Incorporation of fracture directions into 3D geostatistical methods for a rock fracture system

Simulating a rock fracture distribution is an important problem common to various fields in geosciences. This paper presents GEOFRAC, a geostatistical method to simulate a fracture distribution by incorporating the directions (strikes and dips) of the sampled fracture data into the simulation. Fracture locations are generated randomly following fracture densities assigned by a sequential Gaussian simulation. Fracture directions are transformed into an indicator set consisting of several binary (0 and 1) variables and the variables are compressed using the principal component analysis. Ordinary kriging is then employed to estimate the distributions of these principal values and the results are back-transformed into the coordinate system of the original indicator set. Fracture directions are generated randomly using their histograms within the defined directional interval. Finally, facets (fracture elements) are determined from the simulated locations and directions, and the fractures within the angle and distance tolerances are connected to form a fracture plane. From a case study of applying GEOFRAC to the fracture data in Kikuma granite, southwest Japan, GEOFRAC was shown to be able to depict a plausible fracture system because the simulated directions corresponded well to those measured. Furthermore, the simulated fracture system was available to estimate the hydraulic conductivity of the study site, which was roughly in agreement with the average of hydraulic test results.