Journal of Applied Geophysics 111 (2014) 47–58

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Journal of Applied Geophysics

j ourna l homepage: www.e lsev ie r .com/ locate / j appgeo

Channel characterization using multiple-point geostatistics, neuralnetwork, and modern analogy: A case study from a carbonate reservoir,southwest Iran

Seyyedhossein Hashemi a, Abdolrahim Javaherian a,b,⁎, Majid Ataee-pour c,Pejman Tahmasebi d, Hossein Khoshdel e

a Department of Petroleum Engineering, Amirkabir University of Technology, Tehran, Iranb Institute of Geophysics, University of Tehran, Tehran, Iranc Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Irand Department of Energy Resources Engineering, School of Earth Sciences, Stanford University, CA, USAe Department of Geophysics, Exploration Directorate, National Iranian Oil Company, Tehran, Iran

⁎ Corresponding author at: Department of PetroleumEnof Technology, Tehran, Iran. Tel.: +98 21 64545131; fax:

E-mail addresses: javaherian@aut.ac.ir, javaheri@ut.ac

http://dx.doi.org/10.1016/j.jappgeo.2014.09.0150926-9851/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 7 March 2014Accepted 23 September 2014Available online 2 October 2014

Keywords:Facies modelChannel characterizationMultiple-point geostatisticsTraining imageCarbonate tidal flatNeural network

In facies modeling, the ideal objective is to integrate different sources of data to generate a model that has thehighest consistency to reality with respect to geological shapes and their facies architectures. Multiple-point(geo)statistics (MPS) is a tool that gives the opportunity of reaching this goal via defining a training image(TI). A facies modeling workflow was conducted on a carbonate reservoir located southwest Iran. Through a se-quence stratigraphic correlation among thewells, it was revealed that the interval under amodeling processwasdeposited in a tidal flat environment. Bahamas tidal flat environmentwhich is one of themost well studiedmod-ern carbonate tidal flats was considered to be the source of required information for modeling a TI. In parallel, aneural network probability cube was generated based on a set of attributes derived from 3D seismic cube to beapplied into the MPS algorithm as a soft conditioning data. Moreover, extracted channel bodies and drilledwell log facies came to the modeling as hard data. Combination of these constraints resulted to a facies modelwhichwas greatly consistent to the geological scenarios. This study showed how analogy of modern occurrencescan be set as the foundation for generating a training image. Channel morphology and facies types currentlybeing deposited, which are crucial for modeling a training image, was inferred from modern occurrences. How-ever, there were some practical considerations concerning the MPS algorithm used for facies simulation. Themain limitation was the huge amount of RAM and CPU-time needed to perform simulations.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Channel characterization, in a way, that is consistent with geologicalscenarios, is a goal that has always been tried to be achieved during res-ervoir characterization. Modeling of facies variations and reservoir het-erogeneities when channels are present becomes more complex andchallenging. It is mainly because the final facies model should have agood connection to geological facts (channel shapes, facies interactionsand channel connectivity) that are usually present in modern occur-rences. Multiple-point (geo)statistics (MPS) was invented for themodeling of complex geological structures such as curvilinear features,and their facies associations via a training image (TI).

Among all the facies modeling techniques, there are two maincategories including variogram-based and object-based algorithms.

gineering, AmirkabirUniversity+98 21 64543528..ir (A. Javaherian).

Each of the aforementioned algorithms has their own advantagesand disadvantages (Daly and Caers, 2010). In variogram-basedalgorithms, facies types are propagated into cells based on the spatialdistribution function defined through calculating variograms.Variogram-based algorithms have great flexibility in conditioningwith a wide variety of soft and hard data. However, they have greatdifficulty in modeling complex geobodies specially in capturing thecurvilinear features like sinusoidal channels. On the other hand, theobject-based algorithm develops the facies bodies based on the sce-narios defined by geologist. In this algorithm, geologists provide amodel that contains the most probable facies bodies (Deutsch andWang, 1996). The greatest disadvantage for this algorithm is itsdifficulty in conditioning with additional data, especially when an ex-tensive hard data is available to be conditioned with the final model(Liu, 2006). Multiple-point statistics (Guardiano and Srivastava, 1993;Liu et al., 2004; Strebelle and Journel, 2000; Strebelle et al., 2002) is a ro-bust solution that covers the areas where the above mentioned algo-rithms have difficulties.

48 S. Hashemi et al. / Journal of Applied Geophysics 111 (2014) 47–58

The two-point geostatistics owes its popularity due to the simplicityof calculation and mathematical basis of the variogram model. Invariogram-based geostatistics, the variogram is ameasure of the degreeof similarity or dissimilarity of a variable at the given two spatial points.Using a variogram as a measure of geological heterogeneity or continu-ity may lead to the generation of different geological bodies and reser-voir heterogeneities with the same experimental variograms (Caersand Zhang, 2004). On the contrary, using a TI, the MPS algorithmshave the ability to reproduce facies shapes in accordance with geologistexpectations about the facies architecture. TheMPS can combine differ-ent sources of data such as drilled well data, seismic attributes, andother available facies probability curves into a consistent geological

(b)

(a)

Plat

form

Inte

rior

Tida

l Fla

t

Fig. 1. (a) Sequence stratigraphic correlation between wells over the study area. Two wells am(0–100API), NPHI (−0.15–0.45). SB,MFS, the blue triangle, the red triangle, A and B stand for thesea regression phase, respectively. Surfaces “A” and “B” represent the top and bottom of horizositional environment over the study area. Coding of environments corresponds to the color of

scenario explained by geologists. The algorithm proposed byGuardiano and Srivastava (1993) was the first move toward inferringmultiple-point conditional distribution directly from the TI. In their al-gorithm, there was no requirement for prior modeling of MPS or anykriging to calculate conditional probabilities. These probabilities wereobtained directly by scanning the training image. As the algorithmhad to scan the entire TI for simulation of each unknown cell, it was ex-tremely CPU demanding, and this drawback made it impractical. Singlenormal equation simulation (SNESIM) was an algorithm that changedviews to MPS methods (Strebelle, 2002). In SNESIM, the entire TI isscanned once, and a search tree will be constructed afterward. Basedon this search tree, all template patterns are stored and their associated

Ope

n Pl

atfo

rm

Shel

f mar

gin

ong the studied wells presented. Log tracks from left to right in each well section are SGRsequence boundary,maximumflooding surface, the sea level transgression phase, and the

n subintervals in whichmain workflow implemented. (b) Conceptual model for the depo-the log for each environment.

Fig. 2. An aerial photo (Google satellite earth maps) over the Bahamas area. The locationsof the tidal flat areas highlighted by rectangles (Rankey and Berkeley, 2012).

49S. Hashemi et al. / Journal of Applied Geophysics 111 (2014) 47–58

probability will be calculated. Although it had some problems regardingits extensive CPU demand and time execution, the algorithm becamemore practical than before being subjected to many improvements.

Even with implementation of these improvements, the SNESIM isstill suffering from a series of limitations. The method is slow and CPUdemand when dealing with a large area of study and working with a

Fig. 3. A seismic horizon slice inside 3D seismic data over the study area. The area isextremely channelized with different channels in the shape and size. Black bold circlesare the drilling locations over the area.

large number of facies classes. Some limitations of the SNESIM are relat-ed to storing thedata resulted from scanning the TI. In 3D simulation ap-plication, when the grid size is large, and there are numerous faciesclasses, the large search template cannot be used due to this limitation(Straubhaar et al., 2011) and the SNESIM algorithm becomes almost ab-surd. Straubhaar et al. (2011) proposed an alternativeway to store thesesearch events. Their idea was saving the search template into lists in-stead of trees. Their method requires much less memory and allowsfor implementation of a parallel algorithm. However, the list structuredoes not have the advantage of shortcuts (produced by branches ofthe tree) for returning the multiple-point statistics. Therefore, one cansay that the algorithms based on a list structure are slower than atree-based algorithm (Straubhaar et al., 2013). Straubhaar et al.(2013) proposed a new approach using both list and tree structures.The ideawas to index the lists by trees. The leaves of the tree correspondto the individual sublists containing a partition of the entire list(Straubhaar et al., 2013). Another method was proposed by Mariethozet al. (2010) to overcome the SNESIM limitations. In their idea, the TIis sampled directly for a given data eventmaking the scanning databaseunnecessary. OtherMPS algorithms such as cross correlation simulation(CCSIM) (Tahmasebi et al., 2012) and MS-CCSIM (Tahmasebi et al.,2014) have been proposed to cover the SNESIM limitations.

In this study, the SNESIM algorithm was implemented in a faciesclassificationworkflow. The studywas performed in anextremely chan-nelized carbonate reservoir located southwest Iran. The channels belongto the tidal depositional environments. Various geological and geophys-ical sources of data alongwith a thorough study of modern occurrencesof carbonate tidal flat channels were integrated to create a consistent TI.In addition, a neural network analysis was conducted to develop faciesprobability cubes for the different classes of facies. The facies probabili-ties came to workflow as a soft data constraint. These constraints pre-vent the channels and other facies bodies from growing, in a way thatis not consistent with the previously defined geological scenarios inthe TI. Conditional probability for each unknown node was calculatedfrom a combination of neural network probability and multiple-point

Constructing TI based on geologic

data and patterns inspired by the

analogy of modern carbonate

Preparing different seismic

attributes for being used in

neural network step

Preparing facies probability

cube using supervised neural

network

Combining probabilities from

MPS analysis and neural

network using the tau model

Data gathering

Final model

Fig. 4. Themain steps in theworkflow to reach the final facies model. The key step for theworkflow was generating the TI using available geological information, and moderncarbonate occurrence analogies.

A

B

Fig. 5. Regionalizing the study area based on the shapes and patterns of channels. For eachregion “A”, and “B” a separate TI was defined.

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conditional probability. Taumodel (Journel, 2002), was used to performsuch probability combination.

2. Geological settings

The study area is a carbonate oil field located in the southwest ofIran. The area is believed to be on the passive continental margin ofthe Arabian Plate, where shallow marine carbonate sediments havebeenwidely deposited (Sharland et al., 2004). For the purpose of preciseanalysis of depositional environments, a thorough sequence strati-graphic analysiswas conducted. In the process of sequence stratigraphicinterpretation, each depositional sequence was defined based on

(a) (b)

Fig. 6. Process of generating a TI by using aerial photos of modern occurrences (Google satellitein the region “A” of Fig. 5. (b) Result of image processing of (a) by converting the image intensiinto surface elevation. Thus, each pixel has an elevation value based on its color intensity (c) ThFacies codes are as yellow, red, and blue for channel facies, levees, and tight carbonate, respect

maximum landward retreat and seaward advances of shoreline, whichare referred as the maximum flooding surface (MFS), and the sequenceboundary or maximum regression surface (SB/MRS), respectively.

MFS is a time surface that occurs when a rate of sea-level rise attainsmaximum. Therefore, it is typified by the deepest environment in thesequence where sediments such as hemipelagic shale are deposited. Itis commonly true for siliciclastic rocks, and is not necessarily true forthe carbonate environment. Carbonates under shallow marine settingcan aggregate or even prograde to expand the area of deposition duringflooding phase of sea level (Miall, 2010). When the carbonate produc-tivity is sufficient to match the sea level rise, the balance between thesea-level rise and sediment production is formed, which leads to akeep-up succession (Miall, 2010). Fig. 1 shows the keep-up successionsof carbonates in sequence stratigraphic process over the study area.These events were taken as MFS surfaces (MFS2, MFS3, and MFS4). Asreference events, these surfaces were used for correlation among thewells. In this area, sequence boundaries are located at places wherethe succession of clean carbonates changes to shale occurrences. Anoth-er important event is the occurrence of terrigenous sediments justbelow the MPS5. This interval can be regionally correlated with thenearby siliciclastic rocks. The cutting analysis of the wells over thearea suggested that this interval is dominated by clay-rich sediments,without any indication of sand occurrences.

Above sequence stratigraphic analysis along with sedimentologicalinvestigations, resulted in a conceptual model for possible depositionalenvironments in the study area. Dominant depositional environmentswere divided into four distinct environments including tidal flat, plat-form interior, shelf margin, and open platform. The chosen subintervalfor this studywas depositedmainly in the tidal flat environment (inter-val between the surface “A” and the surface “B” as in Fig. 1). Tidal flatsare broad, almost planar areas with an altitude close to the mean sealevel. They are alternately flooded and exposed by tides, and formedby accumulation of muddy sediment transported and deposited in theabsence of appreciable wave energy (Rankey and Berkeley, 2012).Tidalflats are usually developed on areas of shallowwaterwith relative-ly low energy. These conditions may occur in protected areas of high-energy near coastlines associated with estuaries, lagoons, bays, andother areas located behind the barrier islands. Andros Island in theBahamas (Rankey and Berkeley, 2012) is one of the greatest examplesof the modern carbonate tidal flat system, Fig. 2. In summary, one ofthe characteristics of the tidal channel environment is abundance ofchannels. Fig. 3 illustrates a horizon slice of the 3D seismic data overthe study area. There are different channels in shapes and patterns inthe area.

(c)

earth maps). (a) An aerial photo from a typical channel shape in Bahamas that is dominantty into a surface. The idea behind this process is based on the conversion of pixel intensitye final TI model for the region “A” that depicts the dominant channel shape in this region.ively.

Fig. 7.Process of generating the dominant TImodels for region “B” in Fig. 5. Left column shows the aerial photos of regular channels that are present in Bahamas carbonate tidalflat (Googlesatellite earthmaps).Middle column represents the processed image of each aerial photo as discussed in Fig. 6. Right columndepicts thefinal TImodels used representing dominant chan-nel shapes in the region “B”.

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3. Methodology

This study presents a workflow for generating a facies model. Thismodel has the advantage of demonstrating the different channel

(a) (

Fig. 8. (a) Anexample of a typical tidal channel in Bahamas (Google satellite earthmaps). (b) Dischannels, pond related facies, and levees, respectively.

morphologies and their associated facies classes in great details. Fig. 4depicts a flowchart, showing the main steps that have been taken toget the final model. Generating a consistent TI model constructs thefoundation of this modeling workflow. Analysis and study of the

b)

tribution of facies related to the channel overlays to (a). Dark green, blue, and red represent

Table 1The set of seismic attributes used for neural network analysis. Numbers represent the linear correlation coefficient between each two mutual attributes.

Seismic attributes Acoustic impedance Instant frequency Variance Trace gradient RMS amplitude Apparent polarity

Acoustic impedance 1 0.1824 0.017 0.3844 0.0417 0.1874Instant frequency 0.1824 1 0.0987 0.0953 0.006 0.0182Variance 0.017 0.0987 1 0.0988 0.2887 0.1553Trace gradient 0.3844 0.0953 0.0988 1 0.0124 0.1474RMS amplitude 0.0417 0.006 0.2887 0.0124 1 0.0116Apparent polarity 0.1874 0.0182 0.1553 0.1474 0.0116 1

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modern geological occurrences were an excellent source of data formodeling the TI, since they can provide an idea for patterns, morpholo-gy, and facies association of geological structures. As the flowchartshows the neural network study also performed in parallel to producefacies probability cubes. Finally, the MPS facies probabilities and neuralnetwork facies probabilities were combined using the Taumodel. In thefollowing, the details of each aforementioned step are discussed.

3.1. Generating the training image

The TI is a model that describes the expected patterns of geologicalfeatures and their associated facies. Methods such as outcrop mapping,conceptual models and unconditional stochastic methods are usuallyused for constructing a TI model. Pyrcz et al. (2008) provided a libraryof objects to be used in the TI modeling. Maharaja (2008) createdcategorical training images through generating parametric and non-parametric shapes using unconditional Boolean simulation. Jung andAigner (2012) provided a quantitative database on carbonate geobodies.They provided this database by collecting information from extensivestudy of carbonate outcrops, subsurface and satellite images. In thisstudy, modern geological occurrences along with sequence stratigraphicanalysis were used for inferring the state of facies correlation, and themorphology of the channels. Following the sequence stratigraphic anal-ysis, it was found that the chosen reservoir interval for this modeling

((a)

Fig. 9. (a) Volumes of channel bodies resulted froma geobody extractionworkflow. These volumnode. This multiplication highlighted those amplitudes that were related to the channel bodietheir opacity threshold values. These bodies consist of extremely huge amounts of data points. Fed at these point locations. Using the entire points in the training process, makes the neural netwreduce the number of points for neural network implementations. (b) The final point-set is rep

study has been depositedmainly in the tidal flat carbonate environment.Thus, Holcene carbonate tidal flat were considered to be studied in orderto infer the channel morphology and facies classes for further analysisand classification. In other words, thesemodern tidal analogies provideda database for possible channelmorphologies, and their related facies ar-chitectures. It also gave the idea on which types of facies are going to beencountered. Among the modern carbonate tidal flats, Andros Island-Bahamas Bankwas extremelywell studied bymany researchers throughthe recent years (Bergman et al., 2010; Berkeley and Rankey, 2012;Ginsburg and Hardie, 1975; Hardie, 1977; Lowenstam and Epstein,1957; Macintyre and Reid, 1992; Milliman et al., 1993; Neumann andLand, 1975; Rankey and Berkeley, 2012; Robbins et al., 1997; Shinn andLloyd, 1969; Steinen et al., 1988). Shinn and Lloyd (1969) discussed typ-ical channel morphologies that usually occur in various regions ofBahamas tidal flat. Maloof and Grotzinger (2012) also depicted differentchannel shapes through a set of aerial photographs. These studies alongwith satellite images from the Bahamas tidal area constructed a databasefor possible channelmorphologies and facies architecture duringmodel-ing of the TI.

In the SNESIM algorithm, the TI is scanned by a search template tocapture patterns inside the TI. These patterns are stored in the form ofa tree, indicating the probability of each possible event extracted fromthe TI. In circumstances that the size of the TI model is large, thesesearch patterns become gigantic in volume and, therefore, an enormous

b)

eswere obtained frommultiplying the seismic amplitude by its cosine of thephase in eachs. The newly acquired amplitudes were filtered based on their histogram distribution andor neural network analysis, the input training data (attributes)were required to be extract-ork analysis extremely time consuming. Therefore, the channel bodieswere resampled toresenting the channel facies that were used in the training process.

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amount of RAM is required for storing these search results. A practicalsolution for this limitation is to compartmentalize the study area intoregions based on the geobodies and facies architectures that are presentin each region. In the study area, there are two different types of chan-nels regarding their shapes and patterns. The first type is wide, deep,and has a relatively straight pathway that bifurcates into smaller chan-nels, whereas the second type hasmuch smallerwidth and depthwith asinusoid flow line. Based on these differences in channel characteristics,the areawas divided into two regions. For each region, a separate TI wascreated. Fig. 5 shows how these two regions were separated based ontheir channel shapes and patterns. After partitioning the study area, aseparate TI was modeled for each region.

The MPS algorithms like any other geostatistical algorithms arebased on stationary assumption. Therefore, the TIs should be stationary(Caers and Zhang, 2004). Typical sources of data for creating the TImodels including outcrop models, aerial photographs of modern occur-rences, or simple drawings are not usually stationary. It is mainlybecause the sizes of bodies usually vary in vertical or horizontal direc-tions. For example, a channel system and deltaic or turbidite depositsare inherently non-stationary due to change in the channel size and de-positional system over the scale of the reservoir system. Different solu-tions were proposed to account for non-stationary TIs. De Vries et al.(2009) proposed a method in which the TI is subdivided into differentareas, and then the statistics of each area is stored in a separate frequen-cy search trees. In their method, facies probability distribution for eachcell is calculated by weighting the probabilities from the frequencytrees. Chugunova and Hu (2008) used auxiliary continuous data to per-form non-stationary MPS simulations. Their method was based on the

Fig. 10. The training performance of the neural network process. Upper left curves show the noreaches a steady state around 0.4which is an excellent result for training. The bottom left curvesThe horizontal axis on each curve indicates the number of vectors trained during the training prinput training data processed. The right part shows the input seismic attributes used in this studfinal result. The red shows the highest importance and light yellow indicates the lowest importasoftware.

direct inference of the conditional probabilities from joint training im-ages of the principal and the auxiliary variables (facies proportion, frac-ture density, object size, and orientation). The auxiliary variables werealso used in other studies in which the MPS algorithms used non-stationary TIs for generating realizations (Boucher, 2009; De Vrieset al., 2009; Pirot et al., 2014). In this study, the TI models resultedfrom the aerial images were also non-stationary. Some practical strate-gies were implemented to overcome the non-stationary feature of theTIs. They were as (1) regionalizing the reservoir model into zones,based on geometrical features of the channels present in the area,(2) using big search template to scan the TI, (3) extracting channel bod-ies to increase the number of informed nodes, and (4) conditioning tohard and soft data. These strategies also came to support single-objectTIs in which enough repetition of objects in the TI may not be present.The first strategy also came to assist in reducing the amount of RAM re-quirement to store the search patterns as discussed before. Figs. 6 and 7demonstrate the process of generating the TImodels through a series ofaerial images of typical channels that are present in Bahamas tidal flatarea.

For definingmain facies classes in the TI, one should analyze the sed-imentation process over the study area. Through this analysis, sedi-ments can be grouped into classes and used for further modelingprocess. Similar to the channel shape and morphology, modern occur-rences were used to identify the sedimentation process. Tidal currentsdisplace water and their accompanying lime mud into the tidal zone.During ebb tides, water is drained off through the channels leaving be-hind the lime mud (Ahr, 2008). The deposits inside channels extremelydepend on current velocities within channel system. One can say that

rmalized RMS error curves for both training data (in red) and test data (in blue). The errorshow the percentage ofmisclassification. These curves stay to a constant value around 5%.ocess. For the above training process, the training paused after almost 50,000 vectors fromy. The colors beside each input data show the degree of importance of each attribute to thence. The neural network studywas performed by the neural networkmodule of OpendTect

Fig. 11. The final probability model for channel facies resulted from the neural networkprocess. This probability model was used as a soft data to condition the MPS realizationsby using the Tau model.

54 S. Hashemi et al. / Journal of Applied Geophysics 111 (2014) 47–58

the stronger the current, the bigger the size of particles in sediments.Coarse gastropod sand and in some cases lithified dolomitic clasts arecommon in channel deposits (Shinn and Lloyd, 1969). Levees areother facies that are associated with tidal channels. They usually buildup about 1 ft. above the high-tide range. Levees are dominant in outerbanks of channel meanders and also are present on both sides of widestraight main channels, Fig. 8. They are usually composed of sand-sized pellets with light tan to cream in color. The levee sediments canbe easily distinguished by their color (creamy to white) in the aerialphotographs. The use of aerial photos for describing the facies distribu-tion in the Bahamas tidal flat area considered in several studies. Maloofand Grotzinger (2012) prepared an aerial faciesmap inwhich all the fa-cies distributions related to the channels in Bahamas area weredepicted. Moreover, Shinn and Lloyd (1969) and Rankey and Berkeley(2012) presented an excellent description of facies distribution andtheir apparent characteristics through aerial photos. Levees have theirhighest elevation at channel ridge, and they pinch out to the pondsaway the channel bodies. Pond sediments are another class of faciesthat contribute to a considerable percentage of facies in tidal flat envi-ronments. Sediments in ponds are the softest and muddiest sedimentin the entire tidal flat complex (Shinn and Lloyd, 1969). Facies relatedto the ponds can be subdivided into several categories. In general,based on the above description of the sedimentation process, threetypes of facies can be defined as (1) channel facies which have thehighest porosity among the other two classes and thus have the highestreservoir quality, (2) levees which are less porous than channel facies,and (3) tight carbonates which are formed due to lithification ofmuddy carbonate sediments deposited in ponds.

3.2. Neural network analysis

Neural network analysiswas performed on a set of seismic attributesto get facies probability cubes. These probability cubeswere imported assoft data to condition the MPS results. This soft data conditioningprevented the algorithm from a generation of those facies architecturesthatwere not expected to be present according to the related TI. The im-plemented attributes for this process had tomeet two fundamental con-ditions: (1) they must be sensitive to channel bodies, and their faciesassociations and (2) they must have small mutual linear or non-linearcorrelation with each other, to add as much information as possible tothe final probability model. Table 1 describes the implemented seismicattributes and the degree at which they linearly correlated to eachother.

Neural network analysis was conducted using a supervised neuralnetwork algorithm known as multi-layer perception (MLP) with threelayers including an input layer, a hidden layer, and an output layer.The learning algorithm in theMLP is back-propagationwithmomentumand weight decay. Momentum has a filtering role in the gradient de-scent algorithm and improves the training speed. Weight decay avoidsover-fitting of the training data by using a decay factor. Weights aremultiplied by this decay factor to reduce the weight values, which re-sults in smoother functions with improved generalization properties.The training set was created through defining point-sets. The point-sets are point locations at which the input attributes are extracted.The neural network tries to find a relation between these attributesand the facies classes that are represented by these point-sets. In thisstudy, the point-sets representing the channel facies was extractedthrough a geobody extraction workflow. In this workflow, the givenamplitude in each voxel was multiplied by its cosine of the phase. Thenewly acquired amplitudes then were filtered through their histogramanalysis and opacity thresholds. Fig. 9 shows the extracted channel bod-ies through this workflow. In addition, the point-set representing thechannel facies overlying on a seismic horizon slice is represented inFig. 9. The algorithm uses a previously specified proportion of inputtraining data (25% in this study) to test the neural network's per-formance during the training. Fig. 10 depicts the training performance

of the network. This performance is monitored using two graphs:(1) rootmean square (RMS) error curves and (2) the curves for percent-age of misclassification. The normalized RMS error curves indicate theoverall error on the training and test data sets. These curves go downand reach to a steady state as the data training proceeds. Typically theRMS values below0.4, 0.4–0.6, 0.6–0.8, and 0.8 are considered excellent,very good, good and reasonable, respectively. The curve for percentageofmisclassification is a quality control indicator that simply showswhatpercentage of test and training data is categorized into the wrongclasses. After training of the input data, a relationship was establishedbetween input data and facies classes. This neural relation was propa-gated to the entire simulation grid, and a probability cube generatedfor each class of facies. Fig. 11 shows the final probability model thatwas used as a soft data conditioning in the MPS algorithm.

3.3. SNESIM algorithm and conditioning to neural network probabilities

In this study, the SNESIM algorithm that was available inside faciesmodeling package of Petrel was implemented to generate facies simula-tions. This extension of the SNESIM algorithmuses compact search trees(Zhang et al., 2012) to reduce the memory cost for saving search pat-terns. In the SNESIM algorithm, for a random variable Z (e.g., a facies)at an unknown node u, the conditional probability distribution function(cdpf) is estimated from the following equation: (Strebelle, 2002).

F u; zkjdnð Þ ¼ Prob Z uð Þ ¼ zkjdnf g ¼ ck dnð Þc dnð Þ ; k ¼ 1;…; n

� �; ð1Þ

where dn is the data event defined by a template, c(dn) is the number ofreplicates of dn in the training image, and ck(dn) is the number of

55S. Hashemi et al. / Journal of Applied Geophysics 111 (2014) 47–58

replicates in which the centered node value is equal to zk. SNESIM pa-rameters must be applied carefully otherwise the final results will notbe satisfactory. The parameters related to search patterns are of great im-portance because of their critical influence on capturing the structures inthe TI. These parameters also affect the RAM and CPU requirements forperforming the simulation. The search pattern should be large enoughto be able to capture large-scale structures in the TI. However, choosinglarge patterns increases the memory and CPU-time necessary to storethe resulted search template in the form of trees. Tran (1994) used amultiple-grid method for overcoming this limitation. In this study, thenumber of multi-grids was chosen to be three to reasonably increase

Fig. 12. Four realizations of the final facies model. The results of MPS simulation was constraininformation as hard data. Soft data conditioning was performed using the Tau model. The ccube) were assigned, in a way, which the actual reproduction of the channel bodies was guaraneffect relative to MPS facies probability by setting τ2 greater than τ1 (τ1 = 1 and τ2 = 3). Extrbodies reproduced in their exact positions.

the search distance of the template with a small number of grid nodesin the search template. As a rule of thumb, the size of the template waschosen so that it covers 1/3 of geobody (channel) extension in its coars-est grid state. For this work, an ellipsoid search pattern is used because itcontains fewer grid nodes than a rectangular one for a given search radi-us. The template was assigned to be elongated toward the direction ofchannels in the TI to guarantee the connectivity of simulated channelbodies. The other SNESIM parameter is the number of neighbors beingused to simulate a point. Choosing many points will improve the resultsbut will increase the computation time. In this work, 10% of the totalnumber of cells in the search pattern yielded satisfactory results.

ed by neural network probabilities as soft data and extracted geobodies with well faciesoefficients of the Tau model (τ1 for MPS facies probability, and τ2 for facies probabilityteed. The channel facies probability cube as soft data conditioningwas allocated a strongeracted geobodies have performed an anchoring role, in a way, that they forced the channel

Fig. 13. An E-type estimation (average) map of channel facies. This average map was cal-culated from 50 realizations of the final model. As it can be seen the channels are outlinedwith higher order of probability rather than the channel facies probability depicted inFig. 11. The reason for such a difference is the conditioning of the simulations with harddata. As mentioned before, the extracted channel bodies were taken as hard data. Thesechannels were reproduced in every simulation and, therefore, in the averagemap are pre-sented with high probability.

Fig. 14. A 3D view of realization

56 S. Hashemi et al. / Journal of Applied Geophysics 111 (2014) 47–58

The Tau model was used for combining the MPS probabilities withthose probabilities resulted from neural network analysis. The basic re-lation in the Tau model is Eq. (2) where P(Aj|Bj, Cj) is the probability ofoccurrence of a facies at an unknown node j, conditioned to the proba-bility resulted from SNESIM algorithm Bj, and probability resultedfrom neural network analysis Cj (Journel, 2002):

P AjjBj; C j

� �¼ 1

1þ x; ð2Þ

xa¼ b

a

� �x1 ca

� �x2; ð3Þ

a ¼1−P Aj

� �

P Aj

� � ; b ¼1−P AjjBj

� �

P AjjBj

� � ; c ¼1−P AjjC j

� �

P AjjC j

� � ; ð4Þ

where P(Aj) is the prior distribution of the given facies. Parameters a, b,and c are interpreted as a measure of prior uncertainty of the relevantevents or the distance to the occurrence of their relevant events(Journel, 2002). Parameters τ1, and τ2 are weights by which the aboveprobabilities affect the final model; τ1 was assigned for MPS acquiredprobabilities, and τ2 for probabilities resulted from the neural networkanalysis.

4. Results

In order to get themost realistic faciesmodels, two stepswere taken.The first stepwas introducing the extracted channel bodies as hard data.As it is shown in Fig. 3, none of the available wells passed through thechannel bodies. Therefore, the facies logs did not have any informationabout channel facies. They had only information about two other classesof facies. Without any information about channel facies as hard data, it

from the final facies model.

Fig. 15. A 3D view of the E-type map for levees around two arbitrary well locations. The uncertainty behavior around the well location is similar to the facies variations along the upscalefacies log.

57S. Hashemi et al. / Journal of Applied Geophysics 111 (2014) 47–58

was impossible to get a consistent realization with the reality. Even, theconditioning of the MPS results to the soft data (facies probabilitycubes) does not obviate the critical need to anchor the realization tothe hard data. The process of extraction of these bodies was explainedin the neural network section. The algorithm treats these data pointsas informed nodes at the beginning of the simulation process. The sec-ond stepwas conditioning of theMPS realizations to the facies probabil-ities as soft data by implementation of the Tau model. The Tau modelcoefficients, τ1 and τ2, were assigned as the weight of MPS probabilityand channel facies probability (soft data), respectively. In order to getthe most realistic results, the weight of channel facies probability (re-sulted from the neural network) was set to be greater than the MPS fa-cies probabilities. Setting τ2 greater than τ1 (τ1 = 1 and τ2 = 3)increased the influence of soft data conditioning in areas where thechannel facies had the highest probability to occur.

For the simulation of each 2D realization, the first region was gener-ated, then for simulation of the second region, the entire simulation re-sult of the first region was taken as hard data. The connectivity of thesetwo regionswas guaranteed by conditioning of simulation results to thefacies probability cube as soft data. Fig. 12 shows four realizations of thefinal facies model resulting from this modeling. Fig. 13 presents an E-type estimation (average) map of the occurrence of channel bodies,which was calculated through averaging 50 realizations of the finalmodel. Fig. 14 shows the 3D realization of the final facies model show-ing facies variations in the vertical and horizontal directions. This 3Dblock was constructed by stacking of 2D simulations. For each layer ofthis 3D block, 2D facies simulations were conditioned to the hard andsoft data. The hard and soft data were the corresponding layers in theextracted 3D channel bodies, and in the facies probability cubes, respec-tively. Because of this conditioning, the vertical continuity was imposedautomatically. Fig. 15 depicts 3D view of E-type maps for levee aroundtwo arbitrary well locations. The uncertainty behavior around wells isquite similar to variations in the facies well logs. In the other words, inareas where the upscaled facies logs are showing levees, the probabilityfor its occurrence (E-type values) increases and where there is no leveein the facies log, this probability decreases.

5. Conclusions

MPS is a robust solution for delineation of curvilinear geologicalfeatures and their facies associations via generating a training image.The Bahamas tidal flat was used as a source of information for con-structing the TI. This usage of modern occurrences was highly usefulin acquiring the following information. (1) Modern occurrences con-structed a database of all possible channel shapes that were present inthe area of study. (2) It provided the knowledge on what types of faciesusually deposited in geological settings that are similar to the area of

investigation. Reviewing the previous sedimentological studies overthe Bahamas area, constructed a basis for defining the facies classes tobe used in the final model. Conditioning the MPS realizations to thesoft probabilities by using the Tau model gave the opportunity to con-trol the development of facies. Taking well data and extracted channelbodies as hard data, and anchoring the realization to them, guaranteedthe reproduction of facies realization in their correct positions. The con-ditioning role of the soft data became stronger when the Tau model co-efficients were being manipulated based on the geometry of facies.However, there were some practical issues concerning the MPS algo-rithm (SNESIM). The main drawback in this simulation workflow wasthe huge amount of RAM and CPU time required for running theSNESIM algorithm. The results of the TI scanning were required tostore in the form of trees. It was a limitation for implementing largesearch patterns that were necessary for reproducing long-range struc-tures in the TI. Regarding this limitation one may use other recentMPS algorithms (for example the MS-CCSIM, which is a pattern-basedalgorithm) that require much less RAM and CPU for generating theMPS realizations.

Acknowledgment

Authorswish to extend their appreciation to the Department of Geo-physics of National IranianOil Company (NIOC) ExplorationDirectorate,Iran, for making available the required data.

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