USING THE MULTINOMIAL FUNCTION TO INVESTIGATE COMPLEX FRACTURE PATTERNS

This work describes additional aspects of a recently introduced tool that uses the multinomial function to provide a local measure of the degree of organization, and visualize spatial patterns of organization within fracture arrays. Some number of neighbors, n, nearest to a grid point are sampled and the multinomial function applied. Comparison of natural to random strike distributions aids interpretation. Complex fracture patterns may result from the interplay of tectonic and local stress fields, and the history of fracture generation. This tool may help discern the existence, spatial variation, and relative contribution of these multiple factors to the overall complex fracture array. With large n, truly random fracture sets inevitably have some areas of apparent organization, challenging simple interpretations. Such subareas would have locally anomalous mechanical and material properties, but would be more limited in extent than fracture arrays with a preferred orientation component. Histograms of the gridded multinomial value can differentiate between fracture arrays with random, polygonal, and preferred orientations. Polygonal arrays should be shifted to the left of random, while oriented arrays are shifted to the right. This tool was applied to a diverse set of fractures images found in the literature that were digitized into fracture segment strikes. A polygonal fault system from Coorikiana, Australia shows a slight right shift, and locally exhibits a greater degree of local preferred orientation than expected from a random distribution and different than a polygonal pattern. Other polygonal fault patterns are even more strongly right shifted, while another polygonal fault system shows the distribution expected from a polygonal pattern. These can be interpreted as reflecting varying tectonic contributions to a pattern driven by underlying structural diagenesis. The visualization and analysis tool has also been applied to a polygonal fracture pattern from Mars, from chalcedony vein systems from the South Dakota badlands, and to joint patterns, yielding a rich array of results.