The "isogon rosette" method for rapid estimation of strain in flattened folds

Abstract

Dip isogons, drawn on the profile section of a fold by linking the points of equal dip on the inner and outer arcs, can be arranged in a rosette by displacing the isogons without changing their orientation until the mid-point of each isogon becomes the common point of intersection of all isogons. The end points of isogons in the rosette trace a characteristic curve that defines the fold geometry. This curve is a circle in parallel folds, an ellipse in flattened parallel folds, and it reduces to a pair of points in "similar" folds. Since isogons deform as material lines during flattening, the characteristic curve, namely, the ellipse, directly represents the strain ellipse in flattened parallel folds. The method is tested successfully on several examples of natural flattened parallel folds. The "isogon rosette" method allows representation of a given fold by a point on the R_s-θ plot, where R_s and θ are the two-dimensional strain ratio and the angle between the maximum principal strain and the fold axial trace, respectively.