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Fuzzy set concept in structural geology: Example of ductile simple shear

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Abstract

Much of the time, geological data are not accurately known. Instead, geoscientists work with a range of possible data. These data can have a range since they can vary spatially and temporally. In this context, we demonstrate how a well-established structural geological model of velocity profile of ductile simple shear, expressed as an equation, can be furthered by fuzzy set concept. The implementation of fuzzy set concepts in terms of fuzzification in (geo)scientific models takes into consideration the uncertainties of magnitudes of the parameters that define the model. The present study shows that the fuzzified velocity profile of a ductile simple shear zone with parallel boundaries is effectively independent of the dip of the shear zone. This article demonstrates how models of (structural) geological processes can be modelled by fuzzy set approach capable of incorporating a range of magnitudes of parameters.

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Figure 1

Reproduced from figure 1(b) of Mukherjee (2012).

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References

  • Bemis S P, Micklethwaite S, Turner D, James M R, Akciz S, Thiele S T and Bangash H A 2014 Ground-based and UAV-based photogrammetry: A multi-scale, high resolution mapping tool for structural geology and paleoseismology; J. Struct. Geol. 69 163–178.

    Article  Google Scholar 

  • Chakraverty S, Tapaswini S and Behera D 2016 Fuzzy differential equations and applications for engineers and scientists; CRC Press, 240p, ISBN 9781482244731.

  • Deyi F and Ichikawa M 1989 Quantitative estimation of time-variable earthquake hazard by using fuzzy set theory; Tectonophys. 169 175–196.

    Article  Google Scholar 

  • Gaines B R 1978 Fuzzy and probability uncertainty logics; Inf. Control 38 54–69.

    Article  Google Scholar 

  • Ganguly J, Dasgupta S and Cheng W et al. 2000 Exhumation history of a section of the Sikkim Himalayas, India: Records in the metamorphic mineral equilibria and compositional zoning of garnet; Earth Planet. Sci. Lett. 183 471–486.

    Article  Google Scholar 

  • Guo J, Xiao Y and Zhu H 2014 A new method for fracturing wells reservoir evaluation in fractured gas reservoir; Math. Prob. Eng., Article ID 814284.

  • Justman D, Creason C G, Rose K and Bauer J 2020 A knowledge-data framework and geospatial fuzzy logic-based approach to model and predict structural complexity; J. Struct. Geol. 141 104153.

  • Kahraman C, Öztayş B and Onar S C 2016 Comprehensive Literature Review of 50 years of fuzzy set theory; Int. J. Computat. Intell. Syst., https://doi.org/10.1080/18756891.2016.1180817.

  • Kern H and Wenk H-R 1983 Calcite texture development in experimentally induced ductile shear zones; Contrib. Mineral. Petrol. 83 231–236.

    Article  Google Scholar 

  • Means W D 1989 Stretching faults; Geol. 17 893–896.

    Article  Google Scholar 

  • Mukherjee S 2012 Simple shear is not so simple! Kinematics and shear senses in Newtonian viscous simple shear zones; Geol. Mag. 149 819–826.

    Article  Google Scholar 

  • Mukherjee S 2013 Channel flow extrusion model to constrain dynamic viscosity and Prandtl number of the Higher Himalayan Shear Zone; Int. J. Earth Sci. 102 1811–1835.

    Article  Google Scholar 

  • Mukherjee S 2018 Locating center of gravity in geological contexts; Int. J. Earth Sci. 107 1935–1939.

    Article  Google Scholar 

  • Mukherjee S 2019 Kinematics of pure shear ductile deformation within rigid walls: New analyses; In: Problems and Solutions in Structural Geology and Tectonics (eds) Billi A and Fagereng A, Series Editor: Mukherjee S, Developments in Structural Geology and Tectonics Book Series, Elsevier, pp. 81–88, ISSN: 2542-9000.

  • Mukherjee S and Koyi H A 2010 Higher Himalayan Shear Zone, Sutlej section: Structural geology and extrusion mechanism by various combinations of simple shear, pure shear and channel flow in shifting modes; Int. J. Earth Sci. 99 1267–1303.

    Article  Google Scholar 

  • Mukherjee S and Mulchrone K 2012 Estimating the viscosity and Prand.tl number of the Tso Morari Gneiss Dome, western Indian Himalaya; Int. J. Earth Sci. 101 1929–1947.

    Article  Google Scholar 

  • Nilsson B, Højberg A L, Refsgaard J C and Troldborg L 2006 Uncertainty in geological and hydrogeological data; Hydrol. Earth Syst. Sci. Discuss. 3 2675–2706.

    Google Scholar 

  • Park I, Lee J and Lee S 2014 Ensemble of Ground Subsidence Hazard Maps using Fuzzy Logic; Cent. Eur. J. Geosci. 6 207–218.

    Google Scholar 

  • Pradhan B 2011 Use of GIS-based fuzzy logic relations and its cross-application to produce landslide susceptibility maps in three test areas in Malaysia; Environ. Earth Sci. 63 329–349.

    Article  Google Scholar 

  • Schlichting H and Gersten K 1999 Boundary Layer Theory; 8th edn. Springer, Berlin.

    Google Scholar 

  • Shan Y, Li Z and Lin G 2004 A stress inversion procedure for automatic recognition of polyphase fault/slip data sets; J. Struct. Geol. 26 919–925.

    Article  Google Scholar 

  • Xypolias P and Kokkalas S 2006 Heterogeneous ductile deformation along a mid-crustal extruding shear zone: An example from the External Hellenides (Greece); In: Channel flow, extrusion and exhumation in continental collision zones (eds) Law R D and Searle M P, Geol. Soc. London 268 497–516.

  • Zadeh L A 1965 Fuzzy sets; Inf. Control 8 338–353.

    Article  Google Scholar 

  • Zimmermann H-J 2011 Fuzzy set theory and its applications; 2nd edn, Springer Science and Business Media, ISBN 978-94-015-7951-3.

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Acknowledgements

SM was supported by CPDA grant of IIT Bombay. We thank the two anonymous reviewer(s) for raising several concerns. The Associate Editor, Prof Saibal Gupta is thanked for handling and providing language and presentation-related comments.

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Contributions

PA: Worked with numericals and in preparation of the draft ms; SC: Supervision, preparation and corrections in the paper; and SM: supervision, writing and finishing the final version of the paper.

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Correspondence to Soumyajit Mukherjee.

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Communicated by Saibal Gupta

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Anand, P., Chakraverty, S. & Mukherjee, S. Fuzzy set concept in structural geology: Example of ductile simple shear. J Earth Syst Sci 130, 193 (2021). https://doi.org/10.1007/s12040-021-01683-2

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  • DOI: https://doi.org/10.1007/s12040-021-01683-2

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