Characteristic scales of earthquake rupture from numerical models

Numerical models of earthquake rupture are used to investigate characteristic length scales and size distributions of repeated earthquakes on vertical, planar fault segments. The models are based on exact solutions of static three-dimensional (3-D) elasticity. Dynamical rupture is approximated by allowing the static stress field to expand from slip motions at a single velocity. To show how the vertical fault width affects earthquake size distributions for a broad range of fault behaviors, two different fault strength models are used; a smooth model and a heterogeneous asperity model. The smooth model is a simplified version of the Dieterich-Ruina rate and state dependent friction law. The heterogeneous asperity model uses a slip-dependent random powerlaw strength distribution. It is shown that the characteristic scale of fault segmentation is proportional to the vertical width of a seismogenic fault. This conclusion holds for both the smooth and the heterogeneous models. For the smooth models characteristic quake distributions result, with populations of large events that are obviously distinct from smaller events. The distributions of large events have well-defined mean lengths and moments. The heterogeneous models result in Gutenberg-Richter (GR) powerlaw distributions of event sizes up to a characteristic quake size. Quakes larger than the characteristic size fall off the GR distribution such that the powerlaw would greatly overestimate the probability of occurrence of the larger events.