A Methodology to Assess Block Grade Uncertainty
Julián M. Ortiz, Oy Leuangthong, Clayton V. Deutsch,
Quantification of uncertainty of a spatially distributed variable at any scale can be handled through geostatistical simulation. Large computation time, storage, and post-processing of the realizations are required to obtain a final assessment of block uncertainty.
Multi-Gaussian kriging is a flexible alternative to Gaussian simulation. It computes the kriging estimate and variance after normal score transformation of the original samples. Under the multi-Gaussian assumption, all marginal and conditional distributions are Gaussian, hence fully defined by their mean and variance. These Gaussian conditional distributions are obtained by simple kriging and can be back-transformed to the original units of the variable of interest. An estimate and any quantile can be easily retrieved.
The main disadvantage of performing multi-Gaussian kriging is that change of support is not straightforward. We propose a methodology to overcome this limitation of multi-Gaussian kriging by considering a matrix simulation to generate multiple probability fields. Each probability field is used to draw spatially correlated point values from the point-support conditional distributions, and multiple realizations of the average can be obtained. This permits the calculation of the average over the block and its uncertainty. These blocks may correspond to selective mining units or to volumes from longer production periods relevant for engineering decisions. They can even be disjoint blocks, such as when several faces are mined at the same time. POSTMG, a Fortran program to perform these calculations, is described and a case study is provided.
Simulation, Uncertainty, Change of Support, Geostatistics, Multi-Gaussian