Skip to main content
Log in

A Statistical Approach to Geological Mapping

  • Published:
Mathematical Geology Aims and scope Submit manuscript

Abstract

A geological map is the representation, on a two-dimensional plane, of the disposition of three-dimensional rock bodies exposed on the earth's surface. The problem of mapping is essentially that of dividing an area into “homogeneous” subregions on the basis of the exposed rock types. Automatic Bayesian methods of model selection using default Bayes factors have been employed to solve the problem of choosing a set of boundaries between “homogeneous” subregions, assuming no complication excepting low-angle tilting affected rock bodies. The method is tested on two data sets. A sampling scheme for optimum allocation of observation points is also presented.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Aitchison, J., 1986, The statistical analysis of compositional data: Chapman and Hall, London, 416 p.

    Google Scholar 

  • Atkinson, A. C., 1978, Posterior probabilities for choosing a regression model: Biometrika, v. 65, p. 39–48.

    Google Scholar 

  • Berger, J. O., and Pericchi, L. R., 1996, The intrinsic Bayes factor for model selection and prediction: J. Am. Stat. Assoc., v. 91, p. 109–122.

    Google Scholar 

  • Berger, J. O., Pericchi, L. R., and Varshavsky, J. A., 1998, Bayes factors and marginal distributions in invariant situations: Sankhya, Ser. A, v. 60, p. 307–321.

    Google Scholar 

  • Fishman, G. S., 1978, Principles of discrete event simulation: JohnWiley and Sons, New York, 514 p.

    Google Scholar 

  • Geisser, S., and Eddy, W. F., 1979, A predictive approach to model selection: J. Am. Stat. Assoc., v. 74, p. 153–160.

    Google Scholar 

  • Gelfand, A. E., Dey, D. K., and Chang, H., 1992, Model determination using predictive distributions with implementation via sampling-based methods (with discussion), in Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., eds., Bayesian statistics, Vol. 4: Oxford University Press, London, p. 147–167.

    Google Scholar 

  • Ghosh, J. K., Saha, M. R., and Sengupta, S., 1981, Gondwana stratigraphic classification by statistical method, in Merriam, D. F., ed., Down-to-earth statistics: Solutions looking for geological problems: Syracuse University Geology Contributions, Syracuse, New York, p. 47–62.

    Google Scholar 

  • O'Hagan, A., 1995, Fractional Bayes factor for model comparisons: J. R. Stat. Soc., Ser. B, v. 57, p. 99–138.

    Google Scholar 

  • San Martini, A., and Spezzaferri, F., 1984, A Predictive model selection criterion: J. R. Stat. Soc., Ser. B, v. 46, p. 296–303.

    Google Scholar 

  • Sengupta, S., 1970, Gondwana sedimentation around Bheemaram (Bhimaram), Pranhita-Godavari valley, India: J. Sed. Pet., v. 40, p. 140–170.

    Google Scholar 

  • Sengupta, S., Ghosh, J. K., and Mazumder, B. S., 1991, Experimental-theoretical approach to interpretation of grain size frequency distributions, in Syvitski, J. P. M., ed., Principles, methods, and application of particle size analysis: Cambridge University Press, Cambridge, UK, p. 264–279.

    Google Scholar 

  • Spiegelhalter, D. J., and Smith, A. F. M., 1982, Bayes factor for linear and log-linear models with vague prior information: J. R. Stat. Soc., Ser. B, v. 44, p. 377–387.

    Google Scholar 

  • Switzer, P., 1967, Reconstructing patterns from sample data: Ann. Math. Stat., v. 38, p. 138–154.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghosh, J.K., Bhanja, J., Purkayastha, S. et al. A Statistical Approach to Geological Mapping. Mathematical Geology 34, 505–528 (2002). https://doi.org/10.1023/A:1016038710777

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1016038710777

Navigation