Analysis of Fracture Orientation Data From Boreholes

Abstract

Fracture orientation data from boreholes find widespread use in investigations of the subsurface. These data invariably are biased, with in situ fractures at low angles to a borehole being under-represented. Three statistical measures (mean spherical orientation, spherical variance, and moment of inertia), conventionally used to analyze axial data distributed on a sphere without corrections for borehole bias, are used here to analyze fracture pole orientations distributed on a hemisphere, with borehole bias being accounted for. By assuming a particular model for the in situ distribution of fractures, such as a uniform distribution, and then correcting for borehole bias, one can predict the distribution and statistics of fracture poles a borehole survey would yield. The model can then be modified based on the mismatch between observations and predictions. Geologic information on the kinematics and mechanics of fracturing can be incorporated into the model of the in situ distribution. An analysis of fracture orientation data from a complexly fractured granite at the Stripa mine in Sweden shows that this approach provides a useful and straightforward way to investigate fracture distributions in the subsurface. Moment of inertia diagrams and plots of cumulative distribution functions for fracture poles greatly augment equal area projections in analyzing fracture orientation data from boreholes.