Skip to main content
SpringerLink
Log in

Spatial Variability of Rock Depth in Bangalore Using Geostatistical, Neural Network and Support Vector Machine Models

  • Original Paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

Geospatial technology is increasing in demand for many applications in geosciences. Spatial variability of the bed/hard rock is vital for many applications in geotechnical and earthquake engineering problems such as design of deep foundations, site amplification, ground response studies, liquefaction, microzonation etc. In this paper, reduced level of rock at Bangalore, India is arrived from the 652 boreholes data in the area covering 220 km2. In the context of prediction of reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth, Geostatistical model based on Ordinary Kriging technique, Artificial Neural Network (ANN) and Support Vector Machine (SVM) models have been developed. In Ordinary Kriging, the knowledge of the semi-variogram of the reduced level of rock from 652 points in Bangalore is used to predict the reduced level of rock at any point in the subsurface of the Bangalore, where field measurements are not available. A new type of cross-validation analysis developed proves the robustness of the Ordinary Kriging model. ANN model based on multi layer perceptrons (MLPs) that are trained with Levenberg–Marquardt backpropagation algorithm has been adopted to train the model with 90% of the data available. The SVM is a novel type of learning machine based on statistical learning theory, uses regression technique by introducing loss function has been used to predict the reduced level of rock from a large set of data. In this study, a comparative study of three numerical models to predict reduced level of rock has been presented and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Abbreviations

a:

Range of the variogram

b:

The scalar threshold

C:

Capacity factor (for learning machine)

C (0) :

σ Sill of the variogram

C0 :

Nugget of the variogram

l:

The number of training sets

Rn :

n-Dimensional real vector space

w:

The boundary

wi :

Weight assigned to each scater point

x:

The input vector

y:

A binary value representing the two classes

δk :

Actual error

ε:

Error insensitive zone

εk :

Normalized error

ρ(w,b):

Margin

γ (h):

Semi-variogram

σ:

The width of radial basis function

Γ:

Gamma function

References

  • Aleksandar I, Morton H (1990) An introduction to neural computing. Chapman and Hall, London

    Google Scholar 

  • Boser BE, Guyon IM, Vapnik VN (1992) A training algorithm for optimal margin classifiers. In: Haussler D (ed) 5th Annual ACM workshop on COLT. ACM Press, Pittsburgh, pp 144–152

    Google Scholar 

  • Burgress TM, Webster R (1980a) Optimal interpolation and isarithmic mapping of soil properties I. The semivariogram and punctual kriging. J Soil Sci 31:315–331

    Article  Google Scholar 

  • Burgress TM, Webster R (1980b) Optimal interpolation and isarithmic mapping of soil properties II. Block kriging. J Soil Sci 31:333–341

    Article  Google Scholar 

  • Clark I (1979) Practical geostatistics. Applied Science Publishers, Ltd., London, 129 pp

    Google Scholar 

  • Davis JC (2002) Statistics and data analysis in geology, 3rd edn. Wiley, New York

    Google Scholar 

  • Demuth HB, Beale M (1999) Neural Network Toolbox, users guide. The Mathworks, Inc., Natick

    Google Scholar 

  • Dibike YB, Velickov S, Solomatine D, Abbot MB (2001) Model induction with support vector machine: introduction and application. J Comput Civil Eng 15(3):208–216

    Article  Google Scholar 

  • Dowla FU, Rogers LL (1995) Solving problems in environmental engineering and geoscience with artificial neural networks. MIT, Cambridge

    Google Scholar 

  • Drucker H, Donghui W, Vapnik VN (1999) Support vector machine form spam categorization. IEEE Trans Neural Netw 10(5):1048–1054

    Article  Google Scholar 

  • Foody GM, Mathur A (2004) A relative evaluation of multiclass image classification by support vector machines. IEEE Trans Geosci Remote Sens 42(6):1335–1343

    Google Scholar 

  • Furey TS, Cristianini N, Duffy N, Bednarski DW Bednarski, Schummer M Haussler D (2000) Support vector machine classification and validation using microarray expression data. Bioinformatics 16(10):906–914

    Article  Google Scholar 

  • Guillaume A (1977) Introduction a la géologie quantitative: Masson, Paris

  • Gunn S (1998) Support vector machines for classification and regression. Image Speech and Intelligent Systems Technical Report, University of Southampton, UK

  • Gunn R (2003) Support vector machines for classification and regression. http://www.ecs.soton.ac.uk/∼srg/publications/pdf/SVM.pdf

  • Guyon I, Weston J, Steohen B, Vapnik V (2002) Gene selection for cancer classification using support vector machines. Mach Learn 46(1–3):389–422

    Article  Google Scholar 

  • Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5(6):989–993

    Google Scholar 

  • Hagan MT, Demuth HB, Beale M (1996) Neural network design. PWS, Boston

    Google Scholar 

  • Haykin S (1999) Neural networks: a comprehensive foundation. Prentice-Hall Inc., New Jersey

    Google Scholar 

  • Hebb DO (1949) The organization of behavior. Wiley, New York

    Google Scholar 

  • Hertz J, Krogh A, Palmer R (1991) Introduction to the theory of neural computation. Addison-Wesly, Reading

    Google Scholar 

  • Isaaks EH, Srivastava RM (1989) An introduction to applied geostatics. Oxford University Press, New York

    Google Scholar 

  • Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press, New York

    Google Scholar 

  • Khanna T (1989) Foundations of neural networks. Addison-Wesly, Reading

    Google Scholar 

  • Kitanidis PK (1991) Orthonormal residuals in geostatistics: model criticism and parameter estimation. Math Geol 23(5):741–758

    Article  Google Scholar 

  • Kitanidis PK (1997) Introduction to geostatistics: applications in hydrogeology. Cambridge University Press, pp 86–95

  • Kohonen T (1988) An introduction to neural computing. Neural Netw 1(1):3–16

    Article  Google Scholar 

  • Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266

    Article  Google Scholar 

  • Matheron G (1972) Théorie des variables régionalisées in Traité d’Informatique Géologique. Masson, Paris, pp 306–378

  • MathWork, Inc. (1999) Matlab user’s manual, version 5.3. The MathWorks, Inc., Natick

  • McCulloch WS, Pitts W (1943) A logical calculus in the ideas immanent in nervous activity. Bull Math Biophys 5:115–133

    Article  Google Scholar 

  • More JJ (1977) The Levenberg-Marquardt algorithm: implementation and theory. In: Watson GA (ed) Numerical analysis. Springer, Heidelberg, pp 105–116

  • Mukherjee S, Osuna E, Girosi F (1997) Nonlinear prediction of chaotic time series using support vector machine. In: Proceedings of the IEEE workshop on neural networks for signal processing 7. Institute of Electrical and Electronics Engineers, New York, pp 511–519

  • Muller KR, Smola A, Ratsch G, Scholkopf B, Kohlmorgen J, Vapnik V (1997) Predicting time series with support vector machines. In: Proceedings of the international conference on artificial neural networks. Springer-Verlag, Berlin, 999

  • Osuna E, Freund R, Girosi F (1997) An improved training algorithm for support vector machines. In: Proceedings of the IEEE workshop on neural networks for signal processing 7. Institute of Electrical and Electronics Engineers, New York, pp 276–285

  • Radhakrishna BP, Vaidyanadhan R (1997) Geology of Karnataka. Geological Society of India, Bangalore

    Google Scholar 

  • Rendu JM (1978) An introduction to geostatistical methods of mineral evaluation. S African Inst of Min and Metal, Kimberly, 84 pp

  • Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 68:386–408

    Article  Google Scholar 

  • Rubeis VD, Tosi P, Gasparini C, Solipaca A (2005) Application of Kriging technique to seismic intensity data. Bull Seismol Soc Am 95(2):540–548

    Article  Google Scholar 

  • Shahin MA, Jaksa MB, Maier HR (2000) Predicting the settlement of shallow foundations on cohesion less soils using back-propagation neural networks. Department of Civil and Envi Eng, University of Adelaide, Australia, R167

  • Sincero AP (2003) Predicting mixing power using artificial neural network. EWRI World Water and Environmental

  • Smola A (1996) Regression estimation with support vector learning machines. Technische Universitat Munchen, Munchen

    Google Scholar 

  • Vapnik V (1995) The nature of statistical learning theory. Springer, New York

    Google Scholar 

  • Vapnik V, Golowich S, Smola A (1997) Support method for function approximation regression estimation and signal processing. In: Mozer M, Petsch T (eds) Advance in neural information processing system 9. MIT Press, Cambridge

Download references

Acknowledgements

Authors thank Seismology division, Department of Science and Technology, Government of India for funding the project titled “Geotechnical site characterization of greater Bangalore region”. Ref no. DST/23(315)/SU/2001 dated October 2003.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Science, Bangalore, 560 012, India

    T. G. Sitharam, Pijush Samui & P. Anbazhagan

Authors
  1. T. G. Sitharam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pijush Samui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Anbazhagan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pijush Samui.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sitharam, T.G., Samui, P. & Anbazhagan, P. Spatial Variability of Rock Depth in Bangalore Using Geostatistical, Neural Network and Support Vector Machine Models. Geotech Geol Eng 26, 503–517 (2008). https://doi.org/10.1007/s10706-008-9185-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-008-9185-4

Keywords

Search

Navigation