Hausdorff Distance as a 3D Fracture Aperture Metric

We propose Hausdorff distance as a 3D aperture metric for the rough-walled 3D rock fracture. To verify its plausibility, we construct a fracture model from a 3D scanned crystalline rock sample. Comparison with the commonly used vertical aperture reveals significant advantages in imaging of the possible aperture bottlenecks present in the fracture volume. Another advantage stems from the omnidirectional nature of the Hausdorff distance as opposed to the directional true aperture estimation techniques developed previously. Furthermore, we compute aperture distributions for non-sheared and sheared fracture models, highlighting the differences and similarities between both aperture metrics. A parallel can be drawn with the surface roughness estimation method proposed by Grasselli, which also operates on the surface mesh constructed from the 3D scan point cloud. Hausdorff distance is shown to perform best in the highly sloped regions, where the full dip of the mesh polygon becomes significant and vertical aperture inevitably overestimates the true geometric aperture of the fracture.