样本点与距离权重对距离幂次反比法的影响

The Influence of Sample Point and Distance Weight on Inverse Distance Weighting

资源储量估算是勘察工作的重要组成部分,体现了地质勘查工作的价值。为了研究距离幂次反比法在估值过程中偏差与距离权重和样本点数量的关系,使用曼哈顿距离、切比雪夫距离和欧氏距离为权重计算方法,研究样本点数量、距离权重计算方法对距离幂次反比法估值的影响。蛇纹岩矿实例研究结果表明:使用曼哈顿距离、欧氏距离计算权重时,估值的Ni和MgO品位存在被低估的风险;随样本点增加,矿石品位被低估的风险会减小;而切比雪夫距离不适于距离幂次反比法的权重计算。曼哈顿距离用于计算权重时,估值的Ni和MgO品位分布形态与样品品位分布形态更为接近,此时,可以更好刻画矿体内品位分布状态;而欧氏距离估值的Ni和MgO品位均值与样品品位均值更接近,其储量估值精度较高。使用欧氏距离计算权重、7个样本点估值时,对Ni和MgO品位估值的综合效果最好,此时,Ni品位均值偏差为-1.64%、MgO品位为-1.11%。

Reserve estimation is an important component of prospecting work and reflects the value of geological prospecting work. In order to study the relation between the biases and the distance weight with the number of samples in the process of valuation, the Manhattan distance, Chebyshev distance and Euclidean distance were used as the weight to study the influence of the number of samples and the calculation methods of distance weight on the reserves estimation of inverse distance weighting. A case study of serpentine ore was concluded as follows. Firstly, when using the Manhattan distance and Euclidean distance to calculate the weight, the estimation of Ni and MgO grade would be underestimated. With the increase of sample points, the risk of ore grade being underestimated would be reduced. And the Chebyshev distance was not suitable for the weight calcula- tion of the inverse distance weighting. Secondly, when the Manhattan distance was used to calculate the weight, the Ni and MgO grade distributions were closer to the sample grade distribution, and the grade distribution of the ore body could be better described. When the Euclidean distance was used, the Ni and MgO grade values were closer to the mean grade of the samples, and the accuracy of the resource reserves was higher. Finally, when the Euclidean distance was used to calculate the weight, and combining with seven sample points for estimation, the comprehensive estimation effect on the Ni and MgO grade was the best. At this point, the bias of mean values for Ni grade and MgO grade was respectively -1.64% and -1.11%.