the anatomy of avo crossplots - rock...

AVO crossplots are a simple andelegant way of representing AVOdata. Offset variations in amplitudefor reflecting interfaces are repre-sented as single points on a crossplotof intercept and gradient. The advan-tage of this type of plot is that a greatdeal of information can be presentedand trends can be observed in thedata that would be impossible to seewith a standard offset (or angle) ver-sus amplitude plot. The crossplot isan ideal way of examining differencesin AVO responses that may be relatedto lithologic or fluid-type variations.Commonly used techniques forrevealing these differences includecolor-coding samples from the cross-plot and using this as an overlay toa seismic display or creatingweighted (or “equivalent angle”)stacks (i.e., linear combinations ofintercept (R0) and gradient (G).

The early literature approachedAVO crossplots from the point ofview of rock properties. Acentral con-cept that emerged from this work wasthe “fluid line,” a hypothetical trendbased on a consideration of brine-filled rock properties together with

simplifications of the reflectivityequations (Figure 1). If the interceptis plotted on the x axis and the gra-dient on the y axis, then for consoli-dated sand/shale rocks the top andbase reflections form a trend from theupper left to the lower right quadrantof the crossplot that passes throughthe origin. When it was realized thatdata points for equivalent hydrocar-

bon-filled rocks plot to the left of thisline, it became clear that normalizingthe data against the fluid line mightprovide an optimum AVO indicator.

The similarity of the fluid-linetrend to trends on time-window AVOcrossplots generated from seismicwas compelling, and many assumedthese are the same. In fact, both mod-els and real data examples show that

150 THE LEADING EDGE FEBRUARY 2000 FEBRUARY 2000 THE LEADING EDGE 0000

The anatomy of AVO crossplotsROB SIMM, Rock Physics Associates, Harpenden, U.K.ROY WHITE, London University, U.K.RICHARD UDEN, Continuum Resources, Houston, Texas, U.S.

Figure 1. AVO classes and the AVO crossplot.

Figure 2. The anatomy of AVO crossplots. (a) A single class I reflection. (b) The noise associated with the measure-ment of gradient on numerous gathers. (c) The porosity effect. (d) The gas effect. (e) The optimum discriminator.(f) The time-window crossplot.

a) b) c)

d) e) f)

in general this is not the case. Realcrossplot trends depend principallyon the way the crossplot has beenconstructed (i.e., horizon versus time-window crossplots), the amount ofnoise relative to signal, and the mag-nitude of any effect associated withhydrocarbon (i.e., the “gas effect”).While rock-property information iscontained in AVO crossplots, it is notusually detectable in terms of distincttrends, owing to the effects of noise.

Signal and noise. Consider a singlepoint in the lower right quadrant ona crossplot (Figure 2a). This point wasgenerated from the AVO attributes(derived by least squares regression)associated with the maxima of a sin-gle zero-phase reflection on a syn-thetic gather with no noise. Itrepresents a class I response from thetop of a brine-filled consolidated sandat the boundary with an overlyingshale, i.e., the amplitude is decreas-ing with offset. This representationmight be called a “horizon crossplot”as it relates to a single reflecting inter-face.

If data from several gathers withthe same reflection are crossplotted,then the crossplot signature is ofcourse the same—a single point onthe plot. However, if random noise isadded uniformly across the gathers(such that the S/N decreases withoffset), the crossplot responsebecomes an oval distribution ofpoints around the real location(Figure 2b). This is due to the sensi-tivity of the gradient estimation tonoise. Hendrickson has termed thisthe “noise ellipse.” This noise trendis easily recognized on real data, forexample by crossplotting a limitednumber of samples from the samehorizon from a seismic section. Theextension of the trend parallel to thegradient axis is an indication of theamount of noise in the data. On realdata the noise trend usually has aslope of about -5 or more. The effectsof other types of noise (such asRNMO) will not be dealt with here.

Cambois indicated that the slopeof the noise trend is dependent ontwo-way traveltime, velocity struc-ture, and offset. On real data the gen-eral position of a data cluster (suchas that shown in Figure 2b) is depen-dent on the relative scaling of R0 andG (and may be affected by residualmoveout or uncorrected amplitudedecay). However, the slope of thenoise trend is independent of thisscaling.

Although random noise appears

to be the principal component ofnoise on AVO crossplots, other typesof noise can have an influence on theobserved trends (such as RNMO).

Porosity and shale content. Achangein lithology can be modeled by vary-ing the porosity of the sand or theshale content. Increasing the poros-ity has two effects—to decrease theAVO gradient (i.e., the Poisson ratiocontrast with the overlying shale hasbeen reduced) and to decrease theintercept (owing to a decrease in theimpedance contrast). The decrease inintercept gives rise to a low-angleporosity trend that intercepts the gra-dient axis.

Changing the porosity of the sandin the model (but still maintainingthe criteria of noninterfering reflec-tions) results in a crossplot that showsa series of ellipses aligned at an angle

to the gradient axis (Figure 2c). Thetrend imposed by the eye on this datacluster would be somewherebetween the porosity trend and thenoise trend.

A change in lithology due toincreasing shale content of the sandalso lowers the gradient and inter-cept, but the trend is steeper than theporosity trend. It may even be closeto the noise trend. In the case wherethe shale component in the sand isdifferent from the overlying shale (asmight be found at a sequence bound-ary), then the “lithologic trend”would have a nonzero interceptvalue.

This discussion illustrates that agiven area might not have one back-ground trend but a possible varia-tion, depending on the relativecontributions of shale and porositywhich, in turn, are determined by


a)

b)

Figure 3. A real data example. (a) Stacked section illustrating a bright spotwith a top sand pick in green. (b) Time-window crossplot generated from a40-ms window around the top-sand pick.

sedimentary facies. This is a mootpoint, however, given that in practicenoise obscures the lithologic trend.

The gas effect. Figure 2d shows theeffect of fluid substituting the sandsof varying porosity (again the reflec-tions are separate and noninterfer-ing). The effect of the hydrocarbon isnot so much to define a trend as tocreate a separate data cluster occu-pying a position to the left of thebrine-bearing data points. The greaterthe effect of the hydrocarbon on theVP/VS ratio of the sand, the further thedata points will plot away from thebrine-filled data points.

In these models, the optimum dis-

criminator can be determined statis-tically (Figure 2e). This will dependon the amount of noise, the lithologicvariation, and the magnitude of thegas effect. This trend may or may notpass through the zero point. In thereal-world case, knowledge of thenoise trend could be used to modelthe optimum discriminator (assum-ing all other effects on R0 and G couldbe accounted for). If the lithologicvariation is not large, a range oftrends may exist that would dis-criminate equally well.

Time-window crossplots. So far, dis-cussion has centered on the horizoncrossplot. If samples from a time win-

dow are incorporated into the cross-plot, the horizon sample points,together with reflections from thebase of the sand (plotting in the upperleft quadrant), are included in anellipse of points centered on the ori-gin (Figure 2f). The organization ofdata around the origin does not havea physical significance; it is simplythe result of the fact that the mean ofseismic data is zero. Noise related tosampling parts of the waveformsother than the maxima is infilling thearea between the two data clusters.

Cambois has shown that the slopeof what might be called the “time-window” trend (i.e., a line drawnthrough the data which passesthrough the origin) is dependent onthe S/N of the data. The lower theS/N, the steeper the trend. This trendmay be close to the optimum dis-criminator or it may not. The noisierthe data, the closer this time-windowtrend will be to the noise trend.

In the case where S/N is veryhigh, it could be argued that the linederived from a time-windowedcrossplot is equivalent to an averagerock property trend (call it the fluidline if you must) that can be inferredfrom a crossplot derived from welldata. Given the general level of S/Nof most seismic data, this occurrenceis likely to be rare.

Crossplots in practice. It is clear thatthe authors see little value in time-window crossplots, owing to theeffects of noise. However, these cross-plots have successfully recognizedhydrocarbon-related AVO anomalies,usually related to gas where thechange in crossplot position is dra-matic. Oil-related anomalies are usu-ally well hidden in the noise of theplot. Figure 3 shows an example of atime-window crossplot related to abright spot and its correlative reflec-tor. The samples from the bright spotare clearly anomalous in terms oftheir AVO behavior.

On the other hand, the horizoncrossplot clearly targets the reservoirof interest and helps determine thenoise trend while revealing the moresubtle AVO responses. Figure 4shows the horizon crossplot for theportion of reflector marked in Figure3. The responses are characterized bynegative reflections and positive gra-dients (i.e., a class IV response). Thenonbright part of the reflector has ahigh angle slope shown on thenear/far crossplot to be almost totallydue to noise. The bright spot has alower-angled slope on the crossplot


Figure 4. Horizon crossplots. (a) R0/G crossplot for the pick shown inFigure 3 and illustrating the different trends associated with the brightspot and the “background” reflectivity. (b) Near/Far crossplot illustratingthat the background trend on the R0/G crossplot is related to noise and notto lithology.

a)

b)

(owing to higher S/N), and it is pos-sible to see the noise trend as a sec-ond-order effect.

Horizon crossplots can be gener-ated from maps created from AVOattributes or partial stack 3-D inter-pretations. These crossplots need to bemade in a number of locations to makesure that an adequate sample has beenanalyzed. In practice it may not beeasy to identify an optimum discrim-inator from the crossplots, but thenoise trend is usually straightforwardto determine.

AVO anomaly maps can be cre-ated from linear combinations of R0and G. These combinations are usuallyof the form R0+Gx, where x=-G/R0and is determined from the slope of thetrend on the crossplot. Consideringthat the reflection amplitude isdescribed by Rc=R0+Gsin2θ, x repre-sents an “effective” angle. Any slopeon an AVO crossplot is an “effectiveangle stack.” However, which trendshould be used to create the AVOanomaly map?

The answer (as in many issues inseismic interpretation) is that it isimpossible to be definitive. Althoughcrossplots are useful to determinewhich equivalent stack is likely to be

most discriminatory in terms of fluids,they are only a one-dimensional viewof a limited amount of seismic data.The real interpretation issue is whetherthe anomalous responses representporosity or hydrocarbon effects, andthe only way to determine which inter-pretation to make is to analyze the rela-tionship of the anomaly to mappedstructure. In some cases, the equivalentangle stacks representing the noisetrend, the time-window trend, and theoptimum discriminator may give sim-ilar results, owing to the fact that thehydrocarbon effect is a displacementat a high angle to all these trends.

Probably the best approach to theuse of crossplots in interpretation is tobe published by Hendrickson (inpress). He illustrates the use of a rangeof equivalent angle stacks in an inter-pretation, examining the amplitudeconformance to structure on each stackas well as recognizing their signifi-cance in terms of the AVO crossplot.Interpretation is a question of “cover-ing all the angles” so to speak.

Suggestions for further reading. “AVOattributes and noise: pitfalls of cross-plotting” by Cambois (SEG 1998Expanded Abstracts). “Framework for

AVO gradient and intercept interpreta-tion” by Castagna et al. (GEOPHYSICS,1998). “Principles of AVO crossplotting”Castagna and Swan (TLE, 1997).“Another perspective on AVO cross-plotting” by Foster et al. (TLE, 1997).“Stacked” by Hendrickson, (GeophysicalProspecting, 1999). “Yet another perspec-tive on AVO crossplotting” by Sams(TLE, 1998). LE

Acknowledgments: The authors thankEnterprise Oil for permission to publish thispaper and Joel Hendrickson at Shell for hiscorrespondence.

Corresponding author: [email protected].


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