SLIP COMPLEXITY IN EARTHQUAKE FAULT MODELS

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that th e friction laws involve a characteristic distance for slip weakening o r evolution of surface state. That results in a finite nucleation size , or coherent slip patch size, h. Models of smooth faults, using nume rical cell size properly small compared to h, show periodic response or complex and apparently chaotic histories of large events but have n ot been found to show small event complexity like the self-similar (po wer law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic mode ling of earthquake sequences. In contrast, some models of locally hete rogeneous faults with quasi-independent fault segments, represented ap proximately by simulations with cell size larger than h so that the m odel becomes ''inherently discrete,'' do show small event complexity o f the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h = 0 and h ence always fall into the inherently discrete class. We suggest that t he small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an app ropriate length scale leading to a finite h, and a corresponding redu ction of numerical grid size.