How Likely Does an Aftershock Sequence Conform to a Single Omori Law Behavior?

Abstract

The most popular aftershock forecasting model is based on the modified Omori law (MOL), which describes the expected decay of the aftershock given the mainshock’s magnitude. Although such a model is still widely used for operational purposes, it is not unusual that one or more aftershocks break the MOL behavior. In this case, the time evolution of the aftershock sequence becomes much more complicated, and it may be better described by more advanced models, which also account for the triggering capability of all aftershocks. The purpose of this work is to analyze deductively the conditions under which the mean trend of an aftershock sequence, generated by one single mainshock according to the MOL, is satisfactorily described by an inverse power law. Practically, this analysis provides the likelihood that an aftershock sequence will conform to one single MOL; that is, the likelihood of delivering reliable forecasts using a model based on a single MOL. Specifically, we analyze which conditions are present when the triggering capability of a selected aftershock significantly affects the aftershock rate caused by the mainshock. For example, we discuss the application of this scheme to sequences that either conform, or do not, to the MOL behavior, such as the Amatrice– Norcia (Italy 2016–2017), Emilia (Italy 2012), and Tohoku-Oki (Japan 2011) aftershock sequences.