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SUMMARY This paper examines the linear stability of sliding on faults embedded in a 2-D elastic medium that obey rate and state friction and have a finite length and/or are near a traction-free surface. Results are obtained using a numerical technique that allows for analysis of systems with geometrical complexity and heterogeneous material properties; however only systems with homogeneous frictional and material properties are examined. Some analytical results are also obtained for the special case of a fault that is parallel to a traction-free surface. For velocity-weakening faults with finite length, there is a critical fault length $$L^{*}$$ for unstable sliding that is analogous to the critical wavelength $$h^{*}$$ that is usually derived from infinite fault systems. Faults longer than $$L^{*}$$ are linearly unstable to perturbations of any length. On vertical strike-slip faults or faults in a full-space $$L^{*} \approx h^{*}/e$$, where e is Euler’s number. For dip-slip faults near a traction-free surface $$L^{*} \le h^{*}/e$$ and is a function of dip angle $$\beta$$, burial depth d of the fault’s up-dip edge and friction coefficient. In particular, $$L^{*}$$ is at least an order of magnitude smaller than $$h^{*}$$ on shallowly dipping ($$\beta < 10^\circ$$) faults that intersect the traction-free surface. Additionally, $$L^{*} \approx h^{*}/e$$ on dip-slip faults with burial depths $$d \ge h^{*}$$. For sliding systems that can be treated as a thin layer, such as landslides, glaciers or ice streams, $$L^{*} = h^{*}/2$$. Finally, conditions are established for unstable sliding on infinitely-long, velocity-strengthening faults that are parallel to a traction-free surface. 

Abstract 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. Frictional heterogeneity is imposed through alternating velocity‐strengthening 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: (a) the average frictional properties of the fault, and (b) 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.