Seismic Facies Identification and Classification … · Seismic Facies Identification and Classification Using Simple Statistics Abraham K. John,* Larry W. Lake, Carlos Torres-Verdin,

Seismic Facies Identification andClassification Using Simple Statistics

Abraham K. John,* Larry W. Lake, Carlos Torres-Verdin, and Sanjay Srinivasan, The University of Texas at Austin

SummaryThe identification and mapping of rock facies is important to re-liable reservoir characterization. Traditionally, facies identificationand mapping are based on inspection of core data and/or well-logsignatures, a procedure that has subjective aspects because it isrelies on samples from only a very small portion of the reser-voir. Such identification is also difficult to perform at the onsetof the exploration stage because of lack of sufficient well data.This paper demonstrates a simple practical approach to identifyand classify facies from seismic-amplitude data using basic statis-tical concepts.

Within a geologic facies, measured properties [in this caseacoustic impedance (AI)] are assumed to differ mainly as a resultof random additive events and are modeled by a normal distribu-tion, as justified by the central-limit theorem. The facies are iden-tified by estimating the combination of facies volume fractions anddistribution parameters (means and standard deviations of the fa-cies probability-density function) that best fit the population dis-tribution of AI. A simple form of Bayes theorem is then used tocompute the probability of occurrence of each of the facies at themeasured locations. This generates a volume of facies probabilitiescorresponding to the seismic volume. Such a volume can be usedto perform facies-specific petrophysical analysis or be a startingpoint to generate multiple realizations of petrophysical properties.The approach is simple and transparent to use, with no significantcomputational requirements even on large data sets.

We describe an application of the procedure to a syntheticreference data set and a Gulf of Mexico AI data set. Mappedprobabilities of the individual facies show the spatial continuityand geologic character of the underlying depositional environment.Property values within the mapped regions are substantially lessvariable than the original data across the entire region. The within-facies semivariograms exhibit much less spatial correlation thanacross all facies. Since the facies are mapped across an exhaustivedata volume, this approach considerably reduces the need for thegeostatistical construction of property distributions within them aslong as a high correlation exists between the seismic attribute andpetrophysical properties.

IntroductionOne of the first steps involved in building a reservoir model is toidentify the facies present and to map their spatial distribution.This typically is performed using the geological information avail-able from early well logs and cores and the interpretation of seis-mic-amplitude data. Knowledge of the facies present in the area ofstudy results in better application of correlations that are used togenerate spatial maps of petrophysical properties. However, at theonset of the exploration process, accurate identification of thefacies and mapping their distribution across the entire reservoir ischallenging. This is because not enough well data are available tocalibrate and transform the seismic-amplitude data on the basis ofcrossplots of AI and log-measured properties. This motivates theneed to have an automated procedure to help identify directlypossible facies from the seismic-amplitude data and then to be able

to generate maps of their probable spatial distributions using thesame seismic-data volume.

A seismic facies can be defined as a group of seismic amplitudevariations with characteristics that differ distinctly from those fromother facies. A seismic facies is the manifestation of the underlyinggeologic facies or structural feature in the seismic-amplitude data.Different approaches can be used to search and identify these fromthe seismic data. These could be based on analysis of either theseismic waveforms or the seismic attributes.

Statistical classification techniques, which work on seismic at-tributes such as amplitude, have found increasing use within tra-ditional interpretation workflows (Johann et al. 2001; Fournieret al. 2002). The objective of these techniques is to be able todescribe the variability of the data and highlight details of theunderlying geologic features. Statistical classification techniquesmay be supervised on the basis of established identification rulesor they may be unsupervised (Coléou et al. 2003) on the basis ofautomated recognition of patterns in data. The most commonlyused supervised technique is that of artificial neural networks(Saggaf et al. 1984). Supervised techniques, though flexible, needsubstantial training effort based on available data or prior knowl-edge. This is usually time-consuming, case-specific, and, at times,not possible because of the paucity of data. Techniques such ascluster analysis and principal-component analysis, which are un-supervised, are used typically to establish relationships betweendata attributes and to eliminate data redundancy. All of the aboveare essentially similar in that they make use of statistical propertiesof data either to group or to separate them. But they differ in theirability to capture geologic features efficiently, and in their appli-cability and interpretability. Given the large uncertainty at thispreliminary stage of modeling, it is important to have a techniquethat is transparent so that it lends itself to easy interpretation.

This paper demonstrates such an approach, which is based onpartitioning the probability distribution of the measured attributeinto multiple parent distributions (Sinclair 1976). The procedurecan help identify facies only on basis of the probability distributionof AI data. The law of total probability is used along with aparametric mixture model for the facies probability distributions.Bayes theorem is used subsequently to compute the probability ofoccurrence of each facies at every spatial location, given the pres-ence of measured seismic amplitude.

The paper is outlined as follows: The basic theory underlyingthe classification procedure is discussed first. This is followed byan introduction and description of Bayes theorem and its use ingenerating facies probability maps. Application of the technique totwo data sets is shown next.

TheoryFacies Identification. A geologic facies is a sedimentary unit thathas characteristic structural and mineral properties that reflect itsdepositional environment and diagenesis. The resulting set ofpetrophysical properties for a facies is unique; often the propertiescan be used to distinguish between them. But an exhaustive set ofmeasurements is never available; hence, it is desirable to be able toidentify the major facies from a minimal set of attributes or in thiscase, from only the univariate distribution of AI.

If there were only one facies present, then the probability dis-tribution function (PDF) of AI across the reservoir would be uni-modal. If multiple facies are present, the nature of the PDFchanges and new modes arises. The probability distribution of theseismic attribute across the entire reservoir is thus a mixture of theindividual facies distributions whose number, parameters, and pro-

* Now with Shell International Exploration and Production.

Copyright © 2008 Society of Petroleum Engineers

This paper (SPE 96577) was accepted for presentation at the SPE Annual Technical Con-ference and Exhibition, Dallas, 9–12 October, and revised for publication. Original manu-script received for review 14 July 2005. Revised manuscript received for review 7 July 2008.Paper peer approved 26 July 2008.

984 December 2008 SPE Reservoir Evaluation & Engineering

portions are to be estimated. This mixing rule follows from the lawof total probability that states

P�Z � z� = �i=1

N

P�F = i�P�Z � z |F = i�, . . . . . . . . . . . . . . . . . . (1)

where Z is a random variable denoting AI; F is a categoricalrandom variable denoting facies type; P(Z<z) is the observed prob-ability of AI being less than z (cumulative probability); P(F�i) isthe unconditional probability (prior facies proportions) of facies ioccurring; P(Z<z|F�i) is the cumulative probability of observingthe AI value z, conditioned to facies being i; and N is the numberof facies. Eq. 1 assumes that the facies are mutually exclusive; agiven location cannot be in two or more facies.

To use Eq. 1, the conditional probabilities P(Z<z|F�i) must beestimated. We propose to use a parametric model (the Gaussiandistribution) for this purpose. Such a choice is based on the as-sumption that within a facies, it can be expected that measuredpetrophysical attributes (in this case AI) differ only because ofrandom additive events (e.g., noise or subfacies variations) and,hence, can be normally distributed as justified by the central-limittheorem. Therefore, the probability of observing a given value ofAI conditional on facies F being i is given by

P�Z � z |F = i� = N��i, �i�, . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

where �i and �i are the means and standard deviations of the AIwithin facies i. Even though the normal distribution has been pro-posed here, any other appropriate parametric distribution (e.g.,log-normal) can be used. Facies identification and estimation alsomay be achieved using multiple seismic attributes on prestack data(Eidsvike et al. 2004) or by populating the training data withrock-physics equations (Mukerjii et al. 2001).

The left side of the Eq. 1 is the probability-density functioncomputed from all the AI data without regard to facies origin.Unknowns to be estimated are the model parameters (means andstandard deviations) for the measured attribute and the prior prob-abilities for each of the facies. This is accomplished using anoptimization procedure that searches for the model parameters thatfit the data distribution best. The objective function to be mini-mized is

R = �k=1

Ndata

�Pmodel�Z � zk� − Pdata�Z � zk��2, . . . . . . . . . . . . . . . . . (3)

where Pmodel(Z<z) is computed using Eq. 1 and Eq. 2; Pdata(Z<z)is obtained from the cumulative distribution function computedfrom the AI data set; and R is the residual or error of fit betweenthe model and data.

The initial values of the number of facies (N) needed and theirparameters (�i and �i) are set on the basis of the modes existing inthe PDF of the AI data set. The unconditional probabilities (priorfacies proportions) must be set from other data sources like re-gional trends, knowledge of geologic plays, or, as is to be donehere, by an unknown in the optimization routine. They representthe overall volume fraction of each facies present. The procedureis repeated with increasing N until the error of fit no longer de-creases, implying that the variability and character of the distribu-tion has been captured effectively. Estimated model parametersdefine the facies and can now be interpreted in the geological context.

Facies Classification. Once the facies parameters have been iden-tified using the optimization procedure, they can be used to cal-culate the facies probabilities at each location using Bayes theorem(Kapur et al. 2000). Bayes theorem is a simple mathematical ex-pression to calculate conditional probabilities. It relates the di-rect probability of a hypothesis (H) conditioned on a given bodyof data (D), to the inverse probability of the data conditioned onthe hypothesis.

P�H |D� =P�H�P�D |H�

P�D�, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

where P(H) is the prior probability of H. The inverse probabilityP(D|H) is called the likelihood of H on D. It expresses the degreeto which the hypothesis predicts the data, given the backgroundinformation codified in the probability P. Although mathemati-cally simple, Bayes theorem is of great use in computing condi-tional probabilities because, often, likelihood functions are easierto estimate and less subjective than the direct probabilities. In thiscase, for N identified facies we have

P�F = i |Z ∈ z� =P�Z ∈ z |F = i�

�i=1

N

P�F = i�P�Z ∈ z |F = i�

P�F = i�. . . . . . (5)

In Eq. 5, the sign ∈ means “in the neighborhood of” (i.e., theprobability density). The likelihood function is the normal distri-bution, with parameters estimated using the identification proce-dure. P(F) is the prior probability of the facies occurring, whichmay be set on the basis of prior knowledge or from estimatesduring the identification. P(F|Z) is called the posterior, which rep-resents the updated probability of the facies occurring given theobservation of the data at the measured location. Thus, at eachpoint of the seismic cube, a set of facies probabilities is obtained.

If the properties of facies overlap significantly, then each facieswould appear to be equiprobable and the uncertainty in classifica-tion is high. If they are identified as relatively distinct, then aprobability cutoff can be enforced on the facies probabilities, andthe facies type may be coded by an indicator variable.

Seismic processing produces multiple data-attribute volumes,any of which can serve as an input to the classification process.The choice of the attribute used must be made a priori, on the basisof the attribute that captures differences in rock properties betweenpossible facies most effectively.

ResultsCase 1. To test the usefulness of the identification and classifica-tion procedures described above, application to a reference syn-thetic seismic data set is described below. This reference data setwas obtained by first generating an unconditional geological real-ization using the program fluvsim (Deutsch and Wang 1996),populating the geological model with rock properties and finallyobtaining the seismic-amplitude response using a synthetic wave-let and performing filtering and smoothing operations (Mao andJournel 2000). This ideal, multilayer, high-resolution data set wassmoothed further with a window averaging procedure, and ran-dom noise was added in order to obtain a data volume that appearsmore realistic.

The seismic attribute selected as input to the procedure is thecompressional-wave velocity (Vp). For this data set the observedvelocities fall in the range of 2000 to 5000 m/s (Fig. 1). The firsttrial of facies identification is performed by setting up a modelusing two parent facies and finding the parameters that give thebest possible fit to the cumulative distribution function (CDF). Theresults are shown in Table 1, and the PDF of the population and

Fig. 1—Reference velocities from the synthetic data set. Legendis in m/s.

985December 2008 SPE Reservoir Evaluation & Engineering

the two identified facies are shown in Fig. 2. The two faciesidentified have distinct means at the low and high ranges of ve-locities and are similar in variability. Results could be interpretedgeologically as the volume comprising a “slow” facies (channel)with an overall volume fraction of 38% and the rest being a “fast”facies (mudstone). Although the two-facies model captures theoverall variability of the population distribution, some features ofthe population distribution are not represented correctly in themidrange. This motivates the need for another identification trialwith three possible facies.

With the inclusion of one more facies in the model, the popu-lation CDF is fitted much better (lower residual). The algorithmidentifies the new facies as a transition between the previouslyestimated facies (Fig. 3 and Table 1). Such facies could be inter-preted as being the crevasse splay. This facies is between thechannel and mudstone facies spatially as well as being in themidrange of velocity. The border facies could also include channellevees that will also exhibit similar characteristics. The volumefractions of the channel sand and mudstone estimated are reducedas compared to those obtained using the two-facies model.

Using the three-facies model in the classification procedure, theprobability of occurrence of the three facies at each location isgenerated using Eq. 6. A section along the bottom layer is shownin Fig. 4, and the corresponding probability maps are shown inFigs. 5 through 7. Facies 1 represents the channel, which is themost clearly classified. Regions of high probability appear in sinu-ous shapes confirming its geological interpretation. Facies 3, themudstone, is identified by high probabilities outside the channelarea. The probabilities computed for Facies 2 are not as high asthose of Facies 1 or 3, which indicates its relative inabundance inthe region. But it does appear at the edges of the channel. At eachlocation, the facies type is assigned by selecting the facies, whichhas the highest probability value (Fig. 8). The channel and mud-stone are identified distinctly, and the crevasse is located conform-ing to the outer edges of the channel. The computed facies map isin good agreement with the reference facies map (Fig. 9) used togenerate the synthetic data set in the first place, although there aresome misclassifications in the northwest region. Overall, the pro-cedure seems to be capturing the spatial patterns of the facies typeto a reasonable degree of accuracy and reliability.

Case 2. The reservoir under consideration is an active gas fieldlocated in the deepwater Gulf of Mexico, between 8,500 and10,500 ft below sea level. Reservoir units are the lower Pliocenesands interpreted as amalgamated channel sands flanking a saltstructure. 3D post-stack seismic data acquired in the area of studyconsist of traces sampled at 4 ms in the frequency band between 10and 70 Hz, with a central frequency of 25 Hz. The dimensions ofthe reservoir unit are approximately 1.5×1.5 km horizontally, and145 m in the vertical direction (Gambús et al. 2002). For this studya smaller subvolume was extracted for analysis.

The PDF of the acoustic impedance over all measured locationsis shown in Fig. 10. Presence of different facies is evident from theexistence of multiple peaks in the histogram. Some of these peaksare very subtle; however, note that even the subtlest of peaks hashundreds of data points. The CDF of this data set is used as inputto the identification algorithm, and different estimates of faciesparameters are made using different number of facies. Facies 1 isidentified consistently with nearly similar distribution parametersin all trials, indicating its distinct character (Figs. 10 through 12).As the number of facies is increasing, the residual of fit (sum ofsquared errors) decreases (Fig. 13). With more than four facies, thefit did not improve significantly, thereby indicating that all theavailable information in the univariate distribution has been usedin the partitioning. Results from this exercise are summarized inTable 2. From the available scenarios of identified facies (N�2, 3,or 4), the choice of which actually to use as the representativemodel for further work depends on the application. This choicemust be made either by using other data or by geological inter-pretation. In the limit, all different scenarios may be used inde-pendently leading to different facies models of the reservoir, eachhaving its own probabilistic facies distribution maps.

The four-facies model is selected as an input to the classifica-tion procedure. The AI volume of the region of study is shown in

Fig. 2—Partitioning using two facies.

Fig. 3—Partitioning using three facies. Fig. 4—Reference velocities for Layer 1. Legend is in m/s.


Fig. 5—Probability map for Facies 1 (channel) in Layer 1. Fig. 6—Probability map for Facies 2 (crevasse) in Layer 1.

Fig. 7—Probability map for Facies 3 (mudstone) in Layer 1.Fig. 8—Facies indicator map in Layer 1.

Fig. 9—Reference facies indicator map in Layer 1. Fig. 10—Partitioning using two facies.

Fig. 11—Partitioning using three facies. Fig. 12—Partitioning using four facies.


Fig. 14. Note the distinct layering and large AI values in the upperhalf. The posterior probability of each facies occurring is com-puted at each location using the parameters described in Table 2and Eq. 5. The probability volumes for Facies 1 and 2 are plottedin Figs. 15 and 16. On the basis of the probabilities, Facies 1, withAIs in the lower range (10,000 to 15,000 gm-ft/cc-s), is distinctlydemarcated (highly probable) in the lower portion of the regionand is nearly absent (highly improbable) elsewhere. Facies 2with a larger mean AI lies immediately above and seems to berepeated again at the top. Both of the above and the other identi-fied facies are observed to be mappable and open to realistic geo-logical interpretation.

At each location, the presence of facies can now be indicatorcoded on the basis of either a probabilty threshold or by selectingthe facies with the highest probability of occurrence at that point.An indicator plot generated using the latter criterion is shown inFig. 17. Facies 1 and 2 are demarcated as separate layers. Facies3, which has the highest AI, is also distinctly classified and liesabove Facies 2. Facies 4, which was identified with significantoverlap with Facies 1, appears at the top and bottom surfaces ofit, indicating a facies transition. This information can be used asa starting point for applying within-facies correlations and gener-ating maps of properties (e.g., porosity, permeability). Multiplerealizations of facies distributions also may be generated usingMonte Carlo techniques. In the traditional seismic-interpreta-tion workflow, the same end results are realized on the basis ofidentifying the facies using crossplots of multiple attributes (typi-cally from well logs and cores). The AI ranges, which define afacies, are established on the basis of user judgement, which usu-ally involves at least one arbitrary cutoff. The approach describedhere automates the process and removes the arbitrariness in AI-range determination.

Apart from the delineation of the facies in the reservoir, anothersignificant issue is to estimate the heterogeneity and spatial con-tinuity of properties within the facies. Fig. 18 compares the semi-variograms of the AI for the whole data set against those from theclassified facies regions. This semivariogram was computed in thedirection of the bedding plane.

The variograms for Facies 1, 3, and 4 exhibit a lowering of sill(i.e., the variance of the impedance distribution in these facies islow—they appear more homogeneous). Facies 2 follows the trendof the overall AI. This is to be expected in a procedure that con-centrates variability, but the within-facies semivariogram also ex-hibits much less spatial correlation. The lack of correlation indicatesthat the AI within these facies is essentially spatially independent.

DiscussionThe simplicity of the model and the use of univariate distributionentail significant saving of computational effort. The identificationand partitioning steps for both the cases were performed in undera couple of minutes on a personal computer. The parameter esti-mation for the identification was achieved using the built-in opti-mization solver in Microsoft Excel. In both the cases presented, theprocedure seems to be able to identify facies and produce spatialmaps, which are amenable to geological interpretation. This meansthat use of a parametric model based on facies within which prop-erties are assumed to be normally distributed is a reasonable ap-proach for quick and efficient representation of overall probabilitydistributions. The use of Bayes theorem to compute the posteriorprobabilities of the facies, conditioned to the measured data, pro-vides a consistent way of classification.

Although this procedure was developed and applied using uni-variate distributions, it can be extended and applied easily to iden-

Fig. 14—Acoustic Impedance volume used as input. Fig. 15—Probability cube of Facies 1.

Fig. 13—Error of fit and residuals.


tify and classify facies using bivariate distributions (Vrubel 2007).In that case, each facies would be represented by a bivariate nor-mal distribution with four unknown parameters (means and vari-ances of the two attributes in the facies). The inclusion of a secondattribute to the procedure is expected to improve the classification,depending on the validity of the assumption of binormality. Also,the procedure does not require Gaussian distributions for the faciesproperties and the distribution models need not be of the sametype. The only requirement is that of using parametric probabilitydistribution models.

SummaryWe introduced and tested a simple procedure for direct identifica-tion and classification of facies from seismic amplitude data. Theprocedure is based on modeling the probability distribution of themeasured seismic amplitudes using a mixture of facies representedby Gaussian distributions. This is motivated by the need to havesimple, easy-to-compute models and is based on central-limit ar-guments. An optimization procedure is used to find the faciesparameters that fit the measured probability distribution best. Theprocedure is applied successfully to a reference synthetic seismicdata set and to an actual seismic data set from a turbidite reservoirin the Gulf of Mexico. Results show that the approach does pro-vide a simple and computationally efficient means to estimatefacies types together with their probabilitistic spatial distributions.

NomenclatureD � dataf � unconditional probability of facies occurrence

F � random variable denoting facies numberH � hypothesisN � number of faciesP � probability

R � residual or error of fit between model and dataVp � compressional wave velocityZ � random variable denoting acoustic impedance

�j � mean of attribute measured in facies i�i � standard deviation of attribute measured in facies i

Superscripts and Subscripts

data � seismic data seti � facies numberk � data point

model � parametric model used for generating probabilities

Acknowledgments

We thank UNOCAL Corporation for the release of the field dataset reported in this paper. We thank Maika Gambus for her assis-tance in extracting the seismic-amplitude data for Case 2.

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Fig. 16—Probability cube of Facies 2.Fig. 17—Indicator-coded facies probabilities.

Fig. 18—Semivariograms for AI within identified Facies F1through F4.


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Abraham K. John is a PhD degree candidate in the depart-ment of petroleum and geosystems engineering at the Univer-sity of Texas at Austin. He holds an MS degree from The Univer-sity of Texas and a BTech degree from Indian School of Mines,Dhanbad, both in petroleum engineering. Before enteringgraduate school, John worked as a junior field engineer withHalliburton Logging Services India Limited. His interests includereservoir characterization, simulation, and enhanced oil recov-ery. Larry W. Lake is a professor and interim chair in the depart-ment of petroleum and geosystems engineering at the Univer-sity of Texas at Austin. He holds BSE and PhD degrees in chemi-cal engineering from Arizona State University and RiceUniversity, respectively. Lake has been teaching at UT Austinfor 28 years, before which he worked for Shell Development

Company in Houston. He currently holds the W.A. (Monty)Moncrief Centennial Chair in Petroleum Engineering. CarlosTorres-Verdín holds a PhD degree in engineering geosciencefrom the University of California, Berkeley (1991). During 1991–1997, he held the position of research scientist with Schlum-berger-Doll Research. From 1997–1999, Torres-Verdín was res-ervoir specialist and technology champion with YPF (BuenosAires, Argentina). Since 1999, he has been with the depart-ment of petroleum and geosystems engineering of the Univer-sity of Texas at Austin, where he currently holds the position ofZarrow Centennial Professor of Petroleum Engineering. Torres-Verdín is the founder and director of UT Austin’s Research Con-sortium on Formation Evaluation, conducts research on bore-hole geophysics, well logging, formation evaluation, and inte-grated reservoir characterization. He is recipient of the 2003,2004, 2006, and 2007 Best Paper Award by Petrophysics, ofSPWLA’s 2006 Best Presentation Award and 2007 Best PosterAward, SPWLA’s 2006 Distinguished Technical AchievementAward, and SPE’s 2008 Formation Evaluation Award. SanjaySrinivasan is an associate professor of petroleum and geosys-tems engineering and holder of the Frank Jessen Faculty Fel-lowship in Petroleum Engineering at the University of Texas atAustin. His research focus is on reservoir characterization usinggeostatistics, improved flow modeling in heterogeneous reser-voirs, uncertainty assessment, and improved decision-makingin the presence of uncertainty. Srinivasan holds a BTech de-gree in petroleum engineering from the Indian School ofMines, Dhanbad, an MS degree in petroleum engineering fromthe University of Southern California, and a PhD degree in pe-troleum engineering from Stanford University.


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Seismic Facies Identification and Classification … · Seismic Facies Identification and Classification Using Simple Statistics Abraham K. John,* Larry W. Lake, Carlos Torres-Verdin,