The rupture behavior in the beginning of earthquakes provides an important clue to the (1) mechanism of earthquake instability (constitutive and friction laws), (2) fault-zone heterogeneity, (3) fault interaction, and (4) mechanism of rupture growth. To facilitate the study of close-in velocity records for this purpose, we transform time, t, and velocity amplitude, v, to log(t) and v**1/3, respectively. The origin of the time axis is set at 20 msec before the onset. The velocity seismograms displayed with the transformed axes are called "prolograms". On prolograms we can display ground-motion velocity records for earthquakes over a large magnitude range (e.g. M=3 to 7.3) on common scales, 0.01<t<7 sec and -1.5<v**1/3<1.5 (cm/sec)**1/3. Our results suggest that while the simple expanding fault model can explain the overall rupture process, the observed prolograms exhibit rapid oscillations with a period of about 0.1 sec which is probably a manifestation of small scale heterogeneity on the fault plane. The behavior in the rupture beginning varies from event to event, but no obvious systematic difference between small and large earthquakes has been found.
To understand this variability, we considered earthquake models governed by the Griffith type rupture criterion. The essential aspect of the Griffith type model is that under a given driving stress, s, and surface energy, G, of the material, a crack is stable (i.e. does not grow) until its size reaches a threshold value l0. At this point, the crack is in a critical state, and with an infinitesimal increase in s or decrease in G, the crack will grow with a progressively increasing rupture speed. Unless some external mechanism is introduced (e.g. sudden increase in the surface energy), the crack will grow indefinitely. With this basic concept, two classes of models have been considered to represent end-member cases. In the following, "crack" and "fault" are used interchangeably. In the first model, we assume that the surface energy, G(r), varies smoothly as a function of position, r, in the crust which contains pre-existing small faults. The longest fault near r has the critical dimension, l0(r), determined by the surface energy G(r). Under this condition, an earthquake occurs when either s suddenly increases or the material weakens (i.e. G decreases) suddenly, and instability occurs. In this model, faults with small initial dimensions grow in the medium with small surface energy, and those with large initial dimensions, in large surface energy.
In the second model, we assume that the surface energy is constant, G0, throughout the crust except near the ends of faults where it is significantly larger than G0. This model simulates a locked fault. We envisage that there are many preexisting faults in the crust with various length, l0(r) . These faults are stable because they encounter some obstacle at their ends (e.g fault segmentation, strong asperity etc). This situation is modeled with a local increase in the surface energy near the ends of faults. In this model, an earthquake is triggered when the obstacle is suddenly removed (i. e. sudden weakening) or the stress is suddenly increased locally to overcome the obstacle. Once an earthquake is triggered then the fault growth is governed by the "Griffith" type crack propagation in a medium with G0. In contrast to the first model, both short and long faults grow in this model, after having been triggered, in the medium with the same surface energy, G0.
This project is still in progress. The first half of the project was presented at the 1997 Seismilogical Society meeting, and a paper for the second half is being prepared for publication.