Preprints
https://doi.org/10.5194/egusphere-2024-3327
https://doi.org/10.5194/egusphere-2024-3327
08 Jan 2025
 | 08 Jan 2025

Computational modelling and analytical validation of singular geometric effects in fault data using a combinatorial algorithm

Michał P. Michalak, Janusz Morawiec, and Peter Menzel

Abstract. This study analyzes the directional 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 proofs and computational experiments, we explore how triangular surface data can reveal geometric characteristics of 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. This work has significant implications for improving fault modeling in geological studies, particularly when dealing with limited or uncertain data.

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Journal article(s) based on this preprint

08 Oct 2025
Computational modeling and analytical validation of singular geometric effects in fault data using a combinatorial approach
Michał P. Michalak, Janusz Morawiec, and Peter Menzel
Solid Earth, 16, 1025–1040, https://doi.org/10.5194/se-16-1025-2025,https://doi.org/10.5194/se-16-1025-2025, 2025
Short summary
Michał P. Michalak, Janusz Morawiec, and Peter Menzel

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on egusphere-2024-3327', Giacomo Medici, 14 Feb 2025
    • AC3: 'Reply on CC1', Michal Michalak, 23 May 2025
  • RC1: 'Comment on egusphere-2024-3327', Anonymous Referee #1, 10 Mar 2025
    • AC1: 'Reply on RC1', Michal Michalak, 23 May 2025
  • RC2: 'Comment on egusphere-2024-3327', Anonymous Referee #2, 07 May 2025
    • AC2: 'Reply on RC2', Michal Michalak, 23 May 2025

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on egusphere-2024-3327', Giacomo Medici, 14 Feb 2025
    • AC3: 'Reply on CC1', Michal Michalak, 23 May 2025
  • RC1: 'Comment on egusphere-2024-3327', Anonymous Referee #1, 10 Mar 2025
    • AC1: 'Reply on RC1', Michal Michalak, 23 May 2025
  • RC2: 'Comment on egusphere-2024-3327', Anonymous Referee #2, 07 May 2025
    • AC2: 'Reply on RC2', Michal Michalak, 23 May 2025

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload
AR by Michal Michalak on behalf of the Authors (23 May 2025)  Author's response   Author's tracked changes   Manuscript 
ED: Referee Nomination & Report Request started (26 May 2025) by Philip Heron
RR by Giacomo Medici (27 May 2025)
RR by Anonymous Referee #2 (10 Jul 2025)
ED: Publish subject to minor revisions (review by editor) (11 Jul 2025) by Philip Heron
AR by Michal Michalak on behalf of the Authors (14 Jul 2025)  Author's response   Author's tracked changes   Manuscript 
ED: Publish subject to minor revisions (review by editor) (18 Jul 2025) by Philip Heron
AR by Michal Michalak on behalf of the Authors (18 Jul 2025)  Author's response   Author's tracked changes   Manuscript 
ED: Publish subject to minor revisions (review by editor) (21 Jul 2025) by Philip Heron
AR by Michal Michalak on behalf of the Authors (21 Jul 2025)  Author's response   Author's tracked changes   Manuscript 
ED: Publish subject to minor revisions (review by editor) (22 Jul 2025) by Philip Heron
AR by Michal Michalak on behalf of the Authors (22 Jul 2025)  Author's response   Author's tracked changes   Manuscript 
ED: Publish as is (23 Jul 2025) by Philip Heron
ED: Publish as is (23 Jul 2025) by Susanne Buiter (Executive editor)
AR by Michal Michalak on behalf of the Authors (23 Jul 2025)

Journal article(s) based on this preprint

08 Oct 2025
Computational modeling and analytical validation of singular geometric effects in fault data using a combinatorial approach
Michał P. Michalak, Janusz Morawiec, and Peter Menzel
Solid Earth, 16, 1025–1040, https://doi.org/10.5194/se-16-1025-2025,https://doi.org/10.5194/se-16-1025-2025, 2025
Short summary
Michał P. Michalak, Janusz Morawiec, and Peter Menzel

Data sets

Computational modeling and analytical validation of singular geometric effects in fault data using a combinatorial algorithm - Input and processed data Michał Michalak https://doi.org/10.5281/zenodo.13986509

Model code and software

michalmichalak997/3GeoCombine2: v. 1.0 - Initial release Michał Michalak https://doi.org/10.5281/zenodo.13974878

Michał P. Michalak, Janusz Morawiec, and Peter Menzel

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Short summary
This study analyzes geological faults using triangular surface data to model displaced horizons, considering scenarios with and without elevation uncertainties. Formal proofs and computational experiments show that without elevation errors, identical dip directions occur. Even with uncertainties, the expected dip direction remains consistent. The findings offer insights for predicting fault geometry in data-sparse environments, improving fault modeling with imprecise elevation data.
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