Constraining uncertainty of fault orientation using a combinatorial algorithm

Abstract

This study presents experimental results from assessing fault orientation using triangulation and a combinatorial algorithm. We constructed two geological surfaces with vertical and inclined faults. These surfaces were documented by boreholes and represented by triangulated surfaces. We first calculated orientations for a small sample of triangles genetically related to faults that were also members of the Delaunay triangulation. To reduce the epistemic uncertainty regarding the true fault strike, we applied a combinatorial algorithm that allowed us to investigate the orientation distribution of all planes genetically related to the fault. The experiment revealed three unintuitive effects that require further studies: 1) greater concentration of observations about the true dip direction; 2) the same dip direction for different triangles; and 3) triangles that dip in the opposite direction to the fault. To conduct spatial clustering within surfaces, we suggest considering a broader interval of orientations related to faults. This broader interval serves to honor the observation that orientations can be genetically related to faults, even if they indicate a relatively high directional within-dissimilarity. We suggest statistical methods for circular data to investigate the resulting distributions. The computer code associated with this study is open source and freely available.