It may be no exaggeration to claim that this most recent quaddrenium has seen more controversy and thus more progress in understanding the physics of earthquakes than any in recent memory. The most interesting development has clearly been the emergence of a large community of condensed matter physicists around the world who have begun working on the problem of earthquake physics. These scientists bring to the study of earthquakes an entirely new viewpoint, grounded in the physics of nucleation and critical phenomena in thermal, magnetic, and other systems. Moreover, a surprising technology transfer from geophysics to other fields has been made possible by the realization that models originally proposed to explain self-organization in earthquakes can also be used to explain similar processes in problems as disparate as brain dynamics in neurobiology (Hopfield, 1994), and charge density waves in solids (Brown and Gruner, 1994). An entirely new sub-discipline is emerging that is focused around the development and analysis of large scale numerical simulations of the dynamics of faults. At the same time, intriguing new laboratory and field data, together with insightful physical reasoning, has led to significant advances in our understanding of earthquake source physics. As a consequence, we can anticipate substantial improvement in our ability to understand the nature of earthquake occurrence. Moreover, while much research in the area of earthquake physics is fundamental in character, the results have many potential applications (Cornell et al., 1993) in the areas of earthquake risk and hazard analysis, and seismic zonation.

Two important earthquakes occurred during this quadrennium, the June 28, 1992 Landers event (Sieh et al., 1993), and the January 17, 1994 Northridge earthquake (Wuethrich, 1994). While the significance of the latter is yet to be fully understood, effects associated with the Landers earthquake (Hill et al., 1993) indicated that microearthquake activity in geothermal areas as remote as 1000 km epicentral distance (Cascades, Yellowstone) was triggered by the sudden onset of stress increments associated with the Landers event. At distances greater than 250-300 km, the static stress changes are less than the tidal stress changes, which do not correlate with increased microseismicity. The implication is that the susceptibility of increased crustal microseismicity to stress perturbations depends upon spatial wavelength as well as amplitude of the stress perturbation. Effects of this type are often seen in other physical systems near a critical point (Klein and Leyvraz, 1986) as will be discussed below. It may also imply that the correlation length for crustal seismicity is of the order of a thousand kilometers, despite the fact that elastic stresses die off as the inverse cube of the hypocentral distance. Again, the self-organization of physical systems near a critical point is well-known to lead to large correlation lengths, even if the interaction range is small (e.g., Ma, 1985). In addition to these effects, it was established (Harris and Simpson, 1992; Jaume and Sykes, 1992; Stein et al., 1992) that the Landers-Big Bear sequence loaded favorably oriented neighboring faults in the southern California region, shortening the time to failure by perhaps as much as 10 years. The existence of stress relaxation effects in aftershock sequences, leading to stretched exponential distributions, were demonstrated by Kisslinger (1993).

A nonevent with important implications was the missing Parkfield, California, M 6 earthquake, which was originally forecast to occur by January, 1993 (Bakun and Lindh, 1984). Considerable time and effort have been spent on investigations, a sampling of which has been given in Johnson et al. (1992); Karageorgi et al. (1992); Eberhart-Phillips and Michael (1993); and Nadeau et al. (1994). Retrospective studies have concluded that the pattern of occurrence of the the historic Parkfield events is consistent with considerable variation in event interoccurrence time (Savage, 1991; 1993). This theme was echoed in work on the validity of the seismic gap hypothesis by Kagan and Jackson (1992), who concluded that the dominating effect is the tendency of earthquakes to cluster in time. Thus elapsed time since the last event may not necessarily imply a known time interval to the next. Other authors dispute these conclusions (Nishenko et al., 1993). The tendency for earthquakes to cluster in time is supported also by paleoseismic observations of Grant and Sieh (1994). A recent theoretical model by Dieterich (1994) incorporates the clustering idea directly.

An important set of observations relates to the existence of ``slow'' earthquakes precursory to mainshock events that generate seismic radiation, the first of which was observed by Kanamori and Cipar (1974). A number of authors (Jordan, 1991; Ihmle et al., 1993; Kanamori and Hauksson, 1993; Kanamori and Kikuchi, 1993; Kikuchi et al., 1993; Wallace et al., 1991) have found evidence for slow events preceeding mainshocks. However, searches for other kinds of precursory changes, such as variations in earth strain tidal amplitudes prior to the Loma Prieta earthquake (Linde et al., 1992) have been unsuccessful. The degree to which fault plane structure (asperities and barriers) control slip has been investigated by Beck and Christensen (1991) and Ruff (1992), who provide maps of the spatial distribution of enhanced slip on the fault plane. The physical interpretation of asperities in terms of strong regions on the fault depends critically on assumptions about the constancy of rupture velocity and directivity (Rundle and Klein, 1994).

Other laboratory and field observations dealt with the nature of fracture, and of friction on fault surfaces. Chen and Spetzler (1993a,b) studied the scaling and frictional characteristics of fractures in Westerly granite, and found that the power spectrum of topography has an exponent near -2, in agreement with previous work. Marone et al. (1991) demonstrated how earthquake afterslip can be understood via velocity dependent friction laws. Sibson (1992) and Rudniki et al. (1993) discuss the importance of pore water to frictional behavior of faults. A reasonable solution of the apparant stress-heat flow paradox emerged as a result of work by Brune et al. (1993), who showed that for a sufficiently compliant system, which is likely true for a real fault, separation of the interface accompanies slip. Thus sliding friction is nearly zero, and little or no heat is generated. This conclusion is disputed by Dieterich and Linker (1992).

Of major significance was the widespread realization that sliding on faults at roughly constant stress drop does not necessarily imply a Kostrov-type slip distribution. The Kostrov distribution arises when no healing takes place until progression of the rupture front stops. By contrast, the ``Heaton pulse'' model (Heaton, 1990) allows healing just behind the rupture front, and in fact, there is no a priori reason to exclude other more general modes of rupture as well (Rundle and Klein, 1994). Evidence for rupture pulses and non uniform healing behind rupture fronts is now accumulating (Wald et al., 1991; Beroza, 1991; Mendoza et al., 1994; see also the paper by Beroza, this issue).

A controversy emerged over the origin of scaling (power law distributions) in earthquake dynamics, as particularly manifested by the Gutenberg Richter magnitude-frequency relation. Pacheco et al. (1992) used observational data to verify earlier predictions by Rundle (1989) that the b value increases from approximately 1 to 1.5 as the magnitude of the earthquakes increases past about Mw 6 for transform faults, and Mw 7.5 for subduction zone events. Discussions ensued about the physical cause of this change, which occurs when the down dip width of the earthquake roughly equals the thickness of the elastic lithosphere. Rundle (1989), Romanowicz (1992) and Romanowicz and Rundle (1993) attribute the change to a crossover in the scaling of slip. In this view, which is consistent with elastic dislocation theory, slip is always proportional to the minimum diameter of the earthquake, hence slip saturates when the earthquake is large enough to completely rupture the thickness of the elastic lithosphere. In another view, Scholz (1994) maintains that data from field observations of surface slip support the position that slip for large earthquakes grows with earthquake length, thus that slip scales with the maximum diameter of the earthquake. In the latter view, slip for large events grows with length of the earthquake and can in principle become arbitrarily large. Scholz finds support for his viewpoint in a recent theoretical model by Sornette and Virieux (1992), who proposed a nonlinear diffusion equation to describe straining on faults. Their model is a mean field model, the equations describing it do not arise from elasticity, and earthquakes are introduced as fluctuating noise having a power law dependence. More recently, Rundle (1993) rederived and extended his earlier results using a different approach based on statistical mechanics.

A major theoretical theme has been the development of increasingly sophisticated computer simulation techniques for understanding the dynamics of faults. Recent observational work continues to confirm the importance of fault interactions (Bilham and Bodin, 1992; Hill et al., 1993; Sanders, 1993), which of course also exist between patches on the same fault. These interactions cause slip on the fault to self-organize, so that slip occurs in earthquakes obeying the Gutenberg-Richter relation, and not as random events (the existence of power law behavior is incompatible with truly random dynamics). Other work points out that the existence of scaling implies that small earthquakes are as important as large events in redistributing stress (Hanks, 1992), a fact that is clearly seen in simulations. While a few authors use some version of continuum intereactions (stress Green's functions) in their models (Ward, 1992; Ward and Goes, 1993; Rice, 1993; Ben-Zion and Rice, 1993; Ben-Zion et al., 1993), many more use some version of a nearest-neighbor slider block model. Rice (1993) in fact argues that nearest-neighbor models are inappropriate. However, it is known from extensive studies over many years on the statistical mechanics of spin dipole systems (Ma, 1985) that nearest-neighbor models such as Ising systems display much of the same physics as models with dipole (1/r3) interactions. This is a result of the large correlation lengths that appear near a critical point, in association with power law scaling like the Gutenberg-Richter relation. Examples of slider-block models include Carlson et al. (1991); Brown et al. (1991); Carlson (1991); Narkounskaia and Turcotte (1992); Narkounskaia and Turcotte (1992); Huang et al. (1992); Knopoff et al. (1992); Shaw et al. (1992); Vasconcelos et al. (1991); Olami et al. (1992); Rundle and Klein (1993); Ding and Lu (1993); de Sousa et al. (1993); Lomnitz-Adler (1993); Pepke et al. (1994); Rundle and Klein (1994). Some of these papers attempt to put earthquakes into the same category as the self-organized criticality model for sandpiles that has no tuning parameter. Others show that earthquakes are more probably an example of self-organizing systems that can be tuned to approach a critical point, the different physics implying membership in a different universality class and different pattern formation mechanisms. These models typically use concepts from percolation theory to analyze the simulation data. Sahimi et al. (1993) use the percolation idea directly to show that large earthquakes are associated with the backbone of the percolation cluster of fractures forming the fault system in the earth. Others found chaos in the dynamics of their models (Narkounskaia et al., 1992), even in low order systems (Huang and Turcotte, 1992). Models can in principle also be used as testbeds to develop techniques for earthquake forecasting. Ward (1992), Dowla et al. (1992) and Pepke et al. (1994) suggested several methods for testing the predictability of synthetic earthquake sequences, using for example neural networks as well as pattern recognition.

It is apparent that the development and analysis of numerical simulations is very much a field in progress. There is considerable potential for significant advancement because the values of all space-time variables are known, unlike the situation in nature. If adequate theoretical understanding cannot be developed for the simulations, it is unlikely that the dynamics of real faults can be similarly understood.

Acknowledgments. JBR would like to acknowledge support from NASA contract NAG5-2353 to CIRES at the University of Colorado, Boulder.