Simulation is becoming more widely used for mineral resource estimation. There is great interest in quantifying geological uncertainty and understanding geological risk. Let’s review some applications of simulation to long range resource models. Exploration, short-term, underground and other specialized applications will be reviewed separately.
Simulation is the best approach to characterize a mineral deposit because: (1) simulated realizations reasonably represent geological variability, (2) uncertainty can be assessed at any scale, and (3) the information effect and selectivity are accounted for by averaging high-resolution realizations of geology and grade to an appropriate selective mining unit (SMU) block size. The application of simulation considers multiple realizations of SMU grades. In principle, all realizations should be used for all calculations; however, there are many practical applications where summaries of the realizations are used.
Estimate mineral resources on all realizations within the subset of blocks being considered (measured, indicated, or inferred), then report the expected value of the tonnes, grade and metal as the resource. The uncertainty in the resources can be checked relative to expectations, but is rarely disclosed (see March 29, 2020 blog). The reported resources represent all realizations.
Visualize local uncertainty by showing several realizations or summary measures. Cycling through the realizations shows how much the geology and grades could change. Summary measures can be computed at each SMU location such as the local standard deviation, coefficient of variation, P90-P10, the probability to exceed a cutoff grade, or the probability to be higher or lower than arbitrary thresholds. A high probability to exceed a high threshold indicates areas that are surely high. A high probability to be less than a low threshold indicates areas that are surely low. Local uncertainty could be visualized at the data scale, the SMU block size or any larger volume of interest.
Optimize a pit on each realization to understand the impact of geological uncertainty. The results are optimistic since each realization, in turn, is assumed to be the truth. The differences between the optimal pits is an interesting measure of uncertainty. Some of the pit slopes may be more uncertain than others, indicating where more data may be valuable. Uncertainty in economic parameters could be introduced by simulating prices and other parameters.
Create a localized model for the deposit to provide a single deterministic model that matches the expected grade distribution of the realizations. Panels are defined that contain about 50 to 100 SMUs each. The combined distribution of SMU grades is assembled for each panel, then the required number of SMU grades are sampled regularly from the combined distribution. Unique SMU grades are assigned to each location within the panel based on the rank order grade of a localizing variable. The unique localized model could be used in conventional mine planning software.
Run all realizations through the mine plan to understand other aspects of geological uncertainty. The mine plan may be based on a kriged or localized model, then each realization is processed through the plan. The results are pessimistic since the mine plan will evolve in the future as new information comes available; however, the variability in results is informative of the deviations that might be expected. Communicating possible deviations helps manage expectations.
Optimize over all realizations, perhaps with a penalty on risk, is the correct approach for many planning applications, but only available for specialized problems with specialized software. The Heuristic Pit Optimizer (HPO) worked on by various CCG researchers over the years is one tool. This is an active area of development, including a commercial implementation from Resource Modeling Solutions.
Perform sensitivity analysis to understand the first order sources of uncertainty. The realizations are summarized by posterior summary statistics including volumes of different rock types, averages of the grade variables in the domains, variances of grades in the domains, correlations between key variables and so on. Then, a response surface model of the resources as a function of these posterior parameters is constructed to understand what factors are contributing to resource uncertainty. This may lead to additional studies or data acquisition.
Drill Hole Spacing Studies (DHSS) are performed by resampling at different spacings, then resimulating to understand the uncertainty at closer spacings than currently exist. Uncertainty response curves are created, such as, predicting probability of monthly metal production to be within 15% of predicted as a function of drill hole spacing. Different resources, tolerances and production volumes could be considered to understand what spacing would be appropriate for different purposes including classification.
Value of Information Studies (VOIS) are also performed by resampling reference realizations at different spacings, then resimulating and optimizing potential engineering designs. Different data types associated with different inherent error could also be studied. The cost of data acquisition is traded off against improvements in the design. The optimal data spacing maximizes the net value.
Blending studies are undertaken to determine the performance of a particular grade control, mining, stockpiling, stacker/reclaimer scheme. The realistic variability of the simulated realizations is transferred through the entire process to understand the efficacy of the blending scenario. Many different scenarios are considered to optimize system performance.
The modern paradigm of simulation opens possibilities for many other specialized applications including (1) simulation of sampling and grade control to assess the appropriate SMU size, and (2) optimizing parameter selection by simulating with known properties, sampling at realistic data spacing, implementing different parameters, and comparing estimated properties with the known truth.
The Resource Modeling Solutions platform (RMSP) within our more interactive and automatic modeling platform (AMP) facilitate the application of simulation.
