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Optimising noise intervened data processes for
inverse geoelectrical problem using adaptive
neuro fuzzy inference system (ANFIS)
A. Stanley Raj, D. Hudson Oliver, Y. Srinivas & J. Viswanath
To cite this article: A. Stanley Raj, D. Hudson Oliver, Y. Srinivas & J. Viswanath (2021) Optimising
noise intervened data processes for inverse geoelectrical problem using adaptive neuro fuzzy
inference system (ANFIS), NRIAG Journal of Astronomy and Geophysics, 10:1, 138-154, DOI:
10.1080/20909977.2021.1900525
To link to this article: https://doi.org/10.1080/20909977.2021.1900525
© 2021 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Group.
Published online: 25 Mar 2021.
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ARTICLE
Optimising noise intervened data processes for inverse geoelectrical problem
using adaptive neuro fuzzy inference system (ANFIS)
A. Stanley Raj
a
, D. Hudson Oliver
b
, Y. Srinivas
c
and J. Viswanath
d
a
Department of Physics, Loyola College, Chennai India;
b
Department of Physics, Scott Christian College, Nagercoil, India;
c
Centre for
GeoTechnology, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu-India;
d
Department of Mathematics, Vel Tech Rangarajan
Dr. Sagunthala R & D Institute of Science and Technology, Chennai, Tamil Nadu, India
ABSTRACT
Geoelectrical inversion has some problems in inverting data due to the heterogeneous
behaviour of Earth. One of the major concerns in inverting the data is due to the inuence of
noises, which comes from the disturbance due to human interventions, atmospheric variations,
and electromagnetic disturbance, etc. . In this paper, we have presented a concept of Neuro
Fuzzy algorithm which can interpret the noisy data successfully. Moreover, the data were
tested with articially generated random noise, gaussian noise and missing data.
Kanyakumari eld region having complex geological structures and its performance is vali-
dated with a maximum threshold. Kanyakumari eld region having complex geological struc-
tures is used and the performance is validated with a maximum threshold. Neuro fuzzy
technique has the dominant feature of training and testing the data with utmost accuracy.
These implications are made to create the specic Graphical User Interface (GUI) for the
algorithm and it works well for all types of Vertical Electrical Sounding (VES) data with good
performance results.
ARTICLE HISTORY
Received 19 February 2019
Revised 28 January 2021
Accepted 4 March 2021
KEYWORDS
Adaptive Neuro Fuzzy
Inference System; resistivity
inversion; subsurface
modelling; noise intervened
processing; layer model
1. Introduction
Geophysical studies show ample evidences of the suc-
cessful use of the resistivity method in groundwater
prospecting. The geoelectrical resistivity method is
more successful in investigating groundwater studies.
In electrical prospecting, the electrical currents which
are sometimes naturally present in the earth, may be
measured, or one may introduce currents into the
ground artificially by using batteries or generators,
and investigate the electrical field distribution by sui-
table measurements. For aquifer mapping and to esti-
mate the subsurface features direct current resistivity
methods are very useful. Vertical Electrical Sounding
(VES) method is one of the best methods to study
aquifers more reliably.
Due to the non-linear nature of the earth, it is
difficult to estimate the subsurface parameters accu-
rately. It is significant to note that the electrical resis-
tivity values often vary instantaneously from one
formation to the next, and hence the description of
the real earth resistivity model in terms of the linear
model may not be quite appropriate. Several attempts
were made in the last three decades for geoelectrical
resistivity inversion. The prominent inversion results
were obtained from both the forward modelling tech-
niques and direct inversion techniques. A good inver-
sion method must simultaneously minimise the effects
of data error and model parameter errors. Direct
inversion techniques are trustworthy, but this too
will suffer problems in generalisation. For a particular
area under study with more number of training data-
sets available, general soft computing methods works
well, but if moving towards a generalised approach, we
need a specially designed algorithm for carrying out
the computational methods. Geophysical prospecting
methods are commonly used to estimate geological
structures of earth (Wisen et al. 2004; Castilho et al.
2008; Reynolds 2011; Long et al. 2012; Arjwech et al.
2015), hydrogeological characteristics (Zahody et al.
1974; Giang et al. 2013; Trappe et al. 2019), subsoil
investigations, civil engineering structure, agricultural
and industrial regions. Stopinski (2003) studied the
bedrock for the construction of a dam using the elec-
trical resisitivity method. (Niedrleithinger et al. 2008)
applied geophysical techniques for river embankment
in Huang and Mayne. (Al-Fares et al. 2018) studied
about leakage origin in Abu Baara dam using electrical
resistivity tomography. (Ikard et al. 2014) charac-
terised focussed seepage through an earth-fill dam
using geoelectrical methods. Using resistivity logs,
researchers are determining the reservoir characteris-
tics (Archie 1942). Electrical resistivity survey has been
implemented in various parts of the world for different
purposes (ahlin et al. 2004; Friedman 2005; De carlo
2013; Asfahani 2013; Lech et al. 2016; Koda et al. 2017;
Kowalczyk et al. 2017; Rabarijoely 2018). Different
CONTACT A. Stanley Raj stanleyraj_84@yahoo.co.in
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS
2021, VOL. 10, NO. 1, 138–154
https://doi.org/10.1080/20909977.2021.1900525
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
methods were applied to invert electrical resistivity
data (Dahlin 2001; Loke and Dahlin 2002; Loke et al.
2003; Loke and Lane 2004)
A specially designed algorithm was implemented in
this research work using the Adaptive Neuro Fuzzy
Inference System (ANFIS) to invert geoelectrical resis-
tivity data. To evaluate the performance of the algo-
rithm, studies were carried out by adding random
noise and data deletion (missing data) on the inver-
sion of resistivity profile. In this research work, ANFIS
is applied to interpret the geoelectrical resistivity data.
The obtained results are compared with the available
litholog of the study area.
2. Methodology
Many researchers used geophysical exploration stu-
dies using the direct current resistivity method and
identified that this method is more reliable in estimat-
ing the parameters (Kosinky and Kelly 1981; Sri;
Niwas and Singhal 1981; Mazac et al. 1985; Yadav
and Abolfazli 1998). VES data was interpreted using
curve matching procedures and other computational
methods (Flathe 1955; VanDam 1964; Mooney et al.
1966; Ghosh 1971).
In general, the characteristic sounding curves are
represented in multiple layers. Each of the four sets
has particular properties that may be roughly classi-
fied. For H and K-type curves ρ1> ρ2< ρ3 and ρ1< ρ2>
ρ3, respectively, and we may be able to draw some
conclusions about relative values of ρ1 and ρ3 if the
spread has been extended sufficiently. The A and
Q-type curves correspond to ρ1< ρ2< ρ3 and ρ1>
ρ2> ρ3, respectively (Telford 1990).
3. Geophysical method
Geophysical exploration techniques are vibrant and
powerful tools that plays a vital role in the delineation
of aquifer parameters in different geological formations.
In particular, the Geophysical method consisting of
vertical electrical sounding (VES) has been proved to
know the variation of resistivity of the aquifer para-
meters (Rijo 1977). Schlumberger electrode array hav-
ing principle advantage over several types of arrays
(Figure 1) is used to study the electrical resistivity dis-
tribution of the subsurface in order to understand the
groundwater conditions. The Vertical Electrical
Sounding provides a non-destructive, fast and eco-
nomic way to study the properties of aquifers. An
important advantage of VES method is that quantitative
modelling is possible using either model curves or soft-
ware. The resulting models provide accurate estimates
of electrical resistivity, thickness and depth of subsur-
face strata of the Earth. This array (what array?) is a
powerful tool in the delineation of groundwater poten-
tials because of its simple in nature and cost effective.
The field procedure involves as follows: among the four
electrodes that are used, the potential electrodes (M and
N) remain fixed and the current electrodes (A and B)
are expanded symmetrically about the centre of the
spread (Figure 1,Figure 2). With very large values of
current electrodes, however, it is necessary to increase
the potential electrodes. Maximum half current electro-
des (AB/2) separation used in this survey is 100 metres.
Usually, the depth of penetration is proportional to the
separation between the electrodes and varying the elec-
trode separation provides information about the strati-
fication of the ground. Figure 1 shows the Schlumberger
electrode configuration.
Figure 1. Schlumberger electrode configuration for geoelectrical data collection.
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 139
4. Fundamentals of ANFIS – theory and
applications
The intelligent neuro fuzzy inference technique for
data analysis and interpretation are becoming more
powerful tools for making breakthroughs in the
science and engineering fields by transforming the
data into information and information into knowl-
edge in recent days. Masoud Nikravesh (2004) applied
intelligent techniques in the oil and gas industry for
multipurposes such as risk management, uncertainty
analysis and interpretation of geological data. Yasala
Srinivas (2013) applied the ANFIS model to find the
lithology of the study area. The last decade has wit-
nessed significant advances in inverting geosciences
data with associated characteristics. This has been
made possible through improvements in data integra-
tion and quantification of uncertainties.
Neuro-fuzzy modelling is a technique for describ-
ing the behaviour of a system using fuzzy inference
rules within a neural network structure. The model
has a unique feature in which, it can express linguis-
tically the characteristics of a complex non-linear sys-
tem. Geoelectrical resistivity inversion problem was
analysed using the ANFIS model, which produces
less mean square error (Srinivas et al. 2012a, 2012b;
Stanley Raj et al. 2014, 2015). The fuzzy modelling was
first explored by Takagi and Sugeno (1985) and later
ANFIS network was developed by Jang (1993).
In the present work, the electrical resistivity data
collected using the VES (Vertical Electrical Sounding)
method is used for training the dataset. The data
collected from the field is the apparent resistivity,
while on interpretation the subsurface parameters
viz., resistivity and thickness of the individual layers
are obtained. Trained data set is the reference data for
interpreting the subsurface layer parameters of the
earth. This dataset will be used to train ANFIS by
adjusting the membership function parameters that
best model this data, which suits best for this data.
The inherent problems in geoelectrical resistivity
inversion that are to be overcome are as follows.
Precautions to be taken while analysing the geoelec-
trical resistivity inversion data.
●Inadequate data and field errors/noises are also to
be considered while evaluating the subsurface
strata of the earth.
●Framing the appropriate algorithm for inversion
is the most important section involved in apply-
ing these tools.
●Moreover, moving to a generalised approach on
inversion, one should be very careful in validating
the results with different field data.
The application of ANFIS algorithm for the inver-
sion of VES data is demonstrated with different field
datasets. Here, the ANFIS algorithm provides the
necessary database needed for interpretation.
Moreover, the best model of the trained database fits
with the apparent resistivity of the field curve. The
corresponding layer model is produced as an output
with lowest root mean square error in a particular
number of epochs.
4.1. ANFIS methodology
Initially, the data have been subjected to a certain
degree of membership grade so that at each iterations
the firing strength will decide the consequent
parameters.
Figure 2. ANFIS architecture.
140 A. S. RAJ ET AL.
ANFIS system consists of five layers; Output of each
layer is symbolised by O
1,i
with i is a sequence of
nodes and 1 is the sequence showing the lining. Here is
an explanation for each layer (Jang 1993), namely:
4.2. Layer 1
Serves to raise the degree of membership and the
membership used here is Gaussian membership
function.
O
1,i
= μ
A
(x), i = 1,2 . . . .(1)
and
O
1,i
= μ
B
(y), i = 1,2. . . . .(2)
with x is the AB/2 values and y is the apparent resis-
tivity values chosen as the input for the i-th node for
training, whereas, AB/2 and apparent resistivity
values of synthetic data have been chosen as input
and the corresponding true resistivity and depth
values have been chosen as output values for the i-th
node
f x;σ;cð Þ ¼ excð Þ2
2σ2
by {σ and c} are the parameters of membership func-
tion or called as a parameter premise. σ signifies the
cluster bandwidth, and c represents the cluster center.
4.3. Layer 2
Serves to evoke firing-strength by multiplying each
input signal.
O
2,i
= w
i
= μ
A
(x) x μ
B
(y), i =1, 2. . . . .(3)
4.4. Layer 3
Normalizes the firing strength
O
3,i
=w= wi
w1þw2,i =1,2. . . . .(4)
4.5. Layer 4
Calculates the output based on the parameters of the
rule consequent {p
i
, q
i
and r
i
}
O
4,i
=wifi= wi(p
i
x+q
i
y+r
i
). . . . .(5)
4.6. Layer 5
Counts the ANFIS output signal by summing all
incoming signals will produce
P
i
wifi= Piwifi
Piwi . . . . .(6)
ANFIS uses the input data scaling by xbounds =
[min max] command used in MATLAB software
which represents the scaling parameter of the input
function that varies between minimum to maximum
value of the data point. Each data point is scaled for
pre processing of training initially by normalising it.
5. Results and discussion
Many hybrid systems can be built on the combin-
ing platform of neural networks, fuzzy logic and
neuro fuzzy networks. For example, fuzzy logic can
be used to combine results from several neural
networks; although some hybrid systems have
been built, this present work has attained promis-
ing results when combining the fuzzy logic and
neural networks. The field validation proves that
this algorithm can have a bright future for estimat-
ing many non-linear problems. The field data cho-
sen is from one of the four taluks in Kanyakumari
district, located in the southern tip of India. The
total region of Agastheeswaram taluk covers 279.4
km
2
. It lies between the latitude 77°18′ 45″ E to 77°
35′15″ E and 8°4′ N to 8°13′45″ N longitude. The
area is underlain by the crystalline rocks like gneiss
and charnockite of Archaean age. Along the coast
the sands of recent origin are noticed. The geology
map (Figure 3) of the study area is obtained from
Geological Survey of India (GSI 2005). The penin-
sular gneisses occupy the largest area in the district.
The general trend of the strike of this area is in the
N-NW to S-SE direction. Garnetiferous silliminate,
graphite gneiss and garnet biotite gneiss are the
two major groups identified in Kanyakumari
district.
The groundwater occurs in almost all the geolo-
gical formations like crystalline rocks, sedimentary
formations and quaternary alluvium and beach
sands. The groundwater occurrence in the hard
rock region is limited to the weathered mantle of
thickness 10–35 m below ground level. The weath-
ered thickness in hard rock regions is discontinu-
ous both in space and depth. Hence, the
groundwater potentiality is influenced by the inten-
sity of weathering. In the sedimentary formations
having alluvial deposits, the water table is very
shallow which is up to a maximum depth of 10 m
(PWD 2005). Field data chosen from the sounding
location 77.51397 E and 8.108833 N. Figure 4
shows the corresponding multilayer model.
Figure 5 shows the regressed layer model. Figures
6 and 7 show the ANFIS rule architecture and
membership functions, respectively. Figure 8
shows the geoelectric section of the corresponding
layer model.
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 141
5.1. Performance evaluation of algorithm
The performance of the algorithm has been evaluated
by three methods
a) Adding random noise to the data
b) Missing data values to the original field data
c) Adding gaussian noise to the data
5.2. A) Adding random noise to the data
It is very necessary for a system to be fault tolerant and
immune to noise system to enhance the performance
of any problem which is taken into account. Soft
computing techniques would be the better tool to
estimate the subsurface features more clearly than
any other conventional methods. More positively, the
soft computing inversion involves the knowledge-
Figure 3. Geology map of the study area (redrawn after GSI 2005).
Figure 4. Obtained multilayer model inversion of ANFIS algorithm.
142 A. S. RAJ ET AL.
based approach, which proclaims the self-dependent
and pertaining algorithm to solve complex problems
more easily. In this research work, random noises were
added to the original field data with 5%, 10%, 20% and
40% to check the performance of the algorithm. The
results are shown in Figures 9, 10, 11 and 12, respec-
tively, for corresponding the noise percent added. The
results demonstrate that the layer model inversion has
Figure 5. Obtained regressed layer model inversion of ANFIS algorithm.
Figure 6. ANFIS rule architecture.
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 143
been oscillating while increasing the noise percent.
Finally, by adding above 50% noise, the system
becomes unstable. For fixing the solution, ANFIS
tries to fix the membership functions of different
range and the number of rules increment as shown
in Table 1. Thus, it proves that the entire algorithm
itself oscillates for fixing the layer model, the litholog
information of the log doesn’t vary to maximum error
percent. This verifies the ANFIS algorithm tries to
maintain the linearity throughout the program by
adjusting the membership function (gaussian mem-
bership function is used here). It takes much time in
fixing the layer model when increasing the noise per-
cent. But the result showed that only below 20% noise
level, the system can interpret the layer model more
quickly and efficiently with minimum error percent.
So for rapid inversion of optimising the problem, the
system should have maintained the noise percent
below the respective value.
5.3. B) Missing data values (by random data
deletion)
The performance of the algorithm was further tested
by random data deletion. Similar to the noise inter-
vened data, the system is subjected to missing data
Figure 7. Membership functions mapped between the input and output data.
Figure 8. Geoelectric section of the corresponding layer
model.
144 A. S. RAJ ET AL.
values by removing the data randomly from the origi-
nal filed data which is feed as an input.
When 20% of data missing is made, it doesn’t
bring a major problem for inversion. It performs
well at this particular stage. But while going beyond
the 20% missing data, the system subjected to oscilla-
tion and takes more time for fixing the result. The
system cannot interpolate the nearby missing values
of the data when the missing data level reached 40%.
This result is not similar to the noisy data result
Figure 9. Layer model inversion result for five percent random noise added to the input data.
Figure 10. Layer model inversion result for ten percent random noise added to the input data.
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 145
because in the earlier attempt the performance of the
algorithm was maintained constantly up to 40%. The
constraint in missing data interpretation is that,
when it goes beyond the 20% missing data values,
more number of data has to be added to retrieve the
information clearly. This is the prominent result that
this kind of interpretation is directly proportional to
the number of data. More the number of data, the
error percent is low and the inversion hails more
performance.
Figure 11. Layer model inversion result for twenty percent random noise added to the input data.
Figure 12. Layer model inversion result for forty percent random noise added to the inputdata.
146 A. S. RAJ ET AL.
Table 1. Random noise added for ANFIS inversion showing the performance.
S. No. Percentage of random noise added True Resistivity (in Ohm-m) Depth (in m) Error Percent (RMSE) Computational Time (in sec) Number of rules framed while ANFIS inversion
1 5% 44.8704
105.851
65.7963
47.6943
38.0296
31.577
37.600
0.0795
1
5
8
27
30
40
55
0.950 6.866 7 rules
2 10% 41.268
81.988
54.652
43.223
42.042
35.151
36.674
0.073
1
6
10
27
30
40
55
1.381 21.668 8 rules
3. 20% 33.229
62.365
48.666
51.779
18.136
47.056
42.031
39.820
30.330
1234.93
1
5
10
12
20
27
30
40
55
6.26925 21.6611 10 rules
4. 40% 33.994
26.332
23.730
32.296
21.416
22.22
594.02
2
5
27
30
50
55
6.44922 21.7359 10 rules
5. <50% ANFIS System Unstable
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 147
Thus, the ANFIS performance level on comparing
to noisy data and missing data interpretations are
pretty good. At each and every stage the performance
level has been checked with Root Mean Square Error
(RMSE). The algorithm itself possibly tries to reduce
the error percent and it is legible to work in this plat-
form to interpret such data than to rely on a conven-
tional approach.
Figure 13. Layer model inversion result using ANFIS for 20% gaussian noise added to the input data.
Figure 14. Layer model inversion result using ANFIS for 60% gaussian noise added to the input data.
148 A. S. RAJ ET AL.
5.4. C) Adding gaussian noise to the data
In most of the geophysical inversion techniques, we
will perpetually suffer several kinds of noise which
are observed from the field and distort the original
data. In this attempt, gaussian noise was added to
the original data step by step from 10% to 80% and
the results were studied in the case of ANFIS inver-
sion. This proves the stability of the algorithm and
its robustness when it is subjected to numerous
attempts of noise intervened data training.
In previous attempts by various researchers, the
problem of generalisation and choosing initial
model parameters in resistivity inverse problems
was difficult (Ghosh 1971; Zohdy 1989; Qady and
Ushijima 2001; Singh et al. 2005; Ekinci and
Demirci 2008; Carlos et al. 2000). Maiti et al.
(2011) tried a hybrid Monte-Carlo-based approach
with neural networks for inversion of data in for-
ward modelling technique. But in direct inversion,
this algorithm proves to be the worthwhile in
inverting the layer model quickly and efficiently.
This effort was made successful when the inversion
of data with the present algorithm was compared
with the conventional data interpretation. Figures
13, 14 15 16 17 18 and 19 show the gaussian noise
added to the original resistivity data with Signal to
Noise Ratio (SNR) is 20%, 60% and 80% respec-
tively. Above 50% the ANFIS system is unstable.
Thus, it is revealed that the data within 50% of
noise can be interpreted successfully by the
designed ANFIS algorithm.
After this research, the data chosen from the
Kanyakumari field was taken to invert using this well-
performed algorithm. Profile 1 has been chosen in the
Latitude, Longitude of VES 1–8° 7ʹ 34.7988ʹ’ N and 77°
20ʹ 0.0240ʹ’ E, VES 2–8° 7ʹ 31.4004ʹ’ N and 77° 20ʹ
17.4120ʹ’ E, VES 3–8° 7ʹ 27.5016ʹ’ N and 77° 20ʹ
37.5000ʹ’ E, VES 4–8° 7ʹ 24.6000ʹ’ N and 77° 20ʹ
52.9080ʹ’ E, VES 5–8° 7ʹ 17.7996ʹ’ N and 77° 21ʹ
33.9840ʹ’ E. The inversion result with pseudo cross-
section and thickness of the subsurface layer is shown
in Figure 16. Tables 2 and 3 show the respective profile
for ANFIS inverted result and its longitudinal resistivity
variations, respectively.
5.5. Error estimation
L1 norm error estimation is used to minimise the
errors while iteration. This method finds applications
in many fields because of its robustness compared to
L2-norm. L2-norm squares the error and thus the
model is much more sensitive in the case of applying
noisy data. If the amount of noise present in the data
is above a certain percentage as calculated from the
gaussian noise observations in this study, then the
model will be unstable in such cases.
Overfitting problems in ANFIS are avoided by
fixing the permissible error percentage to
Figure 15. Layer model inversion result using ANFIS for 80% gaussian noise added to the input data.
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 149
minimum (below 10% in this study). The permis-
sible error was fixed by the user to choose the
appropriate model parameters while iteration.
6. Conclusions
This kind of geophysical optimising problem includ-
ing the noise and missing data values which works well
with the soft computing approach. Noise and missing
data are the major problems in geophysical data acqui-
sition. Mainly, if the field area chosen to study is
vulnerable or cannot be accessible clearly or more
noises in the field regions, it would be better to opt
for such intelligent techniques for inversion. The
developments and advancements in the field of inver-
sion which is dependable on the intelligent technique
will possibly give the correct definition of the subsur-
face layer model. In these aspects of learning, the
adaptive algorithm becomes accustomed itself for
any kind of field data. The results of the research
work are summarised below
1) The program concerns on the generalised inver-
sion than the conventional ANFIS algorithm inver-
sion. The major difference between the two
approaches is, in the earlier we need more number of
field data that has been subjected for network training.
The solution depends on the number of datasets
involved in training. But in the later part it is not
necessary to have more number of data but the net-
work itself will generate more number of datasets and
it indirectly supports the performance of the algo-
rithm. So this would be the semi-supervised algo-
rithm. Moreover, it depends on the number of
epochs which plays a major role in generating a large
number of synthetic datasets necessary for inversion.
2) This research work concentrates mostly on the
performance of the algorithm by considering (a)
number of epochs, (b) Error percent, (c) Number of
rules assigned to each iteration and (d) Computational
time.
3) The algorithm framed on the generalised plat-
form and tested with the noise intervened data and
missing data values. Performance analysis was
made to check the algorithms reflection on the
disturbed data.
4) The tested algorithm was finally subjected to
coastal data inversion and it proclaims the best algo-
rithm for inverting any non-linear data. Thus, this
algorithm would be the best noise reduction algorithm
and efficient in picking the information necessary for
inversion.
5) Different models can be generated while testing
the ANFIS algorithm at each number of iterations
within a limit of a particular error percent. The more
appropriate model with less error percentage can be
chosen as the reliable model.
6) In general, large number of datasets collected from
a particular study area is
used to train the soft computing methods, and the
remaining data is used to test. However, the training
datasets are generated by changing weights and mem-
bership functions based on the field data in the present
concept. Thus, this approach can be applied to invert
the VES data collected from any study area.
7) The conventional geophysical inversion techniques
can be improved by using a
certain kind of soft computing techniques. Increasing
the number of trained datasets by increasing the num-
ber of iterations (since each iteration will produce a
different layer model), the ANFIS will converge with
the result and make the output to flow towards a
distinctive solution. The ANFIS can also be applied
Figure 16. ANFIS inverted pseudocross section profile.
150 A. S. RAJ ET AL.
Table 2. ANFIS inverted profile.
VES No. True Resistivity (in Ohm-m) Depth (in m) Error Percent (RMSE) Computational Time (in sec)
1. 30.4699
11.0761
13.1531
12.394
71.140
65.940
2142.87
1
3
4
5
40
55
0.33 23.2038
2. 6.0756
12.163
12.416
89.736
82.901
3129.36
1
4
4.2
50
55
0.8320 21.9926
3. 23.313
43.67
36.801
40.878
38.099
62.101
54.671
94.199
0.0879
1
10
12
25
30
50
55
90
0.622 21.3415
4. 18.595
8.532
36.5609
36.2502
2040.17
1
4
25
27
0.1713 3.9226
5. 29.4871
26.3768
68.4449
67.8925
127.378
0.0557
1
11.8
30.7
55
90
0.4692 21.0232
NRIAG JOURNAL OF ASTRONOMY AND GEOPHYSICS 151
Table 3. Longitudinal resistivity variations taken for Kanyakumari profile.
S. No. Percentage of White Gaussian noise added True Resistivity (in Ohm-m) Depth (in m) Error Percent (RMSE) Computational Time (in sec) Number of rules framed while ANFIS inversion
1 10 63.2419
105.387
43.1823
1514.59
1
3
26
0.9132 19.0667 6
2 20 63.2376
106.835
40.7399
1514.54
1
3
26
0.914236 29.4628 12
3 40 63.3428
104.818
40.9337
1514.32
1
3
26
0.939288 18.2351 10
4 60 63.5693
104.792
43.0718
1503.38
1
3
26
0.857434 14.9081 6
5 80 96.0535
96.0535
96.1082
96.1322
95.7721
93.416
88.1523
56.4565
44.1743
36.8733
1517.35
1
1
4
5
6
10
11
20
25
40
6.05378 93.2999 7
6 <80 OPTIMALLY WEIGHTED ANFIS SYSTEM BECOMES UNSTABLE
152 A. S. RAJ ET AL.
to 2D and 3D inversion problems with certain con-
trolling parameters such as learning rate, momentum,
the number of iterations and error percent. Training
database and acquiring knowledge are accomplished
to the best by ANFIS algorithm. More reliable perfor-
mance of ANFIS technique will have the best scope in
the future for estimating many optimisation problems.
Acknowledgements
The authors are willing to thank management of Loyola
College and Physics department for giving the opportunity
to publish this article.
Disclosure statement
No potential conflict of interest was reported by the authors.
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