Artifact Reduced Localization of Uncertainty – Lipstick on a Pig

"INTRODUCTION Conventional mine planning is performed on a single resource model at a selective mining unit (SMU) scale deemed appropriate for the deposit and mining method. Estimation methods such as kriging and inverse distance, commonly used to construct a single model, are susceptible to histogram smoothing (Rossi & Deutsch, 2014). This can be mitigated by limiting the number of composites per estimate, therefore correctly reproducing the distribution of estimates (Boisvert & Deutsch, 2012). Search limiting techniques remedy histogram smoothing at the cost of introducing a problematic conditional bias (Isaaks, 1999) and introduces even greater spatial smoothing. Localization is an alternative, offering histogram reproduction through post processing of more robust probabilistic modeling techniques. A single localized model at the SMU scale is desirable. The correct histogram can be reproduced and a single model allows for the use of conventional mine planning and resource evaluation techniques. Despite the advertized benefits of localization, the necessary reliance on a larger panel scale as a middle step in the localization process yields unsightly “edge-effect” artifacts (Boisvert & Deutsch, 2012). Two approaches to artifact reduction are presented here. The first is a straight forward optimization approach designed to minimize an objective function that penalizes artifacts including panel edge discontinuities to generate a model free of panel edge-effects. The second approach redefines a panel in a less conventional fashion as a randomly chosen set of SMUs throughout the domain. This method produces a model void of any regular panel shape resulting in an artifact free model. Artifact reduction minimizes the obvious “edge-effect” issues of localization but local precision issues described by Boisvert & Deutsch (2012) persist. Localization is not a replacement for quantified uncertainty for comprehensive risk analysis and resource evaluation. LOCALIZATION Initially developed with Uniform Conditioning in mind, localization collapses a distribution of local uncertainty at a panel scale to an SMU scale model for mine planning (Abzalov, 2006). This process has been extended to Indicator Kriging (Hardke, 2011), Sequential Gaussian Simulation (Boisvert & Deutsch, 2012) and MultiGaussian Kriging (Daniels and Deutsch, 2014). The localization process is performed in a similar fashion regardless of which technique is chosen to create the prior model of uncertainty. Methodology There are three scales of importance considered in the localization process. The point scale, otherwise known as the data scale, is the smallest and is the scale at which experimental data is collected. The SMU or block scale is the familiar scale at which mine planning and resource evaluation takes place. Lastly, the panel scale is larger and contains a number of SMUs. Each of the three scales is illustrated in Figure 1."