We provide an overview of the basic models of the aftershock processes and advanced methods used to predict postseismic hazard. We consider both the physical mechanisms for aftershock generation and models of aftershocks and time-dependent models of aftershock processes. In particular, we provide a validation of the aftershock process using a superposition of the Gutenberg–Richter and Omori–Utsu laws. We show that the key role in assessment of postseismic hazard is earthquake productivity, which characterizes the ability of earthquakes to produce subsequent shocks. We discuss the recently established exponential law of earthquake productivity and show that the exponential form is invariant under variations in magnitude and focus depth. Being in discordance with the popular epidemic type aftershock sequence (ETAS) model, the law makes it possible to build a corrected model. We study versions of theoretical validation for the Båth law, which specifies the mean difference between the magnitudes of the main shock and the largest aftershock. We consider also the time-dependent Båth law. We provide a detailed review of modern approaches and methods for dealing with the estimation of the magnitude of the largest aftershock. As well, we review the problem of estimating the duration of aftershocks with magnitudes equal to or greater than a specified value, the hazardous period.

我们概述了余震过程的基本模型和用于预测震后危险的先进方法。我们考虑余震产生的物理机制和余震模型以及余震过程的时间相关模型。特别是，我们使用 Gutenberg-Richter 和 Omori-Utsu 定律的叠加来验证余震过程。我们表明，在评估震后灾害中的关键作用是地震生产力，它表征了地震产生后续冲击的能力。我们讨论了最近建立的地震生产力指数规律，并表明指数形式在震级和震源深度的变化下是不变的。与流行的流行型余震序列（ETAS）模型不一致，法律使得建立一个修正模型成为可能。我们研究了 Båth 定律的理论验证版本，该定律指定了主震震级和最大余震震级之间的平均差异。我们还考虑与时间相关的 Båth 定律。我们详细回顾了处理最大余震震级估计的现代方法和方法。此外，我们还回顾了估计震级等于或大于指定值（危险期）的余震持续时间的问题。我们详细回顾了处理最大余震震级估计的现代方法和方法。此外，我们还回顾了估计震级等于或大于指定值（危险期）的余震持续时间的问题。我们详细回顾了处理最大余震震级估计的现代方法和方法。此外，我们还回顾了估计震级等于或大于指定值（危险期）的余震持续时间的问题。