicpatternrecognitionit matterslittlewhichmethodisused.However, the KSOFM naturally and logically orders its waveformclasses, unlike K-means clustering, and is therefore preferable as itsmaps are easier to interpret.Beware of differences between programs for generating seismicattributes. Aside from incorrect algorithms, which plague instanta-neousfrequency,thesameattributeproducedbycompetingpro-grams can differ substantially due to implementation details. Onesuch detail regards windowing, which is the way an algorithm se-lects seismic data froman interval. Attributes are lters, and like anylter they should employ tapered windows to reduce Gibbs effects.Nontapered or boxcar windows are nonetheless widely used. Box-car windows give rise to banding in the time domain and ringing inthe frequency domain, which are the Gibbs effects. In contrast, ta-pered windows produce sharper images and smoother power spec-tra. Figure 7 demonstrates this with energy half-time. Attributes withringy spectra are poorly designed. Avoid them.Incidentally, energy half-time measures amplitude change. Opti-mistic claims that it indicates lithology are wrong. Prefer standardmeasures of amplitude change to energy half-time see AppendixA.CONCLUSIONSThere are too many duplicate attributes, too many attributes withobscure meaning, and too many unstable and unreliable attributes.This surfeit breeds confusion and makes it hard to apply seismic at-tributes effectively. You do not need them all. Review your seismicattributes and reduce them to a much smaller subset. Discard dupli-cate and dubious attributes, prefer attributes with intuitive geologicor geophysical meaning, understand resolution, distinguish process-es from attributes, and avoid poorly designed attributes. The subsetremaining is both more manageable and more honest.ACKNOWLEDGMENTSI thank Seitel Data Ltd. for permission to publish the seismic datashown in Figures 1, 3, and 6; I thank Landmark for permission topublish the paper; and I thank Paradigmfor supporting the revision. Ialso thank an unknown reviewer and Dengliang Gao for exception-ally helpful and detailed reviews.5 mi 5 mi5 mi 5 mia) b)c) d)Figure 6. Waveform maps produced in a 60 ms window 15 sam-ples. A specic color indicates similar waveforms on a map. Be-tween maps, the same color usually corresponds to different wave-forms. a KSOFM centered at time A, b KSOFM centered at timeB = A + 4 ms 1 sample, c K-means at time B, and d K-meansat time Bwith color scale chosen to match the map in b. The differ-ences caused by the small change in windowexceed those caused bythe competing algorithm.Frequency (Hz)Ringing spectruma) 0.0 1.02.051015202530510152025303540455 kmTime (ms)dB power0 100Frequency (Hz)Smooth spectrumb) 0.0 1.02.05 kmTime (ms)dB power0 100Figure 7. Energy half-time computed with a a boxcar window, andb a Hamming window. Both windows are 60 ms long15 sam-ples. The Hamming windowprevents spectral ringing and producesa sharper image.P36 BarnesAPPENDIX AAMPLITUDE ATTRIBUTESThe amplitude attributes of Figure 1 are computed in an interval ofNsamples taken about a horizon or constant time. Average reectionstrength a is dened asa =1Nn=1Nan, A-1where anis the instantaneous reection strength at time index n. Therms amplitude xrms is dened as the square root of the average of thesquared trace values xn:xrms = 1Nn=1Nxn2. A-2Average absolute amplitude xais given byxa =1Nn=1Nxn . A-3Maximumpeak amplitude is the magnitude of the largest trace valuein the interval. Average energy Eis the total energy of the trace divid-ed by the number of samples, and is dened byE=1Nn=1Nxn2. A-4Average energy is the square of the rms amplitude.Energy half-time measures where in a time interval the seismicenergy is concentrated. As used here, it is dened as the percentageof the interval length at which the center of gravity of the data occurs.This center of gravity is the average time tcdened bytc =n=1Ntnxn2n=1Nxn2. A-5Energy half-time Eht is this average time, referenced from the starttime of the interval, t1, expressed as a percentage of the total intervallength:Eht = 100% tc t1tN t1, A-6where tNis the time at the end of the interval.Relative amplitude change, t, is the time rate of change of thereection strength at normalized by the reection strength:t =1atdatdt. A-7Energy half-time closely resembles an averaged relative amplitudechange.APPENDIX BCONTINUITY ATTRIBUTESBahorichandFarmer 1995 introduceda measure of seismic con-tinuity based on crosscorrelations between three traces in an L pat-tern. Their measure is readily extended to compute continuity in ananalysis window encompassing an arbitrary number of traces. Theresulting correlation continuity attribute is similar in form to sem-blance continuity and comparable to covariance continuity Marfurtet al., 1998; Gersztenkorn and Marfurt, 1999. It is further general-ized by weighting the constituent correlations to produce a weightedcorrelation continuity attribute. I provide the mathematics for thesetwo continuity measures without corrections for reection dip. I im-plicitly use a boxcar windowoperator, though windows could be ta-pered to avoid Gibbs effects. For both measures, continuity Crangesfrom0 for perfectly discontinuous data to 1 for perfectly continuousdata. A corresponding measure of discontinuity D is formed as D= 1 C.I simplify the mathematics by expressing seismic traces as vec-tors. The zero-lag crosscorrelation of two traces xi and xj, each withNsamples, is given byxi xj = k=1Nxikxjk, B-1where k is the trace sample index. The energy Eiof a trace xiis the ze-ro-lag autocorrelation of the trace:Ei = xi xi = k=1Nxik2. B-2Acircumex denotes a unit vector. The unit vector xiis the trace vec-tor xinormalized by the square root of its energy:xi =xiEi. B-3The average trace of a set of M traces is the vector average xa givenbyxa =1Mi=1Mxi. B-4Acorrelation continuity measure C can be dened as the averageof the squared crosscorrelations between every trace with the aver-age trace:C =1Mi=1Mxi xa2. B-5Weighted correlation continuity is the average of the squared cross-correlations between every trace with the average trace, with eachRedundant anduselessseismicattributes P37crosscorrelation weighted by trace energy Ei. Thus, a weighted cor-relation continuity attribute Ccan be expressed asC =i=1Mxi xa2i=1MEi. B-6This continuity measure closely approximates covariance continu-ity, but is computationally faster and does not assume zero-meantraces.REFERENCESBahorich, M., and S. Farmer, 1995, 3-D seismic discontinuity for faults andstratigraphicfeatures: Thecoherencecube: 65thAnnual InternationalMeeting, SEG, ExpandedAbstracts, 9396.Brown, A. R., 1999, Interpretation of three-dimensional seismic data, 5thed.: AAPGMemoir, 42, AmericanAssociation of PetroleumGeologists.Duda, R. O., P. E. Hart, and D. G. Stork, 2001, Pattern classication, 2nd ed.:Wiley Interscience.Gersztenkorn, A., and K. J. Marfurt, 1999, Eigenstructure-based coherencecomputations as an aid to 3-D structural and stratigraphic mapping: Geo-physics, 64, 14681479.Isaaks, E. H., and R. M. Srivastava, 1989, An introduction to applied geosta-tistics: Oxford University Press.Marfurt, K. J., R. L. Kirlin, S. L. Farmer, and M. S. Bahorich, 1998, 3-Dseis-mic attributes using a semblance-based coherency algorithm: Geophysics,63, 11501176.White, R. E., 1991, Properties of instantaneous seismic attributes: The Lead-ing Edge, 10, 2632.P38 Barnes