Abstract The characteristics of coal deposits are relatively homogeneous in general; therefore, their geometric and quality parameters have stationary distributions. However, the geological setting could change this stationarity characteristic; thus, the coal may contain spatially different data trends. These data trends should be treated to derive an accurate estimation of the available coal resources. The general objective of this study is to optimize the drill hole spacing for the non-stationary dataset by applying some approaches to detrend the data. These approaches include spatially dividing the data into several domains (i.e., spatial clustering), extending the existing grid size (drill hole spacing), transforming the data, and using residuals data. The geometric and quality parameters used in this study were the seam thickness and total sulfur, respectively, from one coal seam in the Balikpapan Formation, Kutai Basin, East Kalimantan, Indonesia. The treated dataset was statistically and spatially analyzed to identify the data distribution changes. Nonetheless, the extended spacing, transformation, and residuals approaches resulted in almost similar data trends to the original. The study results indicated that the best approach to detrend the seam thickness and total sulfur at the study site was by dividing the dataset into three spatial domains (i.e., clusters). The global estimation variance method was used in the clustered dataset to produce optimum drill hole spacings of 1000 m, 2000 m, and 2600 m for the northern, central, and southern clusters, respectively, and the measured coal resources at the study site were obtained.

中文翻译：

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煤层厚度和总硫非平稳数据的钻孔间距优化：以东加里曼丹库泰盆地巴厘巴板组煤层为例

摘要 煤层特征总体上较为均质；因此，它们的几何和质量参数具有平稳分布。然而，地质环境可能会改变这种平稳性特征；因此，煤炭可能包含空间不同的数据趋势。应对这些数据趋势进行处理，以得出对可用煤炭资源的准确估计。本研究的总体目标是通过应用一些去趋势数据的方法来优化非平稳数据集的钻孔间距。这些方法包括在空间上将数据划分为多个域（即空间聚类）、扩展现有网格大小（钻孔间距）、转换数据以及使用残差数据。本研究中使用的几何参数和质量参数分别是来自印度尼西亚东加里曼丹库泰盆地巴厘巴板组一个煤层的煤层厚度和总硫。对处理过的数据集进行统计和空间分析，以确定数据分布的变化。尽管如此，扩展间距、变换和残差方法导致了与原始数据趋势几乎相似的数据趋势。研究结果表明，消除研究地点煤层厚度和总硫趋势的最佳方法是将数据集划分为三个空间域（即集群）。在聚类数据集中使用全局估计方差方法，分别为北部、中部和南部集群生成 1000 m、2000 m 和 2600 m 的最佳钻孔间距，