Quantifying the probability of rupture arrest at restraining and releasing bends using earthquake sequence simulations

Fault bends are known to act as barriers to rupture propagation in many earthquakes. A recent compilation of the surface rupture traces of paleo earthquakes quantifies the probability of rupture termination as a function of the bend angle. To understand the physical basis of these unique statistics, we carry out 2D quasi-dynamic earthquake sequence simulations on a fault with either a restraining or releasing (double-) bend. The fault is loaded by steady sliding from an adjacent creeping region, rather than with backslip, together with a stress relaxation method to avoid unphysical stress buildup due to the curvature of faults. This relaxation is a proxy for unmodeled off-fault secondary faulting. This ensures the existence of a long-term steady earthquake cycle and stress field, the latter of which is determined by the balance between the slip-induced stress changes and relaxation terms. We quantify the influence of the bend on rupture propagation by computing passing ratio (i.e., the fraction of ruptures that propagate through the bend). Our simulations approximately reproduce the Biasi-Wesnousky empirical law for a wide range of parameters (e.g., bend width, stress relaxation time, background stress). Also, we reproduce geologic observations that the long-term slip rate of a fault has local minima at restraining bends, without assuming spatially varying loading rates using the backslip approach. Additionally, we find that restraining and releasing bends have different earthquake cycles. For restraining bends, many ruptures are arrested before reaching the center of the bend, and the passing ratio decreases with increasing the bend angle. For releasing bends, ruptures stop after passing the center of the bend, and the passing ratio abruptly drops from near unity to zero at around 20∘. This difference can be qualitatively explained by an energy balance approach. Our model has a potential to understand the seismogenesis of nonplanar faults and we can readily extend our model into 3D specific fault systems for hazard assessment.