Nonlinear analysis of natural folds using wavelet transforms and recurrence plots

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 376; no. 2126; p. 20170257
• Main Authors: Ord, Alison, Hobbs, Bruce, Dering, Greg, Gessner, Klaus
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 13.08.2018
• Subjects: Continuous wavelet transform; Dynamical systems; Geology; Hurst Exponents; Multifractal Geometry; Natural Geological Fold Systems; Nonlinear analysis; Nonlinear Dynamical Systems; Nonlinear dynamics; Nonlinear systems; Photogrammetry; Recurrence Quantification; Redundancy; Three dimensional models; Wavelet analysis; Wavelet Transform; Wavelet transforms; natural geological fold systems; multifractal geometry; Hurst exponents; nonlinear dynamical systems; recurrence quantification; wavelet transform
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2017.0257

Three-dimensional models of natural geological fold systems established by photogrammetry are quantified in order to constrain the processes responsible for their formation. The folds are treated as nonlinear dynamical systems and the quantification is based on the two features that characterize such systems, namely their multifractal geometry and recurrence quantification. The multifractal spectrum is established using wavelet transforms and the wavelet transform modulus maxima method, the generalized fractal or Renyi dimensions and the Hurst exponents for longitudinal and orthogonal sections of the folds. Recurrence is established through recurrence quantification analysis (RQA). We not only examine natural folds but also compare their signals with synthetic signals comprising periodic patterns with superimposed noise, and quasi-periodic and chaotic signals. These results indicate that the natural fold systems analysed resemble periodic signals with superimposed chaotic signals consistent with the nonlinear dynamical theory of folding. Prediction based on nonlinear dynamics, in this case through RQA, takes into account the full mechanics of the formation of the geological system. This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.