Geometric and kinematic models for detachment folds with fixed and variable detachment depths

Abstract

Detachment folds are defined by competent rock units and are cored by incompetent units deformed internally above a detachment horizon. We have developed two geometric models to constrain possible geometries and kinematic paths for ideal detachment folds. The models each independently relate fold geometry to shortening and to detachment depth. Model assumptions include plane-strain, constant competent bedlength, constant cross-sectional area, chevron fold geometry, and no bed-parallel shear outside the fold. Detachment depth is constant in one model but may vary in the other, thus allowing evaluation of the implications for fold geometry and kinematics of fixed vs variable detachment depth. Detachment folds formed above a detachment unit of constant thickness (constant detachment depth) must be initially symmetrical and cannot grow with fixed hinges (fixed arc-length) or a self-similar geometry. Detachment folds formed above a detachment unit of variable thickness (variable detachment depth) must also be initially symmetrical, but any one fold geometry can have a range of possible initial and final detachment depths. Kinematic paths for folds with fixed hinges (fixed arc-lengths), migrating hinges (variable arc-lengths), and selfsimilar geometries are all possible if detachment depth varies. The change in detachment depth during deformation can be determined using the variable detachment depth model if either initial or final detachment depth is known. The models demonstrate a wider range of variability in the geometry and kinematics of ideal detachment folds, particularly for the variable-depth model, than is the case for ideal fault-bend and fault-propagation folds. This variability limits the usefulness of simple geometric models for reconstructing the geometry of natural detachment folds. Balancing cross-sections over a sufficient area and evaluating strain may compensate for these limitations.