Fusion based classification method and its application

© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )

Download PDF

Cite

XML

Abstract

Jin, L., Sen, M.K. and Stoffa, P.L., 2009. Fusion based classification method and its application. Journal of Seismic Exploration, 18: 103-117. Classification algorithms have many applications both in exploration and production seismology. Many classification algorithms have been reported in the literature. However, for facies identification, lithology/fluid prediction etc, improper choice of an algorithm and parameters for a specific problem will create incorrect classification results. Here, we elaborate on some of these issues and propose a new method based on combining multiple classifiers with Dempster-Shafer theory (DS) that increases the accuracy of classification. The philosophy of our approach is that different classifiers offer complementary information about the patterns to be classified. Thus combining classifiers in an efficient way can achieve better classification results than a single classifier alone can. The effectiveness of this method is demonstrated with a real well log data from North Sea.

Keywords

facies classification

lithology prediction

Dempster-Shafer theory

fusion

neural network

back-propagation

References

Fusion based classification
To account for the uncertainties of choosing different classification
algorithms, different parameters, and different input attributes, a fusion based
classification method is presented. The workflow of this method is described in
Fig. 1.
Fig. 1 shows that multiple classifiers can be combined (fusion) using the
DS combination rule (7). The final output from this fusion process is expected
to be better than any of the individual outputs from different classifiers. In this
way, the accuracy of classification can be improved.
In this paper, we choose radial basis function network (RBF) and
backpropagation neural network (BP) as the classifiers; other classifiers can also
FUSION BASED CLASSIFICATION METHOD 107
be used. The outputs of the classifier are considered as the belief functions. The
DS combination rule is applied to get a final result.
In a similar manner, we can reduce the uncertainty of attribute selection
by combining outputs of multiple classifiers with different attributes.
Classifier | >| output 1 |
Classifier 2 tL} Output2
“Na Fusion pio
utput
Classifier 3 | 。 Output3 > (DS)
Classifier n 一說 Output n
Fig. 1. Workflow of fusion based classification.
EXAMPLE
We apply this fusion based classification method on a real dataset. It is
a type well in the oil field which is located in the South Viking Graben in the
North Sea. This exercise uses a method similar to that shown in Avseth and
Mukerji (2002) to classify different facies based on well measurements of Vp
and gamma ray. From the crossplot of Vp and gamma ray, we see that shale can
be classified easily from the sand facies (Fig. 2). A three step classification can
be used, which may increase the accuracy of classification. First, we separate
the sand and shale facies. Then, we discriminate between cemented sand, clean
sand and silty-sand. Finally we separate the silty sand into silty-sandl and
silty-sand2. Here, we choose three sand facies including cemented sand, clean
sand and silty-sand1 as classification targets (Fig. 3). It is similar to the step 2
of a three step classification. We can also group the silty-sand1 and silty-sand2
to be one class for the step 2 classification.
There are 303 samples for the cemented sand, 67 samples for the clean
sand and 106 samples for the silty-sand1. Six samples are randomly chosen as
test data for every facies, which are excluded from the training dataset. A three
layers BP neural network and radial basis network are used as classifiers. Fig.
4 shows the probability of different classes for the test dataset using BP neural
108 JIN, SEN & STOFFA
shale
130 silty-shale
120 cemented sand
clean sand
110 silty-sand1
100 +n silty-sand2
Gamma (API)
Vp (Km/S)
Fig. 2. The crossplot of a well logging data in the North Sea. Six facies are shown in this figure.
The shale and sand facies have a good separation.
network. Fig. 5 is the classification result. One sample is misclassified using BP
neural network. Fig. 6 shows the probability of different classes for the test
dataset using RBF. Fig. 7 is the classification result. Two samples are
misclassified with RBF. Then we combine the outputs of BP (Fig. 4) and RBF
(Fig. 6) to get the fusion result which is shown as Fig. 8, which combines the
two outputs of RBF and BP. The classification result is shown is Fig. 9. It
demonstrates that all the samples are correctly classified.
Next, we perform another experiment. The BP and RBF are run 20 times
by choosing different input parameters. For the BP neural network, we adjust
the size of the second layer. For the RBF, we adjust the spread of the radial
basis functions. Then, compute the mean probability of these 20 runs. The mean
probabilities from the two methods are further combined to get a final result.
Fig. 10 is the mean of the probability for different facies from 20 realizations
FUSION BASED CLASSIFICATION METHOD 109
of BP. Fig. 11 gives the classification result. All the samples are classified
correctly. Fig. 12 is the mean of the probability for different facies from 20
realizations of RBF. Fig. 13 shows the classification result based on Fig. 12. All
the samples are classified correctly. Thus we know that the accuracy of
classification increased by the statistical analysis of multiple runs of classifiers.
We further combine the probabilities shown in Figs. 10 and 12 using DS theory.
The result is shown in Fig. 14 which shows better separation of different facies
than the input probabilities. The classification result is shown is Fig. 15 which
shows that all the samples are classified correctly. We define the classification
variance as the difference between classification probability and output of the
classifier for the corresponding facies. Fig. 16 gives the variances for different
methods. It shows that the fusion result has the lowest variance among the three
methods. We finally note that even though we apply RBF and BP neural
network as classifiers, this fusion based classification method does not depend
on the choice of a specific classifier.
* cemented sand
90 O clean sand
© silty-sand1
Gamma (API)
a ~ co
oOo a
CD
Cn
2 2.5 3 3.5 4
Vp (Km/s)
Fig. 3. The crossplot of our chosen data. The data includes three facies: cemented sand, clean sand
and silty-sand1. The cemented is considered as class 1. Clean sand is treated as class 2. Silty-sand1
is represented as class 3.
JIN, SEN & STOFFA
probability(class 1)
2 4 6 8 10 12 14 16 18
Sample number
probability(class 2)
全
a
T
2 4 6 8 10 12 14 16 18
Sample number
T T T T T T T T
probability(class 3)
全
a
i
2 4 6 8 10 12 14 16 18
Sample number
Fig. 4. Probability of different classes using BP.
70 z T T T T T T T
+ True class
Y_ Result of BP
3h + vs 寢 i
5 上 7
的
加
8 外 yor * * F F FY 4
15+ |
位下审 v 寢字 |
5 4 4 : 上 | x “4 上
2 4 6 8 10 12 14 16 18
Samnla nitmhar
Fig. 5. Classification result of BP neural network based on the probability shown in Fig. 4. One
sample
is misclassified for the class 2.
FUSION BASED CLASSIFICATION METHOD
probability(class 1)
°o
a
probability(class 2)
oO
a
Sample number
2 4 6 8 10 12 14 16 18
Sample number
1 T T T T T T T T
2 4 6 8 10 12 14 16 18
1 T T T T T T T
probability(class 3)
y 4 6 8 10 12 14 16 18
Sample number
Fig. 6. Probability of different classes using RBF.
5 T T T T T T T T
3 v * = =e 里了
5 7
a
eo
8 2 wy 學 + + rv, 事 4
Oo
15 |
1 Md 寢 A ¥ M4 v
True class
Result of RBF
5 4 上 1 上上
2 4 6 8 10 12 14 16
Sample number
Fig. 7. Classification result of RBF based on the probability shown in figure 6. Two samples are
misclassified for the class 2.
N
JIN, SEN & STOFFA
5}
probability(class 1)
2 4 6 8 10 12 14 16 18
Sample number
probability(class 2)
o
a
1 1 4
2 4 6 8 10 12 14 16 18
Sample number
probability(class 3)
2 4 6 8 10 12 14 16 18
Sample number
Fig. 8. The Fusion probability of BP and RBF.
5 T T T T T T T T
3 上 ¥ vo ¥ A 更
5 上 4
a
5 上 4
+ + ¥ ¥ 字字 +
+ True class
7? Result of Fusion
2 4 6 8 10 12 14 16 18
Fig. 9. Classification result of fusion probability shown in Fig. 8. All the samples are correctly
classified.
FUSION BASED CLASSIFICATION METHOD 113
probability(class 1)
o
a
n
2 4 6 8 10 12 14 16 18
Sample number
probability(class 2)
o
a
0 1 1
2 4 6 8 10 12 14 16 18
Sample number
ao 1 T T T T T T T T
g
Ss
£
05+ 4
a
品
2 o 4 1
2 4 6 8 10 12 14 16 18
Sample number
Fig. 10. The mean probability of twenty runs of BP with different parameters.
5 T T T T T T T T
3 7' + ¥ = 前
5 4
F
3}
15 4
1 * ¥ ey, ¥ 4
a
05 L 4 1 1 1 7 Multiple Runs of BP
2 4 6 8 10 12 14 16 18
Sample number
Fig. 11. Classification result based on the probability shown in Fig. 10. All the samples are correctly
classified.
114 JIN, SEN & STOFFA
=
°
probability(class 1)
全
a
1 上
2 4 6 8 10 12 14 16 18
Sample number
=
全
probability(class 2)
全
【
2 4 6 8 10 12 14 16 18
Sample number
T T T T T 可
人
probability(class 3)
全
a
2 4 6 8 10 12 14 16 18
Sample number
Fig. 12 The mean probability of twenty runs of RBF with different parameters.
5 T T T T T T T T
3 wy v= = + >
5+ 4
PA
加
is)
5 上 7
wwsa += <= 时 4
+ True class
了 Multiple Runs of RBF
5 + + n
4 由
2 4 6 8 10 12 14 16 18
Sample number
Fig. 13. Classification result based on the probability shown in Fig. 12. All the samples are correctly
classified.
FUSION BASED CLASSIFICATION METHOD 115
probability(class 1)
o
a
上
2 4 6 8 10 12 14 16 18
Sample number
probability(class 2)
o
a
上
2 4 6 8 10 12 14 16 18
Sample number
1 T T T r T T T T
probability(class 3)
2 4 6 8 10 12 14 16 18
Sample number
Fig. 14. Fusion result using the mean probabilities shown in Fig. 10 and 12.
5 T T T T T T T T
3+ fet + + &
5 上
人
=
15+ 4
伴 + 家 *, Ff ¥ 4
+ True class
i i i i 了? Fusion Result
05 1 4 4
2 4 6 8 10 12 14 16 18
Sample number
Fig. 15. Classification result based on the fusion probability shown in Fig. 14. All the samples are
correctly classified.
116 JIN, SEN & STOFFA
—+— Variance of BP classification
—?— Variance of RBF classification
一 Variance of Fusion classification
0 1 1 1 1
2 4 6 8 10 12 14 16 18
Sample number
Fig. 16. The variance of different classification methods: multiple runs of BP, multiple runs of RBF
and the fusion of multiple runs BP and RBF. The fusion based method can further reduce the
variance of classification.
CONCLUSION
We presented a method that combines multiple classifiers based on DS
combination rules to improve classification accuracy and reduce the uncertainties
related to the choice of suitable classification algorithms and parameters. An
example is presented which is based on the real well log data from the North
Sea. It shows that the fusion based classification does improve the accuracy and
stability of classification of shale and different sand facies. The statistical
analysis of multiple runs of a specific classifier with different parameters is
another way to reduce the uncertainty of the choice of parameters. The fusion
of statistical classification results further reduces the variance of the
classification. We demonstrated that this fusion based classification is a general
method and does not depend on the specific classifiers and therefore, appears
to be a promising tool.
FUSION BASED CLASSIFICATION METHOD 117
ACKNOWLEDGMENTS
Long Jin was supported on a grant from Conoco-Phillips and Jackson
School of Geosciences. We thank Dr. Xiaohong Chen and Dr. Shoudong Wang
for many helpful discussions.
REFERENCES
Avseth, P. and Mukerji, T., 2002. Seismic lithofacies classification from well logs using statistical
rock physics. Petrophysics, 43: 70-81.
Avseth, P. and Mukerji, T., 2005. Quantitative Seismic Interpretation. Cambridge University Press,
Cambridge.
Dowla, F.U. and Rogers, L.L., 1995. Solving Problems in Environmental Engineering and
Geosciences with Artificial Neural Networks. MIT Press, Cambridge, MA.
Holmes, C.C. and Mallick, B.K., 1998. Bayesian radial basis functions of variable dimension.
Neural Computat., 10: 1217-1233.
Li, J. and Castagna, J., 2004. Support vector machine pattern recognition to AVO classification.
Geophys. Res. Lett., 31: L02609.
Martin, D., Buhmann, M. and Ablowitz, J., 2003. Radial Basis Functions: Theory and
Implementations. Cambridge University Press, Cambridge.
Saggaf, M.M., Tokséz, M,N. and Marhoon, M.I., 2003. Seismic facies classification and
identification by competitive neural networks. Geophysics, 68: 1984-1999.
Shafer, G., 1976. A Mathematical Theory of Evidence. Princeton University Press, Princeton.
Shafer, G., 1990. Perspectives on the theory and practice of belief functions. Internat. J. Approxim.
Reason., 3: 1-40.

Previous article in this issue

Next article in this issue

Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing

Publisher's Core Philosophy

We are committed to support the scientific community by publishing impactful research and enhancing communication among scientists. At AccScience Publishing, we are continuously looking for ways to accelerate scientific progress and to strive for transparency and open communication, making knowledge freely accessible without barrier.

9 Raffles Place, Republic Plaza 1 #06-00 Singapore 048619

+65 8182 1586

editorial@accscience.com