dynamics. Combined with insightful physical reasoning and intriguing new laboratory and field data, these investigations promise a better understanding of seismic complexity and predictability.
Earthquakes are clearly complex in both the commonsense and the technical meanings of the word. At the largest scales, complexity is manifested by features such as the aperiodic intervals between ruptures, the power-law distribution of event frequency across a wide range of magnitudes, the variable patterns of slip for earthquakes occurring at different times on a single fault, and the richness of aftershock sequences. Individual events are also complex in the disordered propagation of their rupture fronts and the heterogeneous distributions of residual stress that they leave in their wake. At the smallest scales, earthquake initiation appears to be complex, with a slowly evolving nucleation zone preceding a rapid dynamic breakout that sometimes cascades into a big rupture. Among the many open issues in this field are the questions of whether these different kinds of complexity might be related to one another and, if so, how.
The most ambitious and optimistic reason for considering the ideas of dynamical systems theory is the hope that one might discover universal features of earthquake-like phenomena. Such features would, of course, be extremely interesting from a fundamental scientific point of view. They might also have great practical value, for example, as a basis for interpreting seismic records or for making long-term hazard assessments. Two thought-provoking, complementary concepts that look as if they might bring some element of universality to earthquake science are fractality and self-organized criticality. The first describes the geometry of fault systems; the second is an intrinsically dynamic hypothesis that pertains to the complex motions of these systems. Although each has provoked its own point of view among earthquake scientists—that seismic complexity is, on the one hand, primarily geometric in origin or, on the other hand, primarily dynamic—it seems likely that both concepts contain some elements of the truth and that neither is a complete description of the behavior of the Earth.
There is substantial evidence that fault geometry is fractal, at least in some cases and over some ranges of length scales. Fractality is a special kind of geometric complexity that is characterized by scale invariance (5). That is, images of the same system made with different magnifications are visually similar to one another; there is no intrinsic length scale such as a correlation length or a feature of recognizable size that would enable an observer to determine the magnification simply by looking at the image.