Failure time variation derived from R–S relation:the role of the static stress perturbation

In general, earthquake cycle related to earthquake faulting could include four major processes which could be described by (1) fault locking, (2) self-acceleration or nucleation (possible foreshocks), (3) coseismic slip, and (4) post-stress relaxation and afterslip. A sudden static stress change/perturbation in the surrounding crust can advance/delay the fault instability or failure time and modify earthquake rates. Based on a simple one-dimensional spring-slider block model with the combination of rate-and-state-dependent friction relation, in this study, we have approximately derived the simple analytical solutions of clock advance/delay of fault failures caused by a sudden static <i<Coulomb</i< stress change applied in the different temporal evolution periods during an earthquake faulting. The results have been used in the physics-based explanation of delayed characteristic earthquake in Parkfield region, California, in which the next characteristic earthquake of<i<M</i< 6.0 after 1966 occurred in 2004 instead of around 1988 according to its characteristic return period of 22 years. At the same time, the analytical solutions also indicate that the time advance/delay in <i<Coulomb</i< stress change derived by the dislocation model has a certain limitation and fundamental flaw. Furthermore, we discussed the essential difference between rate- and state-variable constitutive (R-S) model and <i<Coulomb</i< stress model used commonly in current earthquake triggering study, and demonstrated that, in fact, the <i<Coulomb</i< stress model could be involved in the R-S model. The results, we have obtained in this study, could be used in the development of time-dependent fault interaction model and the probability calculation related to the time-dependent and renewal earthquake prediction model.