Fold interaction and wavelength selection in 3D models of multilayer detachment folding

• Multilayer detachment folding is studied with analytical and numerical methods.
• New multilayer-folding domains can be distinguished.
• Wavelength and growthrate scaling laws and domain-limit equations are derived.
• Wavelength in 2D and 3D numerical simulations is in agreement with predicted one.
• Fold interactions causing complex 3D folding patterns in simulations are described.

Many fold-and-thrust belts are dominated by folding and exhibit a fairly regular fold-spacing. Yet, in map-view, the aspect ratio of doubly-plunging anticlines varies considerably from very elongated, and sometimes slightly curved, cylindrical folds to nearly circular, dome-like structures. In addition, the fold spacing often varies significantly around an average value. So far, it remains unclear whether these features are consistent with a folding instability.Therefore, we here study the dynamics of multilayer detachment folding, process by which shortening can be accommodated in thin-skinned fold-and-thrust belts. We start by analysing the physics of this process by using both a semi-analytical thick plate theory and numerical simulations. Results show that several different folding modes occur, about half of which are affected by gravity and have a wavelength that depends on the background deformation rate. Non-dimensional expressions are derived that predict the dominant wavelength and growth rate of each of these folding modes and mechanical phase diagrams are presented that illustrate the applicability of each of the modes.Next, we perform 3D simulations and compare the results with those of 2D models and analytical theory. Both 2D and 3D numerical simulations have wavelengths that are in good agreement with the analytical predictions. In the high-resolution 3D simulations the lateral growth of folds is studied, in particular with respect to fold segment interactions and evolution of fold width–length aspect ratio.The numerical simulations show a number of similarities with the Fars region of the Zagros fold-and-thrust belt including a large range of fold aspect ratio and a normally distributed fold wavelength around a dominant one.

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