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HingeInflex: a MATLAB-based method for precise selection of the hinge and the inflection points in folds

Published online by Cambridge University Press:  30 October 2009

DEEPAK C. SRIVASTAVA  and
VIPUL RASTOGI
DEEPAK C. SRIVASTAVA*
Affiliation:
Department of Earth Sciences, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India
VIPUL RASTOGI
Affiliation:
Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India
*
*Author for correspondence: dpkesfes@iitr.ernet.in
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Abstract

Subjectivity in visual selection of hinge and inflection points leads to significant errors in analyses of fold shapes in profile sections. This article gives a method for precise determination of these points. The method: (1) imports a fold image into Matlab, (2) digitizes points on the image, (3) increases the number of available points by using an interpolation algorithm, (4) fits a polynomial curve to the points, and (5) searches for the hinge and the inflection points mathematically. Tests on several folds confirm that the ‘HingeInflex’ is a rapid, robust and user-friendly method for precise selection of the hinge and inflection points.

Keywords

fold shape analysispolynomial fittinghinge pointinflection pointMatlab
Type
Original Article
Information
Geological Magazine , Volume 147 , Issue 2 , March 2010 , pp. 233 - 241
Copyright
Copyright © Cambridge University Press 2009

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References

Aller, J., Bastida, F., Toimil, N. C. & Bobillo-Ares, N. C. 2004. The use of conic sections for the geometrical analysis of folded profile surfaces. Tectonophysics 379, 239–54.CrossRefGoogle Scholar
Bastida, F., Aller, J. & Bobillo-Ares, N. C. 1999. Geometrical analysis of surfaces using simple functions. Journal of Structural Geology 21, 729–42.CrossRefGoogle Scholar
Bézier, P. 1966. Définition numérique de courbes et surfaces, part 1. Automatisme 11, 625–32.Google Scholar
Bézier, P. 1967. Définition numérique de courbes et surfaces, part 2. Automatisme 12, 17–21.Google Scholar
Biot, M. A. 1961. Theory of folding of stratified viscoelastic media and its implication in tectonics and orogenesis. Geological Society of America Bulletin 72, 1595–1620.CrossRefGoogle Scholar
Coelho, S., Passchier, C. & Grasemann, B. 2005. Geometric description of flanking structures. Journal of Structural Geology 27, 597–606.CrossRefGoogle Scholar
De Paor, D. G. 1996. Bézier curves and geological design in structural geology and personal computers. In Structural Geology and Personal Computers (ed. De Paor, D. G.), pp. 389–417. Oxford: Pergamon Press.CrossRefGoogle Scholar
De Sitter, L. U. 1958. Boudins and parasitic folds in relation to cleavage and folding. Geologie en Mijnbouw 20, 272–86.Google Scholar
Hudleston, P. J. 1973. Fold morphology and some geometrical considerations of theories of fold development. Tectonophysics 16, 1–46.CrossRefGoogle Scholar
Hudleston, P. J. & Lan, L. 1993. Information from fold shapes. Journal of Structural Geology 15, 253–64.CrossRefGoogle Scholar
Lan, L. & Hudleston, P. J. 1996. Rock rheology and sharpness of folds in single layers. Journal of Structural Geology 18, 925–31.CrossRefGoogle Scholar
Lisle, R. J. 1992. Strain estimation from flattened buckle folds. Journal of Structural Geology 14, 369–71.CrossRefGoogle Scholar
Lisle, R. J. 1994. Detection of zones of abnormal strains in structures using Gaussian curvature analysis. American Association of Petroleum Geologists Bulletin 78, 1811–19.Google Scholar
Lisle, R. J. 1997. A fold classification scheme based on a polar plot of inverse layer thickness. In Evolution of Geological Structures in Micro- to Macro-Scales (ed. Sengupta, S.), pp. 323–39. London: Chapman and Hall.CrossRefGoogle Scholar
Lisle, R. J., Martínez, J. L. F., Bobillo-Ares, N., Menéndez, O., Aller, J. & Bastida, F. 2006. FOLD PROFILER: A MATLAB-based program for fold shape classification. Computers & Geosciences 32, 102–8.CrossRefGoogle Scholar
Mertie, J. B. 1959. Classification, delineation and measurement of non-parallel folds. U. S. Geological Survey, Professional Paper 314-E, 91–124.Google Scholar
Pearce, M. A., Jones, R., Smith, S. A. F., McCaffrey, K. J. W. & Clegg, P. 2006. Numerical analysis of fold curvature using data acquired by high-precision GPS. Journal of Structural Geology 28, 1640–6.CrossRefGoogle Scholar
Ramsay, J. G. 1967. Folding and Fracturing of Rocks. New York: McGraw-Hill, 568 pp.Google Scholar
Ramsay, J. G. & Huber, M. I. 1987. The Techniques of Modern Structural Geology, Vol. 2: Folds and Fractures. London: Academic Press Inc.Google Scholar
Shah, J. & Srivastava, D. C. 2006. Strain estimation from flattened parallel folds: application of the Wellman method and Mohr circle. Geological Magazine 143, 243–7.CrossRefGoogle Scholar
Srivastava, D. C. & Lisle, R. J. 2004. Rapid analysis of fold shape using Bézier curves. Journal of Structural Geology 26, 1553–9.CrossRefGoogle Scholar
Srivastava, D. C. & Shah, J. 2006. A rapid method for strain estimation from flattened parallel folds. Journal of Structural Geology 28, 1–8.CrossRefGoogle Scholar
Srivastava, D. C. & Shah, J. 2008. The ‘isogon rosette’ method for rapid estimation of strain in flattened folds. Journal of Structural Geology 30, 444–50.CrossRefGoogle Scholar
Stabler, C. L. 1968. Simplified Fourier analysis of fold shapes. Tectonophysics 6, 343–50.CrossRefGoogle Scholar
Stowe, C. W. 1988. Application of Fourier analysis for computer representation of fold profiles. Tectonophysics 156, 303–11.CrossRefGoogle Scholar
Twiss, R. J. 1988. Description and classification of folds in single surfaces. Journal of Structural Geology 10, 607–23.CrossRefGoogle Scholar
Wojtal, S. & Hughes, G. 2001. Using Bézier curves to analyze the shapes of folded surfaces. Abstracts with Program, Geological Society of America 33 (6), 26.Google Scholar
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