The epidemic‐type aftershock sequence model with tapered Gutenberg–Richter (ETAS‐TGR)‐distributed seismic moments is a modification of the classical ETAS‐GR (without tapering) proposed by Kagan in 2002 to account for the finiteness of the deformational energy in the earthquake process. In this article, I analyze the stability of the ETAS‐TGR model by explicitly computing the relative branching ratio ηTGR⁠: it has to be set less than 1 for the process not to explode, in fact in the ETAS‐TGR model, the critical parameter equals the branching ratio as it happens for the ETAS‐GR, due to the rate separability in the seismic moments component. When the TGR parameter βk=23ln10β is larger than the fertility parameter αk=23ln10α⁠, respectively obtained from the GR and the productivity laws by translating moment magnitudes into seismic moments, the ETAS‐TGR model results to have less restrictive nonexplosion conditions than in the ETAS‐GR case. Furthermore, differently from the latter case in which it must hold β>α for ηGR to exist finite, any order relation for βk and αk (equivalently, for β,α⁠) is admissible for the stability of the ETAS‐TGR process; indeed ηTGR is well defined and finite for any βk,αk⁠. This theoretical result is strengthened by a simulation analysis I performed to compare three ETAS‐TGR synthetic catalogs generated with βk⋚αk⁠. The branching ratio ηTGR is shown to decrease as the previous parameter difference increases, reflecting: (1) a lower number of aftershocks, among which a lower percentage of first generation shocks; (2) a lower corner seismic moment for the moment–frequency distribution; and (3) a longer temporal window occupied by the aftershocks. The less restrictive conditions for the stability of the ETAS‐TGR seismic process represent a further reason to use this more realistic model in forecasting applications.

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具有锥形古腾堡-里希特分布地震矩的流行型余震序列模型的稳定性

具有锥形古腾堡-里希特（ETAS-TGR）分布地震矩的流行型余震序列模型是对Kagan在2002年提出的经典ETAS-GR（无锥度）的修正，目的是考虑地震中形变能的有限性。地震过程。在本文中，我通过显式计算相对分支比ηTGR⁠来分析ETAS-TGR模型的稳定性：对于不爆炸的过程，必须将其设置为小于1，实际上在ETAS-TGR模型中，关键由于地震矩分量的速率可分离性，参数等于ETAS-GR发生的分支比。当TGR参数βk=23ln10β大于通过将矩量级转换为地震矩从GR和生产力定律分别获得的生育力参数αk=23ln10α⁠时，与ETAS-GR案例相比，ETAS-TGR模型的限制性不爆炸条件更少。此外，与后者必须保持β>α才能使ηGR有限存在的情况不同，对于ETAS-TGR过程的稳定性，βk和αk的任何顺序关系（对于β，α⁠而言）都是允许的。实际上，ηTGR定义明确，对于任何βk，αk⁠都是有限的。我进行了模拟分析，比较了用βk⋚αk⁠生成的三个ETAS-TGR合成目录，从而加强了这一理论结果。分支比ηTGR随着前一个参数差的增加而减小，这反映出：（1）余震数量减少，其中第一代冲击的百分比较低；（2）弯矩-频率分布的下角地震弯矩；（3）余震占据的时间窗口较长。