Nonlinear analysis of natural folds using wavelet transforms and recurrence plots

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 suc...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2018-08, Vol.376 (2126), p.20170257-20170257
Main Authors: Ord, Alison, Hobbs, Bruce, Dering, Greg, Gessner, Klaus
Format: Article
Language:English
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
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Summary: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'.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2017.0257