Princeton University Donald R. Hamilton Colloquium Series

Abstract: Earthquakes exhibit complex behavior at all scales, from the evolution of slip during a single rupture lasting seconds to minutes, to the statistics of regional seismicity over years or centuries. The origin of complexity in fault behavior has long been debated: is it a reflection of heterogeneity or geometrical complexity of the underlying fault system, or does it arise spontaneously from the frictional laws that govern fault slip?

In this talk, I will present several case studies supporting the view that complex earthquake behavior can arise even on very simple fault geometries, as a consequence of stress gradients and velocity-dependent friction. In each case, complexity is predicted by simple fracture mechanics arguments, which are validated against numerical simulations of earthquake cycles with rate-state dependent friction.

During the interseismic period, fault slip is characterized by patches of localized creep (or slow slip, with a sliding velocity ≲ mm/yr), next to locked areas (near-zero sliding velocity). The growth of creep patches is described by an energy balance criterion, in which stresses from tectonic loading are balanced by frictional changes within slipping cracks. Eventually, dynamic rupture initiates, and crack propagation is controlled by a balance between the stress intensity factor and a velocity-dependent fracture toughness. I apply these ideas to describe the seismic cycle on a uniform fault loaded by end-point displacement (representing creep at constant velocity on an adjacent fault section), and demonstrate that the stress gradient due to loading results in a broad range of earthquake magnitudes, with a power-law distribution consistent with regional catalogs, without the need for underlying complexity. Furthermore, the model predicts that the same fault can experience both earthquakes and transient slow ruptures at different stages of the seismic cycle, as a consequence of the stabilizing effect imparted by lateral loading; slow transients are reminiscent of slow-slip events frequently observed at the downdip end of megathrust and crustal faults. Finally, I discuss the occurrence of back-propagating fronts within a single earthquake, and argue that this type of complexity is an intrinsic feature of laterally propagating ruptures with a velocity-weakening friction coefficient. Taken together, these results demonstrate that fracture mechanics is a powerful technique to explain fault behavior across a broad range of spatio-temporal scales, and a flexible tool to generalize numerical results beyond a specific realization of elasto-frictional properties.