Fold geometry: a basis for their kinematical analysis

A review of geometrical methods used to describe folds is presented, with special emphasis on methods required to study kinematical folding mechanisms. Several families of mathematical functions that approach the geometry of folded surface profiles are considered; among these functions, conic sections are the most suitable in mathematical modelling. The Ramsay or Hudleston classifications give a detailed functional description of the folded layer profile and are very useful in the kinematical analysis. Nevertheless, simpler classifications of folded layers can be used to describe folds in regional studies; some of them are simplifications of the Ramsay classification. Cleavage distribution through the folded layer, due to its relation with the finite strain ellipsoid, is a key feature in kinematical studies; a useful graphical description of this distribution can be made constructing the curve of cleavage dip variation as a function of layer dip. is of kinematical folding mechanisms requires extensive geometrical information to be obtained from the folds. This analysis can be made attempting to find theoretical folds that fit natural or experimental folds by the use of the point transformation equations for the basic mechanisms. Examples of folds theoretically modelled by tangential longitudinal strain and flexural flow are shown, as well as an example of analysis of kinematical mechanisms in a natural fold. All these examples make it clear how geometry can be the basis for the strain and kinematical analysis of folds.