The scaling laws describing the spatial arrangement of fractures along six deep boreholes penetrating the crystalline rocks in the Rhine Graben were derived using a correlation analysis. Five of the wells, two to 5 km depth, were located at the Soultz geothermal site and one well to 5 km depth was located at Basel, some 150 km from Soultz. Five datasets were derived from borehole imaging logs, whilst one stemmed from the analysis of 810 m of continuous core at Soultz. The two differed inasmuch as the core dataset included essentially all fractures, whereas the image log dataset had few fractures narrower than 1–3 mm. The results of the analysis for all image datasets showed that the spatial arrangement of fractures followed fractal behavior at all scales from meters to several hundred meters, the largest scale amenable to assessment, and that the fractal dimensions were confined to the narrow range 0.85–0.9. However, the core dataset showed significant deviation from fractal behavior, the best-fit fractal dimension of 0.8 being somewhat lower than values obtained from imaging logs in neighboring wells. Eliminating fractures with apertures less than 1 mm from the core dataset to improve comparability led to even lower fractal dimension estimates, indicating the discrepancy was not due to imaging log resolution. Analysis of successive depth sections of the core log suggested the discrepancy was due to the presence of a localized zone between 1750 and 2070 m where the fractal organization is disturbed or takes a lower dimension than elsewhere. Aside from this zone, no systematic variation of fractal dimension with depth was observed in any dataset, implying that a single exponent together with intensity adequately describes the arrangement of fractures along the entire length of the boreholes. The results are relevant to the parameterization of DFN models of deep rock masses.

描述沿着穿过莱茵河地堑结晶岩的六个深钻孔的裂缝空间排列的比例定律是使用相关分析得出的。其中 5 口井深度为 2 至 5 公里，位于 Soultz 地热现场，1 口井深度为 5 公里位于巴塞尔，距离 Soultz 约 150 公里。五个数据集来自钻孔成像测井，而一个来自对 Soultz 810 m 连续岩心的分析。两者的不同之处在于核心数据集基本上包括所有裂缝，而图像测井数据集几乎没有窄于 1-3 毫米的裂缝。所有图像数据集的分析结果表明，裂缝的空间排列在从米到几百米的所有尺度上都遵循分形行为，这是可以评估的最大尺度，并且分形维数被限制在 0.85-0.9 的狭窄范围内。然而，核心数据集显示出与分形行为的显着偏差，0.8 的最佳拟合分形维数略低于从相邻井的成像测井中获得的值。从核心数据集中消除孔径小于 1 mm 的裂缝以提高可比性导致甚至更低的分形维数估计，表明差异不是由于成像日志分辨率。对岩心测井连续深度剖面的分析表明，这种差异是由于在 1750 到 2070 m 之间存在一个局部区域，其中分形组织受到干扰或比其他地方具有更低的维度。除了这个区域，在任何数据集中都没有观察到分形维数随深度的系统变化，这意味着单个指数和强度足以描述沿钻孔整个长度的裂缝排列。该结果与深部岩体 DFN 模型的参数化有关。