Fractal characteristics of fractures in crystalline basement rocks: Insights from depth-dependent correlation analyses to 5 km depth

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.