Non-Gaussian Copula Simulation for Estimation of Recoverable Reserve in an Indian Copper Deposit
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Original Paper
Non-Gaussian Copula Simulation for Estimation of Recoverable Reserve in an Indian Copper Deposit Krishna Dinda1 and Biswajit Samanta2,3 Received 7 March 2020; accepted 23 August 2020
The present study developed a geostatistical simulation technique based on non-Gaussian copula for recoverable reserve estimation considering support effect of a well-known openpit mine of a copper deposit in India. The focus was to examine the efficacy of copula-based simulation model in recoverable reserve estimation. It was assessed by comparing three selectivity curves like grade–ore tonnage, grade–metal tonnage and ore–metal tonnage of reserve constructed using the copula-based simulation, disjunctive kriging and multi-Gaussian kriging with respect to the production data of blasting. The results informed that the copula-based simulation technique provided better accuracy than the nonlinear geostatistical techniques of disjunctive kriging and multi-Gaussian kriging. The root mean square error and standard error analysis indicated that the copula-based simulation model provided more accurate estimates compared with disjunctive kriging and multi-Gaussian kriging. All the three techniques yielded biased estimates, but the least bias was attributed to the copulabased simulation technique. KEY WORDS: Reserve estimation, Copula, V-transformed copula, KendallÕs tau correlation.
INTRODUCTION Recoverable reserve is the proportion of mineral resources that can be techno-economically mined from a deposit. Hence, parameters like cutoff grade and selective mining unit (SMU) size and accessibility of ore would determine actual availability of recoverable reserve (Ravenscroft 1992). As detailed mine planning and subsequent decision on investment largely depends upon estimated figure of recoverable reserve, accurate estimation of this quantity is of paramount importance to a mine planner. Because only limited widely spaced ex1
Advanced Technology Development Centre, Indian Institute of Technology, Kharagpur 721302, India. 2 Department of Mining Engineering, Indian Institute of Technology, Kharagpur 721302, India. 3 To whom correspondence should be addressed; e-mail: [email protected]
ploratory boreholes are available during the planning stage for estimation of such quantity, the problem often becomes very challenging. Traditional linear geostatistical techniques such as ordinary kriging (Matheron 1963a), universal kriging (Huijbregts 1971) and simple kriging (Journel and Huijbregts 1978) provide overly smooth SMU values that frequently result in inaccurate estimation. The methods of nonlinear geostatistics like disjunctive kriging (Matheron 1976b), multi-Gaussian kriging (Verly 1983; Verly and Sullivan 1985) and uniform conditioning with a discrete Gaussian model (Rivoirard 1994) for support effect, which overcome smoothing problem, are highly sensitive to the Gaussianity assumption. Moreover, the theoretical background of these models is so complex that they have not been widely accepted by the field engineers. Only
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