Abstract: Focusing on decay and generation of the aftershock activity,the latest theoretical advancements and applications on the modified Omori law,the ETAS model and the BASS model have been introduced in this paper. Up to now,the modified Omori law is the best formula for fitting the temporal decay of aftershock activity,which has been used to describe the decay characteristics of aftershock sequences quantitatively. Essentially,the modified Omori law is a typical statistical model on observing phenomena,but it has been used widely in practice owing to its less parameters,simple calculation,and higher capability of describing the general features of sequence decay. ETAS model,which takes into account the generation of the high order aftershocks with statistical self-similar characteristics,is a physical expansion of the modified Omori law,and the generation intensity of high order aftershocks is concerned to be related to the magnitude of the father earthquake. Since considering the problems of high order aftershock generation,ETAS model not only has a large improvement in study field of aftershock sequences,but also has many other applications,such as detection of relative quiescence,removing of the cluster aftershock activity,assessment of background seismicity,detection of seismic activity triggered by external factors and so on. BASS model follows the modified Bath's law,while the ETAS model follows the similar rate with the magnitude of the father earthquake,this is the largest difference between ETAS model and BASS model. So,the BASS model is a completely self-similar theoretical model compared with the ETAS,but only few papers concerning its application.

Key words: decay of aftershock sequence, generation of aftershock, modified Omori law, Epidemic Type Aftershock Sequence model(ETAS model), Branching aftershock sequence model(BASS model)

摘要： 着重于序列衰减与余震激发,系统介绍了修改的大森公式、ETAS模型及BASS模型的最新理论研究进展及应用成果。修改的大森公式是迄今为止对序列衰减的最好描述,据此可对序列衰减特征进行定量表述。大森公式本质上是一种典型的现象统计模型,但由于其参数少、计算简单,并且确实能够反映序列衰减的总体特征,因而在实际中应用广泛。ETAS模型考虑了具有统计自相似特征的次级余震激发问题,次级余震激发强度与父地震强度有关,这在物理过程方面对大森公式进行了大大的拓展。由于考虑了次级余震的激发问题,ETAS模型不但在余震序列研究方面比修改的大森公式有了明显的进展,而且在诸如平静检测、余震群集剔除、背景地震活动评估、外因触发地震活动检测等方面也有诸多应用。BASS模型遵循修改的Bath定律,而ETAS模型遵循的是与父地震震级有关的相似率,这是BASS模型与ETAS模型的最大区别,因而相对ETAS模型而言,BASS模型是一种完全自相似的理想化模型,但目前基于BASS模型的应用研究尚不多见。

关键词: 序列衰减, 余震激发, 修改的大森公式, ETAS模型, BASS模型