Stereological analysis of fracture network structure in geological formations

Relationships between three-dimensional fracture networks consisting of polydisperse disks and the corresponding two-dimensional trace maps are systematically analyzed. Bulk densities of disks and disk intersections are related to surface densities of traces and trace intersections; this results in a new relation for the average length of disk intersections. The probability densities of trace lengths and disk intersections are studied for several disk diameter distributions. The inverse problem of deriving the disk distribution from the trace distribution is then solved, assuming only that the disks have uniformly random locations and orientations. These results are applied to a variety of synthetically generated data, as well as to several sets of field data. Analysis of the field data suggests that fracture diameter distributions follow a power law, in agreement with previous conclusions based on trace length histograms, with exponents varying from 1.3 to 2.1.