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Heterogeneity in geometry, stress, and material properties is widely invoked to explain the observed spectrum of slow earthquake phenomena. However, the effects of length scale of heterogeneity on macroscopic fault sliding behavior remain underexplored. We investigate this question for subduction megathrusts, via linear stability analysis and quasi-dynamic simulations of slip on a dipping fault characterized by rate-and-state friction (RSF). Frictional heterogeneity is imposed through alternating velocity-strengthening (VS) and velocity-weakening (VW) patches, over length scales spanning from those representative of basement relief (several km) to the entrainment of contrasting lithologies (100s of m). The resulting fault behavior is controlled by: (1) the average frictional properties of the fault, and (2) the size of VW blocks relative to a critical length scale. Reasonable ranges of these properties yield sliding behaviors spanning from stable sliding, to slow and seismic slip events that are confined within VW blocks or propagate along the entire fault. 

Basal slip along glaciers and ice streams can be significantly modified by external time-dependent forcing, although it is not clear why some systems are more sensitive to tidal stresses. We have conducted a series of laboratory experiments to explore the effect of time varying load point velocity on ice-on-rock friction. Varying the load point velocity induces shear stress forcing, making this an analogous simulation of aspects of ice stream tidal modulation. Ambient pressure, double-direct shear experiments were conducted in a cryogenic servo-controlled biaxial deformation apparatus at temperatures between −2°C and −16°C. In addition to a background, median velocity (1 and 10 μm/s), a sinusoidal velocity was applied to the central sliding sample over a range of periods and amplitudes. Normal stress was held constant over each run (0.1, 0.5 or 1 MPa) and the shear stress was measured. Over the range of parameters studied, the full spectrum of slip behavior from creeping to slow-slip to stick-slip was observed, similar to the diversity of sliding styles observed in Antarctic and Greenland ice streams. Under conditions in which the amplitude of oscillation is equal to the median velocity, significant healing occurs as velocity approaches zero, causing a high-amplitude change in friction. The amplitude of the event increases with increasing period (i.e. hold time). At high normal stress, velocity oscillations force an otherwise stable system to behave unstably, with consistently-timed events during every cycle. Rate-state friction parameters determined from velocity steps show that the ice-rock interface is velocity strengthening. A companion paper describes a method of analyzing the oscillatory data directly. Forward modeling of a sinusoidally-driven slider block, using rate-and-state dependent friction formulation and experimentally derived parameters, successfully predicts the experimental output in all but a few cases.