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Spatial Variability

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Mineral Resource Estimation
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Abstract

An essential aspect of geostatistical modeling is to establish quantitative measures of spatial variability or continuity to be used for subsequent estimation and simulation. The modeling of the spatial variability has become a standard tool of mineral resource analysts. In the last 20 years or so, the traditional experimental variogram has given way to more robust measures of variability. Details of how to calculate, interpret and model variograms or their more robust alternatives are contained in this chapter.

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References

  • Armstrong M (1984) Improving the estimation and modeling of the variogram. In: Verly G et al (ed) Geostatistics for natural resources characterization, part I, Reidel, Dordrecht, pp 1–19

    Google Scholar 

  • Babakhani M, Deutsch CV (2012) Standardized pairwise relative variogram as a robust estimator of spatial structure. Unpublished CCG Research Paper 2012–310

    Google Scholar 

  • Barnes, RJ (1991) The variogram sill and the sample variance. Math Geol 23(4):673–678

    Article  Google Scholar 

  • Christakos G (1984). On the problem of permissible covariance and variogram models. Water Resour Res 20(2):251

    Article  Google Scholar 

  • Clark I (1986) The art of cross-validation in geostatistical applications. In: Proceeding of the 19th APCOM, pp 211–220

    Google Scholar 

  • Clark I, Harper WV (2000) Practical geostatistics. Ecosse North America, Columbus, p 340

    Google Scholar 

  • Cressie N (1985) Fitting variogram models by weighted least squares. Math Geol 17(5):563–586

    Google Scholar 

  • Cressie N (1991) Statistics for spatial data. Wiley, New York, p 900. Reprinted 1993

    Google Scholar 

  • David M (1977) Geostatistical ore reserve estimation. Elsevier, Amsterdam

    Google Scholar 

  • Davis BM (1987) Uses and abuses of cross-validation in geostatistics. Math Geol 17(5):563–586

    Google Scholar 

  • Deutsch CV, Journel AG (1997) GSLIB: geostatistical software library and user’s guide, 2nd ed. Oxford University Press, New York, p 369

    Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York, p 483

    Google Scholar 

  • Gringarten E, Deutsch CV (1999) Methodology for variogram interpretation and modelling for improved reservoir characterization. In: Paper SPE 56654, presented at the SPE annual technical conference and exhibition held in Houston, 3–6 October

    Google Scholar 

  • Isaaks EH (1999) SAGE2001 User’s Manual, Software license and documentation. http://www.isaaks.com

  • Isaaks E, Srivastava RM (1988) Spatial continuity measures for probabilistic and deterministic geostatistics. Math Geol 20(4):313–341

    Article  Google Scholar 

  • Isaaks EH, Srivastava RM (1989). An introduction to applied geostatistics. Oxford University Press, New York, p 561.

    Google Scholar 

  • Journel A (1988) New distance measures: the route towards truly non-Gaussian geostatistics. Math Geol 20(4):459–475

    Article  Google Scholar 

  • Journel AG (1987) Geostatistics for the environmental sciences: An introduction. U.S. Environmental Protection Agency, Environmental Monitoring Systems Laboratory

    Google Scholar 

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

    Google Scholar 

  • Myers DE (1991) Pseudo-cross variograms, positive definiteness and cokriging. Math Geol 23:805–816

    Article  Google Scholar 

  • Omre H (1984) The variogram and its estimation. In: Verly G, David M, Journel AG, Marechal A (eds) Geostatistics for natural resource characterization: NATO ASI series C, v. 122—Part I. Reidel Publication. Co., Dordrecht, pp 107–125

    Google Scholar 

  • Reed M, Simon B (1975) Methods of modern mathematical physics, vol II. Academic Press, New York

    Google Scholar 

  • Rossi ME, Parker HM (1993) Estimating recoverable reserves: is it hopeless? Presented at the Forum ‘Geostatistics for the Next Century’, Montreal, 3–5 June

    Google Scholar 

  • Solow AR (1990) Geostatistical cross-validation: a cautionary note. Math Geol 22:637–639

    Article  Google Scholar 

  • Srivastava RM (1987) A non-ergodic framework for variogram and covariance functions. Unpublished Master of Science Thesis, Stanford University, Stanford, CA

    Google Scholar 

  • Srivastava RM, Parker HM (1988) Robust measures of spatial continuity. In: Amstrong M (ed) Geostatistics. Reidel, Dordrecht, pp 295–308

    Google Scholar 

  • Zhu H, Journel A (1993) Formatting and integrating soft data: stochastic imagining via the Markov-Bayes algorithm. In: Soares A (ed) Geostatistics-Troia. Kluwer, Dordrecht, pp 1–12

    Google Scholar 

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Correspondence to Mario E. Rossi .

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Rossi, M., Deutsch, C. (2014). Spatial Variability. In: Mineral Resource Estimation. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5717-5_6

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