lithology identification of aquifers
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Lithology identification of aquifersTRANSCRIPT
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Computers & Geosciences 31 (2005) 263–275
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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: [email protected] (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 systemwas 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 forlarge 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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