Employing computer simulations and numerical analyses, I investigate earthquake phenomenology using the Rundle-Jackson-Brown (RJB) fault model, which is a cellular automaton version of the Burridge-Knopoff slider-block model. The RJB model consists of a two-dimensional square lattice of inertialess blocks with each block interacting with its neighbors through linear springs. While a tectonic loader plate drives each block via a linear spring, a frictional surface prevents a block from sliding unless the combined stress due to the loader plate and the neighbors overcomes a static frictional threshold. After a sliding block slips, its displacement is proportional to the total stress, which is mostly transferred to the neighbors. The remaining stress dissipates from the system. This stress transfer may cause other blocks to slip, thus initiating an earthquake.; In addition to verifying and extending previous work on the nearest-neighbor RJB model, I modify the RJB model to provide a more realistic description of earthquake faults, in accordance with elasticity theory. This modification entails using a long-range interaction which varies as 1/{dollar}rsp3,{dollar} where r is the distance between the interacting slider-blocks, inside an interaction region, and which equals zero outside this region. For this long-range model, frequency-size distributions of earthquakes, time correlations between earthquakes, dynamic scaling of earthquake growth, and earthquake structure indicate that a spinodal critical point, a point of instability which delineates the boundary between unstable and metastable states, influences the simulated earthquake behavior.; I present a derivation of a coarse-grained theory which probes the long-range RJB system at a length scales longer than the interaction range. Numerical solutions of the time-independent spatially homogenous coarse-grained equation agree with the results from long-range simulations. According to this theory, the long-range RJB model can describe a wide variety of earthquake phenomena, including relatively inactive, almost aseismic faults exhibiting small earthquakes, very active, seismic faults displaying frequency-size distributions similar to the Gutenberg-Richter distribution observed on geological faults, and the possibility of faults which experience spinodal assisted nucleating earthquakes.
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