Controls of Folding on Different Scales In Multilayered Rocks

Folds are a ubiquitous feature of stratified rocks in orogenic belts, and are seen on many different scales. One long-held method used by structural geologists in the field, is to use the asymmetry and vergence of small-scale folds to indicate the geometry of larger scale folds. In this paper, we address the question of why small-scale folds (sometimes termed minor or parasitic folds) initiate in multilayered rocks and are preserved in fold belts, when there is also larger-scale folding. Classical analyses of folding in viscous media, and more recent numerical modelling, show that a multilayer comprising numerous stiff layers will fold with a stronger amplification than a single stiff layer in the same host; and that the buckling instability increases with the number of layers. A reasonable conclusion for stratified rocks might therefore be that large folds, affecting numerous layers, would fold more strongly than smaller folds affecting single or few layers. There would thus appear to be a paradox: how do small folds of one or two layers buckle with a strong enough instability to become the small-scale folds or ‘minor' folds preserved around the larger-scale folds?

We present analytical models of buckling instabilities in multilayers that are less idealized and regular than those usually adopted to examine folding instabilities, to answer the question above. Our results, for modelled ‘structural lithic units', demonstrate which kinds of layer thickness variations, multilayer confinement, and viscosity variations lead to stronger single layer folding of individual layers, than multilayer folding of the whole stack. These results have implications for the mechanics of folding of rocks in nature, and may dispel a few myths about multilayer folding in principle.