Abstract
Imprecise geological information is combined with measured data to perform geostatistical reserve estimation. Fuzzy set theory is used to characterize imprecise information expressed by membership functions. Then the kriging estimator considers both the measurements and the imprecise information. The traditional criteria for the estimator are extended by seeking the minimalization of a measure of imprecision in addition to unbiasedness and minimal estimation variance. The methodology is applied to bauxite quality estimation. It is shown that the incorporation of imprecise geological information into kriging results in a more acceptable reserve estimation that corresponds better to the geologic conditions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bardossy, A., I. Bogardi, and W. E. Kelly, Imprecise (fuzzy) information in geostatistics, Mathematical Geology, 20(4), 287–311. 1988.
Berger, J. O., Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York, 617 p., 1985.
Bogardi, I., L. Duckstein, and A. Bardossy, Trade-off between cost and efficiency of pollution control, Proceedings, VI International Conference on Multiple-Criteria Decision Making, Cleveland, Ohio, June 1984.
De Marsily, G., Spatial variability of properties in porous media; a stochastic approach, Fundamantals of Transport Phenomena in Porous Media, J.Bear (ed. ), The Hague, 1984.
Goicoechea, A., D. R. Hansen, and L. Duckstein, Multi-objective Decision Analysis with Engineering and Business Applications, Wiley, p. 519, 1982.
Journel, A., mAD and conditional quantile estimators, Geostatistics for Natural Resources Characterization, Verly et al. (eds.), D. Reidel Publishing Company, 261–270, 1984.
Journel, A., Constrained interpolation and qualitative information — The soft kriging approach, Mathematical Geology, 18 (3), 269–286, 1986.
Journel, A. and Ch.J. Huijbregts, Mining Geostatistics, Academic Press, New York, 1978.
Kitanidis, P. K., Parameter uncertainty in estimation of spatial functions: Bayesian analysis, Water Resour. Res., 22 (4), 499–507, April, 1986.
Kulkarni, R., Bayesian kriging in geotechnical problems, Geostatistics for Natural Resources Characterization, Verly et al. (eds.), D. Reidel Publishing Company, 775–786, 1984.
Matheron, G., Traité de Geostatistique Appliquée, Editions Techn., Paris, 1962.
Omre, H., Bayesian kriging — merging observations and qualified guesses in kriging, Mathematical Geology, 19 (1), 25–39, 1987.
Zadeh, L. A., Fuzzy sets, Inform. Contr. 8, 338 - -353.
Zimmermann, H. J., Fuzzy Set Theory and its Application, Martinus Nijhoff, p. 363, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Bárdossy, A., Bárdossy, G., Bogárdi, I. (1989). Application of Geological Information to Kriging. In: Armstrong, M. (eds) Geostatistics. Quantitative Geology and Geostatistics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-6844-9_46
Download citation
DOI: https://doi.org/10.1007/978-94-015-6844-9_46
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-6846-3
Online ISBN: 978-94-015-6844-9
eBook Packages: Springer Book Archive