Nucleation process of the one-dimensional Burridge-Knopoff model of earthquakes obeying the rate-and state-dependent friction law is studied both analytically and numerically. The properties of the nucleation dynamics, the nucleation lengths and the duration times are examined together with their continuum limits.

Statistical properties of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes obeying the rate and state dependent friction law are studied by extensive computer simulations. The quantities computed include the magnitude distribution, the rupture-length distribution, the mainshock recurrence-time distribution, the seismic time correlations before and after the mainshock, the mean slip amount, and the mean stress drop at the mainshock, etc. Events of the model can be classified into two distinct categories. One tends to be unilateral with its epicenter located at the rim of the rupture zone of the preceding event, while the other tends to be bilateral with enhanced "characteristic" features resembling the so-called "asperity". For both types events, the distribution of the rupture length Lr exhibits an exponential behavior at larger sizes, ≈ exp[−Lr/L0] with a characteristic "seismic correlation length" L0. The mean slip as well as the mean stress drop tends to be rupture-length independent for larger events. The continuum limit of the model is examined, where the model is found to exhibit pronounced characteristic features. In the continuum limit, the characteristic rupture length L0 is estimated to be ∼100 [km]. This means that, even in a hypothetical homogenous infinite fault, events cannot be indefinitely large in the exponential sense, the upper limit being of order ∼ 10 3 kilometers. Implications to real seismicity are discussed.

Dynamics of earthquake nucleation process is studied on the basis of the one-dimensional BurridgeKnopoff (BK) model obeying the rate-and state-dependent friction (RSF) law. We investigate the properties of the model at each stage of the nucleation process, including the quasi-static initial phase, the unstable acceleration phase and the high-speed rupture phase or a mainshock. Two kinds of nucleation lengths Lsc and Lc are identified and investigated. The nucleation length Lsc and the initial phase exist only for a weak frictional instability regime, while the nucleation length Lc and the acceleration phase exist for both weak and strong instability regimes. Both Lsc and Lc are found to be determined by the model parameters, the frictional weakening parameter and the elastic stiffness parameter, hardly dependent on the size of an ensuing mainshock. The sliding velocity is extremely slow in the initial phase up to Lsc, of order the pulling speed of the plate, while it reaches a detectable level at a certain stage of the acceleration phase. The continuum limits of the results are discussed. The continuum limit of the BK model lies in the weak frictional instability regime so that a mature homogeneous fault under the RSF law always accompanies the quasi-static nucleation process. Duration times of each stage of the nucleation process are examined. The relation to the elastic continuum model and implications to real seismicity are discussed.

No abstract

Slow-slip phenomena, including afterslips and silent earthquakes, are studied using a one-dimensional Burridge-Knopoff model that obeys the rate-and-state dependent friction law. By varying only a few model parameters, this simple model allows reproducing a variety of seismic slips within a single framework, including main shocks, precursory nucleation processes, afterslips, and silent earthquakes.