Most fracture data analysis techniques for attributes such as dip and aperture, treat the attributes independently of their respective spatial locations. A power‐law cumulative frequency for fracture apertures, for example, tells us nothing about their spatial distribution. Lacunarity is a technique for analyzing multi‐scale binary and non‐binary data and is ideally suited for analysis that relates an attribute (e.g., aperture) to its spatial distribution. In a previous study, we showed that scale‐dependent heterogeneity of fracture spacing can be analyzed using lacunarity in order to identify whether fractures occur in clusters. To determine if such clusters contain the largest fractures that control fluid flow through a fracture network, it is imperative that size attribute data be integrated with information about fracture spacing. Here we introduce the novel concept of lacunarity ratio (LR), which is the lacunarity of a given non‐binary data set normalized to the lacunarity of its random counterpart. This technique can delineate the relationship between attributes and spatial clustering by determining scale‐dependent changes in persistence and anti‐persistence. LR is implemented to test if large fractures are statistically found within fracture clusters or if they are randomly distributed at a given scale of observation. The technique is then applied to five different data sets with spacing values together with aperture, length and dip values respectively. The LR‐technique thus developed can help in identifying the occurrence of large or steep fractures with respect to fracture clusters, which in turn, can help improve modeling strategies.

中文翻译：

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空间分布断裂属性的分析：归一化空隙率

大多数针对诸如倾角和孔径的属性的裂缝数据分析技术都独立于其各自的空间位置来对待属性。例如，裂缝孔的幂律累积频率无法告诉我们有关孔洞空间分布的任何信息。腔隙性是一种用于分析多尺度二进制和非二进制数据的技术，非常适合将属性（例如，孔径）与其空间分布相关联的分析。在先前的研究中，我们表明可以使用隐秘性分析裂缝间距的尺度相关异质性，以识别裂缝是否在群中发生。为了确定这些簇是否包含控制流体流过裂缝网络的最大裂缝，必须将尺寸属性数据与有关裂缝间距的信息整合在一起。在这里，我们介绍了“盲度比”（LR）的新概念，它是将给定的非二进制数据集的盲度归一化为其随机对应项的盲度。通过确定持久性和反持久性的比例依赖变化，该技术可以描述属性与空间聚类之间的关系。LR用于测试是否在统计上发现了较大的裂缝，或者在给定的观察范围内它们是否随机分布。然后将该技术应用于五个不同的数据集，分别具有间距值，孔径，长度和倾角值。这样开发的LR技术可以帮助识别相对于裂缝簇的大裂缝或陡峭裂缝的发生，从而有助于改善建模策略。