Constraining uncertainty of fault orientation using a combinatorial algorithm

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 calcul...

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Bibliographic Details
Published in:Computers & geosciences Vol. 154; p. 104777
Main Authors: Michalak, Michał Paweł, Kuzak, Ryszard, Gładki, Paweł, Kulawik, Agnieszka, Ge, Yunfeng
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2021
Subjects:
algorithms
Combinatorial algorithm
computer software
Discontinuity orientation
Fault evidence
Geological modeling
uncertainty
Geological modeling
Fault evidence
Discontinuity orientation
Combinatorial algorithm
ISSN:0098-3004, 1873-7803
Online Access:Get full text
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Summary: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. •Assessing uncertainty on fault orientation using a three point approach.•Combinatorial algorithm was used to constrain the fault strike.•Counterintuitive behavior of the triangles' orientation was demonstrated.•Implications for conducting spatial clustering were given. [Display omitted]
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ISSN:0098-3004
1873-7803
DOI:10.1016/j.cageo.2021.104777