Ore resource estimation based on radial based functions - Case study on União Luiz and Morro do Carrapato Gold Deposits (Alta Floresta Gold Province)

Abstract Radial basis functions can be used as an alternative method for mineral resource estimation when ordinary kriging cannot be done because it is impossible to calculate an experimental variogram. Interpolation based on radial based functions is a method that is similar to ordinary kriging. In this context, this article presents the results of gold resource estimation and modeling of the União Luis and Morro do Carrapato gold deposits located in Alta Floresta Gold Province, Mato Grosso. Experimental variograms in the main direction (90-degree strike) resulted in a pure nugget effect, whereas in the orthogonal direction (180/85), they resulted in a structured variogram. However, the structured variogram for 180/85 is useless because three orthogonal variograms are needed to define the anisotropy ellipsoid for deriving a correlation model used in ordinary kriging. Thus, mineral resource estimation was done using multiquadric equations, a very popular radial based function kernel. The 3D model for gold grades showed a vertical distribution suggesting a structural conditioning for gold mineralization. The grade-tonnage curve with a simulated cutoff of 5.0 g/ton resulted in a gold mineral resource of 2.122 tons. Through the above, the gold estimation and multiquadric equation-based 3D model for the studied area can be considered effective in its objective to estimate ore resources from the available data.摘要：当因无法计算实验变异函数（experimental variogram）而无法采用普通克里金（ordinary kriging）方法时，径向基函数（radial based functions）可作为矿产资源估算的替代方案。基于径向基函数的插值方法与普通克里金方法原理相似。本文针对位于马托格罗索州阿尔塔弗洛雷斯塔金省的União Luis与Morro do Carrapato金矿床，开展了金资源估算与建模研究，并展示了相关结果。主方向（走向90°）下的实验变异函数表现为纯块金效应，而正交方向（180/85°）下的实验变异函数则呈现结构化特征。但180/85°方向的结构化变异函数并无实用价值，因为若要推导普通克里金所用的相关模型，需借助三个正交方向的变异函数以定义各向异性椭球（anisotropy ellipsoid）。因此，本次研究采用应用广泛的径向基函数核——多二次方程（multiquadric equations）开展矿产资源估算。金品位三维模型呈现出垂直分布特征，暗示金矿化受构造作用控制。以模拟边界品位5.0 g/吨计算的品位-吨位曲线（grade-tonnage curve）显示，研究区金矿产资源量为2.122吨。综上，针对研究区开展的金资源估算及基于多二次方程的三维模型，可有效达成利用现有数据估算矿石资源的目标。