Principles of AVO Cross Plotting

Principles of AVO crossplotting

JOHN P. CASTAGNA, University of Oklahoma, Norman, OklahomaHERBERT W. SWAN, ARCO Exploration and Production Technology, Plano, Texas

Shuey’s Two-TermApproximation

R( ) = A + B sin2( ) + ...

R = reflection coefficient= angle of incidence

A = AVO interceptB = AVO gradient

Figure 1. The two-term Shueyapproximation to the Zoeppritzequations represents the angu-lar dependence of P-wavereflection coefficients with twoparameters: the AVO intercept(A) and the AVO gradient (B).In practice, the AVO interceptis a band-limited measure ofthe normal incidence ampli-tude, while the AVO gradientis a measure of amplitude vari-ation with offset. Assumingappropriate amplitude calibra-tion, A is the normal incidencereflection coefficient and B is ameasure of offset-dependentreflectivity.

Hy d rocarbon related “AVO anomalies” may showincreasing or decreasing amplitude variation with offset. Con-versely, brine-saturated “background” rocks may showincreasing or decreasing AVO.

A m p l i t u d e - v e r s u s - o ffset interpretation is facilitated bycrossplotting AVO intercept (A) andgradient (B). Under a variety of reason-able geologic circumstances, As and Bsfor brine-saturated sandstones andshales follow a well-defined “back-ground” trend. “AVO anomalies” are properly viewed asdeviations from this background and may be related tohydrocarbons or lithologic factors.

The common three-category classification developedby Rutherford and Williams is incomplete. We proposethat an additional category (Class IV) be considered. These

are low impedance gas sands for which reflection coeffi-cients decrease with increasing offset; they may occur, forexample, when the shear-wave velocity in the gas sand islower than in the overlying shale. Thus, many “classical”bright spots exhibit decreasing AVO. If interpreted incor-

rectly, AVO analysis will often yield“false negatives” for Class IV sands.

Clearly, the conventional associa-tion of the term “AVO anomaly” withan amplitude increase with offset is

inappropriate in many instances and has led to muchabuse of the AVO method in practice. Similarly, interpre-tation of partial stacks is not as simple as looking for rel-atively strong amplitudes at far offsets. We recommend thatall AVO analysis be done in the context of looking for deviationsfrom an expected background response.

Summary

INTERPRETER’S

April 1997 THE LEADING EDGE

EDGENET HTTP://WWW.EDGE-ONLINE.ORG DECEMBER 1997

Figure 2. For brine-satu-rated clastic rocks over alimited depth range in aparticular locality, theremay be a well-definedrelationship between theAVO intercept (A) andthe AVO gradient (B). Avariety of reasonablepetrophysical assump-tions (such as themudrock trend and Gard-ner’s relationship) resultin linear A versus Btrends, all of which passthrough the origin (B = 0when A = 0). Thus, in agiven time window, non-hydrocarbon-bearingclastic rocks often exhibita well-defined back-ground trend; deviationsfrom this background areindicative of hydrocar-bons or unusual litholo-gies.

Figure 3. This figureshows A versus Btrends for various con-stant ratios of com-pressional (Vp) toshear wave (Vs) veloci-ty. Notice that theAVO gradient (B) andthe AVO intercept (A)are generally nega-tively correlated, andthat the A versus Btrends become morepositive as Vp/Vs

increases. Also, notethat the trendbecomes positive athigh Vp/Vs ratios.Thus, the normalresponse for (nonhy-drocarbon-related)reflections at veryhigh background Vp/Vs

(as we would expectfor very shallowunconsolidated sedi-ments) is an ampli-tude increase versusoffset. Large reflection coefficients associated with shale over porous brine-sand interfaces will exhibit “false posi-tive” AVO anomalies in the sense that they will have larger AVO gradients than weaker reflections lying along thesame background trend. When interpreted in terms of deviation from the background A versus B trend, suchreflections are correctly interpreted as not being anomalous.


Figure 4. Deviations fromthe background petro-physical trends, as wouldbe caused by hydrocar-bons or unusual litholo-gies, cause deviationsfrom the background Aversus B trend. This fig-ure shows brine sand-gassand tie lines for shaleover brine-sand reflec-tions falling along agiven background trend.In general, the gas sandsexhibit more negative Asand Bs than the corre-sponding brine sands(assuming the frameproperties of the gassands and the brinesands are the same). Notethat the gas sands forma distinct trend whichdoes not pass through theorigin.

EDGENET HTTP://WWW.EDGE-ONLINE.ORG DECEMBER

1997

Figure 5. We propose thatthe classification of AVOresponses should bebased on position of thereflection of interest onan A versus B crossplot.First, the backgroundtrend within a given timeand space window mustbe defined. This can bedone with well control ifthe seismic data are cor-rectly amplitude calibrat-ed, or with the seismicdata itself if care is takento exclude prospectivehidden hydrocarbon-bear-ing zones. Top of gas sandreflections then shouldplot below the back-ground trend and bottomof gas sand reflectionsshould plot above thetrend. We can classify thegas sand response accord-ing to position in the A-Bplane of the top of gassand reflections. Our classification is identical to that of Rutherford and Williams (Geophysics, 1989) for Class I(high impedance) and Class II (small impedance contrast) sands. However, we differ from Rutherford andWilliams in that we subdivide their Class III sands (low impedance) into two classes (III and IV). The Class IVsands are highly significant in that they exhibit AVO behavior contrary to established rules of thumb and occur inmany basins throughout the world including the Gulf of Mexico.


Class Relative Impedance Quadrant A B Amplitude vs. Offset

I Higher than overlying unit IV + - Decreases

II About the same as the II, III, or IV + or - - Increase or decrease;overlying unit may change sign

III Lower than overlying unit III - - Increases

IV Lower than overlying unit II - + Decreases

Figure 6. This chart summarizes the AVO behavior of the various gas sand classes. Note that when we say “ampli-tude versus offset” we are referring to the variation of the magnitude of the reflection coefficient. Thus, a negativereflection coefficient that becomes more positive with increasing offset has a decreasing reflection magnitude ver-sus offset. Note that Class IV gas sands are anomalous in that they have a positive AVO gradient and that ampli-tude decreases with increasing offset.


Figure 8. Here are examples of shale over gas-sandand shale over brine-sand reflections. Both decreasein amplitude versus offset and have about the sameAVO gradient, even though the gas sand is a brightspot (it is Class IV). The model parameters are:

Lithology Vp (km/sec) Vs (km/sec) p (gm/cc)Shale 3.24 1.62 2.34Brine Sand 2.59 1.06 2.21Gas Sand 1.65 1.09 2.07

Figure 7. We have superimposed an example of a ClassIV gas sand on a figure taken from Rutherford andWilliams which shows their gas-sand classificationbased on normal incidence reflection coefficient. Thevertical axis is reflection coefficient and the horizontalaxis is local angle of incidence. Note that Class III andIV gas sands may have identical normal incidencereflection coefficients, but the magnitude of Class IVsand reflection coefficients decreases with increasingangle of incidence while Class III reflection coefficientmagnitudes increase.

Plane-wave reflection coefficientat top of gas sand



Figure 9. This figure shows the difference in AVObehavior for a gas sand when overlain by a shale or,alternatively, by a high-velocity tight streak. In bothcases, the gas sand is a bright spot. When overlainby a shale, the gas sand is Class III and amplitudeincreases with increasing angle of incidence. How-ever, when overlain by a tight streak, the gas sand isClass IV and amplitude decreases with increasingangle of incidence. The parameters are:

Lithology Vp (km/sec) Vs (km/sec) p (gm/cc)Shale 2.90 1.33 2.29Brine Sand 3.25 1.78 2.44Gas Sand 2.54 1.62 2.09

The model parameters for this example wereobtained from well log measurements and providedby Jeremy Greene of ARCO Exploration and Pro-duction Technology.

Figure 10. Consider a“bright” gas sandreflection with an AVOintercept (A) of -.4 andan AVO gradient (B) of.4. If the frame proper-ties of the brine sandare not identical to thatof the gas sand, thereflection coefficientfor the shale overbrine-sand reflectionwith an A of, say -.2,could easily have thesame B of .4. This cir -cumstance would con -found most interpretersin that the gas sand is abright spot (A = normalincidence reflectioncoefficient = -.4) but (1)the reflection magni-tude decreases withoffset (B is positive sothe negative reflectionbecomes smaller!), and(2) the AVO gradient is not anomalous with respect to the brine sand. Thus, the result would be a false negative formost interpreters. (Commentary: So this perfectly good bright spot may not be drilled because it has not been “ver-ified” by AVO analysis. Imagine management’s disgust when a competitor who (1) hasn’t bothered doing AVO, or(2) has interpreted the AVO data correctly comes along and drills a discovery. Is it any wonder that AVO has a badname in some quarters? Of course, the problem here is not with AVO, it is with interpreters who cling to naive rulesof thumb; i.e., gas-sand amplitude increases with offset or use partial stacks rather than more sophisticated analysistechniques even though they may have no idea what to look for on a partial stack until after the well has beendrilled and logged. Clearly, one should interpret anomalous AVO behavior in the context of deviation from back-ground gradient AND intercept behavior.)


Reasonable petrophysical assumptions for clasticstratigraphic intervals result in linear background trendsfor limited depth ranges on AVO intercept (A) versus gra-dient (B) crossplots. In general, background B/Abecomesmore positive with increasing Vp/Vs. Thus, if too large adepth range is selected for A versus B crossplotting, andbackground Vp/Vs varies significantly, a variety of back-ground trends may be superimposed, resulting in a lesswell-defined background relationship. For very highVp/Vs, as may occur in very soft, shallow, brine-saturatedsediments, the background trend B/A becomes positive;n o n h y d ro c a r b o n -related re f l e c t i o n smay exhibit increas-ing AVO and showfalse positive anom-alies (especially forl a rge reflection coefficients). Partial stacks, Atimes B pro d-uct indicators, and improperly calibrated fluid-factor sec-tions are all susceptible to such false positives.

Deviations from the background trend may be indica-tive of hydrocarbons. This is the basis for the “fluid fac-tor” of Smith and Gidlow (1987), the “NI versus Poissonreflectivity” of Verm and Hilterman (1995), and relatedindicators.

Inspection of the A versus B plane reveals that gassands may exhibit AVO behavior which differs dramati-cally from conventional rules of thumb. S u re l y, the idea that“gas-sand amplitude increases versus offset” should finally beput to rest for all time.

We suggest that hydrocarbon-bearing sands should beclassified according to their location in the A-B plane,rather than by their normal-incidence reflection coeff i c i e n talone. Class I sands are higher impedance than the over-lying unit. They occur in quadrant IV of the A-B plane. Thenormal incidence reflection coefficient is positive while theAVO gradient is negative. The result is that the reflectioncoefficient decreases with increasing offset. Class II sandshave about the same impedance as the overlying unit.They exhibit highly variable AVO behavior and may occurin quadrants II, III, or IV of the A-B plane. The normal inci-

dence reflection coef-ficient (A) may bepositive or negativeand B is negative.The reflection coeffi-cient becomes in-

creasingly negative versus offset, but the reflection ampli-tude may increase or decrease depending on the sign ofthe reflection coefficient. When the reflection coefficient ispositive at near offset, amplitude will initially decreaseand may reverse polarity and then increase with offset (theClass IIp of Ross and Kinman, where “p” indicates phasereversal). Class II sands often exhibit poor ties betweenconventional synthetic seismograms and the stacked seis-mic data. Our Class III sands differ from Rutherford andWilliams Class III sands in that we include only thosereflections which occur in quadrant III. These sands arelower impedance than the overlying unit and are fre-quently “bright.” They have negative A and B and thereflection coefficient becomes increasingly negative withoffset. These are the quintessential gas sands for whichamplitude increases versus offset. Our Class IV sands arethose low impedance sands which occur in quadrant II.These sands have negative A but a positive B. The reflec -tion coefficient becomes less negative with increasing offset andamplitude decreases versus offset, even though these sands maybe bright spots.

Bear in mind that the two-term Shuey approximationmay not be appropriate for AVO analysis of long-offsetdata. Analysis of such data should include (1) correctionsfor various effects of anisotropy and (2) utilization of thefull Zoeppritz equations.

AVO analysis techniques that rely on AVO product indi-cators (such as Atimes B) or inspection of partial stacks (forweak amplitude at near offsets associated with strong ampli-tudes at far offsets) are designed for Class III sands. Clear-l y, these approaches can easily lead to misinterpretation forother gas-sand classes. A l t e r n a t i v e l y, the fluid factor andrelated indicators will theoretically work for any gas-sandclass. Unfortunately, some algorithms for extraction of A sand Bs are not robust, particularly in the presence of smallNMO errors, so partial stacks are often resorted to. Some-times, for logistical or economic reasons, the interpreter onlyhas access to partial stack data. In these situations, the datashould still be interpreted in the context of the A-B plane anddeviation from some “background” behavior should still bethe means of defining anomalies.

Acknowledgments: This tutorial is based on a more extensive paper(complete with mathematics) co-authored by Doug Foster and CarolynPeddy which was submitted to GEOPHYSICS some months ago and maybe published some day in the distant future. This work was partiallysupported by GRI under contract 5090-212-2050, by ARCO Explo -ration and Production Te c h n o l o g y, and by The University of OklahomaInstitute for Exploration and Production Geosciences.


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Suggestions for further study. TheShuey approximation is described in his 1985 paper inGEOPHYSICS. The “fluid factor” was introduced bySmith and Gidlow in a 1987 article in GeophysicalProspecting. This paper should be required reading foranyone doing AVO analysis. The Rutherford andWilliams classification can be found in their classic 1989paper in GE O P H Y S I C S. This paper gives real world exam-ples of Class I, Class II, and Class III reservoirs. TheRutherford and Williams classification is further dis-cussed in GEOPHYSICS by Castagna and Smith (1994)and Ross and Kinman (1995). AVO crossplotting isdescribed in some versions of Hilterman’s SEG Contin -uing Education Course Notes, beginning in the mid-to-late 1980s. Some superb examples were shown by Fos-ter, Smith, Dey-Sarkar, and Swan at SEG’s 1993 AnnualMeeting. TLE readers were introduced to the subject byCastagna in 1993 and Verm and Hilterman in 1995.N o t a b l y, two papers co-authored by Herb Swan are stillawaiting publication in GEOPHYSICS. One of these wassubmitted in 1993. Jim DiSiena received a best presen-tation award at AAPG’s 1996 convention for applicationof AVO crossplotting techniques to 3-D seismic data.

Would you like to learn more? JohnCastagna is currently performing and compiling casestudies on datasets with Class IV sands and studyingAVO responses at long offsets. He can be reached at405-3256697 or [email protected] for the digitallyinclined, if you are interested in collaborating, cofund-ing, or otherwise participating.

Conclusions and Discussion


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Principles of AVO Cross Plotting