Existing sampling techniques applied within known orebodies, such as sampling along mining drifts, yield element concentration values for larger blocks of ore if they are extended into their surroundings. The resulting average concentration values have relatively small "extension variance". These techniques can be used for multifractal modeling as well as ore reserve estimation approaches. Geometric probability theory can aid in local spatial covariance modeling. It provides information about increase of variability of element concentration over short distances exceeding microscopic scale. In general, the local clustering of ore crystals results in small-scale variability known as the "nugget effect". Parameters to characterize spatial covariance estimated from ore samples subjected to chemical analysis for ore reserve estimation may not be valid at local scale because of the nugget effect. The novel method of local singularity mapping applied within orebodies provides new insights into the nature of the nugget effect. Within the Pulacayo orebody, Bolivia, local singularity for zinc is linearly related with logarithmically transformed concentration value. If there is a nugget effect, moving averages resulting from covariance models or estimated by other methods that have a smoothing effect, such as kriging, can be improved by incorporating local singularities indicating local element enrichment or depletion. Although there have been many successful applications of the multifractal binomial/ip/i model, its application within the Pulacayo orebody results in inconsistencies, indicating some shortcomings of this relatively simple approach. Local singularity analysis and universal multifractal modeling are two promising new approaches to improve upon results obtained by commonly used geostatistical techniques and use of the binomial/ip/i model. All methods in this paper are illustrated using a single example (118 Pulacayo zinc values), and several techniques are applied to other orebody datasets (Whalesback copper deposit, Witwatersrand goldfields and Black Cargo titanium deposit). Additionally, it is discussed that nugget effects exist in a binary series of alternating mostly gneiss and metabasite previously derived from KTB borehole velocity and lithology logs, and within a series of 2796 copper concentration values from this same drill-hole.
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机译：已知矿石中使用的现有采样技术（例如沿采矿巷道采样），如果将较大的矿石块扩展到周围环境中，则会产生较大的矿石块元素浓度值。所得的平均浓度值具有相对较小的“延伸差异”。这些技术可用于多重分形建模以及矿石储量估算方法。几何概率理论可以帮助进行局部空间协方差建模。它提供了有关在超过微观尺度的短距离内元素浓度变异性增加的信息。通常，矿石晶体的局部聚集导致小规模的变化，称为“金块效应”。由于金块效应，用于表征进行化学分析以进行矿石储量估算的矿石样品估算的空间协方差的参数可能在局部范围内无效。在矿体中应用的局部奇异性映射的新方法为金块效应的性质提供了新的见识。在玻利维亚的Pulacayo矿体内，锌的局部奇异性与对数转换的浓度值线性相关。如果存在金块效应，则可以通过合并表示局部元素富集或耗尽的局部奇异点来改善由协方差模型得出的移动平均值或通过其他具有平滑效果的方法（例如克里格法）估计的移动平均值。尽管多重分形二项式/ p 模型已经有许多成功的应用，但是在普拉卡约矿体中的应用导致了不一致，这表明这种相对简单的方法存在一些缺点。局部奇异性分析和通用多重分形建模是两种有希望的新方法，可以改善常用地统计技术和使用二项式/ p 模型获得的结果。本文中的所有方法均通过一个示例（118 Pulacayo锌值）进行了说明，并且将多种技术应用于其他矿体数据集（鲸背铜矿床，Witwatersrand金矿床和Black Cargo钛矿床）。此外，还讨论了金块效应存在于以前从KTB钻孔速度和岩性测井中得出的交替的大部分片麻岩和变位辉石的二元序列中，并且在同一钻孔的一系列2796铜浓度值中。
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