English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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'.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Nonlinear analysis of natural folds using wavelet transforms and recurrence plots