Dynamics of earthquake nucleation process represented by the Burridge-Knopoff model

Abstract

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.

Can the Nucleation Phase be Generated on a Sub-fault Linked to the Main Fault of an Earthquake?

“…Shibazaki and Matsu'ura (1993) further found that the accelerating stage from phase-II to phase-III is related to the presence of nucleation phase in the front of the main P wave. Their results are similar to those obtained by Ueda et al (2014Ueda et al ( , 2015 and Kawamura et al (2018). The results of this study and Wang (2017a) only show two stages which are comparable with the phase-II and phase-II stages proposed by Matsu'ura (1992, 1993).…”

“…Brantut et al (2011) concluded that metamorphic dehydration influences the nucleation of unstable slip and could be an origin for slow-slip events in subduction zones. Ueda et al (2014Ueda et al ( , 2015 and Kawamura et al (2018) pointed out that the nucleation process includes the quasistatic initial phase, the unstable acceleration phase, and the high-speed rupture phase (i.e., a mainshock) and recognized two kinds of nucleation lengths, i.e., L sc and L c which are affected by model parameters, yet not by the earthquake size. The L sc related to the initial phase exists only for a weak frictional instability regime; while the L c associated with the acceleration phase exist for both weak and strong instability regimes.…”

Statistical properties of the one-dimensional Burridge-Knopoff model of earthquakes obeying the rate- and state-dependent friction law

“…In the weak frictional instability regime, seismic events generally tend to possess enhanced characteristic features. The magnitude distribution, for example, changes its character depending on whether in the strong or the weak frictional instability regime: the distribution is eminently single-peaked in the weak frictional instability regime whereas tends to be flat in the strong frictional instability regime 13,44 . Large events of the model can be classified into the two categories which we call type-I and II.…”

“…In the continuum limit where the grid spacing tends to zero, the system is expected to always exhibit a quasi-periodic or a "characteristic" behavior where large earthquakes repeat near-periodically without critical features 35 . Indeed, we recently examined the nature of the nucleation process of the discrete BK model under the RSF law by systematically varying the extent of the discreteness of the model toward the continuum limit, and also by systematically varying various model parameters including the frictional and the elastic parameters 13,44 . It was observed that the model exhibited a quasi-static initial phase in its nucleation process when the frictional instability was weak, i.e., when the normalized frictional-weakening parameter b was less than a critical value b c determined by the elastic-stiffness parameter l as b c = 2l…”

Mapping heterogeneities through avalanche statistics

“…We note that in some other models, including the Burridge-Knopoff and Olami-Feder-Christensen models, nucleation centres are dynamically generated (e.g. [27,28]). In the present context, however, we introduce an asperity-like behaviour in the construction of the model itself.…”