Abstract
A real-world mining application of pair-copulas is presented to model the spatial distribution of metal grade in an ore body. Inaccurate estimation of metal grade in an ore reserve can lead to failure of a mining project. Conventional kriged models are the most commonly used models for estimating grade and other spatial variables. However, kriged models use the variogram or covariance function, which produces a single average value to represent the spatial dependence for a given distance. Kriged models also assume linear spatial dependence. In the application, spatial pair-copulas are used to appropriately model the non-linear spatial dependence present in the data. The spatial pair-copula model is adopted over other copula-based spatial models since it is better able to capture complex spatial dependence structures. The performance of the pair-copula model is shown to be favorable compared to a conventional lognormal kriged model.
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Acknowledgements
This research was funded by the Australian Government’s Cooperative Research Centre for Optimising Resource Extraction Grant P3C-030. The authors thank the reviewers for their comments and guidance, which greatly improved discussion and practical aspects of the application.
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Musafer, G.N., Thompson, M.H., Kozan, E. et al. Spatial Pair-Copula Modeling of Grade in Ore Bodies: A Case Study. Nat Resour Res 26, 223–236 (2017). https://doi.org/10.1007/s11053-016-9314-3
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DOI: https://doi.org/10.1007/s11053-016-9314-3