Scaling and connectivity of joint systems in sandstones from western Norway

The scaling properties of a joint system in Devonian sandstones in western Norway have been investigated using seven maps, covering areas from 18 to 720 m across, which were generated by mapping in the field and from low-level aerial photography taken from different heights. Each map represent a scale ‘window’ on the fracture population, bounded by resolution at small scales and the sample size at large scales. A power-law relationship between fracture trace length and critical observation height (maximum height at which a trace can be identified) is derived and used to create a statistical model for the resolution effects. The model indicates that a continuous smooth curve without a straight-line segment on a log-log cumulative frequency distribution plot does not necessarily rule out a power law as the underlying population distribution. Together, the maps indicate a powerlaw trace-length distribution with an exponent of −2.1. This power law may be valid over four or more orders of magnitude, with natural lower cut-off of around 1 m. The exponent is significantly different from −2.0 (strictly selfsimilar case) and is reflected in a decrease in the abundance of fractures with length comparable to map size, as map scale decreases. The fracture trace-length distribution results in a decrease in apparent connectivity, with decreasing scale. High resolution (large-scale) maps are well connected while the lowest resolution map (smallest scale) is unconnected. Fractures in the smallest scale map are, however, connected by small fractures below the limit of resolution, represented by the largest scale map. The variation in apparent connectivity with scale has implications for fluid flow. When fractures are open to fluid flow the scaling properties of apparent connectivity imply that, beyond a certain scale, the size of fracture controlling flow will be scale-independent. In this fracture system, this appears to occur in sample areas of around 300 m across.