[论文解读] A physical model for aftershocks triggered by dislocation on a rectangular fault

Rodolfo Console, Flaminia Catalli|ArXiv.org|May 4, 2005

earthquake and tectonic studies参考文献 41被引用 7

一句话总结

本文提出一个物理模型，将地震余震率与矩张量和均匀应力降矩形断层的应力变化联系起来。基于速率-状态摩擦模型，结果表明余震率在时间和空间上非均匀衰减——在断层边缘附近迅速达到峰值，但在较大距离处可持续数十年；同时，触发事件总数与地震矩的2/3次方成比例，长期来看断层上的抑制效应几乎与外部触发效应平衡。

ABSTRACT

We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the source. The time-dependent rate of triggered earthquakes is estimated by a rate-state model applied to a uniformly distributed population of faults whose equilibrium is perturbated by a stress change caused only by the first dislocation. The rate of triggered events in our simulations is exponentially proportional to the stress change, but the time at which the maximum rate begins to decrease is variable from fractions of hour for positive stress changes of the order of some MPa, up to more than a year for smaller stress changes. As a consequence, the final number of triggered events is proportional to the stress change. The model predicts that the total number of events triggered on a plane containing the fault is proportional to the 2/3 power of the seismic moment. Indeed, the total number of aftershocks produced on the fault plane scales in magnitude as 10^{M}. Including the negative contribution of the stress drop inside the source, we observe that the number of events inhibited on the fault is, at long term, nearly identical to the number of those induced outside, representing a sort of conservative natural rule. Considering its behaviour in time, our model doesn't completely match the popular Omori law; in fact it has been shown that the seismicity induced closely to the fault edges is intense but of short duration, while that expected at large distances (up to some tens times the fault dimensions) exhibits a much slower decay.

研究动机与目标

• 开发一个基于物理的模型，将主震源参数与余震率和分布联系起来。
• 解决库仑应力变化准则在解释余震时间衰减方面的局限性。
• 将速率-状态摩擦模型整合进静态应力转移框架，以实现更真实的时空余震模式。
• 研究余震生成如何随地震矩和应力降变化，以及长期尺度上净地震活动是否保持平衡。

提出的方法

• 计算弹性半空间中，具有均匀应力降的矩形断层引起的静态位移、应力、应变及修正的库仑破裂应力。
• 应用速率-状态摩擦模型（Dieterich, 1994）模拟受应力变化扰动的预存断层群体的时间依赖性地震活动率。
• 将应力变化作为速率变化的唯一触发机制，假设断层在空间上均匀分布且处于平衡状态。
• 模拟余震率的时空演化，重点关注峰值时间与衰减行为。
• 分析触发事件总数对断层尺寸、应力降和地震矩的依赖关系。
• 将模拟的衰减行为与Omori定律比较，并评估距断层距离在决定衰减 timescale 中的作用。

实验结果

研究问题

• RQ1 与标准的Omori定律相比，速率-状态模型如何改变余震率的时间衰减特性？
• RQ2 触发余震总数与主震地震矩之间的标度关系是什么？
• RQ3 余震活动的空间分布如何随距断层距离变化，特别是峰值时间和持续时间方面？
• RQ4 余震在断层外部的激活与断层本身抑制之间的长期平衡关系如何？
• RQ5 观测到的余震率非均匀衰减是否可由物理摩擦特性而非纯粹统计模型解释？

主要发现

• 触发地震的速率与库仑应力变化呈指数关系，应力变化越大，峰值出现越早（数小时内），应力变化越小则越晚（长达一年）。
• 在断层面触发的余震总数与10^M成比例，当应力降恒定时，余震数的对数与震级呈线性关系。
• 余震总数与地震矩的2/3次方成正比，与观测到的标度律一致。
• 在断层尺寸恒定条件下，触发事件数与应力降成正比。
• 断层边缘附近的余震活动迅速衰减（数天内），而较远距离处（最大达10倍断层尺寸）的活动衰减缓慢，可持续数十年。
• 长期来看，断层上被抑制的事件数几乎等于外部被触发的事件数，导致大空间和长时间尺度上的地震活动率净变化接近零。