Tidally Influenced Stick-Slip in 1D Models of Ice Stream Flow with Rate-and-State Friction

Abstract:

On the shortest time scales, the basal interfaces of glaciers and ice sheets behave elastically. Some of the most prominent consequences of this behavior come from observations of the tidal response at very low effective stresses in the vicinity of sticky spots. Over the short duration of slip events on the Whillans Ice Plain, we can model flow in the vicinity of a sticky spot by equating the sum of elastic and tidal stresses with frictional resistance described by a velocity-weakening, rate-and-state formulation.

Our model domain is approximated as a rectangle with flow-perpendicular width W, and flow-parallel length L. For the background flow we impose a constant rate vice long the up- and down-dip boundaries, and set the flow rate to zero at the ridges that are represented by the flow-perpendicular boundaries. To facilitate a 1D treatment, we assume that stress along the ice base varies only in the direction perpendicular to flow. We examine the elastic response to stress accumulation at a single sticky spot that is centered within the model domain. The frictional constitutive parameters are assumed constant over the entire model domain. The sticky spot is characterized by an increase in the effective stress from its background level of N = σ elsewhere to an enhanced value of N = 10σ – 100σ within the sticky spot itself.

We report simulations where the entire sticky spot ruptures twice per tidal period, and is effectively locked in the intervals between sliding; a few events do not rupture the entire sticky spot. The poorly drained, low stress regions on either side of the sticky spot slide at speeds slightly below vice during the entire simulation, while the sticky spot reaches slip speeds of ~100vice when it ruptures. Sticky spot ruptures occur near both the minimum and maximum tidal stresses. Increasing the tidal forcing amplitude produces more frequent, smaller ruptures, and the behavior becomes less correlated with changes in tidal resistance. Decreasing the sticky spot effective stress causes the behavior to become more chaotic, with the sticky spot showing no obvious periodic response to the tidal signal.