| The functional form of the friction law employed in dynamic earthquake simulations is directly related to the energy partitioning of rupture and slip (e.g., Kanamori and Rivera, 2006). Earthquake ruptures can propagate along geometrically complex faults by bending and jumping along fault segments (Wesnousky, 1988), however, this is dependent on how much energy is available to further rupture propagation and how much energy is needed. For planar fault stepovers with homogeneous stress, rupture can jump segments or it can arrest at the edge of a segment. Since friction laws, along with stress regimes, implicitly specify the energy budget, different laws can lead to different rupture dynamics. Using realistic, laboratory-derived friction laws to simulate rupture is a constant ambition in seismology. The rate-state friction formulation includes intuitive variables such as time, slip speed history, and normal stress history as well as exhibits reasonable properties such as stick-slip sliding, creep, and healing (Dieterich, 1978b, 1979; Linker and Dieterich, 1992). Particularly, including the change in friction coefficient with normal stress history is imperative for earthquakes that produce large dynamic fluctuations in normal stress, including both stepovers and dip-slip faults that penetrate the free surface.;In this study we use FaultMod to run dynamic earthquake simulations on fault stepovers using the various friction formulas listed above. Firstly, we investigate effects of the functional form of the friction laws on jumping rupture at stepovers. The functional forms are associated with unique energy budgets that can determine how far rupture can jump within a given amount of time. We find that making the energy budgets similar between the friction parameterizations makes the rupture processes more similar at the stepover region (e.g., similar maximum jump distances). We also find that for larger jumps the rupture speeds increase to supershear speeds, even though the initial stress conditions would preclude such a result on a planar strike-slip fault (Andrews, 1976b). Secondly, we add to the stepover simulations by introducing the Linker-Dieterich formulation, in which friction coefficient depends on normal stress. It is well known that stepovers exhibit perturbations in normal stress along the offset region during rupture, with the sign being opposite for compressional and dilational stepovers. Adding the normal-stress-dependent state variable to the friction formulation decreases the maximum rupture jump for both types of stepover, however.;Additionally, we apply the Linker-Dieterich formulation to normal and reverse dip-slip faults, both of which are known to exhibit dynamic fluctuations in normal stress due to the free surface (Brune, 1996; Nielsen, 1998; Oglesby et al., 1998). Differences in shear stress direction between normal and reverse faults produce asymmetric normal stress perturbations along the fault during rupture, causing the motion from a reverse fault to be larger than that of an otherwise equivalent normal fault. Adding a normal-stress-dependent state variable serves to mitigate this effect. We also find that decreasing the initial shear stress inhibits rupture more on normal faults than on reverse faults, given that the faults intersect the free surface. |
