Geometrical analysis of folded surfaces using simple functions

Abstract

Several functions have been chosen in order to approximate fold profile geometry. Some of them are valid mainly for alloclinal folds (interlimb angle>0), whereas others are mainly valid for isoclinal folds (interlimb angle=0). In all cases, a fold profile can be characterised by an aspect ratio ( y 0/ x 0) between the height and the width of a limb (fold amplitude), and a shape parameter characteristic of the considered function. The shape parameters have been mutually linked through the area beneath the fold profile. The geometrical analysis enables a graphical classification based on a shape–amplitude diagram in which the most common types of folded surfaces are represented: cuspate, chevron, sinusoidal, parabolic, elliptic and box folds. Any of the shape parameters can be used as x-axis of the diagram in order to approximate the geometries commonly exhibited by natural folds. In the diagram presented in this paper two shape parameters have been combined: the exponent n of a power function for alloclinal folds, and a parameter C/ y 0, defined from a function composed of an elliptic part and a line segment of length C for isoclinal folds. In order to show the suitability of the classification method, it has been applied to some examples of finite-element, experimental and natural folds.