Slip patterns and earthquake populations along different classes of faults in elastic solids

Numerical simulations of slip instabilities on a vertical strike‐slip fault in an elastic half‐space are performed for various models belonging to two different categories. The first category consists of inherently discrete cellular fault models. Such are used to represent fault systems made of segments (modeled by numerical cells) that can fail independently of one another. Their quasi‐independence is assumed to provide an approximate representation of strong fault heterogeneity, due to geometric or material property disorder, that can arrest ruptures at segment boundaries. The second category consists of models having a well‐defined continuum limit. These involve a fault governed by rate‐ and state‐dependent friction and are used to evaluate what types of property heterogeneity could lead to the quasi‐independent behavior of neighboring fault segments assumed in the first category. The cases examined include models of a cellular fault subjected to various complex spatial distributions of static to kinetic strength drops, and models incorporating rate‐ and state‐dependent friction subjected to various spatial distributions of effective stress (normal stress minus pore pressure). The results indicate that gradual effective stress variations do not provide a sufficient mechanism for the generation of observed seismic response. Strong and abrupt fault heterogeneity, as envisioned in the inherently discrete category, is required for the generation of complex slip patterns and a wide spectrum of event sizes. Strong fault heterogeneity also facilitates the generation of rough rupture fronts capable of radiating high‐frequency seismic waves. The large earthquakes in both categories of models occur on a quasi‐periodic basis; the degree of periodicity increases with event size and decreases with model complexity. However, in all discrete segmented cases the models generate nonrepeating sequences of earthquakes, and the nature of the large (quasi‐periodic) events is highly variable. The results indicate that expectations for regular sequences of earthquakes and/or simple repetitive precursory slip patterns are unrealistic. The frequency‐size (FS) statistics of the small failure episodes simulated by the cellular fault models are approximately self‐similar with b ≈ 1.2 and b A ≈ 1, where b and b A are b values based on magnitude and rupture area, respectively. For failure episodes larger than a critical size, however, the simulated statistics are strongly enhanced with respect to self‐similar distributions defined by the small events. This is due to the fact that the stress concentrated at the edge of a rupture expanding in an elastic solid grows with the rupture size. When the fault properties (e.g., geometric irregularities) are characterized by a narrow range of size scales, the scaling of stress concentrations with the size of the failure zone creates a critical rupture area terminating the self‐similar earthquake statistics. In such systems, events reaching the critical size become (on the average) unstoppable, and they continue to grow to a size limited by a characteristic model dimension. When, however, the system is characterized by a broad spectrum of size scales, the above phenomena are suppressed and the range of (apparent) self‐similar FS statistics is broad and characterized by average b and b A values of about 1. The simulations indicate that power law extrapolations of low‐magnitude seismicity will often underestimate the rate of occurrence of moderate and large earthquakes. The models establish connections between features of FS statistics of earthquakes (range of self‐similar regimes, local maxima) and structural properties of faults (dominant size scales of heterogeneities, dimensions of coherent brittle zones). The results suggest that observed FS statistics can be used to obtain information on crustal thickness and fault zone structure.