TY - JOUR
T1 - Nonlinear analysis of natural folds using wavelet transforms and recurrence plots
AU - Ord, Alison
AU - Hobbs, Bruce
AU - Dering, Greg
AU - Gessner, Klaus
PY - 2018/8/13
Y1 - 2018/8/13
N2 - 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 spectrumis 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 continuouswavelet transform comes of age'.
AB - 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 spectrumis 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 continuouswavelet transform comes of age'.
KW - Hurst exponents
KW - multifractal geometry
KW - natural geological fold systems
KW - nonlinear dynamical systems
KW - recurrence quantification
KW - wavelet transform
UR - http://www.scopus.com/inward/record.url?scp=85050358868&partnerID=8YFLogxK
U2 - 10.1098/rsta.2017.0257
DO - 10.1098/rsta.2017.0257
M3 - Article
C2 - 29986911
AN - SCOPUS:85050358868
SN - 1364-503X
VL - 376
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2126
M1 - 20170257
ER -