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Analyses of fold profiles by changing weight parameters of NURB curves

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Abstract

Analyses of Non-Uniform Rational B-spline (NURB) curve by varying weights at its nodal points and projection ratio produce several kinetically plausible symmetric and asymmetric fold morphologies in 2D promptly and efficiently with varied overall geometries, curvature of limbs, sharpness/bluntness of hinges, extent of hinge zone, tightness/interlimb angles, etc. Some of these folds are new geometries what other approaches, such as those with Bézier curve, did not produce so far. Natural fold profiles can be matched with NURB curves from photographs.

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References

  • Aller J, Bastida F, Toimil N C and Bobillo-Ares N C 2004 The use of conic sections for the geometrical analysis of folded profile surfaces; Tectonophys. 379 239–254.

    Article  Google Scholar 

  • Bastida F, Aller J and Bobillo R S 1999 Geometrical analysis of folded surfaces using simple functions; Tectonophys. 21 729–742.

    Google Scholar 

  • Bastida F, Aller J, Bobillo-Ares N C and Toimil N C 2005 Fold geometry: A basis for their kinematical analysis; Earth-Sci. Rev. 70 129–164.

    Article  Google Scholar 

  • Chapple W M 1968 A mathematical theory of finite-amplitude rock-folding; Geol. Soc. Am. Bull. 79 47–68.

    Article  Google Scholar 

  • Chapple W M 1969 Fold shape and rheology: The folding of an isolated viscous-plastic layer; Tectonophys. 7 97–116.

    Article  Google Scholar 

  • Cruikshank K M and Johnson A M 1993 High-amplitude folding of linear-viscous multilayers; J. Struct. Geol. 15 79–94.

    Article  Google Scholar 

  • Evans D G, Schweitzer P N and Hanna M S 1985 Parametric cubic splines and geologic shape descriptions; Math. Geol. 17 611–624.

    Article  Google Scholar 

  • Fletcher R 1979 The shape of single-layer folds at small but finite amplitude; Tectonophys. 60 77–87.

    Article  Google Scholar 

  • Fleuty M J 1964 Description of folds; Proc. Geol. Assoc. 75 461–492.

    Article  Google Scholar 

  • Ghatak A, Sahay A and Srivastava D C 2005 Application of Bézier curves for analysis of symmetric fold shapes; Him. Geol. 26 205–209.

    Google Scholar 

  • Ghassemi M R, Schmalholz S W and Ghassemi A R 2010 Kinematics of constant arc length folding for different fold shapes; J. Struct. Geol. 32 755–765.

    Article  Google Scholar 

  • Ghosh S K 1993 Structural Geology: Fundamentals and Modern Developments; Pergamon Press, Oxford, pp. 217–250.

    Google Scholar 

  • Hudleston P L 1973 Fold morphology and some geometrical implications of theories of fold development; Tectonophys. 16 1–46.

    Article  Google Scholar 

  • Hudleston P L and Lan L 1994 Rheological controls on the shapes of single-layer folds; J. Struct. Geol. 16 1007–1021.

    Article  Google Scholar 

  • Hudleston P L and Treagus S 2010 Information from folds: A review; J. Struct. Geol. 32 2042–2071.

    Article  Google Scholar 

  • Johnson A M and Fletcher R C 1994 Folding of viscous layers: Mechanical analysis and interpretation of structures in deformed rock, Columbia University Press.

  • Lisle R J, Martínez J F, Bobillo-Ares N, Menéndez O, Aller J and Bastida F 2006 FOLD PROFILER: A MATLAB®-based program for fold shape classification; Comput. Geosci. 32 102–108.

    Article  Google Scholar 

  • Liu C, Zhang Y and Wang Y 2009a Analysis of complete fold shape based on quadratic Bézier curves; J. Struct. Geol. 31 575–581.

    Article  Google Scholar 

  • Liu C, Zhang Y and Shi B 2009b Geometric and kinematic modeling of detachment folds with growth strata based on Bézier curves; J. Struct. Geol. 31 260–269.

    Article  Google Scholar 

  • Lorentz G G 1953 Bernstein polynomials; University of Toronto Press, 130p.

  • Marco A and Martínez J-J 2007 A fast and accurate algorithm for solving Bernstein–Vandermonde linear systems; Linear Algebra Appl. 422 616–628.

    Article  Google Scholar 

  • Misra A A and Mukherjee S 2017 Atlas of Structural Geological Interpretation from Seismic Images; Wiley Blackwell, ISBN: 978-1-119-15832-5.

  • Mukherjee S 2010a Structures in meso- and micro-scales in the Sutlej section of the Higher Himalayan Shear Zone, Indian Himalaya; e-Terra 7 1–27.

  • Mukherjee S 2010b Microstructures of the Zanskar Shear Zone; e-journal: Earth Sci. India 3 9–27.

  • Mukherjee S 2011 Flanking Microstructures from the Zanskar Shear Zone NW, Indian Himalaya; YES Bull. 1 21–29.

    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 Higher Himalaya in the Bhagirathi section (NW Himalaya, India): its structures, backthrusts and extrusion mechanism by both channel flow and critical taper mechanisms; Int. J. Earth Sci. 102 1851–1870.

    Google Scholar 

  • Mukherjee S 2014a Atlas of shear zone structures in meso-scale; Springer Geology. Cham., pp. 1–124.

  • Mukherjee S 2014b Review of flanking structures in meso-and micro-scales; Geol. Mag. 151 957–974.

    Article  Google Scholar 

  • Mukherjee S 2015 Atlas of Structural Geology; Elsevier, Amsterdam.

    Google Scholar 

  • Mukherjee S and Koyi H A 2009 Flanking microstructures; Geol. Mag. 146 517–526.

    Article  Google Scholar 

  • 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.

    Google Scholar 

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

    Google Scholar 

  • Mukherjee S, Talbot C J and Koyi H A 2010 Viscosity estimates of salt in the Hormuz and Namakdan salt diapirs, Persian Gulf; Geol. Mag. 147 497–507.

    Article  Google Scholar 

  • Mukherjee S, Punekar J, Mahadani T and Mukherjee R 2015 A review on intrafolial folds and their morphologies from the detachments of the western Indian Higher Himalaya; In: Ductile Shear Zones: From Micro- to Macro-scales (eds) Mukherjee S and Mulchrone K F, Wiley Blackwell, pp. 182–205.

  • Piegl L and Tiller W 1997a Symbolic operators for NURBS; Comp. Aided Design 29 361–368.

    Article  Google Scholar 

  • Piegl L and Tiller W 1997b NURB curves; Springer-Verlag, Berlin.

    Google Scholar 

  • Salomon D 2007 Curves and Surfaces for Computer Graphics; Springer, 11p, ISBN 9780387284521.

  • Sederberg T W 2016 Computer Aided Geometric Design Course Notes; http://www.tsplines.com/educationportal.html.

  • Sederberg T W, Finnigan G T, Li X, Lin H and Ipson H 2008 Watertight trimmed NURBS; ACM Trans. Graphics 27 79.

    Article  Google Scholar 

  • Sederberg T W, Zheng J, Bakenov A and Nasri A 2003 T-splines and T-NURCCs; ACM Trans. Graphics 22 477–484.

    Article  Google Scholar 

  • Sprague K B and de Kemp E A 2005 Interpretive tools for 3-D structural geological modelling part II: Surface design from sparse spatial data; Geoinformatica 9 5–32.

    Article  Google Scholar 

  • Srivastava D C and Lisle R J 2004 Rapid analysis of fold shape using Bézier curves; J. Struct. Geol. 26 1553–1559.

    Article  Google Scholar 

  • Srivastava D C, Rastogi V and Ghosh R 2010 A rapid Bézier curve method for shape analysis and point representation of asymmetric folds; J. Struct. Geol. 32 685–692.

    Article  Google Scholar 

  • Srivastava V and Gairola V K 1997 Classification of multi-layered folds based on harmonic analysis: Example from central India; J. Struct. Geol. 19 107–112.

    Article  Google Scholar 

  • Stabler C L 1968 Simplified Fourier analysis of fold shapes; Tectonophys. 6 343–350.

    Article  Google Scholar 

  • Stowe C W 1988 Application of Fourier analysis for computer representation of fold profiles; Tectonophys. 156 303–311.

    Article  Google Scholar 

  • Tripathy A and Gairola V K 1999 Fold symmetry – a quantitative description; J. Struct. Geol. 21 719–727.

  • Turcotte D L and Schubert G 2002 Geodynamics; Cambridge University Press.

  • Twiss R J 1988 Description and classification of folds in single surfaces; J. Struct. Geol. 10 607–623.

    Article  Google Scholar 

  • Wills B and Willis R 1929 Geologic Structures; \(2\)nd edn, Mc-Graw-Hill Book Co., 518p.

  • Wojtal W 2001 Using Bezier curves to analyze the shapes of folded surfaces; Session No. 9, Structural Geology I: Faulting and Folding: Timing, Geometry, and Processes, GSA Annual Meeting, November 5–8, 2001.

  • Zhong D-H, Li M-C, Song L-G and Wang G 2006 Enhanced NURBS modeling and visualization for large 3D geoengineering applications: An example from the Jinping first-level hydropower engineering project, China; Comput. Geosci. 32 1270–1282.

    Article  Google Scholar 

Download references

Acknowledgements

SM was supported by CPDA grant of IIT Bombay. Associate Editorial assistance and review by Prof. Saibal Gupta (IIT Kharagpur) and detailed comments by an anonymous reviewer and Eugenio Fazio are acknowledged.

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Authors and Affiliations

  1. Department of Geology, Sibsagar College, Joysagar, Sivasagar, 785 665, India

    Manash Pratim Gogoi

  2. Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India

    Soumyajit Mukherjee

  3. Department of Applied Geology, Dibrugarh University, Dibrugarh, 786 004, India

    Tapos K Goswami

Authors
  1. Manash Pratim Gogoi
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  2. Soumyajit Mukherjee
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  3. Tapos K Goswami
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Correspondence to Soumyajit Mukherjee.

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Corresponding editor: Saibal Gupta

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Gogoi, M.P., Mukherjee, S. & Goswami, T.K. Analyses of fold profiles by changing weight parameters of NURB curves. J Earth Syst Sci 126, 98 (2017). https://doi.org/10.1007/s12040-017-0880-5

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