STEREOLOGICAL ANALYSIS OF FRACTURE NETWORK STRUCTURE IN GEOLOGICAL FORMATIONS

Relationships between three-dimensional fracture networks consisting o f polydisperse disks and the corresponding two-dimensional trace maps are systematically analyzed. Bulk densities of disks and disk intersec tions are related to surface densities of traces and trace intersectio ns; this results in a new relation for the average length of disk inte rsections. The probability densities of trace lengths and disk interse ctions are studied for several disk diameter distributions. The invers e problem of deriving the disk distribution from the trace distributio n is then solved, assuming only that the disks have uniformly random l ocations and orientations. These results are applied to a variety of s ynthetically generated data, as well as to several sets of field data. Analysis of the field data suggests that fracture diameter distributi ons follow a power law, in agreement with previous conclusions based o n trace length histograms, with exponents varying from 1.3 to 2.1.