Spatial correlation structures of fracture systems for deriving a scaling law and modeling fracture distributions

An understanding of fracture systems in geological media requires two fracture properties clarification: fracture distributions and the scaling law of fracture systems over different scales. To investigate fracture systems in different scales, we used remotely sensed images from LANDSAT and SPOT satellites, borehole-fracture data in two drilling directions, and a thin-section of rock core sample. The eastern part of the Tohoku district, northeastern Japan, overlain by Cretaceous granite and a Jurassic accretionary complex, was chosen as the study area. Assuming that part of the line features detected in satellite and thin-section images correspond with real fractures, the spatial correlation structures of fractures were clarified by semivariograms to identify an alternative scaling law. For this we focused on joint's line density along boreholes, area density of linear features, and directional relations of strikes between a fracture pair to produce semivariograms of densities and cross-semivariograms of the strikes transformed into binary data sets. The same model independent of the scales could approximate the semivariograms of each parameter. Spatial correlation distances were obtained from the range of the semivariogram model. An important characteristic was that linear trends between representative and correlation distances of fractures were found in log–log plots. Scaling law can contribute to estimating correlation distances at arbitrary fracture scales. A conditional distribution modeling at the borehole-fracture scale was presented as an application of the semivariograms obtained by the three steps: generation of fracture-density map by a sequential gaussian simulation, assignment of strikes to each simulated fracture, and connection of fractures considering distances and differences in strikes between a closely located fracture pair. Additionally, nonconditional simulation at arbitrary fracture scales and changes of permeabilities with scales using a permeability tensor analysis are discussed.