The failure of earthquake failure models

In this study I show that simple heuristic models and numerical calculation s suggest that an entire class of commonly invoked models of earthquake fai lure processes cannot explain triggering of seismicity by transient or "dyn amic" stress changes, such as stress changes associated with passing seismi c waves. The models of this class have the common feature that the physical property characterizing failure increases at an accelerating, rate when a fault is loaded (stressed) at a constant rate. Examples include models that invoke rate state friction or subcritical crack growth, in which the prope rties characterizing failure are slip or crack length, respectively. Failur e occurs when the rate at which these grow accelerates to values exceeding some critical threshold. These accelerating failure models do not predict t he finite durations of dynamically triggered earthquake sequences (e.g., at aftershock or remote distances). Some of the failure models belonging to t his class have been used to explain static stress triggering of aftershocks . This may imply that the physical processes underlying dynamic triggering differs or that currently applied models of static triggering require modif ication. If the former is the case, we might appeal to physical mechanisms relying on oscillatory deformations such as compaction of saturated fault g ouge leading to pore pressure increase, or cyclic fatigue. However, if dyna mic and static triggering mechanisms differ, one still needs to ask why sta tic triggering models that neglect these dynamic mechanisms appear to expla in many observations. If the static and dynamic triggering mechanisms are t he same, perhaps assumptions about accelerating failure and/or that trigger ing advances the failure times of a population of inevitable earthquakes ar e incorrect.