STATISTICAL PHYSICS, SEISMOGENESIS, AND SEISMIC HAZARD

The scaling properties of earthquake populations show remarkable simil arities to those observed at or near the critical point of other compo site systems in statistical physics. This has led To the development o f a variety of different physical models of seismogenesis as a critica l phenomenon, involving locally nonlinear dynamics, with simplified rh eologies exhibiting instability or avalanche-type behavior, in a mater ial composed of a large number of discrete elements. In particular, it has been suggested that earthquakes are an example of a ''self-organi zed critical phenomenon'' analogous to a sandpile that spontaneously e volves to a critical angle of repose in response to the steady supply of new grains at the summit. Tn this stationary state of marginal stab ility the distribution of avalanche energies is a power law, equivalen t to the Gutenberg-Richter frequency-magnitude law, and the behavior i s relatively insensitive to the details of the dynamics. Here we revie w the results of some of the composite physical models that have been developed to simulate seismogenesis on different scales during (1) dyn amic slip on a preexisting fault, (2) fault growth, and (3) fault nucl eation. The individual physical models share some generic features, su ch as a dynamic energy flux applied by tectonic loading at a constant strain rate, strong local interactions, and fluctuations generated eit her dynamically or by fixed material heterogeneity, but they differ si gnificantly in the details of the assumed dynamics and in the methods of numerical solution. However. all exhibit critical or near-critical behavior, with behavior quantitatively consistent with many of the obs erved fractal or multifractal scaling laws of brittle faulting and ear thquakes, including the Gutenberg-Richter law. Some of the results are sensitive to the details of the dynamics and hence are not strict exa mples of self-organized criticality. Nevertheless, the results of thes e different physical models share some generic statistical properties similar to the ''universal'' behavior seen in a wide variety of critic al phenomena, with significant implications for practical problems in probabilistic seismic hazard evaluation. In particular, the notion of self-organized criticality (or near-criticality) gives a scientific ra tionale for the a priori assumption of ''stationarity'' used as a firs t step in the prediction of the future level of hazard. The Gutenberg- Richter law (a power law in energy or seismic moment) is found to appl y only within a finite scale range, both in model and natural seismici ty. Accordingly, the frequency-magnitude distribution can be generaliz ed to a gamma distribution in energy or seismic moment (a power law, w ith an exponential tail). This allows extrapolations of the frequency- magnitude distribution and the maximum credible magnitude to be constr ained by observed seismic or tectonic moment release rates. The answer s to other questions raised are less clear, for example, the effect of the a priori assumption of a Poisson process in a system with strong local interactions, and the impact of zoning a potentially multifracta l distribution of epicentres with smooth polygons. The results of some models show premonitory patterns of seismicity which could in princip le be used as mainshock precursors. However, there remains no consensu s, on both theoretical and practical grounds, on the possibility or ot herwise of reliable intermediate-term earthquake prediction.