Conical folds -- An artifact of using simple geometric shapes to describe a complex geologic structure

"Accurate representation of the 3D shapes of natural folds is essential to characterization of the dynamic models for fold formation. Geometrical analysis of folds commonly relies upon analyzing patterns defined by the variation in the orientation of poles to planar surfaces deformed by a shortening event when plotted using graphical calculators (e.g., stereogram, polar tangent diagrams) to interpret the shape of folds. Stereograms for which orientation data define small circles are classified as non-cylindrical regular folds and are interpreted as "conical folds," where the shape of the fold is represented by a cone that terminates at a point. Utilizing similar two-dimensional geometrical analysis of orientation data extracted from various transects across virtual pericline folds produces high spatial resolution synthetic stereograms with patterns that reproduce those of cylindrical and non-cylindrical conical folds as well as "fish-hook" patterns. Stereograms from natural periclines near Licking, Missouri mimic those of the synthetic stereogram patterns. Reverse engineering to produce three-dimensional shapes from the synthetic stereogram defines cones as this is a permissible solution to this stereogram pattern; however, the shape and orientation of these cones are shown to be poor representations of the shape of the pericline. Additionally, SCAT and differential geometry analyses are used to mathematically demonstrate the difference between periclines and conical folds. In comparison to conical folds, natural pericline folds are common, and their formation is readily reproduced by dynamic modelling without requiring highly non-uniform stress-fields or special mechanical behavior. We suggest that continuing to model the geometrical shape of many natural folds as conical, based upon stereogram patterns that define small circles, is pointless as natural folded rocks are more likely to have the form of periclines"--Abstract, page iii.