Theoretical analysis of large amplitude folding of a single viscous layer

We present a theoretical model for Large Amplitude Folding (LAF) of a single, viscous layer embedded in a viscous matrix. LAF analysis is rooted in the first order thick-plate analysis but extends it by incorporating two growth rate corrections. 1) Following Fletcher (1974), the growth rate is modified according to the evolution of the wavelength to thickness ratio. 2) A growth rate reduction is introduced based on the rate of arclength shortening, as originally developed by Schmalholz and Podladchikov (2000). Through comparison with numerical models, we show that the simultaneous application of the two corrections in LAF provides a good prediction of the evolution of fold geometry parameters up to large amplitudes irrespective of the particular initial perturbation geometry and viscosity ratio. In the case of the multiple waveforms perturbation, we predict a coupling of the evolution of waveforms. We show that the irregular (non-sinusoidal) or localized final fold shape, commonly observed in nature, can be predicted using LAF.

► LAF is a theoretical model for buckling of a single, viscous layer.
► It accurately predicts the evolution of geometrical parameters up to large amplitudes.
► LAF is not restricted to any viscosity ratio and type of perturbation.
► LAF reproduces essential features of the natural fold shapes.