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考察了库仑破裂应力模型和速率一状态摩擦模型的预测效果。我们研究由于阶跃应力扰动(即地震引起的静态应力增加)以恒定速率在时刻t_0时叠加到“背景”应力(如构造加载)上而引起的破裂时间的变化△t(时间提前)。△t的可预测性就意味着地震活动速率r(t)/r_0的可预测性,t_0是取决于构造应力的一恒定速率,地震活动速率可用地震目录来检验。符合余震序列一般特性的r(t)/r_0模型必须能预测出符合大森定律的地震活动性衰减速率,序列的持续时间长度应少于主震轮回周期时间长度的百分之几,并能直接返回到背景活动速率。库仑模型要求一个断层在加载期间保持为闭锁状态,破裂瞬时发生,△t与t_0无关。这些特性意味着地震活动速率会出现瞬时的无限增长,而持续时间为零。对不同的状态演变规则所作的r(t)/r_0的数值计算表明,在主震发震时刻非常接近于破裂状态的断层上会发生余震,这些断层特性必定是“库仑式”的,从而使滑动演变规则可被排除。实际余震的数量特征可以制约速率一状态本构关系的参数:a也许会低于实验值,刚度也许会高,正应力也许会低于静岩压力。我们同时对库仑模型和速率一状态模型作了理论上的比较。当本构关系参量a相对于参量b减少时,速率-状态模型的断层特性就更接近于“库仑式”。这是因为滑动开始是减速的,表明断层接触状态初始是愈合的。当参量。数值较小时,减速更为明显,则断层表现为更加接近于闭锁状态。即使当速率-状态模型的△t具有库仑式特性时,它的大小也仍然可能差一常数,常数大小与b有关。在这种情况下,速率-状态模型的特性类似于一个修正的库仑破坏模型,即弱化使破裂应力临界值降低,从而增加了时间的提前量。与非库仑式响应的偏离也与加载速率、弹性刚度、初始条件以及状态演变规则的假设等有关。
The Coulomb rupture stress model and the rate-state friction model are investigated. We investigate the change in breakup time Δt (time advance) due to a step stress perturbation (ie, an increase in static stress due to an earthquake) at a constant rate superimposed on a “background” stress (such as a tectonic load) at time t_0. The predictability of Δt implies the predictability of the seismic activity rate r (t) / r_0, which is a constant rate that depends on the tectonic stress. The seismic activity rate can be verified by the earthquake catalog. The r (t) / r_0 model that conforms to the general characteristics of aftershock sequences must be able to predict the rate of seismic activity decay consistent with the Omori law. The duration of the sequence should be less than a few percent of the length of the mainshock cycle and should be directly Return to background activity rate. The Coulomb model requires that a fault remain latched during loading, and that rupture occurs instantaneously, with Δt independent of t_0. These characteristics mean that there is an instantaneous infinite increase in the rate of seismic activity, with a duration of zero. The numerical calculation of r (t) / r_0 for different state evolution rules shows that aftershocks will occur on the faults that are very close to the ruptured state at the time of the mainshock quake, and the fault characteristics must be “coulomb” so that Slip evolution rules can be ruled out. The quantitative characteristics of the actual aftershocks can constrain the parameters of the rate-state constitutive relationship: a may be lower than the experimental value, the stiffness may be high, and the normal stress may be lower than the rock pressure. We also made a theoretical comparison between the Coulomb model and the rate-state model. When the constitutive relationship parameter a decreases with respect to the parameter b, the fault-state model’s fault characteristics are closer to “Coulomb’s.” This is because the beginning of the slip is decelerated, indicating that the initial state of the fault contact is healing. When parameters. When the value is smaller, the deceleration is more obvious, then the fault manifests itself closer to the latched state. Even when the Δt of a rate-state model has a Coulomb-like property, its size can still be a constant and the magnitude of the constant is related to b. In this case, the characteristics of the rate-state model are similar to a modified Coulomb failure model, in which weakening reduces the critical value of the fracture stress and thus increases the advancement of time. Deviations from non-coulombic responses are also related to loading rates, elastic stiffness, initial conditions, and the assumption of state evolution rules.