Heavy-mineral assemblages of sediments and sedimentary rocks record information regarding provenance, including the source rocks involved, tectonic setting, climatic conditions, and modifications from source to sink. Drawing conclusions on provenance and provenance changes requires robust quantification of individual heavy-mineral species contents, including error estimates. Nevertheless, it is common practice to count sub-quantities of grains from aliquots and not considering the bias introduced by (a) counting similar numbers of grains from aliquots containing different total numbers of grains, and (b) using variable counting methods. Consequently, reported heavy-mineral contents estimated from counting sub-quantities are affected by errors of unknown extent, making it infeasible to determine whether intra- or intersample variations are statistically significant. Based on 65 heavy-mineral aliquots of variable grain size, mineral species contents, total number of grains, and known composition determined by counting all grains (n = 80,393), here >31 million countings of heavy-mineral sub-quantities are simulated using (a) ribbon counting with varying ribbon size, ribbon position, ribbon orientation, total number of counts, and ways of aggregating counts from multiple ribbons, and (b) a newly proposed counting technique called cluster counting. I show that (a) error estimation for a specific aliquot requires a finite population correction; (b) compared to adjacent ribbons, aggregating counts of spatially distant ribbons reduces the error; (c) cluster counting further reduces the error, showing the best fit with theory; and (d) the Wilson score interval enables error calculation as well as the number of grains to be counted to achieve an operator-specific aim.

中文翻译：

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重矿物颗粒计数：计数技术、误差估计和要计数的颗粒数量

沉积物和沉积岩的重矿物组合记录了有关物源的信息，包括所涉及的烃源岩、构造环境、气候条件以及从源到汇的变化。要得出有关来源和来源变化的结论，需要对各个重矿物种类的含量进行可靠的量化，包括误差估计。然而，通常的做法是对等分试样中的谷物子数量进行计数，并且不考虑由于以下原因引入的偏差：(a)从包含不同谷物总数的等分试样中计数相似数量的谷物，以及(b)使用可变计数方法。因此，通过计数子数量估计的报告重矿物质含量受到未知程度误差的影响，从而无法确定样本内或样本间变化是否具有统计显着性。基于 65 个不同颗粒尺寸、矿物种类含量、颗粒总数以及通过计数所有颗粒确定的已知成分 ( n  = 80,393) 的重矿物等分试样，这里使用以下方法模拟了超过 3100 万次重矿物子数量计数(a) 具有不同色带尺寸、色带位置、色带方向、计数总数以及聚合来自多个色带的计数的方式的色带计数，以及 (b) 一种新提出的称为聚类计数的计数技术。我证明（a）特定等分试样的误差估计需要有限总体校正； (b) 与相邻的色带相比，空间上距离较远的色带的聚合计数减少了误差； (c) 聚类计数进一步减少了误差，显示出与理论的最佳拟合； (d) 威尔逊评分区间能够进行误差计算以及要计数的谷物数量，以实现操作员特定的目标。