Overturned folds in ice sheets: Insights from a kinematic model of traveling sticky patches and comparisons with observations

Overturned folds are observed in regions of the Greenland ice sheet where driving stress is highly variable. Three mechanisms have been proposed to explain these folds: freezing subglacial water, traveling basal slippery patches, and englacial rheological contrasts. Here we explore how traveling basal sticky patches can produce overturned folds. Transitions from low to high stress cause a tradeoff in ice flow between basal slip and internal deformation that deflects ice stratigraphy vertically. If these transitions move, the slip-deformation tradeoff can produce large folds. Those folds record the integrated effects of time-varying basal slip. To understand how dynamic changes in basal slip influence ice sheet stratigraphy, we develop a kinematic model of ice flow in a moving reference frame that follows a single traveling sticky patch. The ice flow field forms a vortex when viewed in the moving reference frame, and this vortex traps ice above the traveling patch and produces overturned folds. Sticky patches that travel downstream faster produce larger overturned folds. We use the model as an interpretive tool to infer properties of basal slip from three example folds. Our model suggests that the sticky patches underneath these folds propagated downstream at rates between one half and the full ice velocity. The regional flow regime for the smaller two folds requires substantial internal deformation whereas the regime for the largest fold requires substantially more basal slip. The distribution and character of stratigraphic folds reflect the evolution and propagation of individual sticky patches and their effects on ice sheet flow.