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Computational modeling and analytical validation of singular geometric effects in fault data using a combinatorial approach.

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Title: Computational modeling and analytical validation of singular geometric effects in fault data using a combinatorial approach.
Authors: Michalak, Michał P.1 (AUTHOR) michalm@agh.edu.pl, Morawiec, Janusz2 (AUTHOR), Menzel, Peter3 (AUTHOR)
Source: Solid Earth. 2025, Vol. 16 Issue 10, p1025-1040. 16p.
Subjects: Triangulation, Combinatorics, Geology databases, Computer simulation, Strike-slip faults (Geology), Data analysis
Abstract: This study analyzes geometrical properties of geological faults using triangulations to model displaced horizons. We investigate two scenarios: one without elevation uncertainties and one with such uncertainties. Through formal mathematical reasoning and computational experiments, we explore how triangular surface data can reveal geometric characteristics of dip-slip faults. Our formal analysis introduces four propositions of increasing generality, demonstrating that, in the absence of elevation errors, duplicate elevation values lead to identical dip directions. For the scenario with elevation uncertainties, we find that the expected dip direction remains consistent with the error-free case. These findings are further supported by computational experiments using a combinatorial algorithm that generates all possible three-element subsets from a given set of points. The results offer insights into predicting fault geometry in data-sparse environments and provide a framework for analyzing directional data in topographic grids with imprecise elevation data. [ABSTRACT FROM AUTHOR]
Copyright of Solid Earth is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Computational modeling and analytical validation of singular geometric effects in fault data using a combinatorial approach.
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  Data: <searchLink fieldCode="AR" term="%22Michalak%2C+Michał P%2E%22">Michalak, Michał P.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> michalm@agh.edu.pl</i><br /><searchLink fieldCode="AR" term="%22Morawiec%2C+Janusz%22">Morawiec, Janusz</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Menzel%2C+Peter%22">Menzel, Peter</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Solid+Earth%22">Solid Earth</searchLink>. 2025, Vol. 16 Issue 10, p1025-1040. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Triangulation%22">Triangulation</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Geology+databases%22">Geology databases</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Strike-slip+faults+%28Geology%29%22">Strike-slip faults (Geology)</searchLink><br /><searchLink fieldCode="DE" term="%22Data+analysis%22">Data analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study analyzes geometrical properties of geological faults using triangulations to model displaced horizons. We investigate two scenarios: one without elevation uncertainties and one with such uncertainties. Through formal mathematical reasoning and computational experiments, we explore how triangular surface data can reveal geometric characteristics of dip-slip faults. Our formal analysis introduces four propositions of increasing generality, demonstrating that, in the absence of elevation errors, duplicate elevation values lead to identical dip directions. For the scenario with elevation uncertainties, we find that the expected dip direction remains consistent with the error-free case. These findings are further supported by computational experiments using a combinatorial algorithm that generates all possible three-element subsets from a given set of points. The results offer insights into predicting fault geometry in data-sparse environments and provide a framework for analyzing directional data in topographic grids with imprecise elevation data. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Solid Earth is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.5194/se-16-1025-2025
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 1025
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      – SubjectFull: Triangulation
        Type: general
      – SubjectFull: Combinatorics
        Type: general
      – SubjectFull: Geology databases
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      – SubjectFull: Computer simulation
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      – SubjectFull: Strike-slip faults (Geology)
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      – SubjectFull: Data analysis
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              M: 10
              Text: 2025
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