Noel C. Toimil

Defining folds on three-dimensional surfaces

We present a new method for the structural analysis of folded surfaces. The method requires a generalized definition of a fold as a patch consisting of contiguous points with Gaussian curvature and mean curvature of consistent sign. Four classes of folds result from this definition: antiforms and synforms each of synclastic and anticlastic forms. This new analysis is illustrated with reference to several examples.

FoldModeler: a tool for the geometrical and kinematical analysis of folds ☆

Abstract FoldModeler is a system constructed in the Mathematica ™ environment that enables strain analysis in the profile of layers folded by the simultaneous or successive superposition of several strain patterns (layer shortening, tangential longitudinal strain, flexural flow and flattening). The fundamentals of the system involve the deformation of an initial grid of quadrilaterals according to the folding mechanisms considered. The main inputs to the system define the number, shape and size of the quadrilaterals, the characteristics of the sequences of incremental strain patterns involved, and the successive variations in form of a reference line named the ‘guideline’. The main outputs of the program are the parameters defining the form of the folded guideline, the drawings of the folded layer with several markers showing the strain distribution, graphics showing the variations in the orientation of the principal directions and the aspect ratio of the finite strain ellipse as functions of the layer dip, and Ramsays classification of the folded layer. FoldModeler has two main geological applications: (a) to predict the geometrical properties of folds produced by the combination of several types of strain patterns and (b) to analyse the strain state in specific natural quasi-symmetrical folded layer profiles and the possible combinations of strain patterns that could give rise to such a fold. This can be done by searching, with a fit and error method, a theoretical fold with the same geometrical characteristics as a given natural fold. The second application requires the existence of cleavage in the natural folded layer, and the best results are obtained when some strain measures are available.

Analysis of folding by superposition of strain patterns

Abstract Two methods have been developed in this paper to model the strain state and the layer geometry of folds. These methods analyse the superposition of strain patterns due to layer shortening, tangential longitudinal strain, flexural-flow and fold flattening. The first method multiplies the deformation gradients of these strain patterns to model the successive superposition of mechanisms. The second method is more general and is based on the transformation of points from the initial configuration to deformed points according to the geometrical properties of the folding mechanisms involved. This method simulates the simultaneous and successive superposition of strain patterns. Both methods generate graphic outputs that describe the strain variation through the folded layer. Another application of these methods is to attempt to find theoretical folds that fit natural or experimental folds and to perform a geometric and kinematical analysis of these folds. Knowledge of the shape of the folded layer and the cleavage pattern is the most common basic information available in natural folds that can be used to perform the analysis. Additional strain data from the folded rocks are valuable for improving knowledge of the kinematical mechanisms involved in the folding.