VANISHING POINTS – THE END OF CONICAL FOLDS (Invited Presentation)

Currently, non-cylindrical folds characterized by small circles on Π-diagrams are considered conclusively as “Conical Folds”. Geometric cones are a mathematically permissible solution to the small circle on a π-diagram; however they are an extremely poor geometric representation of the actual shape of real folds - especially fold terminuses. We analyze the shape of virtual, dynamically modeled, buckle folds (i.e., Periclines), created in a single, uniform, deformation event, using synthetic stereograms, tangent-plots, SCAT, and Geologic Curvature Analysis. The central domain of Periclines are cylindrical folds, whereas the plunging noses are non-cylindrical. Synthetic π-diagrams for virtual periclines are fit by great circles, small circles, ellipses, and “fish-hook patterns. Buckle folds in Ordovician Roubdioux Sandstone from the Ozark Dome have similar Π-diagrams patterns and are best represented as periclines rather than conical folds. “Conical folds” must terminate at a point. This requires the plunge and the ratio of the amplitude (A) to the width (W) of the fold to remain constant (A/W =½) along the crestal line to the terminus of the fold. In contrast, Periclines terminate by a gradual dissipation of the fold and A/W decreases and the plunge varies along the crestal line of the fold. Correctly characterizing how folds dissipate is critical for rheological modeling of folds, and while realistic dynamic models for periclines exist, models for conical fold formation remain conceptual. We suggest an over reliance on the a priori interpretation of small circles in Π-diagrams as being represented only by “cones” has led to overrepresentation and unwarranted elevated status for conical folds at the expense of periclines. In order to advance our understanding of how folds form it is pointless to continue the myth of conical folds as an accurate geometric representation for how folds end.