Journal of Conference Abstracts

Recent Developments in Earthquake Dynamics

Yehuda Ben-Zion (benzion@terra.usc.edu)

Department of Earth Sciences, University of Southern California, Los Angeles, CA., 90089-0740, U.S.A.

The equation of motion for a continuum solid is scale-independent, suggesting that deformation processes in solids should produce self similar patterns manifested in power law statistics (e.g., Andrews, 1980; Kagan and Knopoff, 1980). However, length scales associated with rheology and existing structures can produce deviations from self similarity. An example at small spatial scale is a transition from stable creep to dynamic instability at a nucleation size whose dimensions depend on frictional and elastic parameters (e.g., Dieterich, 1993). This transition, defining a minimum earthquake size, fueled hopes to observe the precursory deformation associated with the nucleation process. However, high resolution geodetic measurements (Johnston et al.,1987) and the existence of very small earthquakes (e.g., M=-1 on the SAF) indicate that, even on major faults, the nucleation zone is too small to produce detectable surface signals. Another, larger size example of a transition breaking self similarity, is the scaling of stress concentration in continuum solids with rupture dimension, which produces a critical event size terminating the power law regime of frequency-size statistics of earthquakes (Ben-Zion and Rice, 1993). This occurs when the effective stress concentration is comparable to the average stress drop, and produces "runaway" events and statistics compatible with the characteristic earthquake distribution. However, if strength heterogeneities have a wide range of size scales, the probability of stopping runaway events is large and the statistics are power law over the entire magnitude range (Ben-Zion and Rice, 1995). These conclusions are compatible with observations of Wesnousky (1994). Statistical physics analysis indicates that power law statistics are also obtained if dynamic weakening effects are not very important (Fisher et al., 1997), or if stress heterogeneities are more clustered than a Brownian field (Rundle et al., 1998).

Ellsworth and Beroza (1995) suggested that observed seismograms contain signatures of dynamic breakouts from earthquake nucleation zones that scale with the final event size. However, this has been disputed (e.g., Mori and Kanamori, 1996) and the subject remains controversial. While prospects for predicting individual earthquakes appear very small (e.g., Geller et al., 1997), it is still possible that the evolution of stress and seismicity patterns generate informative statistical measures for intermediate-term forecasting of large events. This is supported by pattern recognition analysis of observed (e.g., Keilis-Borok and Kossobokov, 1990; Knopoff et al., 1995) and synthetic (e.g., Pepke et al., 1994; Eneva and Ben-Zion, 1997) earthquake catalogs based on space-time clustering and other signals, and time-to-failure analysis employing observed cumulative Benioff strain (Bufe and Varnes, 1993) with possible log periodic fluctuations (Sornette and Sammis, 1996; Bowman et al., 1998). Relevant to these are model calculations showing establishment and destruction of long range correlation of stress with large earthquake cycles (Ben-Zion, 1996), approach and retreat from criticality (Heimpel, 1997; Sammis and Smith, 1998), and creation of log periodic signals in systems with discrete hierarchical structures (Huang et al., 1997).

A challenging front in fracture mechanics is the proper understanding of energy partition at crack tip, and trajectory (including branching) of dynamic ruptures. Classical theory (e.g., Yoffe, 1951) and high resolution experiments of tensile cracks (e.g., Sharon and Fineberg, 1996) indicate a transition, at rupture speed of about 0.5 the Rayleigh velocity (C_R) or less, to rough crack surfaces and branching. This is compatible with the strongly disordered structures of immature fault systems. However, it is not compatible with the commonly inferred earthquake rupture speeds of 0.8-0.9 C_R, and the long straight fault traces characterizing mature fault zones. A possible explanation may stem from dynamic reduction of normal stress that accompanies slip on a material interface (Weertman, 1980; Andrews and Ben-Zion, 1997). This may trap ruptures in fault zones with well developed interfaces. In such structures, the same mechanism produces self-healing ruptures with short rise times and small amount of frictional heat, in agreement with data and ideas summarized by Heaton (1990) and Brune et al. (1993). A quasistatic reduction of fault strength during a large earthquake cycle can result from evolving fluid pressure (e.g., Sibson, 1992; Rice, 1992; Byerlee, 1993), as was demonstrated by Miller et al. (1996). Quasistatic evolution of fault structures, seismicity patterns, and associated fields, have been studied by Lyakhovsky et al. (1997; this meeting), using a model consisting of a brittle upper crust governed by damage rheology over a viscoelastic substrate. Their simulated statistics depend on the space-time size of the observational domain, i.e., the response is non ergodic. For some parameters, the results exhibit overall switching of response, from periods of intense seismic activity to periods with aseismic deformation. An overall response switching is also found in a mean field analysis of earthquakes on a strike-slip fault in a 3D half space (Dahmen et al., 1998; this meeting), and is compatible with some long records of earthquake histories (e.g., Marco et al., 1996).

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