Nonlinear analysis of natural folds using wavelet transforms and recurrence plots

Area of Science:

• Geology
• Geophysics
• Complex Systems

Background:

• Geological fold systems are complex natural phenomena.
• Understanding their formation processes requires advanced analytical techniques.
• Previous studies often simplified fold dynamics.

Purpose of the Study:

• To quantify natural geological fold systems using nonlinear dynamics.
• To identify the underlying processes responsible for fold formation.
• To compare natural fold signals with synthetic models.

Main Methods:

• Photogrammetry for 3D model creation.
• Wavelet transforms and wavelet transform modulus maxima for multifractal spectrum analysis.
• Recurrence Quantification Analysis (RQA) for recurrence quantification.

Main Results:

• Natural fold systems display multifractal geometry and recurrence patterns.
• Analysis revealed similarities to periodic signals with superimposed chaotic signals.
• These findings align with nonlinear dynamical theories of folding.

Conclusions:

• Geological folding can be effectively modeled as a nonlinear dynamical system.
• RQA provides insights into the mechanics of fold system formation.
• This approach enhances predictive capabilities in geological studies.