Copula-based spatial modelling of geometallurgical variables

Musafer, G. N., Thompson, M. H., Kozan, E. and Wolff, R. C. (2013). Copula-based spatial modelling of geometallurgical variables. In: Simon Dominy, Proceedings: The Second AusIMM International Geometallurgy Conference (GeoMet) 2013. GeoMet 2013: The Second AusIMM International Geometallurgy Conference, Brisbane, QLD, Australia, (239-246). 30 September-2 October, 2013.

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Name Description MIMEType Size Downloads
Author Musafer, G. N.
Thompson, M. H.
Kozan, E.
Wolff, R. C.
Title of paper Copula-based spatial modelling of geometallurgical variables
Conference name GeoMet 2013: The Second AusIMM International Geometallurgy Conference
Conference location Brisbane, QLD, Australia
Conference dates 30 September-2 October, 2013
Proceedings title Proceedings: The Second AusIMM International Geometallurgy Conference (GeoMet) 2013
Place of Publication Carlton, VIC, Australia
Publisher The Australasian Institute of Mining and Metallurgy (AusIMM)
Publication Year 2013
Sub-type Fully published paper
ISBN 9781921522970
Editor Simon Dominy
Start page 239
End page 246
Total pages 8
Collection year 2014
Language eng
Formatted Abstract/Summary
The most important aspect of modelling a geological variable, such as metal grade, is the spatial correlation. Spatial correlation describes the relationship between realisations of a geological variable sampled at different locations. Any method for spatially modelling such a variable should be capable of accurately estimating the true spatial correlation. Conventional kriged models are the most commonly used in mining for estimating grade or other variables at unsampled locations, and these models use the variogram or covariance function to model the spatial correlations in the process of estimation. However, this usage assumes the relationships of the observations of the variable of interest at nearby locations are only influenced by the vector distance between the locations. This means that these models assume linear spatial correlation of grade. In reality, the relationship with an observation of grade at a nearby location may be influenced by both distance between the locations and the value of the observations (ie non-linear spatial correlation, such as may exist for variables of interest in geometallurgy). Hence this may lead to inaccurate estimation of the ore reserve if a kriged model is used for estimating grade of unsampled locations when non-linear spatial correlation is present. Copula-based methods, which are widely used in financial and actuarial modelling to quantify the non-linear dependence structures, may offer a solution. This method was introduced by Bárdossy and Li (2008) to geostatistical modelling to quantify the non-linear spatial dependence structure in a groundwater quality measurement network. Their copula-based spatial modelling is applied in this research paper to estimate the grade of 3D blocks. Furthermore, real-world mining data is used to validate this model. These copula-based grade estimates are compared with the results of conventional ordinary and lognormal kriging to present the reliability of this method.
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Document type: Conference Paper
Collections: W.H. Bryan Mining Geology Research Centre
Official 2014 Collection
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Created: Thu, 14 Nov 2013, 14:56:34 EST by Jon Swabey on behalf of WH Bryan Mining and Geology Centre