using artificial intelligence to corellate multiple...

Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Annual Technical Conference andExhibition held in Houston, Texas, 3–6 October 1999.

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AbstractWell data gives precise information on reservoir properties atspecific field locations with high vertical resolution. 3Dseismic surveys cover large areas of the field but reservoirproperties are not directly observable due to poor verticalresolution. For this paper, a new methodology has beendeveloped and tested for relating reservoir properties at thewell-bore to sets of seismic attributes, in order to predictreservoir properties in two zones of the Nash Draw field in SENew Mexico. Over 350 seismic attributes can be used inregression analyses of reservoir properties. Since using allattributes is computationally unfeasible and labor intensive,fuzzy logic is used to select the most statistically significantattributes for developing regression equations for individualreservoir properties. Non-linear regressions were used, asindividual attributes had low correlation coefficients whencross-plotted with reservoir properties, and neural networkarchitectures were developed to relate the selected attributes toeach property. In each case the output data used for trainingwas a reservoir property, porosity (φ), water saturation( Sw),or net pay, from 19 wells in the field. Each property wasestimated using a neural network trained to CC=0.8 or higherusing the highest ranking seismic attributes as inputs. Thevalidity of the solutions were tested by removing three wellsfrom the training data, re-computing the weights, andpredicting the three absent points. These tests were appliedthree times for each reservoir property, with different pointsremoved. Each network accurately predicted these nine testpoints and the solutions are considered robust. φ, Sw, and netpay maps were generated using the regression relationships

and the seismic attributes at each seismic bin location. Porevolume (φh) and hydrocarbon pore volume (hφSo) maps werederived from those reservoir property maps. These newtechniques maximize both the well control and seismic dataand generated useful maps for targeted drilling programs inthe field.

IntroductionThe Nash Draw field1 in SE New Mexico produces oil andwater from two sandstones of the Delaware Mountain group.The field is currently being developed, and overlying Playalakes and Potash mining concerns require the use of horizontaldrilling to target un-drained areas of the reservoir beneaththese surface features. Since long horizontal wells areexpensive it was decided to pursue advanced reservoircharacterization prior to drilling. In 1996 a high quality 3Dseismic survey was shot over the field covering an area ofabout eight square miles. Initially, amplitude alone was usedas an indicator of reservoir grade porosity2, however, a welldrilled on the basis of amplitude data alone was not aneconomic success. Geostatistics can provide good interpretedestimates of interwell reservoir properties, but existing NashDraw wells primarily cover the center part of the availableseismic survey, so a new technique to extrapolate reservoirproperties beyond the area directly constrained by wells wasdeveloped. The new technique utilizes non-linearmultivariable regression (artificial neural networks) usingseismic attributes as inputs and porosity, water saturation, andnet pay as outputs. The regression equations allow theprediction of these three reservoir properties in areas withoutdirect well control, using the laterally extensive seismicattribute data, and the computation of related maps such as φhand hφSo.

Seismic Attribute SelectionThe two primary sources of data required for this method arewell and seismic attribute data. The well data used in thisstudy is tabulated in Table 1. Over 80 seismic attributes wereextracted from the Nash Draw seismic data for the twohorizons of interest. Extracted attributes were averaged acrossthe entire interval for each of the horizons of interest (theBrushy Canyon K and L Sands), and the well data from each

SPE 56733

Using Artificial Intelligence to Corellate Multiple Seismic Attributes to ReservoirPropertiesR. S. Balch, SPE, New Mexico Petroleum Recovery Research Center, and B. S. Stubbs, SPE, Pecos PetroleumEngineering, and W. W. Weiss, SPE, and S. Wo, SPE, New Mexico Petroleum Recovery Research Center

SPE 56733 USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 2

of the 19 wells used in the study were also averaged across therespective intervals. Thus the output maps presented later inthis paper represent interval-averaged values for the respectivereservoir properties.

It is both statistically dangerous and notcomputationally feasable to use all 80 attributes to formregression relationships, therefore we have developed softwarebased on a fuzzy-ranking algorithm3 to select attributes bestsuited for predicting individual reservoir properties. Thealgorithm statistically determines how well a particular input(seismic attribute) could resolve a particular output (reservoirproperty at the well bore) with respect to any number of otherinputs using fuzzy curve analysis. To illustrate the technique asimple example is given.

Consider a set of random numbers in the range {0,1}using x={xi}, i=1,2,…,99, and xi=0.01*i, and plot each value(yI= Random(xi)) (Figure 1a). Next add a simple trend to therandom data (yi=(xi)^0.5+Random(xi)) and plot those values(Figure1b). For each data (xi, yi) a “fuzzy” membershipfunction is defined using the following relationship

Sample fuzzy membership functions are shown inFigures 1a-b. Here, b=0.1, since b is typically taken as about10% of the length of the input interval of xi. A fuzzy curve isbuilt up using a summation of all individual fuzzy membershipfunctions in (xi, yi), and this final curve can be interpreted forthe utility of given inputs for linear or non-linear regressions.The fuzzy curve function is defined below:

Where N is the size of the data set or the total numberof fuzzy membership functions. Figure 2 shows the curvesfor the data sets shown in Figures 1a-b. This simple exampleillustrates the ability of the fuzzy ranking approach to screenapparently random data for obscure trends such as thecorrelation between seismic attributes and reservoir properties.

Based on the deviation from a flat curve, eachattribute is assigned a rank, which allows a direct estimation ofwhich attributes would contribute the most to a particularregression. The fuzzy ranking algorithm was applied to selectthe optimal inputs (attributes) for six output cases: K porosity,K net pay, K water saturation, L porosity, L net pay, and Lwater saturation.

Having selected the most statistically significantattributes, an important question remains. How physicallysignificant are the attributes? A thorough literature reviewshows some direct relationships between attributes and

properties in lab-scale experiments.4 But, in generalrelationships are very complex and vary from field to field,and even between formations within a single field so the exactrelationship between frequency and porosity, for example,may be ill defined. Ideally, the rigorous use of rock physicscould demonstrate fundamental quantitative relationshipsbetween seismic attributes and reservoir properties usingforward modeling. However, though it seems obvious that allfeatures of seismic signals are a result of changes in rockproperties through which the seismic energy is transmitted,these relationships are not straightforward, even for relativelyeasily computed attributes such as instantaneous frequency.However, individual attributes have been used for a number ofyears in diverse reservoirs around the world to indicatevariations in stratigraphy, porosity and other reservoirproperties, and as such are generally accepted as meaningful.5

At present, any study which uses seismic attributes needs toevaluate individual attributes for statistical significance andthoroughly test results.

Multivariable Non-Linear RegressionLinear regression for reservoir properties was not feasible forthis study, as the relationships between input and outputs werepoorly defined by individual attributes (Figure 3). It wasdecided to use non-linear regressions using software wedeveloped based on the fast-converging, feed-forward, back-propagation conjugate gradient algorithm6 (neural network).Input attributes were selected using the fuzzy rankingalgorithm (Figure 4). Figure 5 shows a sample neuralnetwork architecture, circles represent “neurons”, or locationsof non-linear functions, while each line represents acoefficient applied to these neurons. A back-propagationfeed-forward algorithm such as the conjugate gradientalgorithm used here is “trained” using known inputs andoutputs in an iteritive fashion, with weights being sequentiallyadjusted until the desired fit (if possible) is achieved. Thesample architecture displayed in Figure 5 is a 2-2-1architecture, since there are two neurons in the input layer, 2neurons in the hidden layer, and one output neuron. Theregression equation (inverse model) for this network is asfollows:

Out1=f(v1∗f(w1∗in1+w2∗in2)+v2∗f(w2∗in1+w4∗in2))

Two neural network architectures were utilized in the study, a3-2-1, and a 4-2-1 (Figure 6), both of which were minimizedin order to maintain a satisfactory ratio of training data toweights (coefficients of the regression equation). For thisstudy, reservoir properties are well known at the locations ofthe well-bore intersections with the K and L intervals. Seismicdata that covers a much larger area is also available, and hasdata at the locations of the well-bore intersections as well.Seismic attribute data from the same seismic bin that containsthe well is correlated to well-bore values of porosity, net payor water saturation in an iterative process using either a 3-2-1,

ii

i yb

xxxF ∗

−−= ))(exp()( 2

∑

∑

=

==N

iii

N

ii

yxF

xFxFC

1

1

/)(

)()(


or a 4-2-1 neural network. Table 2 shows which of the 80attributes and two networks were used in regressions for eachreservoir property in the K and L intervals

Training and TestingIt is desireable to test how robust a regression relationship isby holding some data out for testing. Since there were 19control points (wells) it was decided to test by removing setsof three wells, training the network with 16 control points, andthen using that network to predict the three withheld points.This exercise was applied three times for each property andinterval, withholding differing sets of three points for eachtest. Figure 7a-d shows the final results of training with all19 points, and the three test sets for the L interval porosityregression. It is evident from these cross-plots that thenetwork has resolved porosity in a robust fashion, and that theresulting regression equation may be used to predict porosityin other areas of the field. Figure 8a-e shows the 19 pointnetworks for the other reservoir properties of the L and the Kintervals. These regressions were also tested in the samemanner, and had similar results.

ResultsThe regression relationships (architecture and weights) wereused to compute maps of field wide porosity, net pay, andwater saturation for the K and L intervals. Additionaldiagnostic φ*h and h*φ*So maps were also computed to aiddesign of a development program. In general these maps fitthe expectations from earlier geostatistical studies1, and thereservoir understanding of the operator.

Figure 9a-b shows L and K interval porosity mapspredicted using the computed regression relationships. Both Kand L horizons show patterns of distinct, or isolated porosity,and the L porosity map compares favorably with compartmentmaps produced independently.1 Figure 10a-b shows L and Kinterval net pay maps. The K horizon shows much morevariation in net pay thickness than the L, which is reasonableconsidering that the K is considered discontinuous and thinsand thickens in the field, while the L thickness is considered tobe continuous across the study area. Figure 11a-b shows Land K interval water saturation maps. In general the Kappears wet, except in distinct pods, which may representpossible drilling targets. The L zone water saturation isuniform, at about 45% across the field except in the northwestand southeast. The increased saturation in the northwestcorner, which is up-dip, may be due to compartmentalizationas indicated in Figure 8a.

Figure 12a-b and Figure 13a-b show φh and hφSomaps for the L and K horizons. The φh maps in Figure 12a-bare useful as an indicator of where sufficient pore volumeexists within the field. The K horizon shows a good deal ofvariability, with relatively lower φh in areas where the K isinterpreted to pinch out. The L interval φh shows a moreuniform distribution of pore volume, though some thinner andthicker areas do exist. Fine detail across the map may assist indetermining compartmentalization of porosity, as net pay is

relatively uniform across the study area. The hydrocarbon porevolume maps in Figure 13a and Figure 13b for the L and Kintervals, respectively, include information on oil saturation(1-Sw) and essentially illustrates where the oil was in the fieldat the time the seismic survey was collected. Pressurevariations are yet to be mapped. The wet K interval showsonly isolated pods of good producing potential, while the lesswet L interval shows strong undrilled potential production inthe SE corner of section 11, the SW and NW corners ofsection 7, and the west half of section 14. Areas to avoiddrilling for the L interval might include the east half ofsections 7 and 18, the SW corner of section 13, the SE cornerof section 14 and the northern half of section 11.

ConclusionNon-linear regression for reservoir properties using multipleseismic attributes as inputs was found to be useful forextrapolating φ, Sw, and net pay across the Nash Draw field,even though wells were predominantly located only in thecenter of the study area. These three reservoir properties,along with associated maps (φh and hφSo) allowed theoperator to make more informed decisions on the drillinglocations of planned expensive horizontal wells as theycontinue field development.

AcknowledgementsWe would like to thank Mark Murphy of Strata ProductionCompany for allowing us to present these results. Mr.Murphy gave valuable insights for interpreting and validatingour predictions. New Mexico Tech has a generous softwaregrant from Landmark which has greatly enhanced our researchcapabilities. This work was part of DOE Cooperativeagreement DE-FC95BC14941 with Strata Production Co.

References1. Final Technical, Phase I Report: “Advanced Oil

Recovery Technologies for Improved Recovery FromSlope Basin Clastic reservoirs, Nash Draw BrushyCanyon Pool, Eddy County, NM.” Department of Energy.PRRC Report (98-47).

2. Hardage, B. A., Simmons, J. L., Pendleton, V. M., Stubbs, B. A., and Uszynski, B. J.: “3D Seismic Imaging and interpretation of Brushy Canyon Slope and Basin Thin Bed Reservoirs, Northwest Delaware Basin,” Geophysics (v63, no 5, 1998), 1507-1519.3. Lin, Y., and Cunninham, G. A.: “A new approach to Fuzzy-Neural System Modeling,” IEEE Transactions on Fuzzy Systems, (v3 no 2, 1995), 190-198.3. Rafipour, B.J.:”Seismic Response for Reservoir Fluid Evaluation,” SPE Formation. Eval. (Mar 1989), 45-48.5. Schultz, P.S., Ronen, S., Hattori, M. and Corbett, C.: “Seismic-guided estimation of log properties,” The Leading Edge, (may 1994), 305-315.6. Moller, M. F.: “A Scaled Conjugate Gradient Method for Fast Supervised Learning,” Neural Networks, (v6 1993), 525-533.


Table 1

Well Data for K and L intervalsWell K Net Pay K Porosity K Sw L Net Pay L Porosity L SwU-1 40.5 5.9 80.8 35.5 10.1 41.7U-5 65.0 8.7 87.3 31.0 10.5 59.1U-6 44.5 11.1 87.9 25.0 13.4 41.4U-9 63.5 8.7 88.7 31.5 7.2 76.1U-10 47.0 10.2 91.1 14.5 12.5 43.2U-11 37.0 10.9 81.3 28.0 12.8 37.9U-12 59.5 9.1 90.9 46.5 11.3 53.6U-13 52.5 12.3 70.1 38.5 13.6 40.6U-14 45.0 11.5 72.9 26.5 13.1 42.5U-15 39.0 10.8 93.3 28.0 13.7 40.3U-19 67.5 4.2 93.6 19.5 12.4 39.9U-20 22.5 12.6 84.6 20.5 13.1 47.8U-23 34.5 10.5 79.0 6.5 13.0 38.8U-24 52.5 11.8 75.1 23.0 12.9 47.7U-25 35.0 11.2 81.5 12.0 9.2 88.5U-29 52.5 11.7 92.7 31.5 12.1 42.1U-38 57.0 14.3 96.5 23.5 11.0 97.0

T-FEE-1 56.5 8.5 98.2 43.0 10.7 75.4T-FED-1 71.0 6.6 99.4 67.0 10.5 75.9

Table 2Average interval attributes used for the non-linear regressions

Reservoir Property Architecture CC Attributes

K PorosityNetwork 1 0.89

Max peak frequencyAvg absolute frequency

Isochron

K Net-Pay Network 2 0.86

Max peak frequencyAvg absolute frequencyAvg absolute amplitude

Isochron

K Water Saturation Network 1 0.83

Avg reflection strengthAvg peak frequency

Isochron

L Porosity Network 1 0.88

IsochronAvg instantaneous frequency

Energy half-time

L Net Pay Network 1 0.80

Avg max peak amplitudeAvg RMS amplitudeAvg Peak amplitude

L Water Saturation Network 1 0.84

Avg instantaneous phaseAvg trough amplitude

Energy half-time


Fig. 1a—One Hundred random points between 0 and 100, two sample Fig. 1b—Same one hundred random points with a simple trendfuzzy membership functions are illustrated. added, two sample fuzzy membership functions are shown.

Fig. 2—Fuzzy curves for the two data distributions in figure 1. Curves are the summationOf the fuzzy membership functions for each point. Value is given to trends with monotonicVertical variations.

y=Random(x)

0

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FC of (x) 0̂.5 +random data in[0,1]

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FC of randomdata in [0,1]

trend of 0.5


Fig. 3—Sample crossplots illustrating the best (instantaneous phase) and worst (peak ampltude) individual correllation of seism ic attributesto water saturation for the L interval. This figure illustrates the need for multivariate analysis to better resolve reservoir properties.

Fig. 4—Fuzzy curves for the sample attribute crossplots in Figure 3. Note the continuous and semi-monotonic nature of the curv e forInstantaneous phase, which indicates correlability to Sw. The curve for Peak amplitude is discontinuous and primarily flat, in dicating a poorcorrelability with Sw.

R 2 = 0.2734

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Fig. 5—Schematic neural network using 2-2-1 architecture. Out1 (output) is described in the text. f, the activationfunction is a predefined step function designed to simulate the response of a real neuron to a stimulus.

Fig. 6—Actual network architectures used in this study. Table 2 shows which network and input attributes wereused to characterize each reservoir property of interest in both the K and L intervals.

f

fw3

w2

w1

w4

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v2

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in2

in1

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f

) exp(1

1)( ,

xxffunctionactivationtherepresentsfwhere

α+=

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A1

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Network 1

Network 2 φ, h, Sw

A4


7a 7b

7c 7d

Fig. 7-- Results of training for L interval porosity. The 7a cross-plot shows normalized values of actual well-bore porsity vs.well-bore porosity computed by the non-linear regression. Perfect results would have all points exactly on the line between 0,0and 1,1. Real world noise and generalization makes the coefficient of correlation, cc=0.875, acceptable for predicting intra andextra well porosities. b), c), and d), show the results of exclusion testing for the L interval porosity regression, with gray points,excluded, and then predicted, by the subset neural networks.

L Porosity training - All 19 points

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8a 8b

8c

8d 8e

Fig. 8--Full regressions for L interval net pay and Sw, and K interval porosity, net pay, and Sw. These networks were tested in the same manneras the L interval porosity in Figure 7, with similar results.

K Porosity training- all 19 points

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K Net Pay Training- All 19 points

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K Saturation training- all 19 points

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L Net Pay Training- all 19 points

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Fig. 9a—L interval predicted porosity map. Porosities are good throughout the center of the field, low in south central sectio n of the field. Aninteresting, laterally extensive porosity feature (11%) is located in the northwest corner, updip of higher porosities in the c enter of the field.

Fig. 9b—K interval predicted porosity map. Discrete areas can have large porosity compared to adjacent regions.


Fig. 10a—L interval predicted net pay map. Primarily uniform across the field with 30-35 ft thickness.

Fig. 10b—K interval predicted net pay map. Note the discontinuous depositional thicknesses.


Fig. 11a—L interval predicted water saturation map. Generally water saturation is less than 45%, and fairly uiform.

Fig. 11b—K interval predicted water saturation map. Water saturation is generally high (85% or more), but locally low.


Fig. 12a—L interval pore volume map generated from predicted porosity and net pay maps. Greatest pore volume is denoted by the darkestgray’s, and indicate that some good potential drill sites remain.

Fig. 12b—K interval pore volume map generated using predicted porosity and net pay maps. Wide variations in pay are due to thi nning andthickening of the K interval in the study area as well as wide variations in porosity.


Fig. 13a—K interval hydrocarbon pore volume map generated from predicted property maps. The far northwest and southeast appear to benon-productive (wet), but a number of good targets still exist in other areas.

Fig. 13b—K interval hydrocarbon pore volume map generated from predicted property maps. Only a few small targets exist.

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