The stability of frictional sliding on dip-slip and finite length faults

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.