Rotation of fold-hinge lines associated with simple shear during southerly directed thrusting, Ouachita Mountains, southeastern Oklahoma

The Broken Bow uplift in southeastern Oklahoma contains the oldest rocks exposed in Ouachita orogenic belts and has experienced tour phases of deformation. First generation folds are tight, overturned, Sverging. and have a well developed slaty cleavage. Second-generation folds are coaxial with first-generation structures, are open to tight, are inclined, and reveal S-vergence. Northerly dipping faults truncate second generation fold limbs. Third-phase structures, including recumbent folds and pencil structures, are interpreted to be contemporaneous with S-directed thrusting. The hinges of earlier folds documented in the area least affected by thrusting are horizontal and trend E-W. The hinges of folds of the same generation within fault zones plunge 30–50 ° toward the north or northwest. Thus, it is concluded that the earlier folds have been passively rotated during S-direeted thrusting, as have the contemporaneous folds and pencil structures. A simple-shear model associated with S-directed thrusting is proposed to explain these geometrical relations. The rotated fold hinges provide quantifiable shear-strain gauges which can be used to quantify shear strain in the Broken Bow uplift as well as in other orogenic belts. A model for shear-strain calculation is developed using the general geometric relationship between fold-hinge lines, the shear direction, and the shear plane.