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Computers & Geosciences 31 (2005) 263–275

www.elsevier.com/locate/cageo

Lithology identification of aquifers from geophysical well logsand fuzzy logic analysis: Shui-Lin Area, Taiwan$

Bieng-Zih Hsieh, Charles Lewis, Zsay-Shing Lin�

Department of Resources Engineering, National Cheng Kung University, Tainan, Taiwan

Received 7 July 2003; received in revised form 7 July 2004; accepted 16 July 2004

Abstract

The purpose of this study is to construct a fuzzy lithology system from well logs to identify formation lithology of a

groundwater aquifer system in order to better apply conventional well logging interpretation in hydro-geologic studies

because well log responses of aquifers are sometimes different from those of conventional oil and gas reservoirs. The

input variables for this system are the gamma-ray log reading, the separation between the spherically focused resistivity

and the deep very-enhanced resistivity curves, and the borehole compensated sonic log reading. The output variable is

groundwater formation lithology. All linguistic variables are based on five linguistic terms with a trapezoidal

membership function.

In this study, 50 data sets are clustered into 40 training sets and 10 testing sets for constructing the fuzzy lithology

system and validating the ability of system prediction, respectively. The rule-based database containing 12 fuzzy

lithology rules is developed from the training data sets, and the rule strength is weighted. A Madani inference system

and the bisector of area defuzzification method are used for fuzzy inference and defuzzification. The success of training

performance and the prediction ability were both 90%, with the calculated correlation of training and testing equal to

0.925 and 0.928, respectively. Well logs and core data from a clastic aquifer (depths 100–198m) in the Shui-Lin area of

west-central Taiwan are used for testing the system’s construction. Comparison of results from core analysis, well

logging and the fuzzy lithology system indicates that even though the well logging method can easily define a permeable

sand formation, distinguishing between silts and sands and determining grain size variation in sands is more subjective.

These shortcomings can be improved by a fuzzy lithology system that is able to yield more objective decisions than

some conventional methods of log interpretation.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Groundwater; Aquifer characterization; Hydrogeology; Artificial intelligence; Soft computing

e front matter r 2004 Elsevier Ltd. All rights reserve

geo.2004.07.004

ble from server at http://www.iamg.org/CGE-

.

ing author. Tel.: 886-6-275-7575� 62825; fax:

.

resses: wink@ms31.url.com.tw (B.Z. Hsieh),

cku.edu.tw (Z.S. Lin).

1. Introduction

Fuzzy logic analysis of well logs has been recently

applied extensively in many reservoir characterization

studies. For example, Fung et al. (1997) applied a self-

generating fuzzy rule extraction and inference system to

the prediction of petrophysical properties from well log

data, whereas Huang et al. (1999) presented a useful

fuzzy interpolator for permeability prediction based on

d.

ARTICLE IN PRESSB.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275264

well logs from the North West Shelf in Australia. Fuzzy

logic has also been used to determine hydrocarbon

formation lithofacies and permeability from well log

data in the southern North Sea (Cuddy, 2000). Cuddy’s

results gave near-perfect differentiation among aeolian,

fluvial, and sabkha rock types (the major lithofacies in

several North Sea fields) from basic logs such as gamma-

ray (GR) and porosity logs. The techniques of fuzzy

logic analysis from well logs can be applied to both

consolidated and unconsolidated sediments, as well as

for water applications in oil exploration.

Although conventional geophysical well logging is an

ideal method for hydro-geologic studies involving

aquifer characteristics, such as porosity and hydraulic

conductivity (Temples and Waddell, 1996; Lin et al.,

1997), the identification of aquifer lithology from well

log data depends upon the ability to distinguish between

soils/rocks with grain sizes varying from clay to gravel,

and this method is still largely subjective in the absence

of core data. Well logging also provides in situ and

continuous data, as well as yielding a number of

economic benefits by saving the cost and time of core

analyses. However, well logging is limited because

lithology identification is still a subjective task that

depends largely on the experience of the log analyst.

Identification of hydrocarbon formation lithology

from geophysical logs commonly employs lithology

crossplots (such as ‘‘M–N lithology plot’’ which requires

a sonic log, density log, and neutron log) or the

combination gamma-ray neutron-density log method

(Asquith and Gibson, 1982). However, consideration

must be given to the idea that groundwater aquifers can

be contaminated by the radioactive sources required for

these two types of logs, and the large hydraulic

conductivities might create an adverse environment for

decentralized neutron and density logs (Peng, pers.

comm., 2003). Furthermore, the lithologies involved in

water wells versus oil/gas wells might require different

log suites.

Identification of groundwater (shallow aquifer) for-

mation lithology from well log data largely depends on

expert experience and rather subjective rules, such as,

‘‘IF the natural GR reading is high and the separation in

readings between shallow formation resistivity and deep

formation resistivity is small, then the formation

lithology is probably shale (Chapellier, 1992; Hsieh,

1997). Moreover, groundwater aquifer systems involving

rocks with grain sizes ranging from clay to sand are

often characterized by well logging methods as simply:

sands (including fine-, medium-, or coarse-grained

sands: the major components of an aquifer) and shales

(including silts, clays, and ‘‘muds’’: the major compo-

nents of an aquitard). This type of analysis from well

logging is simple and subjective. One way to reduce this

subjectivity is with the fuzzy logic technique, a type of

artificial intelligence (AI) technology that has been

successfully used to determine hydrocarbon sediment

lithology (Cuddy, 2000). Similar to conventional com-

puterized well log analyses, fuzzy logic allows all

pertinent log data, core analyses, mud analyses, etc. to

be examined simultaneously by the interpreter.

Although the fuzzy logic method uses the same data as

conventional log analysis, it is unlike conventional

analyses which still demands qualitative determination

of lithology. Instead, fuzzy logic adopts a set of rules

insuring objectivity in determination of soil/rock type

whilst incorporating the expertise of the interpreter.

The purpose of this study is to construct a fuzzy

lithology identification system based on the GR log, the

resistivity logs, and the sonic log from the Shui-Lin area

of Taiwan to identify formation lithology of a ground-

water aquifer. The fuzzy logic lithology identification

system can provide a more objective approach for log

analysts in determining lithology in the ‘‘gray areas’’

(areas involving clastic rocks with grain sizes between

sand and shale) of the system of interest.

2. Basic Theory

2.1. Conventional Well Log Analysis

The hydro-physical logs used in this study are: (a) the

GR, (b) borehole compensated sonic (BHC) with sonic

porosity (SPHI) curve, (c) spontaneous potential (SP),

and (d) phasor induction (PI). The PI includes four

curves: medium very-enhanced resistivity (IMER), deep

very-enhanced resistivity (IDER), spherically focused

resistivity (SFLU), and apparent formation water

resistivity (Rwa). The lithologic results of core analysis

were also used in this study. This study limits the

following explanation of conventional well log analysis

basic theory to clastic sedimentary rocks, focusing on

shales and sandstones and the different responses of

logging tools to ‘‘salt water versus fresh water’’ zones.

The following describes the basics of the log types used

in this study to acquaint the general reader.

2.1.1. Gamma-ray (GR) log

The GR log is designed to measure the natural

radioactivity of soils and rocks, and is particularly useful

in distinguishing between shales and sandstones and in

determining depositional environments. Shales usually

exhibit high GR readings if they contain sufficient

quantities of accessory minerals containing isotopes like

potassium (40K), uranium (238U) or thorium (232Th). On

the other hand, sands normally exhibit low GR

responses (Fig. 1).

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Table 1

Average interval transit time and velocity in rocks (after Sheriff and Geldart (1995); Chapellier (1992); Dewan (1983); Asquith and

Gibson (1982))

Lithology Transit time, Dt (ms/ft) Velocity of matrix (ft/s) Velocity of matrix (m/s)

Clays 167–62.5 6000–16,000 1830–4880

Shale 167.6–62.5 5900–16,065 1800–4900

Sandstone 66.7–51.5 15,000–19,500 4575–5950

Limestone 47.6–43.5 21,000–23,000 6400–7015

Dolomite 43.5–38.5 23,000–26,000 7015–7930

Fig. 1. Lithology determination from gamma-ray and resistivity logs.

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275 265

2.1.2. Borehole compensated sonic (BHC) log with

porosity curve (SPHI)

Because of the overlap in velocities between sand-

stones and shales (Table 1), the primary function of a

sonic log is seldom determination of lithology; however,

it can sometimes provide useful information regarding

rock type and porosity, particularly if this log is used in

conjunction with other logs. For clean sandstones

saturated with oil, salt water or fresh water, the sonic

log may give similar responses, but gas usually has a

more pronounced effect on this log. The bulk compres-

sional wave velocity in rocks is also heavily dependent

upon porosity, that decreases the velocity, and the

primary wave velocity may depend upon degree of

consolidation or packing as well. Generally, the velocity

of acoustic waves is slower in clays than in sandstones

(Table 1).

2.1.3. Spontaneous potential (SP) log

The secondary potential or SP log requires a

conductive drilling mud for best results. According to

Asquith and Gibson (1982), ‘‘the magnitude of SP

deflection depends upon the difference in resistivity

between the mud filtrate and formation water, and if

these two fluids have the same resistivity, there is no

deflection of the SP from the shale baseline.’’ Clean

sandstones containing oil, gas and salt water have

negative deflections (with salt waterooilogas), whereas

clean sandstones containing fresh water might have zero

or even positive SP responses. If the formation water is

fresher than the mud filtrate, the curve will show a

positive deflection, with the amount of deflection

proportional to the difference in salinity between the

formation water and mud filtrate.

2.1.4. Phasor induction (PI) log with apparent formation

water resistivity (Rwa) curve

The most useful log in this study for distinguishing fresh

water aquifers from salt water reservoirs is the PI log. It

consists of curves for shallow, medium and deep

resistivities, along with a curve for apparent formation

water resistivity of the uninvaded zone where the

formation water is uncontaminated by mud filtrate.

Although induction logs do not work well in highly

conductive muds, they can be run in holes filled with air,

oil, or freshwater muds. Aquifers tend to be more resistive

than aquitards. For a well drilled with salt water based

drilling mud, the resistivity of the invaded zone, that

consists of rock, mud filtrate, formation water (either salt

or fresh water), and possibly residual hydrocarbons, will

generally be smaller than the resistivity of the uninvaded

zone containing fresh water. For this situation, porous and

permeable sandstones are characterized by a wide separa-

tion between the shallow (invaded zone) and deep

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Fig. 3. Linguistic input variable model. Each linguistic input

variable is constructed from five linguistic terms: VL (very low);

L (low); M (medium); H (high); and VH (very high).

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275266

(uninvaded zone) resistivity curves. On the other hand,

under the same conditions above, a shale would exhibit a

small separation between the shallow resistivity curve and

the deep resistivity curve (Fig. 1). If, however, the drilling

mud is fresh water based, the separation between the

spherically focused (shallow) resistivity curve and the deep

resistivity curve will be considerably less (the invaded zone

resistivity can be approximately equal to that of the

uninvaded zone since both contain fresh water) than if the

drilling fluid were salt water based. The separation between

the two resistivity curves is therefore an important

parameter in lithology determination involving a ground-

water aquifer, provided the type of drilling mud is known.

2.2. Fuzzy lithology system

Fuzzy set theory, a method to distribute linguistic

fuzzy information by mathematics, distributes a set by

using a membership function, and extends the concepts

of classical set theory. Fuzzy logic can be defined as: ‘‘a

logical system that generalizes classical two-valued logic

for reasoning under uncertainty’’ (Yen and Langari,

1999). Therefore, fuzzy logic theory eliminates the

problem of two-valued logic reasoning in classical set

theory (Klir and Yuan, 1995).

The major procedures in a fuzzy lithology system

developed in this study include (i) fuzzification, (ii) fuzzy

‘‘if-then’’ rules database, (iii) fuzzy inference system and

(iv) defuzzification (Fig. 2). During fuzzification, well

log data (such as the GR reading, the separation

between resistivity curves (DR), and the interval transit

time (Dt)) are transformed to linguistic input variables

constructed by linguistic terms and a membership

function. The fuzzy ‘‘if-then’’ rules database contains

several lithology identification rules; the form of

lithology identification rules is constructed by ‘‘if A, B

and C, then D’’ where A, B, C, and D are fuzzy sets.

Fuzzy approximate reasoning is then determined by a

fuzzy inference system. A fuzzy lithology value is

obtained by a defuzzification method, and finally the

lithology of groundwater formation can be determined.

2.2.1. Fuzzification

The fuzzy lithology system in this study contributes

the linguistic variables from the original domain

Fuzzy “if-then”

rules database

Fuzzy inference

system

Fuzzification Defuzzification

Linguistic

input

variables

Well log

reading

Lithology

Fuzzy

lithology

value

Fig. 2. Fuzzy lithology system.

variables. The linguistic input variables include ‘‘GR,’’

‘‘DR,’’ and ‘‘Dt,’’ which are some of the most important

basic parameters in lithology identification of ground-

water formations. Every linguistic input variable in-

volves five linguistic terms, such as very low (VL), low

(L), medium (M), high (H), and very high (VH) as

shown in the trapezoidal membership function (Fig. 3).

The linguistic output variable is ‘‘lithology’’, consist-

ing of five linguistic terms: C (clay), Z (silt), FS (fine

sand), MS (medium sand), and CS (coarse sand). The

reference boundary of the output variable linguistic term

is defined as an ‘‘exponent’’. The grain size range is

presented by an exponential function (of the form 2n,

where ‘‘n’’ is a negative integer) (Table 2). From the

range of grain size, the exponent ‘‘n’’ for the upper and

lower boundaries is adopted to define the reference

boundary of linguistic terms. The membership function

adopted for the linguistic output variable is a trapezoi-

dal membership function (Fig. 4).

2.2.2. Fuzzy ‘‘if-then’’ rules and rule-based database

The rule-based database consists of several general

lithology identification rules. The format of the lithology

identification rule is

If ‘‘GR’’ is A, and ‘‘DR’’ is B, and ‘‘Dt’’ is C, then

‘‘lithology’’ is D.

Where GR, DR, and Dt are linguistic input variables;

‘‘lithology’’ is the linguistic output variable; A, B, C are

linguistic terms of input variables (VL, L, M, H, or VH);

and D are the linguistic terms of output variables (C, Z,

FS, MS, or CS).

The number of lithology identification rules depends

on the training data. For example, if all combinations

between every two input variables are considered, the

rule-based database consists of a total 125 (=53) ‘‘if-

then’’ rules. Therefore, an appropriate reduced rule-

based database must be incorporated into the system

training step.

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Table 2

Grain size range of matrix and reference boundary setting

Linguistic term of output variable Grain size range of matrix (cm) Reference boundary of linguistic term

CS (coarse sand) 204AGS*42�1 [0, �1]

MS (medium sand) 2�14AGS42�2 [�1, �2]

FS (fine sand) 2�24AGS42�4 [�2, �4]

Z (silt) 2�44AGS42�8 [�4, �8]

C (clay) 2�84AGS42�12** [�8, �12]

*AGS=Average grain size.**2�12 represents the value of zero.

Fig. 4. Linguistic output variable ‘‘lithology’’ constructed from

five linguistic terms: C (clay); Z (silt); FS (fine sand); MS

(medium sand); and CS (coarse sand).

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275 267

2.2.3. Fuzzy inference system

A Madani inference system was chosen for this study.

Madani fuzzy inference uses a linguistic reasoning

process that has been extensively applied to engineering

studies (MATLAB, 2001). Because the output variable

in this study is defined by fuzzy sets, the process of fuzzy

reasoning belongs to a type of linguistic reasoning.

Therefore, the Madani inference system is an appro-

priate method for this study.

2.2.4. Defuzzification

The input for the defuzzification process is a fuzzy set

and the output is a crisp set. The purpose is to derive a

crisp value which can represent the result of fuzzy sets in

linguistic output variables. The bisector of area method is

introduced into the defuzzification process (MATLAB,

2001). This method bisects the aggregate output area and

obtains the output crisp value from the center of the area.

3. Case study

3.1. Regional geology

The Shui-Lin area, used for identifying lithologies of a

groundwater aquifer system in this study, is located

southwest of Yun-Lin, Taiwan (Fig. 5). The area is part

of the south branch of the Chou-Shui River alluvial fan

system, whose deposits consist of unconsolidated sand,

silt, and clay from the Chou-Shui River and its

tributaries. The upper section of the alluvial fan consists

primarily of gravel deposits, whereas the lower section

(Shui-Lin area) consists mainly of sand or clay. The

interbedded shale aquitard and the sand aquifer were

deposited because of alternating transgression and

regression. All of the sedimentary formations in the

investigation area are Pleistocene-Recent in age. In the

Shui-Lin area, the shale materials (silt and clay) are

aquitards, and the sands (FS, MS, and CS) are aquifers.

3.2. Data Collection

The geophysical logs from SL-2 well used in this study

(Fig. 6) include the GR log, a PI log consisting of three

‘‘usual’’ resistivity curves (the medium very-enhanced

curve was not used in this study) plus an Rwa curve (not

shown in Fig. 6), and a BHC log with SPHI curve

(porosity curve not shown in Fig. 6). Lithologic types

from core analyses from the SL-monitoring well include

C, Z, FS, MS and CS.

Both the geophysical logs from SL-2 well and the core

analysis lithology from SL-monitoring well represent

continuous data over the depth range from 100 to 198m.

Also, these two wells are located very close to each other

(Fig. 5). The distance between the two wells is about

400m. Because of their close proximity, it is assumed

that their lithologies and depths are equivalent.

4. Procedure

4.1. Data digitization

For the SL-2 wells, log curves were read every 2m for

the depth range from 100 to 198m (drill depths with

ground level equal to 7.1m) and then converted to

digital data sets. A total of 50 data sets were digitized

(Table 3). Every log data set included the GR log, the

SFLU and the IDER curves from the PI log, and the

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Fig. 5. Study area and well locations.

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275268

BHC log. The input parameters used in the fuzzy

lithology system, GR and Dt, were directly taken from

the digitized data of the GR log and the BHC log,

respectively. The other input parameter, DR, is the value

of the IDER (deep) curve reading minus the SFLU

(shallow) curve reading.

According to the core analysis from the Central

Geological Survey of Taiwan, the lithology of the Shui-

Lin area groundwater aquifer includes C, Z, FS, MS,

and CS. In the fuzzy lithology system, the lithology type

must be converted to a crisp set for system mathematical

estimation. A code number from 1 to 5, ranging from

coarse sand to clay, respectively, was assigned for each

lithology (Table 4).

Therefore, the input variables used in the fuzzy

lithology system were ‘‘GR, DR, and Dt.’’ And the

output variable used in the fuzzy lithology system was

‘‘lithology.’’ For the depth interval from 100 to 198m, a

total 50 datasets were collected and digitized (Table 3).

4.2. Data cluster

The 50 data sets were clustered into two parts:

training data sets and test data sets. The training data

sets were used to construct the fuzzy lithology system for

Shui-Lin area by carefully adjusting the fuzzy sets of the

fuzzy input variables, by reducing the fuzzy lithology

rules, and by constructing the rule-based database. The

test data sets were used to validate the ability of system

prediction. Based on the 80/20 rule for the total of 50

data sets, the amount of the training data sets and the

test data sets were 40 and 10, respectively. The following

steps are necessary to extract the 10 test data sets: (1)

arrange all sets in order of increasing depth (Table 3); (2)

choose a random depth value among the 50 data sets

(122m was chosen at random in this study); (3) pick up

the test data sets every 10m spaced in the ‘‘up’’ direction

from the chosen depth value (in this study, the testing

data sets started from 122m by random choice, the 112

and 102m were extracted in the up direction) (Table 3);

(4) pick up the test data sets every 10m spaced in the

‘‘down’’ direction from the chosen depth value (in this

study, based upon the 122m depth selected by random

choice, 132, 142, 152, 162, 172, 182, and 192m were

extracted in the down direction) (Table 3). Step (3)

involving depths of 100, 102, 104, 106 and 108m (chosen

by random) can be ignored because no test data sets can

be found in the ‘‘up’’ extracted direction. Step (4) can be

ignored for depths of 190, 192, 194, 196 and 198m

(chosen by random) because no any test data sets can be

found in the ‘‘down’’ extracted direction.

By the way of test data set extraction, 10 test data sets,

at depths of 102, 112, 122, 132, 142, 152, 162, 172, 182,

and 192m, were extracted. The reason for not extracting

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Fig. 6. Geophysical logs from SL-2 well and core analysis from SL-monitoring well.

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275 269

all test data sets by random is to avoid the test data sets

from becoming too concentrated in some depth intervals.

4.3. Fuzzy lithology system construction

Based on the 40 training data sets, the linguistic input

variables, including ‘‘GR,’’ ‘‘DR,’’ and ‘‘Dt,’’ can be

constructed (Figs. 7–9). Every linguistic input variable is

based on five linguistic terms: ‘‘VL,’’ ‘‘L,’’ ‘‘M,’’ ‘‘H,’’

and ‘‘VH,’’ respectively. The membership function

adopted for linguistic input variable analysis is a

trapezoidal membership function.

The linguistic output variable is ‘‘lithology’’, which is

differentiated by five linguistic terms: C, Z, FS, MS and

CS, respectively (Fig. 4). From the reference boundary

defined (Table 2) and the trapezoidal membership

function, an output fuzzy set, ‘‘lithology,’’ can be

constructed (Fig. 4).

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Table 3

Digitized well log data and resulting lithologies

Depth GR* DR* Dt* Lithology** Depth GR DR Dt Lithology

100 72 10 182 4 150 82 3 177 4

102 67 20 171 3 152 87 11 182 5

104 77 5 176 3 154 88 4 183 5

106 75 9 180 4 156 88 8 184 5

108 78 17 176 4 158 90 6 190 5

110 83 12 179 4 160 79 9 170 4

112 82 14 179 4 162 69 18 165 3

114 79 10 178 4 164 68 21 166 3

116 79 5 174 4 166 82 2 155 4

118 78 13 174 4 168 82 10 174 4

120 81 11 178 4 170 78 9 178 4

122 68 15 180 3 172 74 12 173 3

124 67 16 177 3 174 82 13 170 3

126 72 14 178 3 176 82 10 179 4

128 71 17 177 3 178 83 8 182 4

130 76 14 176 3 180 83 11 176 4

132 77 14 176 4 182 85 13 177 5

134 78 10 178 4 184 79 10 177 4

136 76 11 178 4 186 75 13 171 3

138 83 9 177 4 188 75 23 168 2

140 81 7 182 4 190 73 11 176 3

142 82 7 176 3 192 69 14 175 3

144 68 23 175 3 194 67 12 167 3

146 60 20 177 3 196 53 29 179 1

148 67 14 173 3 198 62 19 178 3

*Digitized well logs: GR: Gamma-ray log reading, API; DR: Value of deep curve reading minus shallow curve reading, O-m; Dt:

Borehole compensated sonic (BHC) log reading, ms/ft.**Lithology abbreviation: 5 (clay); 4 (silt); 3(fine sand); 2 (medium sand); 1 (coarse sand).

Table 4

Lithology code used in fuzzy lithology system

Lithology (Shui-Lin area) Grain size range of matrix (cm) Correlated lithology code

Coarse sand 204AGS42�1 1

Medium sand 2�14AGS42�2 2

Fine sand 2�24AGS42�4 3

Silt 2�44AGS42�8 4

Clay 2�84AGS42�12** 5

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275270

A reduced fuzzy lithology rule-based database was

developed from the 40 training data sets. The rule-based

database contains 12 fuzzy lithology rules (Table 5),

which are all in the form of an ‘‘if-then’’ model. A rule

weighting concept was introduced in this study for

carefully adjusting the rule strength (MATLAB, 2001).

Every rule can define a rule weight, which is a number

between 0 and 1. A rule weight used in this study not

only reflects the strength of the rule, but also expresses

the relative importance between rules.

Fuzzy reasoning for all rules in this study was based

upon a Madani inference system. After the process of

output aggregation, the bisector of area defuzzification

method derives a crisp value which represents the result

of aggregate output area. By using the reference

boundaries for lithology types (Table 2), a crisp set

derived from defuzzification can be converted to a

specific lithology; thus, the lithology of the groundwater

aquifer can be identified from the fuzzy lithology system.

5. Results

By using the 40 training data sets, the specific fuzzy

sets of input variables were constructed. A fuzzy

lithology rule-based database, containing 12 fuzzy

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Fig. 9. Linguistic input variable, Dt, includes five linguistic

terms (for definitions, see Fig. 3).

Fig. 8. Linguistic input variable, DR, includes five linguistic

terms (for definitions, see Fig. 3).

Fig. 7. Linguistic input variable, GR, includes five linguistic

terms (for definitions, see Fig. 3).

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275 271

lithology ‘‘if-then’’ rules with its specific rule weighting,

was established in this study for the Shui-Lin area.

After the training work of the fuzzy lithology system

was completed, the performance of training and the

ability of prediction were validated.

5.1. Performance validation of fuzzy lithology system

training (training results)

The performance validation was employed to check

the system’s training performance by placing all or part

of the training data sets into the trained fuzzy lithology

system. In this study, a total of 40 training data sets were

used to check the performance of system training.

The results of lithology from this fuzzy lithology

system (named ‘‘fuzzy lithology’’) were compared with

the results of lithology from core analysis (named ‘‘true

lithology’’). In Fig. 10, the square marks (also connected

by a line) represent the true lithology, the star marks

represent the fuzzy lithology, the vertical axis shows the

depth interval from 100 to 200m, and the numbers from

1 to 5 on the horizontal axis represent the different

lithologies from CS, MS, FS, Z, and C, respectively.

Thirty-six training data sets were identified correctly

from the total 40 training data sets (Fig. 10), for a

success rate of 90%.

In the performance validation of the system training,

all of the sand types (CS, MS, and FS) were successfully

identified (Fig. 10). Only four layers were not well

trained. Even though the training performance was not

‘‘perfect’’ (success rate of 100%), but, in this study, the

real performance of the system depended on the

predictive ability as well; therefore, an ‘‘appropriate’’

training performance to avoid over-training (means the

system had a perfect training result but poor predictive

ability) was considered. On the other hand, achieving

the best predictive ability of the system was the desired

target.

5.2. Predictive ability of fuzzy lithology system (test

results)

Ten non-trained test data sets were introduced into

the fuzzy lithology system for validating the predictive

ability of the system. Nine test data sets were predicted

correctly from the total 10 testing data sets (Fig. 11) with

90% success. The predictive ability of 90% is considered

high, and only one silt type was predicted incorrectly. It

is possible that heterogeneous and/or anisotropic con-

ditions existed at this depth between the two wells and

resulted in the wrong prediction of the silt zone. Another

possible reason could be due to some factors that were

not considered in this study such as lacking the SP log

information.

6. Discussion

The original well survey of the SL-monitoring well

included the GR log, the short (spacing) normal (16")

resistivity and long (spacing) normal (64’’) resistivity

curves. Because mud recycling was not adopted in

drilling, and the plastic casing was installed quickly to

avoid well collapse in some depth intervals, the logging

data quality was of poor quality to identify lithology.

The vicinity well, SL-2, recycled the mud (GELMUD

consisting of brackish water and bentonite) during

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Table 5

Fuzzy ‘‘if-then’’ lithology rules after fuzzy system training

Rule 1 If GR is VL and DR is VH and Dt is (N/A)* Then Lithology is CS (1)**

Rule 2 If GR is L and DR is H and Dt is (N/A)* Then Lithology is MS (1)

Rule 3 If GR is (N/A)* and DR is H and Dt is M Then Lithology is MS (0.8)

Rule 4 If GR is M and DR is M and Dt is M Then Lithology is FS (1)

Rule 5 If GR is M and DR is M and Dt is L Then Lithology is FS (1)

Rule 6 If GR is (N/A)* and DR is H and Dt is H Then Lithology is FS (0.8)

Rule 7 If GR is H and DR is L and Dt is H Then Lithology is Z (0.6)

Rule 8 If GR is H and DR is M and Dt is H Then Lithology is Z (0.4)

Rule 9 If GR is H and DR is M and Dt is M Then Lithology is Z (0.4)

Rule 10 If GR is VH and DR is L and Dt is H Then Lithology is C (0.4)

Rule 11 If GR is VH and DR is VL and Dt is H Then Lithology is C (1)

Rule 12 If GR is VH and DR is VL and Dt is VH Then Lithology is C (1)

Abbreviation identify: VL (very Low) ; L (low) ; M (medium) ; H (high) ; VH (very high) CS (coarse sand); MS(medium sand); FS(fine

sand); Z(silt); C(clay).

(N/A)*: Rule did not use this component after system training (a reduced rule works here).**The rule weighting value.

Fig. 10. Comparison between true lithology and fuzzy lithology in training period.

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275272

drilling, and the well was logged by Schlumberger

Corporation. The log quality was sufficient to identify

lithology. It should be noted that the mudcake resistivity

(Rmc) and mudfiltrate resistivity (Rmf), both with

values of about 4O-m as determined from the log

header, indicate that the drilling mud in the SL-2 well

was ‘‘just salty enough’’ to act as a conductive fluid for

the SP to operate and to yield sufficient contrast between

the invaded and uninvaded zones, thereby allowing the

Induction Phasor log to operate. Results from the fuzzy

lithology system for the SL-2 well were then correlated

with the core analysis lithologies from the SL-monitor-

ing well in this study.

In the performance validation of the system training,

36 training data sets were identified correctly from the

total 40 training data sets. The training performance was

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Fig. 11. Comparison between true lithology and fuzzy lithology in testing period.

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275 273

90%. In the results of the system prediction ability

validation, nine test data sets were predicted successfully

from the total 10 test data sets. The predictive ability

was 90%, and it is considered high compared to Cuddy’s

(2000) and Fung et al.’s (1997) studies. Another way to

check the prediction accuracy for both training and

testing is based on the coefficient of correlation (Fung et

al., 1997). A high value of the coefficient of correlation

means the system results have high correlations to the

original core data. In this study, the calculated training

correlation was 0.925, and the calculated testing

correlation was also high (up to 0.928). In the (Fung

et al.’s (1997) study, the best training correlation was

0.917, and the best testing correlation was 0.865.

Compared with their results (even though they had a

different output variable to be ‘‘porosity’’) we can

conclude that the prediction accuracy of our fuzzy

lithology system is acceptable.

The lithologic results from core analysis, well logging

and fuzzy lithology are compared in Fig. 12, in which

the three major columns represent lithologies from the

three methods. The groundwater formations between

100 and 198m (drill depths) in the SL-2 well were

divided into either sands or shales based on conven-

tional well logging analysis of the log curve shapes and

two basic rules:

(Rule 1) IF the GR reading is low, IF the separation

of deep and shallow resistivity curves (DR) is wide, and

IF the interval transit time (Dt) is short, THEN the

lithology of the formation is sand.

(Rule 2) IF the gamma-ray GR is high, IF the

separation of deep and shallow resistivity curves (DR) is

narrow, and IF the interval transit time (Dt) is long,

THEN the lithology of the formation is shale.

The words used in the above sentences, low and high,

mean the relative degree of GR reading. Usually,

maximum values of GR readings are used to infer a

shale base line, and minimum values will be used to set

up a sand base line. The word ‘‘low’’ means close to the

sand base line, and the word ‘‘high’’ means close to the

shale base line. The words ‘‘wide and narrow’’ refer to

the relative degree of separation between the deep and

shallow resistivity curves. The word ‘‘wide’’ means the

value is close to the maximum separation for the given

depth interval, and the word ‘‘narrow’’ is just the

opposite. Also, the words ‘‘short and long’’ refer to the

relative values of the interval transit times measured in

BHC log.

The well logging method can easily delineate a

permeable sand formation from log characteristics

(Fig. 12), but identification of silts and determination

of sands with varying grain sizes (from coarse to fine)

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Fig. 12. Lithology results: comparison of core analysis, well logging, and fuzzy system.

B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275274

are more subjective and difficult. This shortcoming can

be improved by our fuzzy lithology system analysis.

This study’s lithology system included C, Z, FS, MS,

and CS, all of which are common in Shui-Lin area.

Because gravels are not found in the depth range from

100 to 198m in this area, they were omitted. On the

other hand, this fuzzy lithology system cannot recognize

a gravel lithology because the system did not include any

experience while system training. In this case, the fuzzy

lithology system is not appropriate for gravel formations

ARTICLE IN PRESSB.Z. Hsieh et al. / Computers & Geosciences 31 (2005) 263–275 275

(like those close to the upper section of the Choushui

River alluvial fan). Furthermore, this study involves a

‘‘clastic’’ aquifer rather than a ‘‘carbonate’’ aquifer;

however, some studies have developed similar method

can be applied to carbonate reservoirs (Chang et al.,

1997; Cuddy, 2000). This might be of interest to middle-

Eastern oil field analysts.

7. Conclusions

A fuzzy lithology system based on well logs from the

Shui-Lin area of Taiwan was constructed for identifying

formation lithology with varying grain sizes of a

groundwater aquifer in this study. The specific fuzzy

sets of input variables were established, and a fuzzy

lithology rule-based database containing 12 fuzzy

lithology ‘‘if-then’’ rules with its specific rule-weighting

was formulated for the Shui-Lin area. The conclusions

are:

(1)

The prediction accuracy of fuzzy lithology system

was fairly good (‘‘90%’’ for predictive ability and

‘‘90% or better’’ for the coefficient of correlation)

based on the results of the testing performance, and

the calculated coefficient of correlation of training

and testing.

(2)

The compared lithologic results by core analysis,

well logging and fuzzy lithology show that the

conventional well logging method can easily distin-

guish a permeable sand formation from log char-

acteristics, but identification of silts and

determination of sands with varying grain sizes are

more subjective and difficult. As illustrated in this

research, our fuzzy lithology system can improve the

definition of grain size. Although there is some

subjectivity in the fuzzy lithology system, it enables

the log analyst to make a more objective final

decision than by conventional well log analysis.

(3)

This methodology can be particularly useful for

large aquifers involving multi wells where only a few

core analyses are available.

Acknowledgments

The authors thank Chinese Petroleum Corporation of

Taiwan for supplying logs from the SL-2 well. We

appreciate the core analyses furnished by Central

Geological Survey of Taiwan, and the groundwater

aquifer information in the Shui-Lin area from the

groundwater monitoring network set up by Water

Resources Agency, Ministry of Economic Affairs,

Taiwan. We also give special thanks to John Doveton

and an anonymous reviewer for their valuable review

comments that made our study more integrated.

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