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  • Probabilistic lithofacies prediction from prestack seismic datain a heterogeneous carbonate reservoir

    Luanxiao Zhao1, Jianhua Geng2, Jiubing Cheng2, De-hua Han3, and Tonglou Guo4

    ABSTRACT

    We mapped probabilities of lithology and fluid based onseismic and well observations in a heterogeneous carbonate res-ervoir of the Sichuan Basin, southwest China, thus characteriz-ing the reservoir complexity and identifying the potential sweetspot. Rock physical analysis showed that the presence of avuggy-fracture porosity system combined with the fluids effectcomplicate the elastic responses of heterogeneous carbonates.This also gives physical insight into how the elastic propertiesof different lithofluid classes can be distinguished. With the ap-plication of Bayesian linearized amplitude variation with offsetinversion, we found that the posterior distribution of P- and S-wave velocities were reliably extracted, whereas the inverted

    density tended to show high uncertainty due to a lack of wideangle data in the migrated seismic gathers. Finally, a Bayesianapproach was implemented to propagate uncertainty fromprestack seismic data to lithofluid classes in an integratedframework. The gas-carbonate predictions with high posteriorprobabilities were consistent with well observations at thewell location and the present geological continuity. The prob-ability distributions for the anhydrite, limestone, and dolostonewere essential to understand the reservoir architecture anddelineate the reservoir heterogeneities. We also ascertained thatthe uncertainty of lithofacies prediction is determined by theuncertainty of seismic inversion as well as the uncertaintyof the link between lithofacies to their corresponding elasticresponses.

    INTRODUCTION

    Seismic characterization of carbonate reservoirs is challenging.This is mainly because carbonates constantly undergo physical,chemical, and biological changes during sedimentation and postde-positional diagenesis, thereby causing significant heterogeneities inrock properties. Quantitative lithofacies delineation from seismicdata is considered to be an important tool for understanding suchcomplexities and heterogeneities in carbonate reservoir. In this ar-ticle, we present a case study to show how to predict probabilitydistributions of lithology and fluid from prestack seismic data ina Paleozoic marine carbonate reservoir, Sichuan Basin, southwestChina. This geologically complex carbonate reservoir exhibits thecharacteristics of very deep burial depth, overmatured source rock,and strong heterogeneities due to the extensive diagenesis in geo-logic history (Ma et al., 2008b).

    Many factors can cause uncertainties for lithofacies predictionfrom seismic data, such as data noise from geophysical measure-ments and processing, approximation of physical models and alsothe associated scale changes (Mukerji et al., 2001; Houck, 2002;Avseth et al., 2005; Grana and Rossa, 2010). This is especially truefor carbonate reservoirs, which display wide variations in rock prop-erties due to the complicated geologic processes. From the statis-tical point of view, such uncertainties can be reduced if moredisparate sources of data, such as geologic knowledge, seismic data,rock physics, and core information, can be combined. A Bayesiansetting will be a natural choice to integrate all the available infor-mation to characterize the inversion uncertainty (Tarantola, 1987;Eidsvik et al., 2004; Gunning and Glinsky, 2007; Bosch et al.,2010). In general, probabilistic lithology and fluid prediction fromprestack seismic data entails the uncertainty of seismic inversionand rock-physics inversion, and it has been studied by many authors

    Manuscript received by the Editor 2 November 2013; revised manuscript received 25 March 2014; published online 5 August 2014.1Tongji University, State Key Laboratory of Marine Geology, Shanghai, China, and University of Houston, Department of Earth and Atmospheric Sciences,

    Houston, Texas, USA. E-mail: [email protected] University, State Key Laboratory of Marine Geology, Shanghai, China. E-mail: [email protected]; [email protected] of Houston, Department of Earth and Atmospheric Sciences, Houston, Texas, USA. E-mail: [email protected], Exploration Southern Branch, Sichuan, China. E-mail: [email protected] 2014 Society of Exploration Geophysicists. All rights reserved.

    M25

    GEOPHYSICS, VOL. 79, NO. 5 (SEPTEMBER-OCTOBER 2014); P. M25M34, 12 FIGS.10.1190/GEO2013-0406.1

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  • through proposed methodologies and case studies (Eidsvik et al.,2004; Larsen et al., 2006; Buland et al., 2008; Gonzlez et al., 2008;Rimstand and Omre, 2010; Ulvmoen and Omre, 2010; Rimstadet al., 2012). However, most of those studies focus on sandstonereservoirs with relatively less heterogeneities, and it is still verychallenging to demonstrate its application in the studied carbonatereservoirs, which present strong heterogeneities. This is mainly dueto two factors described in the following two paragraphs.First, the burial depth of the studied carbonate reservoir is deeper

    than 6 km, and hence the signal-to-noise ratio (S/N) in the seismicdata is reduced significantly. Also, the deep targeted reservoirmakes it hard to obtain wide-angle gathers, resulting in difficultiesto extract reliable elastic parameters (P-wave velocity, S-wavevelocity, and density) through seismic inversion. To reveal thereliability of the seismic inversion results for further quantitativelithology prediction, it is necessary to evaluate their associated un-certainties. In this study, we perform amplitude variation with offset(AVO) inversion in the Bayesian framework to estimate the pos-terior distribution of the inverted elastic parameters (Buland andOmre, 2003).Second, the complex diagenesis complicates the rock-physics

    relationship in carbonates, which in turn makes seismic responsepoorly understood. Therefore, understanding the sensitivity of theelastic properties of carbonates to the fluids effect is critical to testthe feasibility of lithology and fluid prediction from seismic attrib-utes. The elastic responses in carbonates are often considered to beless sensitive to the fluids effect because carbonate rocks are oftenvery stiff. However, the fluids effect on the seismic rock propertiesof carbonates can be dramatically amplified due to the presence ofheterogeneities and fractures (Li et al., 2003; Han, 2004). Rock-physics modeling is used to study how the elastic properties of dif-ferent lithofluid classes in this heterogeneous carbonate reservoircan be distinguished, thereby providing physical insights into lith-ology and fluid prediction from seismic data.The intent of this paper is not to focus on the details of the prob-

    abilistic inversion methodologies. Rather, through a case study, ourgoal is to investigate how the geologic understanding and rock-physics analysis can help us better understand and constrain the lith-ofacies prediction from seismic data in a probabilistic framework.The paper is structured as follows: We first introduce the geologic

    background and related data set in the carbonate reservoir of theSichuan Basin, southwest China. The categorical lithology andpore-fluid scenarios, which are termed as lithofacies classes, are de-fined based on geologic information and well-log analysis prior tothe inversion. We then use rock-physics modeling to physically linkthe defined lithofluid classes to the elastic properties. Next, a fastBayesian simultaneous AVO inversion approach is performed toestimate elastic properties and their associated uncertainties in a2D inline section extracted from a 3D migrated seismic data set.Finally, we present and analyze the probabilistic lithology and fluidinversion results from this 2D seismic data set.

    GEOLOGIC SETTING AND DATA DESCRIPTION

    The studied Yuanba gas field is the deepest marine strata gas fieldfound in China, and it is located in the northern end of the gentlydeformed structural belts in the central Sichuan Basin (Long et al.,2011). The reservoir rocks in the Lower Triassic formation areprimarily controlled by the oolitic shoal facies developed on theevaporitic carbonate platform edge. The evaporate beds of thelagoon-tidal flat facies in the Lower and Middle Triassic strataformed the cap rock for the underlying gas accumulations (Ma et al.,2008b). The deep buried reservoirs suffer multiphase tectonicmovements after deposition, which make the secondary diageneticprocesses very complex and thereby strongly reorganize the porespace of reservoir rocks. The main diagenetic processes includecompaction-pressure solution, selective dissolution, fracturing, do-lomitization, and recrystallization.A stacked image of the seismic data is shown in Figure 1, in

    which the red vertical line indicates the location of the availablewell. The structures within the targeted seismic inversion zone ap-pear relatively flat. For the purpose of AVO inversion, the seismicdata have been processed by a processing contractor with an am-plitude-preserving workflow, ensuring that prestack data representthe true offset dependent reflectivity. The quality of the seismic datacan be characterized as good with an S/N of around four.Well logs play an important role in linking rock properties to

    seismic data, which should be extensively analyzed prior to thelithofacies inversion. The well-log data of lithology content, P-wavevelocity, S-wave velocity, density, and water saturation after depth-to-time conversion, are displayed as functions of two-way travel-time in Figure 2. As we can see from the curve of the watersaturation, gas-saturated dolostones are trapped between the layersof brine saturated dolostone from the depth of 2680 to 2730 ms.Here, dolomitization is considered to play a large role in improvingreservoir quality through increasing particle size in the mud-domi-nated fabrics by replacing the lime mud with medium-size dolomitecrystals (Lucia, 1999). In addition, dolostone is less compactableand hence more favorable for porosity preservation. There are sev-eral layers of anhydrite deposition, which are attributed to the fre-quent sea-level fluctuations. The occurrence of anhydrite is oftenlinked to diagenetic processes of evaporite mineralization. Note thatthe overburden anhydrite that ranges from 2650 to 2680 ms, whichis considered the seal for the underlying dolostone reservoir, con-tains some thin shale and dolostone layers. The well-log also showsa thick limestone formation that is controlled by a relatively stabledepositional environment. More shale content is found in this lime-stone unit, which is often associated with the low energy deposi-tional environment, possibly in a lagoonal or central platformsetting. Nonetheless, the dolostone reservoir is pretty clean, which

    Figure 1. Stacked seismic image of inline 209 (the negative ampli-tudes are red, and the positive amplitudes are black). The dashedrectangle identifies the targeted inversion zone, and the red lineidentifies the position of well A.

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  • suggests that the depositional environment is probably related to thehigher energy setting such as platform margins. Based on the geo-logic knowledge and petrophysical interpretation of well-log data,we define four lithofacies in the targeted inversion zone: anhydrite,dolostone, gas-carbonates, and limestone. The lithofacies showfairly strong vertical variations based on this single well analysis,implying that the reservoir exhibits complex depositional anddiagenesis in the geologic history. Rock properties can also be dis-cerned from well-log data. For example, the trapped gas-carbonatespresent elastic features of low velocity and low density. Further-

    more, dolostone generally has higher P- and S-wave velocities,whereas anhydrite tends to have higher density.

    ROCK-PHYSICS ANALYSIS

    The prediction ability is strongly dependent on the degree ofseparation for lithofacies given seismic-derived elastic properties.Statistical rock-physics relationships that are derived from well-logdata represent the link between the lithofacies to their correspond-ing elastic properties. More importantly, it is critical to understand

    Figure 2. P-wave velocity, S-wave velocity, density, and water saturation are displayed as a function of two-way traveltime in well A. Litho-fluid classes are defined. Green, red, yellow, and blue represent lithofacies of anhydrite, dolostone, gas-carbonates, and limestone, respectively.

    Figure 3. Core photos of reservoir rocks in the Yuanba gas field of Sichuan Basin, southwest China. Red parts represent pore space. (a) Fine-medium crystal dolomitic limestone with microfractures, (b) power crystal dolostone with vuggy pores and microfracture, and (c) power crystaldolostone with vuggy pores and microfractures.

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  • why the inverted elastic attributes can physically be used to identifythe lithofluid classes based on the geologic understanding of thisreservoir. In this section, we perform rock-physics analysis to dem-onstrate how the heterogeneities of rock properties affect the result-ing elastic responses.

    Vuggy-fracture porosity system

    Geologic observations suggest that the diagenetic product of frac-turing, dissolution, compaction, and dolomitization significantlyimprove the deep-buried reservoir quality. The pore space is hencedominated by the secondary porosity. Figure 3 shows core plugsrepresentative of the carbonate reservoir formation in the SichuanBasin. The heterogeneous pore systems are closely related to small-scale touching vugs (grain molds) and microfractures. Typically,most of the fluid storage is in the vuggy system and most of theflow capacity is in microfractures.Vugs or moldic porosities are often formed from dissolution

    processes by selectively dissolving grains composed of unstableminerals. Such dissolution processes can occur within the meteoricenvironment associated with fresh water or in the burial environ-ment (Lucia, 1999). Moreover, the rich sour gas, such as H2S in thisreservoir, is believed to enhance the dissolution effect. Normally,the vugs, or grain molds are often isolated and have poor connec-tivity. Fortunately, the well-developed microfractures increase theconnection between the separate vugs and enhance the permeabilitydramatically. This is supported by the fact that the reservoir rockshave an average porosity of about 4%5%, but the effective per-meability could be as high as several hundred millidarcies basedon the core measurements. Microfractures in this reservoir could beassociated with dolostones brittleness and differential stress due tothe multiphase tectonic movement. Additionally, the developed mi-crofractures, which serve as fluid conduits, are favorable for disso-lution to take place. Overpressure is another important factor thatshould be considered to facilitate the development and preservationof the secondary porosity. First, overpressure can increase the solu-bility of acid gas (CO2 and H2S), and it thereby enhances the dis-solution ability of formation water. Second, overpressure tends topreserve vuggy-fracture porosity system during the process ofburial compaction (Ma et al., 2008a).

    Rock-physics modeling

    Rock physics modeling is used to learn how the vuggy-fractureporosity system and fluid behavior together affect the elastic proper-ties. The dry-rock elastic moduli are computed using the differentialeffective medium theory (Mavko et al., 2009; Xu and Payne, 2009;Zhao et al., 2013). This scheme simulates porosities in a compositeof two phases by incrementally adding a small amount of pores(phase 2) into a matrix (phase 1). The coupled system of ordinarydifferential equation can then be written as

    1 dK K2 KP2; (1)

    1 d 2 Q2. (2)

    With the initial conditions K0 K1 and 0 1, whereK1 and 1 are the matrix bulk and shear moduli, respectively;

    K2 and 2 are the bulk and shear moduli of the inclusion phase,respectively; is the porosity and d is the incremental changein porosity; and P2 and Q2 are the geometric factors dependingon the aspect ratios of the elliptical pores. In this case, the porespace is assumed to consist of a combination of stiff matrix porosity(vuggy pores) and microfractures with aspect ratios of 0.4 and 0.01,respectively. The solid matrix is assumed to be dolomite based, thematrix porosity is assumed to be 0.05, and the crack density variesfrom 0 to 0.30, which is calculated from the crack-induced porosityand the aspect ratio of the cracks (Hudson, 1981). The gas-brine car-bonate reservoir is assumed to be partially saturated, and the effectivefluid modulus is computed based on the Voigt average approximation(Domenico, 1976; Mavko et al., 2009):

    Kf SwKw SgKg; (3)

    where Kf is the effective bulk modulus of the fluid mixture; Kw andKg, respectively, denote the bulk moduli of the brine and gas phases;and Sw and Sg, respectively, denote the water saturation and gas sat-uration. Finally, Gassmanns fluid substitution method is performedto add the fluid mixture to obtain the elastic response of the satu-rated rock.The simulated elastic properties of the carbonates VPVS ratio

    versus P-impedance superimposed with well-log data are displayedin Figure 4. The rock-physics modeling result explains the scatter-ing point in terms of fluids and porosity heterogeneities. Figure 4aand 4b mainly illustrates the effect of crack density and water sat-uration, respectively. It turns out that the vuggy-fracture porositysystem combined with the fluids effect complicate the elastic re-sponses of the heterogeneous carbonates. They show that the gashas a strong effect on reducing P-impedance and VPVS ratiofor fractured carbonates, and this effect becomes stronger withhigher crack density. However, the brine-saturated fractured carbon-ates exhibit slight increase in VPVS ratio and slight decrease in P-impedance for intensely fractured carbonates. Physically, when thefractures are dry or filled with gas, the seismic propagation velocitythat is normal to the fracture will be significantly decreased. In con-trast, the brine drastically stiffens the very compliant fractures(Schoenberg and Sayers, 1995). Consequently, it is physically rea-sonable to understand that gas-carbonates in this reservoir can havea good separation with the other three lithofacies. Figure 4b showsthat well-log data from the gas-carbonate interval nicely complywith the different water saturation lines. It seems to be hard toseparate the saturation effect at low crack density (

  • PROBABILISTIC LITHOFACIES PREDICTION

    In this section, we make inferences about the defined categoricallithofacies from prestack seismic data. The lithofacies f and seismicdata d can be linked via a set of elastic parametersm. In a Bayesianinversion setting, the posterior distribution for f given the seismicgather d is generally expressed as (Buland et al., 2008)

    pfjd Z

    Z

    pfjmpmjddm: (4)

    Note that this equation only holds with the assumption of condi-tional independence pfjm; d pfjm, which implies that theseismic data do not give any additional information for the litho-facies prediction when the elastic parameters are already known.

    It is clear to see that equation 4 propagates uncertainty from seismicdata to lithofluid classes by integrating two posterior probabilities.The first is the posterior probability of elastic attributes given seismicdata obtained by a Bayesian inversion approach (Buland and Omre,2003). The second is the posterior probability of lithofacies condi-tioned by elastic attributes based on the rock-physics inversion.

    Bayesian seismic inversion

    According to Bayes theorem, the posterior distribution of elasticparameters given seismic data pmjd in equation 4 is defined as

    pmjd pdjmpm; (5)

    where pdjm is the seismic likelihood function and pm is theprior model for the elastic parameters. The seismic likelihood is de-fined by the convolutional model with discrete matrix formulationin Buland and Omre (2003) and Buland et al. (2008). The priormodel pm combines the contribution of the rock-physics likeli-hoods and prior probabilities for all the defined lithofacies:

    pm XNf1

    pmjfpf; (6)

    where pmjf is the rock-physics-likelihood function, pf is theprior lithofacies model, and N is the total number of lithofacies.The rock-physics likelihood is simulated from statistical rock-phys-ics analysis of the available log data in Well A. Because the priorgeologic and spatial information about the lithofacies distribution inthe targeted zone are not taken into account, the prior probabilitiesassigned to the each defined lithofacies classes are set as 0.25. Ob-viously, pm has the multimodal distribution with each mode rep-resenting each lithofacies, which is mathematically inconveniently

    Figure 4. A rock-physics template presented as crossplots ofVPVS versus P-impedance, which is used to illustrate the effectof (a) crack density and (b) fluid saturation. The two black linesindicate 100% gas saturated and 100% brine saturated, the dashedpink lines in panel (a) represent modeling results with differentcrack densities, and the red solid lines in panel (b) indicate the im-pact of different fluid saturation. Scattering data points in panel(b) are only from the well-log data of gas carbonate interval, andthey are color coded by water saturation.

    Figure 5. The angle gather at the well position, which is trans-formed from the offset-domain common-image gathers. The maxi-mum incident angle obtained here is 33.

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  • used as a prior model for seismic inversion. Consequently, we ap-proximate pm to pm with Gaussian distribution, which ischaracterized by the expectation vector, the covariance matrix, andthe spatial-correlation function (Buland and Omre, 2003; Larsenet al., 2006; Buland et al., 2008).To perform Bayesian amplitude variation with angle (AVA) in-

    version, we transform migrated prestack seismic gathers from theoffset domain to the reflection angle domain. Figure 5 shows thetransformed angle gather at the well position. Because the targeted

    carbonate reservoir is very deep, the largest incident angle obtainedis about 33. The wavelet used in the inversion is extracted fromseismic data in the well-tie setting, as shown in Figure 6. Note thatthe wavelet in this case is angle independent, which is mainly basedon the fact that the prestack gathers have been preconditioned in-cluding offset and spectral balancing of the seismic amplitudes. To acertain degree, this can mitigate the impact of wavelet stretch andincrease the fidelity of angle gathers for AVA inversion. However, toget more reliable inversion results, angle-dependent wavelets arerequired to correct for uncertainties due to anisotropy effects, over-burden effects, attenuation effects, and so on. Moreover, the low-frequency information used to constrain seismic AVA inversioncomes from the expectation of the prior model of elastic parameters,which assumes smoothing variations of elastic properties in the tar-geted inversion window. Nonetheless, for lithofacies having largecontrasts and rapid variations of elastic properties, it is also reason-able to give separate prior models for different lithofacies to providebetter discriminability of the low-frequency background trend.The inversion results at the well position (Figure 7) show that the

    inverted P- and S-wave velocities fit well with the well-log trends,and some details of the vertical change can even be captured. How-ever, the inverted density is not accurate enough to be retrieved. The0.9 confidence intervals indicate that the uncertainty of the inverteddensity is much higher than that of the inverted P- or S-wave veloc-ity. This is likely to be caused by the realistic noise levels of seismicdata and lack of wide-angle reflectivity gather in the deep targetedformation. The maximum a posteriori solution within the targetedzone is shown in Figure 8. According to the previous rock-physicsanalysis, the very low acoustic impedance and VpVs ratio from2690 to 2740 ms in the seismic inversion result can be regardedas the potential gas reservoir. The next step is to map the probabilityof the gas carbonate reservoir.

    Assessment of the posterior model

    Following the approach presented in Buland et al. (2008), theapproximate likelihood model for the seismicdata given lithofacies can be written locally forthe time sample i as

    pdjfi ZZ

    pmijfipmijdpmi

    dmi;

    (7)

    where pmijd is the posterior seismic inversionresult using the Gaussian prior model pmi.Here, we do not use density information for re-liable lithofacies prediction due to its poor inver-sion result as shown in Figure 7, even though itis an important input to constrain the lithofaciesprediction, especially for the separation of gas car-bonates. Thus, only P- and S-wave velocities areused as links to estimate lithofacies probabilitiesfrom seismic data. Recall that the relationshipof P- and S-wave velocities in this heterogeneouscarbonate reservoir exhibits significant variationdue to the presence of the complex vuggy-fractureporosity system as well as the fluids effect; there-fore, we assume that the P- and S-wave velocitiesindependently provide information to constrain

    Figure 7. Seismic inversion result at the well position. The black line indicates the ac-tual well-log data, the green line indicates well-log trend, the red thick line indicates amaximum solution, and the red thin lines indicate an 0.9 prediction interval.

    Figure 6. The angle-independent wavelet used in the inversion.

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  • the lithofacies prediction. This entails the conditional independencebetween P- and S-wave velocities, and the rock-physics likelihoodcan be consequently expressed as

    pmijfi pVpijfipVsijfi. (8)

    The histograms of four lithofacies P- and S-wave velocities inwell A are shown in Figure 9a. The rock-physics likelihoods dis-played in Figure 9b are assumed to follow the Gaussian distributionand can be calculated from the associated expectation and varian-ces. As expected, the elastic properties of gas-carbonates can sep-arate well with the other three lithofacies, but the variance andassociated uncertainty tend to be higher. Also, the elastic propertiesof the anhydrite, limestone, and dolostone are overlapping eachother to a certain degree, but they present relatively lower varianceand associated uncertainty.The approximate likelihood function in equation 7 and prior

    probabilities of lithofacies define the approximate posterior litho-facies distribution:

    pfijd pdjfipfi; (9)which can be normalized as

    XNf1

    pfijd 1: (10)

    To efficiently solve the integral in equation 7 (see Buland et al.,2008), the likelihood function pdjfi can be considered as a con-volution of the ratio hmijfi pmijfipmi, with the Gaus-sian kernel gmi mi pmijd:

    pdjfi ZZ

    hmijfigmi midmi: (11)

    Here, m mjd represents the posterior expectation of Bayesianseismic inversion. Now, the convolution in equation 11 can be

    Figure 9. (a) Histograms for the four lithofacies P- and S-wavevelocities. The curves are used to plot the boundary of the histogramfor each lithofacies. The data used are from the well log A in thetargeted reservoir. The yellow, green, blue, and red colors representthe lithofluid classes of gas-carbonates, anhydrite, limestone, anddolostone, respectively. (b) The rock-physics likelihoods for thefour lithofacies and the probability distributions for the P- andS-wave velocity are assumed to be Gaussian.

    Figure 8. Maximum a posteriori seismic inversion results of P-wavevelocity, S-wave velocity, and VPVS ratio within the targeted zone.

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  • numerically realized in the Fourier domain by the use of fast Fouriertransform. Consequently, we can compute the posterior probabil-ities of lithofacies by looking up the precalculated likelihood afterBayesian seismic inversion. In addition, we do not make any as-sumptions about spatial dependency of lithofacies in neighboringcells to assess the posterior model in this case study.

    Results of the posterior probabilities for the lithofacies

    Figure 10 displays the posterior probability for anhydrite, dolo-stone, gas-carbonates, and limestone at the well position. The sumof posterior probability of all lithofacies is equal to one. For a per-fect prediction, the probability would be one in the position of refer-

    ence lithofluid classes and zero otherwise. Generally, the predictedposterior probabilities for the lithofacies are acceptable comparedwith the actual lithology profile defined at the well position. It isobserved that the probabilities of gas-carbonates occurrence atthe reservoir zones (27002740 ms) are about 0.60.7, which dem-onstrates that the gas-carbonates are highly predictable. This ismainly due to two reasons: First, the inverted elastic properties fromseismic data have a good match with the actual log data and theassociated uncertainty is low in the gas-carbonate zone; second,the rock-physics relationships for the gas-carbonates have a goodseparation with other lithofacies. The prediction ability for thedolostone is high at depths ranging from 26902700 ms and28202850 ms. However, it is reduced at depths ranging from

    27402750 ms and 28902900 ms, where theyare mistaken as limestone. A possible explanationfor this may be attributed to the poor elastic prop-erty inversion results at the corresponding depths.Even though the rock properties of the dolostone,limestone, and anhydrite can be discriminated to acertain degree, errors occasionally occur for dis-criminating anhydrite, dolostone, and limestone.The posterior probabilities of gas-carbonate,

    anhydrite, dolostone, and limestone for the tar-geted zone are displayed in Figures 11 and 12.The lithofacies profile from well A is also markedfor easy comparison with the predicted result. Theinversion result suggests that the gas carbonates inthe top of the targeted zone (27002750 ms) showvarying posterior probabilities ranging from 0.5 to0.8. Although the inversion procedure goes traceby trace, without considering the lateral continu-ity, the predicted probabilities about the gas-carbonate area still show spatial continuity geo-logically. Also, the reservoir rocks tend to beheavily cracked based on the previous rock-phys-ics analysis. In conjunction, those factors increaseour confidence to identify the gas carbonatereservoir with high posterior probability as the po-tential sweet spots. We also map the posteriorprobabilities of anhydrite, dolostone, and lime-stone. The targeted zone shows significant hetero-geneities in terms of the lithology distribution,which in turn gives feedback about the varyingdepositional environment and strong diagenesisthat reorganized the reservoir in geologic history.Even though the prediction uncertainty may behigh in certain areas, it is still useful for the delin-eation of the reservoir architecture and construc-tion of the geologic model.

    DISCUSSION

    The main limitation in this case study is thatthe prior information about the spatial correlationfor the lithofacies model has not been taken intoaccount. Generally, the prior model for the seis-mic lithofacies inversion can be constructedbased on the available geologic information,well-log data, and seismic interpretation. Nu-merically, the prior model on the lithofacies

    Figure 10. (Left) The reference lithology and fluid profile, with anhydrite (green), dolo-stone (red), gas-carbonates (yellow), and limestone (blue), is defined based on the well-log analysis. (Right) Posterior probabilities for lithofacies prediction from seismic dataat the well position. The sum of posterior probability of each lithofacies is equal to 1.

    Figure 11. Posterior probability for gas-carbonate distributions in the targeted reservoir.The corresponding lithofacies profile from well A is plotted for comparison with theinversion results.

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  • classes can be characterized by a Markov random field that capturesthe locally vertical and horizontal continuities (Eidsvik et al., 2004;Larsen et al., 2006; Rimstad and Omre, 2010; Ulvmoen and Omre,2010). This should be considered in future work. Also, in this case,we only use P- and S-wave velocities to infer the lithofacies prob-abilities from seismic because the density is not reliably extractedbased on the three-term AVO inversion. It is also practically pos-sible to use the elastic attributes of P-impedance in combinationwith the VPVS ratio, which can be readily estimated using two-term AVO information. This might enhance the prediction abilityto distinguish gas-carbonate from anhydrite because they have lessoverlap if the information of P-impedance is included as illustratedin Figure 4a. In addition, we assume the conditional independenceof P- and S-wave velocities in the rock-physics likelihood to predictposterior probabilities of lithofacies. Strictly speaking, this assump-tion is considered to be not in accordance with the seismic inversionresult because there exist some dependencies for the P- and S-wavevelocities inverted from the AVO attributes. It is important to note

    that this should be considered as a special case for this hetero-geneous carbonate reservoir where the presence of complex poresystem and fluid saturation effect result in strong P- and S-wavevelocity variations. However, such a treatment may subjectively en-hance the prediction certainty because we do not account for theredundancy in the information of elastic parameters.The rock-physics likelihood and the prior elastic model used for

    seismic inversion are better be estimated from several wells in thisarea to include the lateral heterogeneities. Nonetheless, only onewell is available for this inversion test, which could increase theuncertainty for lithology and fluid prediction. Also, due to the lim-ited access to the well-log data, a blind well test, which wouldstrengthen the applicability of this method to characterize the car-bonate reservoir, could not be performed. Finally, it is necessary topoint out that the uncertainties related to scale change and disper-sion effects are not included in this study. Because when the com-pliant fractures and stiff vuggy pores coexist in the heterogeneouscarbonates, velocity dispersion can be induced by an internal porepressure equilibration that takes place with fluid flowing from themore compliant high-pressure regions to the relatively stiffer low-pressure regions. Besides, patchy saturation in the gas carbonatereservoirs may also contribute velocity dispersion. All those factorsshould be cautiously calibrated to allow more reliable lithofaciesprediction.

    CONCLUSIONS

    Lithology and fluid prediction from seismic data in SichuanBasin, southwest China is significantly challenging due to its deepburial depth and substantial heterogeneities. With integration of thegeologic information, rock-physics analysis, well-log, and seismicdata, we applied a Bayesian inversion approach to predict the pos-terior probabilities for the defined lithofluid classes. We demon-strate that it is important to perform rock-physics analysis beforeconducting lithology and fluid prediction, in particular for theheterogeneous carbonate reservoir. Based on our geologic under-standing of the reservoir, the rock-physics modeling scheme weused gives physical insight into how the lithofluid classes with dif-ferent rock properties can be related to their corresponding elasticresponses. We conclude that the elastic responses of carbonates canbe sensitive to the fluids due to the presences of vuggy-fracture poresystem in this reservoir. Bayesian seismic inversion helps to char-acterize the uncertainty of the extracted seismic attributes. For thestudied deep targeted carbonate reservoir, it is found that the densityprediction is not reliable with high uncertainty. Therefore, we onlyuse P- and S-wave velocities for lithology and fluid prediction. Theposterior probabilities for the four defined lithofacies are mapped inthe target zone, which aid the identification of the potential gas-car-bonate formation with geologic continuity. The case study also il-lustrates that the prediction strength is controlled by the uncertaintyof the rock-physics likelihood and the accuracy of the seismic in-version results.

    ACKNOWLEDGMENTS

    We thank SINOPEC for permission to publish the data. Theauthors greatly appreciate M. Bosch and the other, anonymous, re-viewers for their constructive comments that significantly improvedthe work. Special thanks also go to A. Buland and O. Kolbjrnsenfor the illuminating discussions on the topic of Bayesian inversion.

    Figure 12. Posterior probabilities for anhydrite, dolostone, andlimestone distributions in the targeted reservoir. The correspondinglithofacies profile from well A is plotted for comparison with theinversion results.

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