avo classification

Elastic properties of rocks are stronglyinfluenced by local geologic trends andcan change markedly even within asedimentary basin. Critical geologicfactors that control elastic propertiesare either related to depositional envi-ronment or burial history. Knowledgeabout the expected change in seismicresponse, as a function of depositionalor compactional trends, will increasethe ability to predict hydrocarbons,especially in areas with little or no welllog information. In other words, byunderstanding the geologic constraintsin an area of exploration, one canreduce the range of expected variabil-ity in rock properties and hence reducethe uncertainties in seismic reservoirprediction. Figure 1 depicts this prob-lem, where we assume there is well logcontrol only in the shallow interval onthe shelf edge. Before extending theexploration into more deeply buriedzones, or to more distal deepwaterenvironments, it is important to under-stand the rock physics trends in thearea.

In this paper, we present a techniqueto calculate expected AVO (amplitudevariation with offset) responses as afunction of lithofacies, pore fluid, andburial depth. First, we calculateexpected depth trends in rock physicsproperties for different lithologies andpore fluids. These trends are calculatedfrom empirical porosity-depth modelsrepresenting the local burial and com-paction history. Next, we calculate thecorresponding AVO depth trends fromthe depth trends in rock properties.Different models are generated basedon the knowledge of local geology anddepositional environment. AVO uncer-tainties are included and take intoaccount the expected or observed nat-ural variability in the rock properties.In this way one can obtain AVO prob-ability density functions (pdfs) for anygiven depth of burial. Finally, the mod-eled AVO pdfs are used to predict themost likely lithology and pore fluidsfor different depth intervals from realseismic data. We apply this techniqueto an unconsolidated, mud-rich deep-water turbidite system offshore WestAfrica (Figure 2).

Rock physics depth trends. In order tounderstand the expected seismic

response of a siliciclastic reservoir, atany given depth, it is of key interest toknow the expected contrast in elasticproperties between shales and sands asa function of depth. However, rockphysics and AVO depth trends can bevery complicated depending on min-eralogy, lithology, diagenesis, pore pres-sure, effective stress, and fluidproperties. In areas with good well cov-erage, one can establish empirical rockphysics depth trends for differentlithologies from statistical regressions towell log data (VP, VS, and density).However, in this paper we want tostress the importance of modelingdepth trends. Rock physics modelsallow for extrapolation of observedtrends to depositional settings anddepth ranges that are not covered bywell log data. This is often the case inan early exploration stage. Furthermore,

modeled depth trends help us to betterunderstand observed depth trends, andto detect anomalous zones that do notfollow the expected depth trends,whether these are pressure anomalies,unexpected lithologies, or abrupt dia-genetic events.

In general, seismic velocities anddensities of siliciclastic sedimentaryrocks will increase with depth due tocompaction and porosity reduction.Consequently, the very first step of theproposed AVO classification techniqueis to establish local porosity-depthtrends for sands and shales. For manysedimentary basins, porosity-depthtrends for siliciclastic sediments areshown to follow fairly simple andempirical functions, following expo-nential or linear forms (see appendix).Applying the empirical equation givenin the appendix, porosity-depth trends

1004 THE LEADING EDGE OCTOBER 2003

AVO classification of lithology and pore fluids constrained by rockphysics depth trendsPER AVSETH, HARALD FLESCHE, and AART-JAN VAN WIJNGAARDEN, Norsk Hydro Research Centre, Bergen, Norway

Figure 1. Rockphysics propertieschange with deposi-tional environmentand burial depth.These geologic trendsmust be taken intoaccount duringhydrocarbon recon-naissance of seismicdata.

Figure 2. Seismic stack section intersecting a well penetrating a turbiditic gas and oil field, offshoreWest Africa. The geologist’s core description is superimposed showing the vertical sequences ofsands and shales encountered in the well (red = poorly sorted conglomerates; orange = clean tur-bidite sands; yellow = shaly sands; black/white streaks = mixed, thin-bedded sands-shales and lami-nated shales (heterolithics); green= shale). Gas was encountered in the upper sandy interval,whereas oil was found in the middle sand interval. Brine was encountered in the lower sandy inter-val. The seismic data are zero-phase where red (with dark extremes) represents negative amplitudesand black represents positive amplitudes.

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are calibrated using reasonable critical(depositional) porosity values at thesurface, and inverted density logs forany burial depth. At deposition, shalestend to have relatively high porositiescompared to sands. Sands will havedepositional porosities of approxi-mately 0.4, while shales can have depo-sitional porosities of more than 0.8(Figure 3). Shaly sands and heterolithics(i.e., mixed sands and shales) can haveeven lower depositional porosity than

0.4, as clay particles will fill the porespace of the sand frame. During earlyburial, porosity is reduced mainly dueto change of grain packing and ductilegrain deformation. Shales tend to com-pact more easily than sands, causing acrossover of the porosity-depth trendsof sands and shales. At greater depths,different diagenetic processes occur.Sands lose porosity mainly due tocementation, while bound water isreleased and intrinsic clay porosity is

reduced in shales. Secondary porositymay occur in sands due to dissolutionof mineral grains. Hence, porosity-depth trends can become very complexat great depths.

The rock physics depth trends (i.e.,VP, VS, and density versus depth) cor-responding to the porosity-depthtrends mentioned above can be rathercomplex due to the competing effectsof porosity, pressure, mineralogy, tex-ture, and pore fluids. In fact, we mayobserve more than one crossover invelocity-depth trends of sands andshales. Rock physics models can bevery useful to better understand thesedepth trends. However, the modelshave to be calibrated to local geologybefore they can be used for further pre-diction of hydrocarbons and lithology.Geologic constraints include expectedlithofacies and facies associations, sandand shale mineralogy (to determineeffective elastic moduli and densitiesfor the solid phase), fluid properties(oil density, GOR, gas gravity, brinesalinity), and information about pres-sure and temperature gradients. Forunconsolidated rocks we apply Hertz-Mindlin contact theory (see appendix)to calculate elastic moduli of uncon-solidated sediments as a function ofporosity and pressure. Based on theelastic moduli, we calculate VP and VSversus depth. Density (ρ) is calculateddirectly from the porosity trends. Fromthese parameters we can calculateacoustic impedance and VP/VS ratiosversus depth. We calculate depth trendsfor clean sands, shaly sands, and shales.We assume 100% quartz and 0% clayfor the clean sand trend and 80% quartzand 20% pore filling clay (smectite) forthe shaly sand trend. Effective mineralmoduli are estimated using Hill’s aver-age (see Mavko et al., 1998). Bulk andshear moduli of quartz are 36.8 GPaand 44 GPa, respectively. Similar para-meters for smectite are 15 GPa and 5GPa. Figure 4 shows calculated trendlines of AI and VP/VS versus depthcompared with observed well log datafrom the well intersected by the seis-mic line in Figure 2. We observe a verygood match between the shale trendand the log data in the shaly intervals(i.e. zones with high gamma ray val-ues), both in terms of acoustic imped-ance and VP/VS. Deviations from themodeled shale trend may reflect vari-ation in silt content within the shales.The sandy reservoir zone nicely fol-lows the shaly sand trend. Deviationsfrom the clean sand and shaly sandtrends reflect both presence of hydro-carbons (the trend lines are calculatedfor brine-saturated rocks) as well as


Figure 3. Schematic illustration of porosity-depth trends for sands and shales. Both the sand andshale trends can vary significantly due to composition, texture, pore fluids, temperature, and pres-sure gradients. Hence, no attempt is done to assign absolute scales. However, there are a few rules ofthumb: (1) The depositional porosity of shales is normally higher than that of sands. (2) The poros-ity gradient with depth is steeper for shales than for sands during mechanical compaction (i.e. atshallow depths). (3) The porosity gradient with depth will be steeper for sands than for shales dur-ing chemical compaction (i.e. quartz cementation of sands normally occurs at greater burial depth,beyond 2-3 km).

Figure 4. Predicted seismic depth trends based on empirical porosity trends, compared to well logdata from the Tertiary deep-water turbidite field shown in Figure 2.

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variability in clay content. A few localpeaks of high impedance anomaliesmay reflect local cementation. Rockphysics depth trends for cementedsandstone could be calculated usingthe Dvorkin-Nur cement model (seeMavko et al., 1998). However, in addi-tion to the porosity, we would thenneed to know the amount of cement asa function of depth before calculatingthe elastic properties. To do thisrequires reliable information from geol-ogists about the expected cement vol-ume at a given depth.

Statistical AVO modeling constrainedby rock physics depth trends. Theestimated acoustic impedance and

VP/VS trends in Figure 4 can be usedto calculate the expected AVO responsewith depth, for sand-shale interfaces.The example in this study is from adeepwater turbidite setting, and weassume 12 different interface categories.These are based on realistic layer con-figurations in a turbiditic environment,and are depicted in Figure 5. Thismodel of facies associations is rathersimplified compared to the true sedi-mentologic observations in the area,but we attempt to reduce the amountof interface categories while still hon-oring geologic variations that may beseismically significant. If we includetoo many interface categories, we mayintroduce too much overlap between

individual classes in a binary AVOcrossplot.

Next, we extract VP, VS, and den-sity for clean brine sand, pure shale,and shaly sand, from the calculateddepth trends in the previous section.These are assumed to be the mean val-ues for the different facies at the targetlevel. We assume multiGaussian dis-tributions where the variances areselected based on information fromanalog areas, or from nearby wells. Inthis example we have used nearbywells to calculate the variances.Moreover, we use Gassmann theory toestimate the rock properties for gas andoil saturated sands (see Mavko et al.,1998). (Fluid properties used for theturbidite field: Gas gravity = 0.7, oilreference density = 28 API, and brinesalinity = 80 000 ppm). The resultinghistograms of VP, VS, and density fordifferent facies and fluids are shown inFigure 6.

For each interface category, theexpected AVO response at a targetdepth is calculated using a commonapproximation given by Shuey, validfor angles less than 30°:

R(θ) ≈ R(0) + G · sin2 θ,

The zero offset reflectivity, R(0), iscontrolled by the contrast in acousticimpedance across an interface. The gra-dient, G, is mainly controlled by thecontrast in VP/VS ratio. We do a MonteCarlo (MC) simulation to estimate thedistribution of zero-offset reflectivity(R(0)) versus AVO gradient (G), basedon the mean and covariances in VP, VS,and ρ for the different interface cate-gories. The structure of the covariancematrix determines the dependenciesbetween the variables VP, VS, and ρ.Normally, there is a higher correlationbetween VP and VS than between VPand ρ. The resulting AVO scatter plotsrepresentative of the target depth, fromwhich the AVO pdfs can be estimated,are shown in Figure 7.

Seismic calibration and AVO classifi-cation. The final step in the AVO clas-sification technique is to apply themodeled AVO pdfs to predict the mostlikely facies and pore fluid from seis-mic data. We did a blind test of the wellintersecting the line in Figure 2, usingthe AVO pdfs derived from the mod-eled depth trends. R(0) and G estimatedfrom pre-stack gathers along the lineare calibrated to the modeled AVO pdfsin Figure 7. We identify a background“window” in the seismic section nearor around the target interval. For thestudied turbiditic environment we


Figure 5. Simple facies association model for mud-rich turbidite channel-levee complex and relatedinterface categories.

Figure 6. Histograms of VP,VS and density for differentlithologies and fluids at thetarget depth level correspond-ing to the reservoir sandspenetrated by the well inFigure 4. The mean values aredetermined by the depthtrends, while the variances areassumed to be depth-indepen-dent and are taken from anearby well.

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assume the background trend to becharacterized by interface categories10-12, as most seismic horizons in amud-rich turbiditic environment aremade up of these categories. We cali-

brate the covariance matrix of R(0) andG for the background trend in the seis-mic data with the covariance matrix ofR(0) and G for the background trend inthe model, either by matching the

covariances or by univariate variancematching. This calibration is thenapplied to seismic data in the targetarea (Figure 8).

After calibrating the seismic datawith the modeled AVO pdfs, we per-form the AVO classification. We use theMahalanobis distance to estimate themost likely layer category for each datasample in the data (see appendix). Theclassification result is shown in Figure9, where we lump the 12 layer interfacecategories into 5 facies and fluid groups(tops and bases together). We obtain agood match with the observations inthe well (compare with Figure 4). Thetop reservoir is successfully identifiedas gas bearing, while zones of oil sandsare identified below the gas reservoir.However, significant parts of the reser-voir are characterized as water-bearing.This could reflect the great overlap andambiguities between oil and brine sandsin terms of AVO properties. The caprock is predicted to be predominantlyheterolithics and shales. Bear in mind,however, that the final result in Figure9 represents classification of interfaces,not layers. However, the methodologypresented in this paper can also beapplied to layer inversion results. Forinstance, elastic inversion could be clas-sified using pdfs of AI versus VP/VS. Inthat case, the calibration of the seismicdata is not necessary. Also note in Figure9, that a few data points have been cat-egorized as “no class,” and depicted inblack. In the classification procedure,data points located a certain distanceaway from any of the modeled interfacecategories in the R(0)-G crossplot, arerejected. The unclassified units couldeither represent noise in the data orlithologies/facies not included in themodeling. We suspect these to be thinunits of cemented sands. This would bein accordance with the well log data inFigure 4, where we observe a few anom-alous high velocity peaks in the sandytarget interval. One future extension ofthis AVO technique will be to includedepth trends for cemented sandstone.It is also important to note that fluidproperties will be depth dependent.Pressure and temperature control thecompressibility of fluids but also thechemical properties of fluids can changewith depth. In particular, relative den-sity of oil (API gravity) tends to bedepth dependent, where biodegrada-tion of oil decreases with depth. Hence,shallow reservoirs will normally con-tain relatively thick oil, compared todeeper reservoirs. Trend lines of APIgravity versus depth would be valu-able information to be included in thisAVO classification technique. Another


Figure 8. Calibration of AVO attributes extracted from prestack seismic data with modeled AVOpdfs in Figure 7. The black stars represent the AVO attributes estimated from the real data (i.e.crossplot of each sample in upper R(0) versus lower G section), while the colored dots represent themodeled AVO responses for the various interface categories. The modeled heterolithics (i.e., shalysands) and shales in green and blue, respectively, represent the modeled background trend, whichhas been calibrated with the background trend in the real data.

Figure 7. Modeled AVO scatter plots of R(0) versus G for different interface categories for thetarget depth level. (See Figure 5 for explanations of the interface categories).

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future extension will be to include faciestransition probabilities and spatial sta-tistics to improve the constraints on theclassification of vertical and lateral geo-logic variations from seismic data.

Conclusions. The seismic signature ofhydrocarbons can be very differentfrom one depth to another due to dif-ferent compaction trends for differentlithologies. Therefore, it is necessary toinclude depth as a parameter when weuse AVO analysis to predict lithologyand pore fluids from seismic data. Wehave developed a depth dependentprobabilistic AVO technique thatenables us to predict the most likelylithology and pore fluid from seismic data,even in areas with sparse local well loginformation. Nevertheless, presence oflocal well log data will improve on themodeling of AVO pdfs, and give bettercontrol on the seismic calibration. Themain limitations of the methodologyinclude tuning and overburden effects,as well as the inherent ambiguities inrock physics properties and AVOresponse. The technique presented inthis paper is an extension of themethodology presented by Avseth et al.(2001).

Suggested reading. “Seismic reservoirprediction using Bayesian integration ofrock physics and Markov random fields:A North Sea example” by Eidsvik et al.(TLE, 2002). “Seismic reservoir mappingfrom 3-D AVO in a North Sea turbiditesystem” by Avseth et al. (GEOPHYSICS,2001). “Mapping lithofacies and porefluid probabilities in a North Sea reser-voir: Seismic inversions and statisticalrock physics” by Mukerji et al .(GEOPHYSICS, 2001). “Examination of AVOresponses in the eastern deepwater Gulfof Mexico” by Smith and Sondergeld(GEOPHYSICS, 2001). “Rock physics andAVO analysis for lithofacies and porefluid prediction in a North Sea oil field”by Avseth et al. (TLE, 2001). “Statistical

rock physics: Combining rock physics,information theory, and geostatistics toreduce uncertainty in seismic reservoircharacterization” by Mukerji et al. (TLE,2001). “Geostatistical integration of rockphysics, seismic amplitudes, and geologicmodels in North Sea turbidite systems”by Caers et al. (TLE, 2001). “Rock physicsand seismic properties of sands andshales as a function of burial depth” byAvseth et al . (SEG 2001 ExpandedAbstracts). The Rock Physics Handbook byMavko et al. (1998). “Significance of geo-pressure in predicting lithology” by Vermet al. (TLE, 1998). “Porosity/depth trendsin reservoir sandstones: assessing thequantitative effects of varying pore-pres-sure, temperature history and mineral-ogy, Norwegian Shelf data” by Rammand Bjørlykke (Clay Minerals, 1994).

Appendix.Porosity-depth trends. Ramm and

Bjørlykke (1994) suggested a claydependent regression model for poros-ity versus depth of sands, due tomechanical compaction:

φ=φc·e-(α+β·Cl)·Z

where φc is the critical (i.e., deposi-tional) porosity, and α and β are regres-sion coefficients representing aframework grain stability factor for

clean sandstones (Cl=0) and a factordescribing the sensitivity towardincreasing clay, respectively. The clayindex, Cl, is defined as the volume oftotal clays relative to the total volumeof stable framework grains.

Hertz-Mindlin contact theory. Elasticmoduli of the dry rock are calculatedusing the following equations:

where KHM and GHM are the bulk andshear moduli at porosity φ, respec-tively; P is the differential pressure; K,G, and v are the bulk and shear mod-uli of the solid phase, and its Poisson’sratio, respectively; and n is the coordi-nation number (i.e., number of graincontacts per grain). The wet rock mod-uli are calculated using the Gassmanntheory (see Mavko et al., 1998).

Classification using Mahalanobis dis-tance. The Mahalanobis distance isdefined as follows:

M2 = (x-µi)T Σi-1(x-µi),

where x is the sample vector, µi are thevectors of means for the differentclasses, and Σi is the training datacovariance matrix for class i. TLE

Acknowledgments: We thank Norsk Hydro andTotalFinaElf for allowing publication of the dataused in this study. Thanks to Erling Vågnes andJohn Gjelberg, both at Norsk Hydro, for valu-able geologic input, and Tapan Mukerji atStanford University for helpful comments thatimproved the manuscript.

Corresponding author: [email protected]

OCTOBER 2003 THE LEADING EDGE 1011

Figure 9. The most likely lithology and pore fluid along the seismic section in Figure 2.

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