identification of lithofacies using kohonen self-organizing maps

Computers & Geosciences 28 (2002) 223–229

Identification of lithofacies using Kohonenself-organizing maps

Hsien-Cheng Changa,*, David C. Kopaska-Merkelb, Hui-Chuan Chenc

a Department of Computer Science, University of Alabama, Tuscaloosa, AL 35487, USAbGeological Survey of Alabama, P.O. Box 869999, Tuscaloosa, AL 35486, USA

cDepartment of Computer Science, University of Alabama, Tuscaloosa, AL 35487, USA

Received 30 October 2000; received in revised form 5 June 2001; accepted 10 June 2001

Abstract

Lithofacies identification is a primary task in reservoir characterization. Traditional techniques of lithofacies

identification from core data are costly, and it is difficult to extrapolate to non-cored wells. We present a low-cost

automated technique using Kohonen self-organizing maps (SOMs) to identify systematically and objectively lithofacies

from well log data. SOMs are unsupervised artificial neural networks that map the input space into clusters in a

topological form whose organization is related to trends in the input data. A case study used five wells located in

Appleton Field, Escambia County, Alabama (Smackover Formation, limestone and dolomite, Oxfordian, Jurassic). A

five-input, one-dimensional output approach is employed, assuming the lithofacies are in ascending/descending order

with respect to paleoenvironmental energy levels. To consider the possible appearance of new logfacies not seen in

training mode, which may potentially appear in test wells, the maximum number of outputs is set to 20 instead of four,

the designated number of lithofacies in the study area.

This study found eleven major clusters. The clusters were compared to depositional lithofacies identified by

manual core examination. The clusters were ordered by the SOM in a pattern consistent with environmental gradients

inferred from core examination: bind/boundstone, grainstone, packstone, and wackestone. This new approach

predicted lithofacies identity from well log data with 78.8% accuracy which is more accurate than using a

backpropagation neural network (57.3%). The clusters produced by the SOM are ordered with respect to

paleoenvironmental energy levels. This energy-related clustering provides geologists and petroleum engineers with

valuable geologic information about the logfacies and their interrelationships. This advantage is not obtained in

backpropagation neural networks and adaptive resonance theory neural networks. r 2002 Elsevier Science Ltd. All

rights reserved.

Keywords: Neural networks; Carbonate rocks; Paleoenvironmental energy; Well log

1. Introduction

Lithofacies identification is important for many

geological and engineering disciplines. Lithofacies, rock

or sediment units characterized by certain textures or

other features, can be used to correlate important

characteristics of a reservoir, such as permeability and

porosity. Identifying various lithofacies of the reservoir

rocks is a primary task for petroleum reservoir

characterization. The purpose of this paper is to describe

an automated method of predicting reservoir rock

characteristics from frequently available data and expert

geological knowledge.

Traditionally, lithofacies are identified from cores.

Core data provide direct observations of lithofacies;

*Corresponding author. Fax: +205-3480219.

E-mail addresses: [email protected] (H.-C. Chang),

[email protected] (D.C. Kopaska-Merkel), [email protected]

(H.-C. Chen).

0098-3004/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 9 8 - 3 0 0 4 ( 0 1 ) 0 0 0 6 7 - X

however, cores are costly to collect and core recovery is

often less than 100%. Moreover, core description can be

time consuming and dependent on geologists’ experi-

ence. Therefore, a lower-cost method not requiring cores

but providing similar or improved accuracy and resolu-

tion is desirable.

For this paper we use a suite of well logs, which

provide indirect information about the subsurface and

are less expensive than using core determination. Well

log measurements can be classified to logfacies. Logfa-

cies, reflecting both rock and fluid properties, allow

discrimination among beds or sedimentary units. Log-

facies often correspond to lithofacies when they are

calibrated with core descriptions. Thus, logfacies may be

constructed as surrogates for lithofacies. Classifications

of identified logfacies can then be used to predict

lithofacies in non-cored wells or non-cored intervals in

cored wells.

Associating well log data with lithofacies can be

difficult due to the heterogeneous nature of rocks,

especially carbonate rocks. Lithofacies can be defined

using any set of rock properties. However, only

lithofacies defined by variations in properties that affect

well log response can be identified using well log data.

Moreover, some useful rock properties such as porosity

and permeability affect well log response.

Conventional computing algorithms or statistical

methods have been shown to be inadequate for certain

geological problems (Moline and Bahr, 1995), especially

in carbonate reservoir characterization. Some research-

ers in the field of geology and petroleum engineering

have recently employed artificial neural networks

(ANNs) to improve on past performance in solving

such problems (Baldwin et al., 1990; Raiche, 1991;

Rogers et al., 1992; Chang et al., 1998, 2000). ANNs are

classified into two major types on the basis of learning

modesFsupervised and unsupervised. For supervised

networks, back-propagation neural networks (BPNNs)

are the most widely used; for unsupervised networks,

Kohonen self-organizing maps (SOMs) and Adaptive

Resonance Theory (ART) networks are the two most

frequently applied (Doveton, 1994; Chang et al., 1998,

2000).

BPNNs have several significant drawbacks. For

example, outputs are confined by a predetermined

number of nodes; it is difficult to interpret relationships

among output nodes, and it is difficult to incorporate

geological knowledge into networks. Among these

problems, the restriction of output to predetermined

clusters is a major concern. When test data are located

outside the training data range, BPNN cannot classify

them; thus, the discriminating ability is not assured.

BPNN adequately deal with well-bounded and stable

problems, because training sets may cover the entire

expected input space. Unfortunately, in reservoir char-

acterization problems, variables frequently are neither

well-bounded nor stable. New lithofacies and new values

of important rock properties are often encountered. This

is particularly true of carbonate reservoirs such as the

Smackover Formation, because carbonate reservoirs

exhibit patchy heterogeneity at a variety of spatial scales

(e.g., Kopaska-Merkel and Mann, 1992).

Incorporating unsupervised networks with pattern-

recognition principles researchers have overcome some

disadvantages in BPNNs and achieved some promising

results (Baldwin et al., 1990; Chang et al., 2000). These

principles involve extracting significant features from

inputs in training mode, and in production mode,

clustering inputs based on extracted features (Looney,

1996). SOMs (Baldwin et al., 1990) and ART networks

(Chang et al., 2000) have their own strengths. SOMs

cluster inputs to ordered features, using one, two or

more dimensions, providing intuitive or explicit expla-

nation/knowledge of the output clusters. Further, the

distance between two different clusters can tell the user

how ‘‘close’’ these two clusters may be in terms of

certain physical or chemical properties such as environ-

mental energy levels. For example, in the cluster pairs 2

and 10, and 2 and 4, clusters 2 and 4 are more closely

related than 2 and 10. ART networks let the user control

the degrees of similarity among prototyped clusters

stored in networks and inputs. However, the order of

clusters in ART networks does not provide any useful

geologic information for geologists or petroleum en-

gineers.

Further, the ordering feature of SOMs provides

transition information between neighboring clusters;

for example, where grainstone grades into packstone.

This property can alleviate the ‘‘hard’’ boundary effect.

Using traditional hard-boundary clustering methods, a

datum can belong to only one cluster, even if its

characteristics are intermediate. Using this ordering

feature, geologists and petroleum engineers can more

easily understand the relationships among clusters.

Thus, we employ SOMs in this paper.

2. Kohonen self-organizing maps

Kohonen self-organizing maps are unsupervised

artificial neural networks developed by Kohonen

(1982), who intended to provide ordered feature maps

of input data after clustering (Freeman and Skapura,

1991; Ripley, 1996). That is, SOMs are capable of

mapping high-dimensional similar input data into

clusters close to each other. SOMs are two-layer, fully

connected networks with a weight matrix. SOMs are

also called ‘‘topology-preserving maps’’, assuming a

topological structure among the cluster units. This

property is observed in the brain, but is not found in

other ANNs, such as BPNN and ART neural networks.

The resulting maps provide users an intuitive and

H.-C. Chang et al. / Computers & Geosciences 28 (2002) 223–229224

familiar way of correlating and illustrating input data

sets.

Combining this topological concept and geologists’

knowledge, we proposed a five-input and

one-dimensional output SOM. One of the best-known

applications of multiple-input and one-dimensional

output SOM is the solution of the traveling salesman

problem (TSP) (Ang!eniol et al., 1988). The TSP

is a difficult constrained optimization problem that

is often solved using heuristic methods (Ritter et al.,

1992).

The architecture and algorithm of SOMs implemented

in this work are detailed in the Appendix (Fausett,

1994). The weight vector represents the exemplar of the

input patterns and the maximum number of clusters to

be formed. After several experiments our maximum

number of output clusters was set to a large number, 20,

instead of the designated number (4 in this study) of

lithofacies. One advantage of this maximum number of

output clusters is that it contains all possible distinct

logfacies in the studied areas but the number is not so

big as to separate similar inputs. This also considers the

possible appearance of new clusters not seen in the

training mode but that may potentially appear in test

wells. If test-data clusters are located within the

same cluster range as training data, the training data

possibly cover the entire data range. If the test-data

clusters are located on end-clusters (the first or the

last clusters), the training data may not contain the

proper range and other sets of training data may be

needed. Output clusters may contain empty elements

when a large number of clusters are used in training

mode. If these empty clusters appear between two

occupied clusters, there may be another potential

lithofacies not observed in the data used. If empty

clusters lie at one end of the range of clusters and span a

large number of clusters, a smaller number of clusters

may be sufficient.

Baldwin et al. (1990) implemented an eight-dimen-

sional SOM to classify eight inputs into eight large-scale

(coarse) lithofacies (e.g., limestone, sand, and shale).

Their output lithofacies are assumed to be interrelated.

In this paper, we present an architecture of SOM, five

inputs and one-dimensional output, based on the

geological knowledge that the environmental energy

level is related to lithofacies (outputs) in ascending/

descending order. In other words, the output nodes

located closer to each other in a one-dimensional form

have closer energy levels. However, in an eight-dimen-

sional form with eight output nodes, there is no

distinction of the closeness of each output; each node

has the same effects on its seven neighboring nodes.

Furthermore, our SOM is used to distinguish small-scale

(finer) lithofacies: mudstone (MS), wackestone (WS),

packstone (PS), and grainstone (GS) which are textural

classes of carbonate rocks.

3. Source of data

The cores and well logs used in this paper were

from wells (Alabama State Oil and Gas Board

Permit Numbers 3986, 3854, 4633, 4835, and 6247) in

Appleton Field, located in north-central Escambia

County, Alabama (Markland, 1992; Kopaska-Merkel

and Hall, 1993). The field produces oil from variable

carbonate strata of the Smackover Formation at a

subsea depth of approximately 3,900m. Cores were

sampled at 0.3 m intervals, except the core from well

#6247, which is continuous. There are 157 core data

points available in the training well and 241 in the test

wells.

Core examination revealed four major lithofacies in

the training well (#3986) using the Dunham classifica-

tion (Dunham, 1962). These are wackestone, packstone,

grainstone, and bind/boundstone. In Appleton Field,

bind/boundstone is stratigraphically associated with

grainstone in reef-shoal complexes. Mudstone is

not found in the training well but appears in test well

#6247.

For each data point, there are five input variables:

depth, neutron porosity, density porosity, sonic,

and ‘‘velocity-deviation’’ logs (Anselmetti and Eberli,

1999). The data preprocessing stage incorporates

prior knowledge of the Smackover FormationFdepth

of top and bottom of Smackover Formation and

approximate boundaries between the upper and middle

sections, and middle and lower sections of Smackover

Formation.

The SOM program was trained on the data from well

# 3986 and was tested on wells #3854, #4633, #4835, and

#6247 to verify performance. Well #3986 was chosen as

the training well because it has the most complete set of

core and log data for the whole thickness of the

Smackover Formation. The output clusters (logfacies)

produced from the SOM program were associated with

lithofacies previously identified by a geologist (Mark-

land, 1992).

4. Results and discussion

Eleven major, two minor, and seven ‘‘null’’ logfacies

are numbered between 0 and 19 (because a maximum of

20 output clusters are possible). The relationship

between logfacies identified by SOMs and lithofacies

determined by a geologist are shown in Table 1. These

logfacies were mapped to the four major lithofacies:

bind/boundstone, grainstone, packstone, and wackes-

tone. After calibrating with the core analysis, relation-

ship between logfacies (SOM) and permeability (from

commercial core analyses) is shown in Table 2. It is

noted that the logfacies 0, 1, 5, and 6 possess

permeability values over 100 md. The maximum

H.-C. Chang et al. / Computers & Geosciences 28 (2002) 223–229 225

permeability values found in these four logfacies are in

descending order of paleoenvironmental energy level.

The prediction and corresponding geologist’s core

descriptions (Markland, 1992) are shown in Fig. 1. The

lithofacies predicted by the SOM match those identified

by the geologist for nearly 80% of the test-well

data (Table 3). The order of clusters follows the

paleoenvironmental energy level in descending order:

bind/boundstone, grainstone, packstone, and wackes-

tone. That is, the larger the number of a given logfacies,

the lower the energy that logfacies represents. The 11

major logfacies are distributed consecutively in the

lower number logfacies, implying data in the study

area are continuously distributed in environmental

space. There are 6 empty clusters between logfacies 10

and 17. This gap resulted from the choice of 20 possible

logfacies in the training mode. However, some data are

located in logfacies, 17 and 19, justifying the use of 20

potential facies. If the analysis were re-run, using 11

(numbered from 0 to 10) distinct possible logfacies in the

training mode, then data previously assigned to logfacies

17 and 19 would be reassigned to the highest-number

logfacies, 10. Two minor logfacies contain only 3 data

points (1 and 2 points for logfacies 17 and 19,

respectively). Of these three points, two are from the

training well (#3986) and only one comes from a test

well (# 3854). These two logfacies consist of algal

laminite, which is a minor variety of bind/boundstone

that is not necessarily found in a high-energy setting.

According to the energy level trend implied by logfacies

number these should be low-energy logfacies, which is

consistent with the known environmental distribution of

algal laminite.

SOM predicted lithofacies identity from well log

data with 78.8% (190 of 241 points) accuracy.

This degree of accuracy is comparable to that (79.3%,

191 of 241 points) achieved by an ART2 neural network

on the same data (Chang et al., 1998, 2000). However,

the clusters (logfacies) produced by the SOM are

ordered with respect to paleoenvironmental energy

levels, which provides valuable geologic information.

Further, the SOM is more accurate than BPNNs

(57.3%) (Chang et al., 2000). Because this SOM predicts

lithofacies identity from well log data with a high

degree of accuracy, it may permit improved prediction

of lithofacies in non-cored intervals and non-cored

wells.

Table 1

Logfacies identified by SOMs and lithofacies determined by

geologist

Logfacies (SOM) Lithofacies (Geologist)

0 Grainstone 1/Bind/boundstone 1

1 Grainstone 2/Bind/boundstone 2

2 Grainstone 3/Packstone 1


4 Grainstone 5

5 Grainstone 6



8 Wackestone 1/Packstone 5



11 a

12 a

13 a

14 a

15 a

16 a

17 Algal Laminite 1

18 a

19 Algal Laminite 2

aNo-valued output nodes.

Table 3

Statistics of prediction of lithofacies for test wells

Well

number

No. of

available

data points

Match

(#)

Mismatch

(#)

Match

(%)

3854 60 44 16 73.3

4633-B 74 69 5 93.2

4835-B 49 39 10 79.6

6247 58 38 20a 65.5

Total 4 wells 241 190 51 78.8

aTwenty mismatched points, including 8 data points of

mudstone, which was not seen in training well #3986.

Table 2

Relationship between logfacies (SOM) and permeability

Logfacies (SOM) Permeability (md)

0 0.01–4000

1 3–1545

2 Not permeablea

3 Not permeable

4 Not permeable

5 0.01–618

6 0.01–50

7 Not permeable

8 Not permeable

9 Not permeable

10 Not permeable

17 Not permeable

19 Not permeable

aBelow measurement limit (0.01md).


Fig. 1. Comparisons between geologist’s description and predictions from self-organizing map.


5. Conclusions

We have presented a SOM incorporating geologists’

knowledge of paleoenvironmental energy level. This

approach possesses the following advantages over

supervised-learning BPNNs and unsupervised-learning

ART neural networks in the determination of lithofa-

cies. First, the one-dimensional topological architecture

of the SOM is consistent with the geologists’ lithofacies

knowledge, in that the geologist’s expertise is embedded

in the structure. Second, the distribution of the SOM

nodes provides ascending/descending energy informa-

tion about the lithofacies, not provided by BPNN and

ART neural networks. Third, the distances between

nodes provide information about the relative energy

level of lithofacies represented by those nodes. Finally,

the SOM may be extended to two- or three-dimensional

topology, according to the geologists’ knowledge, to

map other geophysical properties from well logs and

provide convenient visualization using two- or three-

dimensional plots.

Acknowledgements

This work is supported, in part, by the US Depart-

ment of Energy through their Alabama DOE/EPSCoR

Program.

Appendix A. Kohonen self-organizing mapFArchitec-

ture and Learning Algorithm

The basic architecture of the one-dimensional SOM

employed in this work is shown in Fig. 2. The network

consists of two layers: input (Xi; i ¼ 1yn) and output

(Yj ; j ¼ 1ym), where n denotes the number of input

nodes and m stands for the maximum number of clusters

to be formed. In the case of this study, n ¼ 5 and m ¼

20: Wij is a weight vector for input Xi and output Yj :The learning algorithm is summarized as follows:

(1) At the beginning of the trial, randomly assign

values to Wij ranging from 0 to 1.

(2) Set learning rate, topological neighborhood para-

meters and maximum number of clusters to be

formed.

(3) Input an Xi and compute Euclidean distance DðjÞ of

each cluster Yj :

DðjÞ ¼X

i

ðWij � XiÞ2:

(4) Find the minimum DðJÞ; J is the index of Yj with

minimum distance.

(5) Update weights for all units j within a specified

neighborhood of J and for all i:

WijðnewÞ ¼ WijðoldÞ þ learning rate�½Xi � WijðoldÞ�:

(6) Repeat steps (3) and (5) until all inputs have been

presented to the SOM once.

(7) Test stopping condition.

(8) Update learning rate and go to (3).

References

Ang!eniol, B., de La Croix Vaubois, G., Le Texier, J.-Y., 1988.

Self-organizing feature maps and the traveling salesman

problem. Neural Networks 1, 289–293.

Anselmetti, F.S., Eberli, G.P., 1999. The velocity-deviation log:

a tool to predict pore type and permeability trends in

carbonate drill holes from sonic and porosity or density

logs. American Association of Petroleum Geologists Bulle-

tin 83, 450–466.

Baldwin, J.L., Bateman, A.R.M., Wheatley, C.L., 1990.

Application of neural network to the problem of mineral

identification from well logs. The Log Analyst 3, 279–293.

Chang, H.-C., Chen, H.-C., Kopaska-Merkel, D.C., 1998.

Identification of lithofacies using ART neural networks and

group decision making. Proceedings of Artificial Neural

Networks in Engineering Conference, St. Louis, Missouri,

USA, pp. 855–860.

Chang, H.-C., Kopaska-Merkel, D.C., Chen, H.-C., Durrans,

S.Rocky, 2000. Lithofacies identification using multiple

adaptive resonance theory neural networks and group

decision expert system. Computers & Geosciences 26(5),

591–601.

Doveton, J.H., 1994. Applications of artificial intelligence in log

analysis. In: Geologic Log Analysis Using Computer

Methods, American Association of Petroleum Geologists,

Tulsa, OK, pp. 151–165.

Dunham, R.J., 1962. Classification of carbonate rocks accord-

ing to depositional texture. In: Ham, W.E. (Ed.), Classifica-

tion of Carbonate Rocks. American Association

of Petroleum Geologists Memoir 1. The American Associa-

tion of Petroleum Geologists, Tulsa, OK, pp. 108–121.

Fig. 2. Architecture of Kohonen one-dimensional self-organiz-

ing map.


Fausett, L.V., 1994. Fundamentals of Neural Networks:

Architectures, Algorithms, and Applications. Prentice-Hall

Inc., Englewood Cliffs, NJ, 461 pp.

Freeman, J.A., Skapura, D.M., 1991. Neural Networks:

Algorithms, Applications, and Programming Techniques.

Addison-Wesley, Reading, MA, 401 pp.

Kohonen, T., 1982. Self-organized formation of topologically

correct feature maps. Biological Cybernetics 43, 59–69.

Kopaska-Merkel, D.C., Hall, D.R., 1993. Reservoir

Characterization of the Smackover Formation in

Southwest Alabama. Alabama Geological Survey Bulletin

153, 111 pp.

Kopaska-Merkel, D.C., Mann, S.D., 1992. Regional variation

in microscopic and megascopic reservoir heterogeneity in

the Smackover Formation, Southwest Alabama. Transac-

tions of Gulf Coast Association of Geological Societies 42,

189–212.

Looney, C.G., 1996. Pattern Recognition Using Neural Net-

works: Theory and Algorithms for Engineers and Scientists.

Oxford University Press, New York, 458 pp.

Markland, L.A., 1992. Depositional history of the Smackover

Formation, Appleton Field, Escambia County, Alabama:

M.Sc. Thesis, University of Alabama, Tuscaloosa, AL,

145 pp.

Moline, G.R., Bahr, J.M., 1995. Estimating spatial distribu-

tions of heterogeneous subsurface characteristics by regio-

nalized classification of electrofacies. Mathematical

Geology 27, 3–22.

Raiche, A., 1991. A pattern recognition approach to geophy-

sical inversion using neural nets. Geophysical Journal

International 105, 629–648.

Ripley, B.D., 1996. Pattern recognition and neural networks.

Cambridge University Press, Cambridge, 403 pp.

Ritter, H., Martinetz, T., Schulten, K., 1992. Neural Computa-

tion and Self-organizing Maps: An Introduction. Addison-

Wesley, Reading, MA, 306 pp.

Rogers, S.J., Fang, J.H., Karr, C.L., Stanley, D.A., 1992.

Determination of lithology from well logs using a neural

network. American Association of Petroleum Geologists

Bulletin 76, 731–739.


identification of lithofacies using kohonen self-organizing maps

Documents