Nonlinear analysis of natural folds using wavelet transforms and recurrence plots. (9th July 2018)

• Record Type: Journal Article
• Authors: Ord, Alison; Hobbs, Bruce; Dering, Greg; Gessner, Klaus
• Is Part Of: Philosophical transactions. Volume 376:Number 2126(2018)
• Publication Date: 2018-07-09
• Subjects: natural geological fold systems -- nonlinear dynamical systems -- multifractal geometry -- wavelet transform -- recurrence quantification -- Hurst exponents; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2017.0257
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : 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'.