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Fusion based classification method and its application

LONG JIN,  MRINAL K. SEN,  PAUL L. STOFFA
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Jackson School of Geosciences, The University of Texas at Austin, Austin, TX, U.S.A.,
JSE 2009, 18(2), 103–117;
Submitted: 13 February 2008 | Accepted: 16 January 2009 | Published: 1 April 2009
© 2009 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/ )
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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
  1. To account for the uncertainties of choosing different classificationalgorithms, different parameters, and different input attributes, a fusion basedclassification method is presented. The workflow of this method is described inFig. 1.
  2. Fig. 1 shows that multiple classifiers can be combined (fusion) using the
  3. DS combination rule (7). The final output from this fusion process is expectedto be better than any of the individual outputs from different classifiers. In thisway, the accuracy of classification can be improved.
  4. In this paper, we choose radial basis function network (RBF) andbackpropagation neural network (BP) as the classifiers; other classifiers can alsoFUSION BASED CLASSIFICATION METHOD 107be used. The outputs of the classifier are considered as the belief functions. The
  5. DS combination rule is applied to get a final result.
  6. In a similar manner, we can reduce the uncertainty of attribute selectionby combining outputs of multiple classifiers with different attributes.Classifier | >| output 1 |Classifier 2 tL} Output2“Na Fusion pioutputClassifier 3 | 。 Output3 > (DS)Classifier n 一 說 Output nFig. 1. Workflow of fusion based classification.EXAMPLE
  7. We apply this fusion based classification method on a real dataset. It isa type well in the oil field which is located in the South Viking Graben in the
  8. North Sea. This exercise uses a method similar to that shown in Avseth and
  9. Mukerji (2002) to classify different facies based on well measurements of Vpand gamma ray. From the crossplot of Vp and gamma ray, we see that shale canbe classified easily from the sand facies (Fig. 2). A three step classification canbe used, which may increase the accuracy of classification. First, we separatethe sand and shale facies. Then, we discriminate between cemented sand, cleansand and silty-sand. Finally we separate the silty sand into silty-sandl andsilty-sand2. Here, we choose three sand facies including cemented sand, cleansand and silty-sand1 as classification targets (Fig. 3). It is similar to the step 2of a three step classification. We can also group the silty-sand1 and silty-sand2to be one class for the step 2 classification.
  10. There are 303 samples for the cemented sand, 67 samples for the cleansand and 106 samples for the silty-sand1. Six samples are randomly chosen astest data for every facies, which are excluded from the training dataset. A threelayers 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 neural108 JIN, SEN & STOFFAshale130 silty-shale120 cemented sandclean sand110 silty-sand1100 +n silty-sand2Gamma (API)Vp (Km/S)
  11. 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 BPneural network. Fig. 6 shows the probability of different classes for the testdataset using RBF. Fig. 7 is the classification result. Two samples aremisclassified 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 thetwo outputs of RBF and BP. The classification result is shown is Fig. 9. Itdemonstrates that all the samples are correctly classified.
  12. Next, we perform another experiment. The BP and RBF are run 20 timesby choosing different input parameters. For the BP neural network, we adjustthe size of the second layer. For the RBF, we adjust the spread of the radialbasis functions. Then, compute the mean probability of these 20 runs. The meanprobabilities from the two methods are further combined to get a final result.
  13. Fig. 10 is the mean of the probability for different facies from 20 realizationsFUSION BASED CLASSIFICATION METHOD 109of BP. Fig. 11 gives the classification result. All the samples are classifiedcorrectly. Fig. 12 is the mean of the probability for different facies from 20realizations of RBF. Fig. 13 shows the classification result based on Fig. 12. Allthe samples are classified correctly. Thus we know that the accuracy ofclassification increased by the statistical analysis of multiple runs of classifiers.
  14. We further combine the probabilities shown in Figs. 10 and 12 using DS theory.
  15. The result is shown in Fig. 14 which shows better separation of different faciesthan the input probabilities. The classification result is shown is Fig. 15 whichshows that all the samples are classified correctly. We define the classificationvariance as the difference between classification probability and output of theclassifier for the corresponding facies. Fig. 16 gives the variances for differentmethods. It shows that the fusion result has the lowest variance among the threemethods. We finally note that even though we apply RBF and BP neuralnetwork as classifiers, this fusion based classification method does not dependon the choice of a specific classifier.* cemented sand90 O clean sand© silty-sand1Gamma (API)a ~ cooOo aCDCn2 2.5 3 3.5 4Vp (Km/s)
  16. Fig. 3. The crossplot of our chosen data. The data includes three facies: cemented sand, clean sandand silty-sand1. The cemented is considered as class 1. Clean sand is treated as class 2. Silty-sand1is represented as class 3.JIN, SEN & STOFFAprobability(class 1)2 4 6 8 10 12 14 16 18Sample numberprobability(class 2)全aT2 4 6 8 10 12 14 16 18Sample numberT T T T T T T Tprobability(class 3)全ai2 4 6 8 10 12 14 16 18Sample number
  17. Fig. 4. Probability of different classes using BP.70 z T T T T T T T+ True classY_ Result of BP3h + vs 寢 i5 上 7的加8 外 yor * * F F FY 415+ |位 下 审 v 寢 字 |5 4 4 : 上 | x “4 上2 4 6 8 10 12 14 16 18Samnla nitmhar
  18. Fig. 5. Classification result of BP neural network based on the probability shown in Fig. 4. Onesampleis misclassified for the class 2.FUSION BASED CLASSIFICATION METHODprobability(class 1)°oaprobability(class 2)oOaSample number2 4 6 8 10 12 14 16 18Sample number1 T T T T T T T T2 4 6 8 10 12 14 16 181 T T T T T T Tprobability(class 3)y 4 6 8 10 12 14 16 18Sample number
  19. Fig. 6. Probability of different classes using RBF.5 T T T T T T T T3 v * = =e 里 了5 7aeo8 2 wy 學 + + rv, 事 4Oo15 |1 Md 寢 A ¥ M4 vTrue classResult of RBF5 4 上 1 上 上2 4 6 8 10 12 14 16Sample number
  20. Fig. 7. Classification result of RBF based on the probability shown in figure 6. Two samples aremisclassified for the class 2.NJIN, SEN & STOFFA5}probability(class 1)2 4 6 8 10 12 14 16 18Sample numberprobability(class 2)oa1 1 42 4 6 8 10 12 14 16 18Sample numberprobability(class 3)2 4 6 8 10 12 14 16 18Sample numberFig. 8. The Fusion probability of BP and RBF.5 T T T T T T T T3 上 ¥ vo ¥ A 更5 上 4a8 2 上 © 县 + & + 讓 a5 上 4+ + ¥ ¥ 字 字 ++ True class7? Result of Fusion2 4 6 8 10 12 14 16 18
  21. Fig. 9. Classification result of fusion probability shown in Fig. 8. All the samples are correctlyclassified.FUSION BASED CLASSIFICATION METHOD 113probability(class 1)oan2 4 6 8 10 12 14 16 18Sample numberprobability(class 2)oa0 1 12 4 6 8 10 12 14 16 18Sample numberao 1 T T T T T T T TgSs£05+ 4a品2 o 4 12 4 6 8 10 12 14 16 18Sample number
  22. Fig. 10. The mean probability of twenty runs of BP with different parameters.5 T T T T T T T T3 7' + ¥ = 前5 4a 2 w 9 于 5 + © 4F3}15 41 * ¥ ey, ¥ 4a05 L 4 1 1 1 7 Multiple Runs of BP2 4 6 8 10 12 14 16 18Sample number
  23. Fig. 11. Classification result based on the probability shown in Fig. 10. All the samples are correctlyclassified.114 JIN, SEN & STOFFA=°probability(class 1)全a1 上2 4 6 8 10 12 14 16 18Sample number=全probability(class 2)全【2 4 6 8 10 12 14 16 18Sample numberT T T T T 可人probability(class 3)全a2 4 6 8 10 12 14 16 18Sample number
  24. Fig. 12 The mean probability of twenty runs of RBF with different parameters.5 T T T T T T T T3 wy v= = + >5+ 4PA加8 2 7, F F © F © 4is)5 上 7wwsa += <= 时 4+ True class了 Multiple Runs of RBF5 + + n4 由2 4 6 8 10 12 14 16 18Sample number
  25. Fig. 13. Classification result based on the probability shown in Fig. 12. All the samples are correctlyclassified.FUSION BASED CLASSIFICATION METHOD 115probability(class 1)oa上2 4 6 8 10 12 14 16 18Sample numberprobability(class 2)oa上2 4 6 8 10 12 14 16 18Sample number1 T T T r T T T Tprobability(class 3)2 4 6 8 10 12 14 16 18Sample number
  26. Fig. 14. Fusion result using the mean probabilities shown in Fig. 10 and 12.5 T T T T T T T T3+ fet + + &5 上人8 2 下 * © © © © |=15+ 4伴 + 家 *, Ff ¥ 4+ True classi i i i 了? Fusion Result05 1 4 42 4 6 8 10 12 14 16 18Sample number
  27. Fig. 15. Classification result based on the fusion probability shown in Fig. 14. All the samples arecorrectly classified.116 JIN, SEN & STOFFA—+— Variance of BP classification—?— Variance of RBF classification一 Variance of Fusion classification0 1 1 1 12 4 6 8 10 12 14 16 18Sample number
  28. Fig. 16. The variance of different classification methods: multiple runs of BP, multiple runs of RBFand the fusion of multiple runs BP and RBF. The fusion based method can further reduce thevariance of classification.CONCLUSION
  29. We presented a method that combines multiple classifiers based on DScombination rules to improve classification accuracy and reduce the uncertaintiesrelated to the choice of suitable classification algorithms and parameters. Anexample is presented which is based on the real well log data from the North
  30. Sea. It shows that the fusion based classification does improve the accuracy andstability of classification of shale and different sand facies. The statisticalanalysis of multiple runs of a specific classifier with different parameters isanother way to reduce the uncertainty of the choice of parameters. The fusionof statistical classification results further reduces the variance of theclassification. We demonstrated that this fusion based classification is a generalmethod and does not depend on the specific classifiers and therefore, appearsto be a promising tool.FUSION BASED CLASSIFICATION METHOD 117ACKNOWLEDGMENTS
  31. Long Jin was supported on a grant from Conoco-Phillips and Jackson
  32. School of Geosciences. We thank Dr. Xiaohong Chen and Dr. Shoudong Wangfor many helpful discussions.REFERENCES
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  34. Avseth, P. and Mukerji, T., 2005. Quantitative Seismic Interpretation. Cambridge University Press,Cambridge.
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  36. Geosciences with Artificial Neural Networks. MIT Press, Cambridge, MA.
  37. Holmes, C.C. and Mallick, B.K., 1998. Bayesian radial basis functions of variable dimension.Neural Computat., 10: 1217-1233.
  38. Li, J. and Castagna, J., 2004. Support vector machine pattern recognition to AVO classification.Geophys. Res. Lett., 31: L02609.
  39. Martin, D., Buhmann, M. and Ablowitz, J., 2003. Radial Basis Functions: Theory and
  40. Implementations. Cambridge University Press, Cambridge.
  41. Saggaf, M.M., Tokséz, M,N. and Marhoon, M.I., 2003. Seismic facies classification andidentification by competitive neural networks. Geophysics, 68: 1984-1999.
  42. Shafer, G., 1976. A Mathematical Theory of Evidence. Princeton University Press, Princeton.
  43. Shafer, G., 1990. Perspectives on the theory and practice of belief functions. Internat. J. Approxim.Reason., 3: 1-40.
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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