Proportions

An enhanced co-simulation technique for resource modelling using grade domaining: a case study from an iron ore deposit

“…Truncated Gaussian modelling is a stochastic approach that was first formulated by Matheron et al (1987) that constructs realisations of the categorical variables. The following workflow can be applied to simulate the grade domains (Armstrong et al 2011), after definition of a variogram model: Perform Gibbs sampler (Geman and Geman 1984) to convert the grade domain at data locations into a Gaussian random field. Employ a multi-Gaussian simulation algorithm to simulate the Gaussian random fields at the target locations conditioned to the Gaussian data obtained from Gibbs sampler. Apply a truncation rule (already defined by a cut-off grade) to convert the obtained Gaussian maps into the corresponding grade domains. …”

“…waste and ore) is as follows: Split the original grade distributions into the grade domains (e.g. waste and ore) based on the corresponding cut-off values. Simulate grade domains using a truncated Gaussian simulation algorithm to obtain the simulated grade domains: Convert categorical data at sample location, namely grade domain i , into indicators: Calculate the truncation thresholds and infer the variogram model of the Gaussian random field through the corresponding indicator variograms. Transform the categorical data into a Gaussian random field by applying a Gibbs sampler algorithm (Armstrong et al 2011): Simulate the obtained Gaussian random field via turning bands simulation at the target location Truncate the simulated values into the poor and rich ore grade domains considering the pre-defined threshold. Simulate partial grades at each grade domain via the turning bands co-simulation algorithm: Transform the resultant partial grades into two different standard normal score distributions, with the Gaussian distribution with mean 0 and variance 1. Convert the declustered continuous variable ( ) into a Gaussian variable ( ) via modelling the anamorphosis function (Rivoirard 1994) Check the multi-Gaussianity hypothesis. Calculate the direct and cross-covariance functions of the normal score variables and obtain the fitted model through a linear model of coregionalisation. Co-simulate the partial grades conditionally to the heterotopic sample data. Obtain the realisations of the continuous variables (waste and ore grades) by inverse transformation of simulated values via the anamorphosis function. Juxtaposing the obtained simulated values of partial grades into the corresponding grade domain, realisation by realisation, to obtain the final models. …”

“…Simulate grade domains using a truncated Gaussian simulation algorithm to obtain the simulated grade domains: Convert categorical data at sample location, namely grade domain i , into indicators: Calculate the truncation thresholds and infer the variogram model of the Gaussian random field through the corresponding indicator variograms. Transform the categorical data into a Gaussian random field by applying a Gibbs sampler algorithm (Armstrong et al 2011): Simulate the obtained Gaussian random field via turning bands simulation at the target location Truncate the simulated values into the poor and rich ore grade domains considering the pre-defined threshold. …”

“…Transform the categorical data into a Gaussian random field by applying a Gibbs sampler algorithm (Armstrong et al 2011): …”

“…Grade domains can be interpreted by any deterministic approach, such as explicit and implicit modelling (Rossi and Deutsch 2014); however, this does not incorporate quantification of the uncertainty related to the domain definition. Stochastic approaches such as Sequential Indicator simulation (Deutsch 2006), truncated Gaussian simulation (Matheron et al 1987), and Plurigaussian simulation (Armstrong et al 2011) can be used to quantify uncertainty. For the modelling of a continuous variable, it is a common practice to model each grade variable separately within each grade domain using deterministic or stochastic approaches.…”