Sensitivity of 3d Rupture Dynamics to Fault Geometry and Friction Parameters the Friction Law

We scale the various parameters deening a 3D fault model (i.e. characteristic distance and time of a state friction law, size and aspect ratio of the fault, medium impedance) and derive two dimensionless parameters governing the typical dynamics of the fault through single or multiple ruptures. The diier-ent faulting regimes are illustrated by a series of numerical simulations. As the parameters are varied the model crosses over from a regime which exhibits narrow, self-healing slip pulses, to one which exhibits broad, crack-like solutions that only heal in response to edge eeects. In the crack-like regime we observe periodic systemwide events. For self-healing pulses, the system exhibits self-roughening which leads to dynamical complexity. The behavior also changes from periodicity or quasi-periodicity to more complex time sequences as the total fault size or the length to width ratio are increased. Our results are in good qualitative agreement with analogous results which we obtain for a one dimensional Burridge{Knopoo model, where the variations in the stiiness of the transverse spring are related to variations in the width of an equivalent two dimensional fault, and radiation eeects are approximated by viscous dissipation. For our studies we deene a rate and state friction law which incorporates a characteristic distance for slip weakening, a characteristic time for healing, and a velocity weakening steady state. We choose the simplest functional representation for these features: The friction is given by