[1] Earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales. In addition, many aspects of regional seismicity appear to be stochastic both in space and time. However, within this complexity, there is considerable self-organization. We argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics. Concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models. Examples include sandpile models, forest fire models, and, particularly, slider block models. These models exhibit avalanche behavior very similar to observed seismicity. A fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes. Several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts, some of which show promise. INDEX

In many places, earthquakes with similar characteristics have been shown to recur. If this is common, then relatively small deformations associated with individual earthquake cycles should accumulate over time to create geological structures. Following this paradigm, we show that existing models developed to describe leveling line changes associated with the seismic cycle can be adapted to explain geological features associated with a fault. In these models an elastic layer containing the fault overlies a viscous half‐space with a different density. Fault motion associated with an earthquake results in immediate deformation followed by a long period of readjustment as stresses relax in the viscous layer and isostatic equilibrium is restored. Deformation is also caused as a result of the loading and unloading due to sediment deposition and erosion. In this paper, the parameters that control the growth of dip‐slip structures are identified. We find that the flexural rigidity of the crust (or the apparent elastic thickness) provides the main control of the width of a structure. The loading due to erosion and deposition of sediment determines the ratio of uplift to subsidence between the two sides of the fault. The flexure due to sediment load is much more important in this respect than whether the fault is normal or reverse in character. We find that, in general, real structures are associated with apparent elastic thicknesses of 4 km or less and thus with very low flexural rigidities.

Threshold systems are known to be some of the most important nonlinear self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization in earthquake threshold systems at two distinct scales: (i) The ''microscopic'' laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive the results obtained from sliding friction experiments, and (ii) the ''macroscopic'' earthquake faultsystem scale, in which the physics of strongly correlated earthquake fault systems can be understood by using time-dependent state vectors defined in a Hilbert space of eigenstates, similar in many respects to the mathematics of quantum mechanics. In all of these systems, long-range interactions induce the existence of locally ergodic dynamics. The existence of dissipative effects leads to the appearance of a ''leaky threshold'' dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of background fluctuations. At the macroscopic earthquake fault-system scale, these ideas show considerable promise as a means of forecasting future earthquake activity.