ishola et al pure and applied geophysics 2014

7/24/2019 Ishola Et Al Pure and Applied Geophysics 2014

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See discussions, stats, and author profiles for this publication at:http://www.researchgate.net/publication/275670745

Combining Multiple Electrode Arrays for

Two-Dimensional Electrical Resistivity

Imaging Using the Unsupervised

Classification Technique

ARTICLE in PURE AND APPLIED GEOPHYSICS JUNE 2015

Impact Factor: 1.62 DOI: 10.1007/s00024-014-1007-4

READS

53

3 AUTHORS:

Kehinde S. Ishola

University of Science Malaysia

7PUBLICATIONS 1CITATION

SEE PROFILE

Mohd Nawawi


55PUBLICATIONS 70CITATIONS

SEE PROFILE

Khiruddin Abdullah


219PUBLICATIONS 176CITATIONS

SEE PROFILE

Available from: Mohd NawawiRetrieved on: 01 November 2015
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Combining Multiple Electrode Arrays for Two-Dimensional Electrical Resistivity ImagingUsing the Unsupervised Classification Technique

K. S. ISHOLA,1,2 M. N. M. NAWAWI,1 and K. ABDULLAH1

AbstractThis article describes the use ofk-means clustering,

an unsupervised image classification technique, to help interpret

subsurface targets. Thek-means algorithm is employed to combine

and classify the two-dimensional (2D) inverse resistivity models

obtained from three different electrode arrays. The algorithm is

initialized through theselection of the number of clusters, numberof

iterations and other parameters such as stopping criteria. Automat-

ically, it seeks to find groups of closely related resistivity values that

belong to the same cluster and are more similar to each other thanresistivity values belongingto other clusters. The approach is applied

to both synthetic and field data. The 2D postinversions of the

resistivity data werepreprocessed by resamplingand interpolating to

the same coordinate. Following the preprocessing, the three images

are combined into a single classified image. All the image prepro-

cessing, manipulation and analysis are performed using the PCI

Geomatics software package. The results of the clustering and

classification are presented as classified images. An assessment of

the performance of the individual and combined images for the

synthetic models is carried out using an error matrix, mean absolute

error and mean absolute percent error. The estimated errors show

that images obtained from maximum values of the reconstructed

resistivity for the different models give the best representation of the

true models. Additionally, the overall accuracy and kappa values

show good agreement between the combined classified images and

true models. Depending on the model, the overall accuracy ranges

from 86 to 99 %, while the kappa coefficient is in the range of

5498 %. Classified images with kappa coefficients greater than 0.8

show strong agreement, while images withkappa coefficients greater

than 0.5but less than 0.8give moderate agreement. Forthe field data,

the k-mean classifier produces images that incorporate structural

features of the three electrode array configurations. Consequently,

some clusters that overwhelmingly correspond to the lithologic units

of the investigated areas are better identified than the tomographic

images of each data set considered separately, underscoring the

relevance of the unsupervised classification technique in this study.

Key words: Unsupervised classification, electrode arrays,

k-means clustering, clusters, overall accuracy, lithologic units.

1. Introduction

In geophysical investigations involving hydroge-

ology, subsurface exploration, mining, geotechnical

and archaeological prospecting, electrical resistivity

imaging has remained a vital tool for some decades

(DAHLIN 1996; SEATON and BURBEY 2000; CANDANSA-YAR and BASOKUR 2001; LOKE et al. 2013). The

advancements made in the use of this tool by

allowing resistivity data to be collected and processed

in a short period of time using a suitable electrode

array are worthy of commendation. This is coupled

with the advent of multielectrode resistivity recording

systems that have popularized the use of electrical

resistivity imaging. However, one of the problems of

resistivity investigations is the choice of a suitable

electrode configuration that will give the best

response to the observed targets in the subsurface

(ZHOU and GREENHALGH 2000; ZHOU and DAHLIN

2003). Several electrode arrays have been used in

resistivity investigations, including, but not limited

to, the Wenner, Wenner-Schlumberger, dipole-

dipole, pole-pole and pole-dipole arrays (DAHLIN

1996; CHAMBERS et al. 1999; STORZet al.2000). Each

electrode array has its advantages and limitations

regarding field operations and interpretation capabil-

ities (LOKEet al.2003; DAHLINand ZHOU2004; ABER

and MESHIN CHIASL 2010). Also, the depth of inves-tigations (ROY and APPARAO 1971; BARKER 1989;

OLDENBURG and LI 1999; SZALAI and SZARKA 2008),

sensitivity to horizontal or vertical variations, and

signal strength (LOKE 2001; SEATON and BURBEY

2002; DAHLIN and ZHOU 2004; CANDANSAYAR 2008)

are some of the other factors needing to be taken into

consideration in using these arrays. In addition, the

geological structures to be mapped, heterogeneities of

the subsurface, sensitivity of the resistivity meter

1 Geophysics section, School of Physics, Universiti Sains

Malaysia, 11800 Pulau Pinang, Penang, Malaysia. E-mail: saidi-

[email protected]; [email protected];

[email protected] Department of Geosciences, University of Lagos, Akoka,

Lagos, Nigeria.

Pure Appl. Geophys.

2014 Springer Basel

DOI 10.1007/s00024-014-1007-4 Pure and Applied Geophysics


3/29

(FURMAN et al. 2003), sensitivity of the arrays to

vertical and lateral variations in the resistivity of the

subsurface, horizontal data coverage and signal

strength of the array (DAHLINand ZHOU2004) should

be considered before embarking on field surveys.

In conducting an electrical resistivity survey over

a noisy site, the Wenner array is preferred because of

its high signal strength and high resolution of hori-

zontal structures, but it is less easily applicable when

mapping 3D structures where the dipole-dipole, pole-

dipole and pole-pole arrays are given preference

(DAHLINand LOKE1997; ZHOUand DAHLIN2003). The

Wenner array also has a good vertical resolution, thus

making it suitable for imaging horizontal structures

(IBRAHIMet al.2003). The dipole-dipole array is most

sensitive to resistivity variations beneath the elec-

trodes in each dipole length and is very sensitive tohorizontal variations. The dipole-dipole array is rel-

atively insensitive to vertical variations in the

subsurface resistivity (GRIFFITHS and BARKER 1993).

As a result, the dipole-dipole array is given priority

for mapping of vertical structures such as dykes and

cavities (LOKE 2001; EL-QADY et al. 2005). In prac-

tice, electrical resistivity imaging involves the use of

either four electrode arrays (e.g., the Wenner Sch-

lumberger and dipole-dipole) or the three electrode

type typical of the pole-dipole with a polarity-

reversed array for all possible currents and potential

electrode combinations. To gain knowledge of the

relative potentials of these electrode arrays, several

researchers have worked in this direction. SZALAI and

SZARKA (2008) classified about 100 electrode arrays

into eight classes based on three parameters; they are

superposition, focusing and collinearity. Also, STUM-

MERet al.(2004) opined that electrical resistivity data

acquired using a large number of four-point electrode

arrays gave substantial subsurface information com-

pared to the data sets obtained from both individualarrays, such as the Wenner, dipole-dipole or a com-

bination of the Wenner and dipole-dipole arrays.

Moreover, DE LAVEGAet al.(2003) used a combined

inversion algorithm for different electrode array data

sets with the combined inversion images outper-

forming the inversion results obtained from separate

electrode arrays. ATHANASIOUet al.(2007) introduced

a weighting factor to the two-dimensional (2D)

combined inversion algorithm, which prevented the

dominance of one array type over another as the

applied parameter allowed equal participation of the

data from an individual array.

In previous studies, attempts have been made at

comparing the ability of different electrode arrays to

resolve, map or identify subsurface targets (SEATON

and BURBEY 2002; DAHLIN and ZHOU 2004; CAN-

DANSAYAR 2008). Several researchers have compared

different electrode arrays individually on the basis of

their sensitivity analysis, depth of investigations, and

responses to resolving vertical or horizontal struc-

tures (SASAKI 1992; DAHLIN 2001; BENTLEY and

GHARIBI 2004; FIANDACA et al. 2005; CAPIZZI et al.

2007; BERGE and DRAHOR 2009; MARTORANA et al.

2009; NEYAMADPOUR et al. 2010; RUCKER 2012).

Meanwhile, in related studies, the use of joint

inversion techniques have been introduced and usedfor combining two or more geophysical data into a

single image for the cross gradients (GALLARDO and

MEJU 2003, 2004, 2007) and structural approach

(HABER and OLDENBURG 1997). The efficacy of the

joint inversion method hinges on the complementary

nature of the geophysical data sets (DOETSCH et al.

2010). In addition, concerted efforts have been geared

toward optimizing different electrode arrays for

electrical resistivity surveys in order to obtain as

much information as necessary in the detection and

imaging of subsurface structures within a short period

of time (STUMMER et al. 2002,2004; WILKINSONet al.

2006a, b; COSCIA et al. 2008; LOKE et al. 2010; HA-

GREY and PETERSEN 2011; HAGREY 2012). In view of

this, COSCIA et al. (2008) proposed an experimental

design method involving an independent comparison

between the information provided by one electrode

array with others using crosshole electrical resistivity

imaging. In another work, LOKEet al.(2010) adopted

four methods to automatically select an optimal set of

array configurations that provided maximum subsur-face model resolution for an electrical imaging

applied to both synthetic and field surveys.

In the present study, however, we focus on the

combination of the 2D post-inversion resistivity

models from three different electrode arrays, namely,

the dipole-dipole (Dpd), Wenner-Schlumberger

(Wsc) and pole-dipole (Pdp), reflecting a wide range

of geological situations, using an unsupervised image

classification technique. To this end, the capability

K. S. Ishola et al. Pure Appl. Geophys.


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and functionality of an image processing technique

are explored to generate a single integrated image for

both synthetic and real-field examples.

In this article, we present a review of the different

electrode arrays used in electrical resistivity imaging

with emphasis on the advantages and their limita-

tions. Also, a technique for combining the images

from some commonly used electrode array configu-

rations is mentioned. The remainder of the article is

organized into the traditional theoretical background,

method, results and discussion followed by directions

for further work. In Sect. 2, we introduce the image

classification technique, which emphasizes two broad

groups of classification techniques. Section3 dis-

cusses the methodology, which includes numerical

modeling, merging of post-resistivity inversion data

sets, clustering and classification procedures. Also,the other aspects of the methodology presented are

the assignment of resistivity to the classification

images and criteria for evaluating the accuracy of the

clustering technique. Section4presents the results of

the application of the clustering technique to both

synthetic and field examples. In addition, the dis-

cussion section interprets the results, and suggestions

for continued research are provided.

2. Image Classification Techniques

Mechanistically, image classification is a process

that translates the raw data into more meaningful

and understandable forms (TSO and OLSEN 2005).

The image classification technique involves cluster-

ing the pixels of an image, where a pixel is the

smallest unit of digital image data that can be

individually processed, into a relatively small set of

clusters, such that pixels in the same class have

similar statistical properties. Image classificationrelies on distinctive signatures or spectral contents

of the classes as well as the ability to reliably dis-

tinguish these signatures from others (EASTMAN

2003). The image classification techniques stand out

from other data integration methods, such as artifi-

cial neural networks, self-organizing maps and joint

inversion methods, to mention but a few. This is

because of its predictive abilities (KVAMME 2006) in

subsurface target detection using scattered fields

(CHATURVEDI and PLUMB 1995). In the joint inversion

method, an external constraint is imposed on the

models (e.g., PRIDE 1994; TRYGGVASON et al. 2002;

LINDE et al. 2006; LINDE and DOETSCH 2010) as the

approach seeks an existing empirical or mathemati-

cal relationship between the models, whereas the

image classification technique looks for a natural

grouping/pattern in the data sets.

Generally, image classification can be grouped as

either supervised or unsupervised classification, and

both groups are used especially in remote sensing

for image analyses. In supervised classification, the

pixel classes are controlled by the analyst through

the process of selecting training sites in advance in

order to train the classifier (CAMPBELL 2002; TSO and

OLSEN 2005). On the other hand, unsupervised

classification works by objectively extracting variousfeatures of an image. The detailed information

derived from an image is guided by the number of

clusters into which the image is partitioned. The

preference of unsupervised over supervised classifi-

cation schemes in this study is a result of knowledge

of the site to be classified being immaterial at the

initial separation of the image pixels. Meanwhile,

the classification process is less prone to human

error as an analyst is not at liberty to make as many

decisions during the classification process and the

classes in the data are not overlooked (LILLESAND

and KIEFER1994; EASTMAN 1995; ENDERLE and WEIH

2005).

Among the commonly used algorithms for parti-

tioning of image data sets in unsupervised

classification techniques are the k-means, iterative

self-organizing data analysis (ISODATA) and fuzzy

c-means. The ISODATA algorithm is similar to the k-

means with the distinct difference that it allows for

the minimum-maximum number of clusters, while

the k-means assumes that the number of clusters isknown a priori. On the other hand, the fuzzy c-means

is an alternative way of assigning data to specific

clusters with an absolute in or out value based on

degree of membership of the data into clusters (WARD

et al.2014). Each of the clustering algorithms uses an

iterative procedure for organizing objects into a pre-

defined fixed number of clusters while attempting to

optimize the distance between the observational data

set and cluster centers (CHENG 2003; KHAN and

Combining Multiple Electrode Arrays


5/29

AHMAD 2004). Thus, unsupervised classification

techniques partition data sets into clusters by ensuring

that intercluster variability is maximized and mini-

mizing intraclass variability without recourse to field

knowledge (LILLESANDand KEIFER2000).

2.1. The k-means Clustering Algorithm

Thek-means is a clustering algorithm (MACQUEEN

1967) that partitions multidimensional pixels in the

model space of the image, usually in a vector form

into prespecified k clusters. In the context of this

study, the clusters consist of resistivity values, and

the grouping is performed such that pixels within a

cluster are similar (i.e., intracluster variability) and

are dissimilar from pixels belonging to another

cluster (i.e., intercluster) with each cluster repre-sented by cluster centers. Thus, clustering techniques

are popularly used for finding interesting features or

patterns in a data set that may not be obvious (RANA

et al. 2010).

The theoretical background of the k-means algo-

rithm is as follows: suppose there are N input data

points such thatx1; x2; . . .; xm2 Rn is a finite number

of patterns existing in the model space of the model;

then the k-clustering aims at partitioning these data

points into kdisjoint subsets or clusters C1; . . .; Ck;

withk\Nsuch that optimization is performed based

on the clustering criterion. The criterion used for the

optimization is the sum of the squared of Euclidean

distances between each data point, xi, and the cluster

center, mk, of the subset Ck, which contains xi. This

optimization criterion is called the clustering error,

and it depends on the cluster centers m1, , mk. At

the k-th iterative step, the N observations are

partitioned into k clusters using the relation,

x2 Cjk,

provided x mjk \ x mikk k 1

for all i 1; 2; . . .; k; i 6j, where Cjk denotes the

set of observations whose cluster center is mj(k). In

the next step, a new cluster center mjk 1; j

1; 2; . . .; k is computed such that the sum of the

squared distances from all points (pixels) in Cj(k) to

the new cluster center is minimized. A measure that

minimizes this is the observation mean ofCj(k). Thus,

the new cluster center formed is given by:

mjk 1 1

Nj

Xx2Cjk

x; j 1; 2; . . .; k 2

where Nj is the number of pixels in the image. The

cluster centers are reference points used by the algo-

rithm to group the observation data points (pixels) into

clusters. The cluster centers, also called centroids, are

computed as the average of the observations in a

particular cluster. Being a point-based algorithm, the

k-means starts with the cluster centers that are initially

placed at arbitrary positions and proceeds by moving

the cluster centers at each step so that it minimizes the

clustering error. For clustering of the data set, a large

number of dimensions contains more information, and

the clusters obtained tend to increase with increasing

dimensionality in the data set.

The k-means algorithm calculates its clustercenters iteratively by initializing the centers in mkand decides membership of the pixels in one of thek-

clusters according to the closest neighbor, i.e., the

minimum distance from the cluster center. Then, it

calculates the new mkby repeating the steps above

until there are no changes in the cluster centers. Thus,

the goal is to minimize the sum of squares error

within each cluster represented by its Euclidean

distance as:

dx; mk XNi1

Xmj1

xi mj 2

3

where kk2 is a measure of the minimum distance

between a pixel, xi, and the cluster center, mj. In

Eq.3, high membership values are assigned to pixels

that are close to the cluster center for a particular

cluster, while low membership values are assigned to

pixels that are far from the centroid (PHAMand PRINCE

1999).

2.2. Selection of the Number of Clusters

In most clustering situations, an important step in

the implementation of the clustering procedures is to

specify the number of clusters into which the image is

to be partitioned. In this regard, an analyst is faced

with the dilemma of selecting the number of clusters

or partitions in the final solution as there is no

existing benchmark in the literature regarding the

selection of an optimal number of clusters. To



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overcome this nagging problem in clustering, a

variety of procedures has been proposed and used

for determining the number of clusters in data sets

(MILLIGAN and COOPER 1985; HALKIDI et al. 2001;

KVAMME 2006; WARD et al. 2014). Doing so will

assist in the final interpretation of the classification

image. In practice, the appropriate number of clusters

for a given data set is based on trial and error. The

subjective nature of deciding what constitutes correct

grouping by this method makes the selection difficult.

Another approach is to run the clustering algorithm

many times with the number of clusters gradually

being increased from a certain initial value to some

threshold values and the partitioning of data resulting

in the best validity measure being selected (HALKIDI

et al. 2001). WARD et al. (2014) used the number of

peaks obtained from the application of the kerneldensity estimation method to the data set to provide a

statistically grounded analysis of the data that in turn

was assumed to represent the appropriate number of

clusters required to group the data.

Grouping of the pixels into a few prespecified

clusters could result in a loss of important details

about the models during clustering of the data sets. In

order to ensure at the outset that no important

information in the image data sets is ignored,

clustering is often prepared with a large number of

clusters to reflect the specific characteristics of the

data sets (CIHLARet al. 1998; PHAMet al. 2004; GAO

2009). However, using a large number of clusters also

poses a problem, as too many details that could give

irrelevant interpretations of the targets may be

created (FIGUEIREDO and JAIN 2002; ERNENWEIN

2009). Therefore, finding an optimum number of

clusters in a data set could be very challenging since

it requires a priori knowledge of the data in some

cases. The performance of the k-means clustering

algorithm in terms of adequate interpretation of theclassification image depends on the selection of an

optimal number of clusters, types of attributes (i.e.,

measured parameters), types of data sets and scales of

attributes.

2.3. Stopping Rules of the k-means Algorithm

The convergence of the k-means algorithm is

guided by the cost function or sum of the square

error, which reduces to a local minimum. At this local

minimum, the correct number of cluster centers

converges into an actual cluster center as other initial

centers move away from the input data set (ZALIK

2008). A satisfactory clustering result is obtained

when the number of iterations as a prerequisite is

indicated before the user/analyst runs the algorithm.

A number of convergence conditions are possible in

the execution of clustering algorithms. These include:

(1) the search may stop when a given or defined

number of iterations is reached, (2) stopping when the

partitioning error is not reduced because of the

relocation of the centers is an indication that the

partition is locally optimal, (3) when there is no

exchange of data points between clusters, exceeding a

predefined number of iterations, and (4) when a

threshold value is attained. This convergence thresh-old corresponds to the maximum percentage of pixels

whose clusters remain unchanged from the previous

iteration (REIGBERet al. 2010; LI et al. 2013). At this

stage, the clusters are saved as the best cluster

solution for the clustering. Also, the threshold

parameter, T, typically a specific value, is stated or

selected by the user. Thek-means algorithm based on

a user-supplied parameter can modify the threshold

value by either increases or decreases depending on

the number of clusters required to represent the data

set.

3. Methodology

Subsurface imaging over a target using different

electrode configurations produces tomographic mod-

els of the target. Each inverse resistivity image gives

different information about the investigated area.

This is due to nonuniqueness in the inversion process

leading to ambiguity in the interpretation of theresults. To reduce the ambiguity, there is a need for

all the information from the different electrode con-

figuration images to be integrated into a single image.

To this end, an unsupervised classification technique

using the k-means algorithm that automatically par-

titions the 2D inverse resistivity model data sets into

some prespecified number of clusters with each

cluster linked to a particular geological or hydro-

geological (i.e., electrofacies) unit that makes up the



7/29

resistivity image is employed. The procedure used in

this study can be grouped into four stages: (1)

numerical modeling, (2) clustering and classification

procedures, (3) assignment of resistivity and (4)

accuracy assessment.

3.1. Numerical Modeling of Synthetic Data

3.1.1 Forward Modeling

The synthetic models used in this study were created

through forward modeling. Forward modeling, also

known as the forward solver, involves a mapping

from the model space to the data space (SCHWARZBACH

et al. 2005). Forward modeling estimates/predicts

data on the basis of the known distribution of model

parameters and electrode configuration used. Theforward modeling for the DC potentials is accom-

plished using a finite difference (FD) technique to

solve the partial differential equation for charge

distribution. The program that performs this calcula-

tion is the RES2DMOD software package (GEOTOMO

2005). This forward solver is used to calculate the

apparent resistivity data for a user-defined 2D

subsurface model (i.e., it computes the electric

potential difference for a particular resistivity model).

In the FD approach, a resistivity model of the

subsurface is first discretized into several rectangularmesh or grids. Then, the FD method determines the

potentials at the nodes of the rectangular mesh in both

directions. The DC resistivity forward modeling was

performed with the synthetic data shown in Fig. 1ae

generated over the 2D resistivity structures. The

potential differences were computed for the three

electrode arrays, namely the Wenner-Schlumberger

(Wsc), dipole-dipole (Dpd) and pole-dipole (Pdp)

arrays. In all the simulations, 40 surface electrodes at

an electrode spacing of 1 m were used.

In this study, five synthetic models were used to

simulate a typical field survey and test the image

classification approach for the integration of different

electrode arrays images. These include:

1. A resistivity block prism (target) with a resistivity

value of 500 X-m (light blue) embedded in a

homogeneous medium of 10 X-m (deep blue)

(Fig.1a).

2. Two resistivity blocks having resistivity values of

100 X-m (green) and 300 X-m (orange) embedded

in a homogeneous medium of 10 X-m (deep blue)

(Fig.1b).

3. Three blocks with resistivity values of 100 X-m

(left), 300 X-m (middle) and 500 X-m (right) all

embedded in a homogeneous background of 10 X-

m (Fig.1c).

4. A vertical fault juxtaposing a conductive top layer

(hanging wall) with resistivity of 10 X-m (blue)

and a resistive bottom layer (foot wall) with

resistivity of 100 X-m (green) (Fig.1d)

5. A resistivity dyke of 500 X-m (light blue)intruding in a homogeneous background 100 X-m

(green) (Fig.1e).

3.1.2 Inverse Modeling

The determination of the model parameter (i.e.,

resistivity estimates) using the data space and model

space is known as inversion. Unlike forward model-

ing, inverse modeling is the mapping from the data

space to the model space (OLDENBURG and ELLIS

1991). Inversion is used to reconstruct the subsurface

resistivity distribution from the measurements of

voltage and current data. Inversions of the apparent

resistivity data sets from forward modeling were

carried out using the commercially available

RES2DINV software (GEOTOMO 2005). During the

inversion process, 5 % Gaussian noise was added to

reflect field conditions. The inversion of the apparent

resistivity data from forward modeling into 2D

resistivity models was carried out using RES2DINV,

a commercially available inversion program. Thissoftware program uses two different inversion rou-

tines for the generation of earth models from the

resistivity data. The inversion routines are based on

the blocky or L1-norm optimization (LOKE et al.

2003) and Gauss-Newton smoothness-constrained

least-squares method for L2-norm optimization (DEG-

ROOT-HEDLIN and CONSTABLE 1990; ELLIS and

OLDENBURG 1994). The L1-norm optimization method

Figure 1Synthetic resistivity models used for stimulation of a a resistive

block,b two resistive blocks, c three resistive blocks, d a vertical

fault and e a resistive dyke

c



8/29



9/29

allows earth resistivity models with relatively sharp

variations across boundary resistivity to be recon-

structed as it tries to minimize the sum of absolute

values of the models resistivity. It is a better

optimization choice when geological discontinuities

are expected (SEATON and BURBEY 2002; LOKE et al.

2003). On the other hand, the L2-norm based on the

least-squares optimization method attempts to mini-

mize the sum of squares of the spatial variations in

the resistivity of the models and the data misfit

leading to earth resistivity models with gradual

transitions across zones of different resistivities

(LOKE et al. 2003). Although the default inversion

routine used by this program is based on an L2-norm,

both optimization techniques were used initially, but

the L2-norm was observed to have smearing effects

on the boundaries (LOKE et al. 2003) of the models.As a result, the L1-norm was preferred throughout the

inversion process in the synthetic examples.

3.1.3 Regularization Parameters

Inverse problems are ill posed because of the

nonuniqueness resulting from sparse noisy data and

the need to finely parameterize the earth so that

enough variation is allowed in the solution (MEJU

1994; HABER and OLDENBURG 2001). To overcome ill-

posedness in the inversion, regularization schemesare usually applied (DOESTCH et al. 2010). Examples

of the regularization constraints that allow for

stabilization of the inversion process are damping

and smoothing (BLOME et al. 2011). The common

perspectives in these regularization schemes are that

the data are given and inversion should produce a

single model that fits the data (ELLIS and OLDENBURG

1994). A 2D earth model is parameterized by means

of a grid of rectangular prisms, each having a uniform

resistivity. As a tradition, each block is made smaller

than the data resolution length so that the position of

the block boundaries does not affect the final model.

The regularization parameter is a trade-off between

data misfit and model roughness as a large value

results in a smooth model and weak data misfit, while

a small value leads to a highly rough model with

good data misfit (TIKHONOVand ARSENIN 1977; LOKE

et al. 2003). Several methods exist to compromise

data misfit and model constraints (FARQUHARSON and

OLDENBURG2004). In order to obtain a solution for the

inverse problem, an important factor to consider is

the damping factor (k), which depends among other

factors on the distribution of the resistivity data.

An estimation of the damping factor is based on

the trial and error method (LOKE and BARKER 1996;

OLAYINKAand YARAMANCI 2000). The selection of an

appropriate damping factor is important for subsur-

face imaging inversion in order to avoid local

minima. Using low damping values could lead to

low data misfit, but produce high instability in the

values of the estimated resistivity between adjacent

cells; this in turn could result in erroneous assump-

tions of the model resistivity in the area under study

(LOKEet al.2010). To establish an optimum value of

the damping factor that gives the best inversion

results after successive iterations, OLAYINKA andYARAMANCI (2000) suggest the use of a damping

factor in the range of 0.050.25 with a 20 %

increment between successive iterations. Also, Eas-

ton (1987) opined that higher damping values should

be used at the beginning and lower the damping

values on subsequent iterations.

In this article, the suggestion provided by OLAY-

INKA and YARAMANCI (2000) in respect to the

value(s) for the damping factor for models inversions

was adopted. The inversions were carried out with an

initial damping factor of k =0.25, which was

reduced to a minimum of 0.015 after successive

iterations. Tables1and2display the data points for

the three electrode arrays used for providing infor-

mation about the inverse models and parameters used

for the resistivity inversion with the RES2DINV

software package, respectively. The propagation

factor, n, for the dipole-dipole array increases from

1 to 6 (Table1). It is advisable not to use n values

greater than 6 for the dipole-dipole array in order to

increase the depth of investigation because of theweak signal strengths of this array (LOKE 2009).

Table 1

Modeling parameters for the three electrode arrays used

Parameter/electrode array Dpd Wsc Pdp

Number of data points 308 253 319

Number of model layers 6 8 8

Number of blocks 178 204 240



10/29

3.2. Assignment of Resistivity Without Clustering

The reconstructed inverse resistivity values of the

three electrode array configurations were combined

using Eqs.4,5,6and7. This combination yields four

new images (i.e., minimum, maximum, median and

average), which are illustrated as:

Rminxi;yi minRdpd;Rwsc;Rpdp 4

Rmaxxi;yi maxRdpd;Rwsc;Rpdp 5

Rmedxi;yi medRdpd;Rwsc;Rpdp 6

Ravgxi;yi Rdpd Rwsc Rpdp

3

7

where Rdpdxi;yi; Rwscxi;yi andRpdpxi;yi are the

resistivity values for the dipole-dipole, Wenner-Sch-

lumberger and pole-dipole electrode arrays. Also, for

the models images, the mean resistivity values

denoted by Rmax, Rmin, Rmed and Ravg for the maxi-mum, minimum, median and average images,

respectively, were assigned to the blocks and back-

ground of the models.

3.3. Clustering and Classification Procedures

The 2D post-inverse resistivity models saved in

text files format, i.e., as xyz, where x represents the

electrode position,y is the depth of investigation, and

z represents the resistivity values, were exported into

an image-processing environment using the PCI

Geomatics software for further manipulations and

analysis. The PCI Geomatics used throughout this

article has a variety of functionality that enables users

or analysts to get more from imagery in support of a

wide range of geospatial applications. It is used in the

remote sensing environment for imagery processing,

geographic information systems and photogrammetry

(PCI2001).

To implement the k-means algorithm, the follow-

ing input parameters were used in addition to the

three input images from the electrode configurations:

(1) the number of clusters, which is usually a priori

defined, was 16. To avoid the difficulty in the

selection of an appropriate number of clusters, in this

article the prior information obtained during the 2Dinversion process was used to specify the number of

clusters, k, for the clustering. By this an objective

evaluation measure to suggest suitable values for the

number of clusters, thus avoiding the need for trial

and error, is implied. Moreover, the use of prior

knowledge from the inversion results provided an

automatic decision rule eliminating the problems of

human subjectivity. This was to ensure that adequate

information needed for the interpretation of the

model was obtained: (2) the stopping criteria (i.e.,

the number of iterations and the convergence thresh-

old were set to 20 and 0.01, respectively). After

convergence, thek-means algorithm creates an output

image file with a thematic raster layer as a result of

clustering, and this is stored in the PCIDSK program.

The PCIDSK is a data structure for holding images

and related data. When this convergence threshold is

attained, the program terminates. Prior to classifica-

tion of the combined images, we masked the region

of the models images that did not have data points

manually. This was necessary to ensure that only thecoregistered part of the images was classified.

3.3.1 Assignment of Resistivity to Clusters

Each cluster formed is associated with three resistiv-

ity values from the three electrode array

configurations. These resistivity values are denoted

by Rc1, Rc2 and Rc3 in contrast to the resistivity

assigned to the images obtained without clustering in

Table 2

Summary of parameters used during 2D resistivity inversions

Initial damping factor 0.25

Minimum damping factor 0.015

Convergence limit 1

Minimum change in absolute error \10 %

Number of iterations 38Jacobian matrix is recalculated for the first

two iterations

Increase of the damping factor with depth 1.05

Robust data inversion constraint is used with

the cutoff factor

0.05

Robust model inversion constraint is used with

the cutoff factor

0.005

Extended model is used

Effect of side blocks is not reduced

Normal mesh is used

Finite difference method is used

Number of nodes between adjacent electrodes 4

Logarithm of the apparent resistivity used

Reference resistivity used is the average of minimum

and maximum values



11/29

Sect.3.2. To assign a single resistivity value, we used

the minimum, maximum, median and average ofRc1,

Rc2 and Rc3 represented by Rcmin; Rcmax; Rcmed and

Rcavg, respectively, using Eqs. 8, 9, 10and11.

Rcminxi;yi minRc1;Rc2;Rc3 8

Rcmaxxi;yi maxRc1;Rc2;Rc3 9

Rcmedxi;yi medRc1;Rc2;Rc3 10

Rcavgxi;yi Rc1 Rc2 Rc3=3: 11

Also, overall resistivity values denoted by

Rcmin; Rcmax; Rcmed and Rcavg were assigned to the

blocks and background of the classified images. The

final step in the classification campaign was merging

of clusters.

Another important stage in image classification

process involves aggregation or merging of clusters in

the classified images and then ascribing the merged

clusters to desirable classes according to similarity in

their spectral properties. To this end, merging was

confined to spatially adjacent clusters by comparison

of one cluster with its neighbor(s) and assigning it to

the same class on the basis of their pixel values. This

was carried out through the class merging submenu

available at the Geomatica Focus window of the PCI

software. Also, the spatial context (i.e., boundary) of

the individual pixels can be used. This is particularlyrelevant when the spectral signatures of the clusters are

reasonably similar. Thus, as the clusters were merged,

the data structure of the classified image was updated

by reestimating the resistivity value of each class.

3.4. Accuracy Assessment

After assigning resistivity values to the clusters,

an assessment of the accuracy/performance of the

classified images was carried out. This was carried

out relative to the true model images. There are many

criteria for assessing the performance of models

images in the literature. These include: R-square,

semi-partial R-square, absolute error (AE), root-

mean-square, standard deviations, mean absolute

error (MAE) and mean absolute percentage error

(MAPE). In this article, however, accuracy assess-

ment being an important step in the classification

process is necessary in order to evaluate the quality of

the classified images. With this end in view, the error

matrix or contingence tables were used for quantita-

tive evaluation of the images. The error matrix table

displays statistics for assessing the accuracy of

classification images using the number of pixels that

represent the features in the image (SINGH 1989;

CONGALTON and GREEN 1999; LILLESAND and KEIFER

2000; LIUet al. 2003; MELGANIand BRUZZONE 2004).

To construct the error matrix table, every pixel in the

classified images was compared with the pixel in the

reference images (i.e., true models) for the blocks and

background of the models images. Then, percentages

obtained from the table gave the accuracies of the

classification (CONGALTON 1991; LILLESAND and KEIF-

ER 2000; LIU et al. 2003; ENDERLE and WEIH 2005;

HASMADI et al.2009; PERUMALand BHASKARAN 2010).

In interpreting classification accuracy, it is importantnot only to note the percentage of correctly classified

pixels but also to determine the nature of errors of

omission and commission on a pixel-by-pixel basis.

Producers accuracy (PA) is obtained by dividing

the number of correctly classified pixels in each

category by the total number of pixels in the

corresponding column. Users accuracy (UA) is

computed by dividing the number of correctly

classified pixels by the total number of pixels in the

corresponding row (i.e., it is concerned with what

percentage of the cluster has been correctly classi-

fied). The PA and UA were obtained using Eqs. 12

and13, respectively, as follows:

PA % 100 error of omission % 12

UA % 100 error of commission % : 13

In these equations, both the PA and UA are

related to errors of omission and commission,

respectively. Pixels that are incorrectly excluded

from a particular cluster are defined as an error ofomission, while pixels that are incorrectly assigned to

a particular cluster that actually belong in other

classes are defined as an error of commission

(BOSCHETTI et al. 2004).

Also, the percentage of overall accuracy (OA)

was estimated using Eq. 14given by:

O:AU

W 100 % 14



12/29

where U is the total number of correctly classified

pixels in the same category (i.e., sum of diagonal

pixels) and W is the total number of pixels (i.e., sum

of pixels in a row or column) in the classified image.

There are situations where the correct classification is

made by chance. In this case the most widely used

statistics for the estimation of the effect of change

agreement is known as the kappa coefficient (j). The

kappa coefficient was calculated using Eqs.15 and

16a,16bas follows:

ja1 a2

1 a215

a1

PNi1

xij

N16a

and

a2

PNi1

yizi

N2 16b

wherea1 is the overall accuracy, a2is the percentage

of items that has been classified correctly by chance,

xij is the number of pixels in the ijth cell of the

contingence table, yi marginal total of row,

zi =marginal total of column, N =the total number

of pixels in the image under consideration.

Furthermore, the AE was computed by making

pixel-by-pixel comparison between the true models

and the combined images. With this end in view,

both MAE and MAPE were calculated. First, the

absolute error (AE) of the model features (i.e., for

the blocks and background) was computed. This was

carried out by estimating the difference in resistivity

between the true model and classified image on a

pixel-by-pixel basis. For all the pixels within the

blocks, for instance, MAE was estimated as the

average of all AEs. Also, the MAPE was estimatedfor the blocks and background of the models

images. AE, MAE and MAPE are given in Eqs.17,

18, 19 as follows:

A:E xi; yi qi qij j 17

MAE 1

N

XNi1

qi qij j 18

MAPE 1

N

XNi1

qi qiqi

100 19

whereqi is the true resistivity of the block(s) and qi is

the calculated resistivity of the block; N is the total

number of pixels in the image.

4. Results and Discussion

4.1. Synthetic Results

A tabulated set of reconstructed resistivity values

for each block and background of the models in

Fig.2 are presented in Table3. The images

obtained using Eqs.4, 5, 6 and 7 to merge the

resistivity values of the three individual electrode

arrays (i.e., the dipole-dipole, pole-dipole and Wen-

ner-Schlumberger) are shown in Fig.2dg. It is

observed from the table that for all the models, the

reconstructed resistivity values of the blocks are

underestimated compared to the resistivity of the

true models, while for the background the recon-

structed resistivity values are an overestimation. In

essence, the amplitude of resistivity has been

dampened and is a known feature inherent in

resistivity imaging (RUCKER 2012). For the individ-

ual electrode arrays, it is observed that the dipole-dipole images give better results than Wenner-

Schlumberger and pole-dipole images. This means

that the reconstructed blocks resistivity for dipole-

dipole images is closer to the true models resistivity

than the resistivity for Wenner-Schlumberger or

pole-dipole images. Also, for the combined images,

the reconstructed resistivity of the maximum images

is higher than that of the remaining images (i.e.,

minimum, median or average). Thus, the maximum

outperforms any of the other combination as well as

the individual images in attempting to reproduce thetrue models.

The classification results after the pixels (i.e.,

resistivity values) had been grouped into 16 clusters

by the classifier algorithm together with their mean

resistivity values are presented in Table4. It is seen

that each cluster has three mean resistivities associ-

ated with it. These resistivity values show that each



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cluster contains information about the three electrode

configurations used. Furthermore, a gradual increase

in resistivity from one cluster to another is noted.

This gradual increase might be due to the electrical

contrast between the blocks and the background of

the models images as the classifier recognizes

certain patterns in resistivity that are grouped to aparticular cluster and other patterns to another cluster.

Also, the classification results of the combined

classified images obtained for the model of a single

block embedded in a homogeneous background are

shown in Fig.3ad. The rest of the classified images

containing thematic information are shown in Figs. 4,

5, 6and7.

The aggregation of the clusters into classes shows

that, for a single block model, cluster 1 is assigned to

the background and clusters 216 to the block leading

to a model with two classes. Class 1 corresponds to

the background and class 2 to the block (Fig. 3). For

the two-block model, clusters 24 are assigned to the

first block (left), clusters 516 to the second block

(right) and cluster 1 to the background. As a result

three classes are produced, and each class corre-sponds to a particular feature of the model (Fig. 4).

The three-block model images are such that cluster 1

is assigned to the background, clusters 24 are

assigned to the left block, while clusters 5 through

10 are assigned to the middle block; clusters 1116

are assigned to the right block with a total of four

classes representing this model. Class 1 represents the

background, while classes 24 represent the blocks of

the model (Fig.5). In Fig.6, clusters 13 are

Figure 2Two-dimensional inverse images of a block model for individual arrays: a Dpd,b Pdp,c Wsc and combined images,d max,e min,fmed and

g avg



14/29

assigned to the conductive top layer, and clusters

416 are assigned to the resistivity bottom layer. As a

result, two classes are obtained for the fault model:

class 1 is typical of the top layer, and class 2

corresponds to the bottom layer of the model. In the

resistivity dyke model, clusters 216 are assigned to

the intrusive block, while cluster 1 belongs to the

background. This implies that only two classes are

desirable to represent these models. Again, class 1

represents the background, while class 2 represents

the intruding block (Fig.7). In consequence, the

number of clusters aggregated/merged into a partic-

ular class depends on the structural features identified

in the models image.The overall resistivity obtained after assigning the

mean resistivity values obtained in Table3 to the

blocks and background of the classified images is

summarized in Table5. From this table, two deduc-

tions could be drawn. For instance, for a one-block

model type (1) the resistivity values range from a

minimum of 180 X-m to a maximum of 340 X-m.

With this range, it shows that after classification of

the images, the overall resistivity values obtained for

Table 3

Summary of reconstructed resistivity for the different models

without classification

Model

type

True model Reconstructed mean resistivity (X-m)

Resistivity

(X

-m)

Dpd Pdp Wsc Rmax Rmin Rmed Ravg

Oneblock

Block (500) 320 250 160 330 160 260 250Background

(10)14 13 12 11 13 12 12

Twoblocks

Block 1(100)

110 100 87 120 89 110 110

Block 2(300)

360 330 260 370 260 330 320

Background(10)

17 18 15 19 15 17 17

Threeblocks

Block 1(100)

59 57 53 61 55 59 58

Block 2(300)

170 130 84 180 83 140 130

Block 3

(500)

240 150 120 250 130 150 180

Background(10)

18 16 14 18 13 15 16

Fault Hanging wall(10)

13 12 13 14 12 13 13

Foot wall(100)

95 93 92 100 86 92 93

Dyke Block (500) 470 460 460 470 460 460 460Background

(100)100 100 100 100 100 100 100

Table4

Summaryofclustering

forsyntheticmodelswithmeanresistivity

inX-m

ModeltypeArray

type

Cluster

1

Cluster

2

Cluster

3

Cluster

4

Cluster

5

Cluster

6

Cluster

7

Cluster

8

Cluster

9

Cluster

10

Cluster

11

Cluster

12

Cluster

13

Cluster

14

Cluster

15

Cluster

16

Oneblock

Dpd

9

29

58

90

120

150

190

220

300

340

390

340

380

420

430

460

Pdp

9

24

45

68

92

120

140

170

170

220

240

260

290

320

340

360

Wsc

8

27

41

56

72

85

100

120

130

160

160

180

200

210

220

220

Twob

locks

Dpd

9

37

71

110

140

190

230

280

320

360

400

450

480

520

560

590

Pdp

10

41

72

100

130

180

220

260

300

340

370

410

440

470

500

530

Wsc

9

29

51

76

100

120

160

190

220

250

290

310

350

380

410

440

Three

blocks

Dpd

10

10

29

52

68

90

120

140

170

180

210

220

250

280

310

340

Pdp

10

10

25

43

63

60

82

100

130

120

160

140

160

170

180

140

Wsc

10

11

21

34

59

41

61

77

79

110

100

120

130

130

140

140

Fault

Dpd

11

19

30

41

52

62

72

82

91

99

110

100

110

110

110

110

Pdp

12

17

25

33

42

51

59

67

76

86

95

110

120

120

120

130

Wsc

11

16

24

32

40

48

56

64

73

82

91

110

120

130

140

140

Dyke

Dpd

100

120

150

180

200

230

260

290

310

340

360

390

420

440

470

500

Pdp

100

120

150

170

200

230

260

290

310

350

370

400

430

460

480

490

Wsc

99

130

150

180

210

240

270

290

320

350

370

400

430

470

480

490



15/29

the maximum images are closer to the true models

resistivity (i.e., 500 X-m) than the resistivity values

obtained for the rest of the models images. Also, the

rest of the models images show similar trends, and

(2) in comparison with the models images obtained

without classification, it is noted that there is anincrease in resistivity values of the combined classi-

fied images resulting from the unsupervised

technique. This could suggest that the unsupervised

classification technique finds patterns or features

residing in the original models that might not be

obviously known by any of the individual electrode

array configurations before the unsupervised classi-

fication technique is utilized (ERNENWEIN2009; RANA

et al. 2010).

Furthermore, the error matrices generated for

statistical evaluation of the performance of the

classified images relative to the true models are

presented in Tables6,7,8,9and10. PA indicates the

degree to which the reference pixels are classified

(LILLESAND and KEIFER 2000). UA indicates theprobability that a given cluster is actually present

on the ground (LILLESAND and KEIFER 2000). Gener-

ally, both the users and producers accuracies

indicate good classification of the models as the

errors of commission and omission during the

classification were less than 40 %. The accuracy

assessment from the unsupervised classification tech-

nique further shows that the overall percentage

accuracy is greater than 70 %. Overall accuracy

Figure 3Two-dimensional integrated classified images for a resistivity block model: a max, b min, c med and d avg



16/29

evaluates the percentage of cases correctly classified,

i.e., the probability that a pixel is classified correctly

in the classified image. This indicates a good

agreement between the classified images and the true

model images used as reference data. According to

LANDIS and KOCH (1977), the ranking of the kappa

coefficient (j) ranges from 1 to 1. As a result, three

groups can be obtained: (1) j greater than 0.8

represents strong agreement between the classifica-

tion and the true models images; (2) j between 0.4

and 0.8 represents moderate agreement; (3) j less

than 0.4 represents poor agreement between the

classified and the true model images. By this

standard, j shows that for the one-, two- and three-

block images, substantial agreement exists between

the classified images and true models with kappa

accuracy from 76 to 83 %, while for the fault and

dyke models, the j values are 90 and 93 %,

respectively. This implies that there is perfect agree-

ment between the classified and true model. Thus, j

compensates for chance agreement in the classifica-

tion and provides a measure of how much better the

classification performs in the probability of randomly

assigning pixels to their correct classes.

Figure 4Two-dimensional integrated classified images for the resistivity two-block model: a max, b min, c med and d avg



17/29

In addition, an assessment of the accuracy of the

combined images, employing both MAE and MAPE,

shows that for all the synthetic models, the maximum

resistivity values assigned to the models give the least

errors, as presented in Tables 11and12, respectively.Thus, the maximum approach is considered the best

representative of the true models as it reproduces the

true model with the least possible errors compared to

the other models images. Although our focus in this

article was on classified images, more details on the

quality of images obtained without clustering in

terms of MAE and MAPE for the synthetic models

can be found in ISHOLAet al. (2014).

4.2. Application to Field Examples

As feasibility tests of the application of the

aforementioned unsupervised classification tech-

nique on synthetic data, we also extended the

clustering technique to real field data. In fieldexample 1, electrical resistivity imaging was con-

ducted to delineate subsurface lithological units that

control the hydrogeology of the study area for

groundwater resources development. Also, in field

example 2, electrical resistivity imaging was applied

to demarcate regions of leachate infiltration in a

septic field.

Figure 5Two-dimensional integrated classified images for the resistivity three-block model: a max, b min, c med and d avg



18/29

4.2.1 Field Example 1

A 2D electrical resistivity survey was performed at

Universiti Sains Malaysia Engineering campus, Ni-

bong Tebal, in Penang, Malaysia. The ABEM Lund

Imaging system comprising a Terrameter SAS 4000

supplemented with an automatic multielectrode

selector ES 10-64C system was used in the acquisi-

tion of electrical resistivity data. A resistivity profile

of about 420 m was established. Along this profile,

four cable reels, each 100 m long and trending in the

west-east direction, were used. Sixty-two takeouts

electrodes were deployed at 5-m spacing for the two

inner cable sets (100300 m), i.e., short (S) and 10-m

electrode spacing for the outer cable sets, i.e., long

(L) corresponded to distances of 0100 m and

300400 m on the standard 400 m (ADIAT et al.

2013). Two cable joints were used to link the cables to

ensure continuity. The first cable joint was used to

connect cables 1 and 2, while the second cable joint

connected cables 3 and 4. The other terminals ofcables 2 and 3 were connected to the Terrameter used

for the measurements. The three electrode array

configurations used were the dipole-dipole (LS),

pole-dipole (LS) and Schlumberger (LS). A forward

modeling subroutine was used to calculate the appar-

ent resistivity values, and a nonlinear least-squares

optimization technique was used for the inversion.

Like in the synthetic example, the RES2DINV

program was employed. In the dipole-dipole array,

Figure 6Two-dimensional integrated classified images for a resistivity fault model: a max, b min, c med and d avg



19/29

with a minimum electrode spacing of 5 m, a total of

770 data points were used for measurements of

resistivity (i.e., 414 data points for L, 356 data points

for S), for the pole-dipole array 792 data points (516

for L, 276 for S) and for the Schlumberger array 748data points (418 for L, 330 S). For all three arrays,

after the seven iterations, the inversion converged

with misfit error less than 20 %. The misfit errors were

for the dipole-dipole (17 %), pole-dipole (13 %) and

Schlumberger (10 %) arrays. Inversion results for the

noise-contaminated data sets were saved in text file

format in order to allow for further manipulation and

analysis using the image processing program package

of the PCI Geomatics 10.3 software.

The reconstructed tomographic images of the

three electrode array configurations are shown in

Fig.8ac. From a geophysical viewpoint, the geo-

logical structures delineated behave like a three-layer

model for all the three arrays. With the dipole-dipolearray, the inversion image (upper panel) shows that a

low resistivity layer is detected close to the surface.

The low resistivity zone has a surface layer thickness

between 3 and 10 m. This zone is underlain by a layer

with higher resistivity, while the third layer, which

seems to extend throughout the model, is character-

ized by an intermediate resistivity. Using the pole-

dipole array, the inverse image (middle panel) reveals

that the first layer is a low-resistivity pocket-like

Figure 7Two-dimensional integrated classified images for a resistivity dyke model: a max, b min, c med and d avg



20/29

structure haloed by a more resistive layer that extends

downward to a depth of about 60 m. This layer

appears to be separated by a less conductive layer

with depth from 15 to 40 m. The Schlumberger array

image (lower panel) shows that the first layer is a

conductive zone that extends through the model. It

surrounds a more conductive pocket-like structure.

Also, a high-resistivity structure of finite extent is

observed, while the deeper portion of the inverse

image is a zone that corresponds with an intermediate

resistivity. For resistivity imaging, the difference in

the imaging abilities of the three electrode arrays

when applied to the geological model is underscored.

The difference in the imaging capability is controlled

by the array parameters electrode spacing (a) and

propagation factor (n) (DAHLIN and ZHOU 2004). We

should also mention that the differing effects of the

electrode arrays on the 2D inverse images are due to

the arrangement of the electrodes, spreading patterns

and density of the data.

The aforementioned electrical imaging empha-

sizes the nonuniqueness of the inversion process

(TARANTOLAand VALETTE1982; NARAYANet al.1994).

To reduce the ambiguity in the tomographic images,

the three 2D inverse resistivity images were com-bined using an unsupervised image classification

technique. The three images in Fig. 8ac were used

as inputs to the k-means algorithm alongside other

initial parameters used in the synthetic modeling

section. Also, like the synthetic examples, the number

of clusters into which the combined images should be

partitioned was set at 16, while the number of

iterations and convergence threshold where 20 and

0.01, respectively. Again, the prior knowledge of the

inversion results for these models guided the choice

of the number of clusters used. The clustering result

is presented in Table13. Following the assignment of

resistivity values to the clusters, the clusters were

merged into six desirable classes. The resulting

classification image with a superimposed borehole

lithologic log for the assignment of lithologies is

shown in Fig. 9.

Cluster 1 was assigned to class 1; clusters 2 and 3

were merged to class 2; clusters 46 were merged to

class 3. Also, clusters 7 and 8 were merged to class 4,

and clusters 912 were merged to class 5, whileclusters 1316 were assigned to class 6. This

aggregation/merger of the clusters corresponded with

the subsurface geological units of the study area.

Though the unavailability of resistivity log data (i.e.,

as ground truth) made it impossible to evaluate the

accuracy of the classified image using the error

matrix table as in the synthetic examples, neverthe-

less a qualitative approach involving the available

borehole lithologic log was used. The electrical

Table 5

Summary of overall resistivity for classified images

Model type Model description

(X-m)

Overall resistivity (X-m)

Rcmax Rcmin Rcmed Rcavg

One block Block 1 (500) 340 180 260 260Background (10) 14 11 12 13

Two blocks Block 1 (100) 130 92 120 110

Block 2 (500) 380 260 330 320

Background (10) 19 15 17 16

Three blocks Block 1 (100) 74 59 67 67

Block 2 (300) 200 90 140 150

Block 3 (500) 250 150 160 190

Background (10) 12 5 8 8

Fault Hanging wall (10) 14 11 12 13

Footwall (100) 100 86 93 93

Dyke Block 1 (500) 480 460 470 470

Background (100) 100 100 100 100

Table 6

Error matrix/contingency table for a one-block classified image on

a pixel-by-pixel basis

j = 0.80 Block 1 Background Row total UA

Block1 108,658 6,568 115,226 0.94

Background 51,351 751,003 802,354 0.99

Column total 160,009 757,571 917,580

PA 0.68 0.99 O.A = 0.94

Table 7

Error matrix/contingency table for two-block classified image on a

pixel-by-pixel basis

j = 0.76 Block

1

Block

2

Background Row

Total

UA

Block 1 54,965 11,775 37,360 104,100 0.53

Block 2 0 56,136 10,298 66,434 0.85

Background 2,035 89 690,060 692,184 0.99

Column

total

57,000 68,000 737,718 862,718

PA 0.96 0.83 0.94 O.A = 0.93



21/29

contrast in the geologic units delineated, on corrob-

oration with the representative borehole lithologic log

information, showed that the geology of the area

consists of clay, sandy clay, clayey sand and sand.

The range of resistivity values to the depth of

investigation was between 5 and 55 X-m. The

relationship that links the various classes with the

litho-resistivity values for the subsurface character-

ization of the study area is summarized in Table 12.

A conductive anomalous body that presumes to be aniron material was identified as class 1. This material

is buried in a less conductive layer that corresponds

with clay (class 2). Class 3 corresponds with sandy

clay. Because it is less cohesive, the groundwater

potential of this layer might be low. The promising

zones for probable groundwater exploitation in the

area are clayey sand (i.e., class 4) and sand units

belonging to classes 5 and 6. In general, the

Table 8

Error matrix/contingency table for the three-block classification model on a pixel-by-pixel basis

j = 0.83 Block 1 Block 2 Block 3 Background Row total UA

Block 1 28,381 18,562 10,989 55,014 112,946 0.25

Block 2 0 20,475 25,256 2,260 47,991 0.43

Block 3 0 2,892 7,255 0 10,147 0.71Background 1,619 571 0 689,447 691,637 0.99

Column total 30,000 42,500 43,500 746,721 862,721

PA 0.95 0.48 0.17 0.92 O.A = 0.86

Table 9

Error matrix/contingency table for a fault classified image on a

pixel-by-pixel basis

j = 0.90 Top layer Bottom layer Row total UA

Top layer 37,408 35,050 72,458 0.52

Bottom layer 2

ishola et al pure and applied geophysics 2014

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