EARTHQUAKE FAILURE SEQUENCES ALONG A CELLULAR FAULT ZONE IN A 3-DIMENSIONAL ELASTIC SOLID CONTAINING ASPERITY AND NONASPERITY REGIONS

Numerical simulations of earthquake failure sequences along a discrete cellular fault zone are performed for a three-dimensional (3-D) model representing approximately the central San Andreas fault. The model c onsists of an upper crust overlying a lower crust and mantle region, t ogether defining an elastic half-space with a vertical half-plane faul t. The fault contains a region where slip is calculated on a uniform g rid of cells governed by a static/kinetic friction law and regions whe re slip is prescribed so as to represent tectonic loading, aseismic fa ult creep, and adjacent great earthquakes. The computational region mo dels a 70-km-long and 17.5-km-deep section of the San Andreas fault to the NW of the great 1857 rupture zone. Different distributions of str ess drops on failing computational cells are used to model asperity (' 'Parkfield asperity'') and nonasperity fault regions. The model is ''i nherently discrete'' and corresponds to a situation in which a charact eristic size of geometric disorder within the fault (i.e., cell size, here a few hundreds of meters) is much larger than the ''nucleation si ze'' (of the order of tens of centimeters to tens of meters) based on slip weakening or state evolution slip distances. The computational gr id is loaded by a constant plate motion imposed at the lower crust, up per mantle, and creeping fault regions and by a ''staircase'' slip his tory imposed at the 1857 and 1906 rupture zones. Stress transfer along and outside the fault due to the imposed loadings and failure episode s along the computational grid is calculated using 3-D elastic disloca tion theory. The resulting displacement field in the computational reg ion is compatible with geodetic and seismological observations only wh en the asperity and nonasperity regions are characterized by significa ntly different average stress drops. The frequency-magnitude statistic s of the simulated failure episodes are approximately self-similar for small events, with b - 1.2 (the b value of statistics based on ruptur e area b(A) is about 1) but are strongly enhanced with respect to self -similarity for events larger than a critical size. This is interprete d as a direct manifestation of our 3-D elastic stress transfer calcula tions; beyond certain rupture area and potency (seismic moment divided by rigidity) release values, the event is usually unstoppable, and it continues to grow to a size limited by a characteristic model dimensi on. This effect is not accounted for by cellular automata and block-sp ring models in which the adopted simplified stress transfer laws fail to scale properly with increasing rupture size. The simulations sugges t that local maxima in observed frequency-magnitude statistics corresp ond to dimensions of coherent brittle zones, such as the width of the seismogenic layer or the length of a fault segment bounded by barriers . The analysis indicates that a single cell size, representing approxi mately a single scale of geometric disorder, cannot induce self-simila rity in a 3-D elastic model over a broad range of magnitudes. A repres entation of geometric disorder covering a range of scales may thus be required to generate a wide domain of self-similar Gutenberg-Richter s tatistics. Our simulations show a great diversity in the mode of failu re of the Parkfield asperity; the earthquakes themselves define an irr egular sequence of events. The modeling, like many other discrete faul t models, suggests that expectations for periodic Parkfield earthquake s and/or simple precursory patterns repeating from one event to the ot her are unrealistic.