<p>This study introduces a non-stationary v-transformed copula model for simulating orebodies and estimating recoverable reserves, addressing the limitations of traditional stationary models in the case of mineral deposits with gradational contact points (referred to as soft boundaries) between ore and waste domains. The fundamental assumption of the proposed model is that cumulative distribution function (CDF) of the random function is stationary within a specific panel, and the model is stationary with respect to that panel. This assumption enables that the model to reflect non-stationary features by allowing CDF to vary from one panel to another. Thus, the concept of piecewise stationarity on each panel is introduced into the development of non-stationary v-transformed copula-based simulation model. Since the correct representation of soft boundaries is essential for this kind of non-stationary model, an automatic boundary detection algorithm is developed to detect ore and waste contacts. This proof-of-concept has been applied to a case study mine, to evaluate the effectiveness of non-stationary v-transformed copula-based simulation model for reserve estimation by comparing selectivity curves with those of stationary copula model and ground-truth blast hole data. These findings highlight the superiority of the non-stationary model over its stationary counterpart.</p>

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Recoverable reserve estimation using non-stationary and non-Gaussian copula-based simulation model

  • Krishna Dinda,
  • Biswajit Samanta,
  • Debashish Chakravarty

摘要

This study introduces a non-stationary v-transformed copula model for simulating orebodies and estimating recoverable reserves, addressing the limitations of traditional stationary models in the case of mineral deposits with gradational contact points (referred to as soft boundaries) between ore and waste domains. The fundamental assumption of the proposed model is that cumulative distribution function (CDF) of the random function is stationary within a specific panel, and the model is stationary with respect to that panel. This assumption enables that the model to reflect non-stationary features by allowing CDF to vary from one panel to another. Thus, the concept of piecewise stationarity on each panel is introduced into the development of non-stationary v-transformed copula-based simulation model. Since the correct representation of soft boundaries is essential for this kind of non-stationary model, an automatic boundary detection algorithm is developed to detect ore and waste contacts. This proof-of-concept has been applied to a case study mine, to evaluate the effectiveness of non-stationary v-transformed copula-based simulation model for reserve estimation by comparing selectivity curves with those of stationary copula model and ground-truth blast hole data. These findings highlight the superiority of the non-stationary model over its stationary counterpart.