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Simulated Block Variance for 3D Drillhole Infill


Drillhole infill has an important role in the mining industry, especially when its aim is to enhance the assessment of variance representativeness of a mineralized rock or any other measured characteristics. Some infill optimization methods propose the use of kriging variance, which is feasible when the goal is to search for sub-sampled regions, but those methods may fail in more complex situations given that a fundamental limitation of kriging variance is to only depend on neighboring samples nearby the estimate location. This paper proposes a method to infer the best location for new drillholes through optimization using as objective function the sum of simulated block variance (SBV), which does not have the same limitation as to the kriging variance. The SBV is reached by stochastic simulation (sequential Gaussian simulation) to compute the variance of each block along with the grid model, and the values are summed to attain the objective function. The objective function minimization is computed by three different methods of search: random search, simulated annealing, and particle swarm optimization. Due to smaller objective function values when applied to a synthetic deposit, simulated annealing with fast cooling schedule algorithm performed better than the others. Further tests led to the conclusion that simulated annealing had more representation of the population. These methods were also applied to a real sampled site, the Capanema Mine, and the simulated annealing with fast cooling also produced the best results with regard to representativeness.

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Data Availability

The synthetic data can be shared by the corresponding author.

Code Availability

The codes written for the paper and the editions to existing software (GsLib) can be shared by the corresponding author.


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The authors acknowledge the funding received from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), the availability of software Studio RM provided by Datamine used in developing this work, utilized in agreement between the software developers, and the Laboratório de Informática Geológica from the Instituto de Geociências Universidade de São Paulo.


The research was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

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Correspondence to Gustavo Z. Ramos.

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See Table

Table 8 Results of each optimization method for a given number of holes. Values are ratios of the optimized values to the initial objective function, given as a value of 1 for the 0 number of new holes


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Ramos, G.Z., da Rocha, M.M., Correia, A.E. et al. Simulated Block Variance for 3D Drillhole Infill. Nat Resour Res 31, 1245–1263 (2022).

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  • Optimization
  • Infill
  • Uncertainty
  • Mining
  • Simulation
  • Heuristic