Simple and Ordinary Multigaussian Kriging for Estimating Recoverable Reserves

Author: Emery, Xavier

Source: Mathematical Geology, Volume 37, Number 3, April 2005 , pp. 295-319(25)

Publisher: Springer

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Abstract:

Multigaussian kriging is used in geostatistical applications to assess the recoverable reserves in ore deposits, or the probability for a contaminant to exceed a critical threshold. However, in general, the estimates have to be calculated by a numerical integration (Monte Carlo approach). In this paper, we propose analytical expressions to compute the multigaussian kriging estimator and its estimation variance, thanks to polynomial expansions. Three extensions are then considered, which are essential for mining and environmental applications: accounting for an unknown and locally varying mean (local stationarity), accounting for a block-support correction, and estimating spatial averages. All these extensions can be combined; they generalize several known techniques like ordinary lognormal kriging and uniform conditioning by a Gaussian value. An application of the concepts to a porphyry copper deposit shows that the proposed “ordinary multigaussian kriging” approach leads to more realistic estimates of the recoverable reserves than the conventional methods (disjunctive and simple multigaussian krigings), in particular in the nonmineralized undersampled areas.

Keywords: Hermite polynomials; conditional expectation; discrete Gaussian model; local stationarity; lognormal kriging; multigaussian model

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s11004-005-1560-6

Affiliations: Department of Mining Engineering, University of Chile, Avenida Tupper, 2069, Santiago, Chile, Email: xemery@cec.uchile.cl

Publication date: April 1, 2005

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