Increased earthquake rate prior to mainshocks

Eitan E. Asher, Shlomo Havlin, Shay Moshel, Yosef Ashkenazy

Research output: Contribution to journalArticlepeer-review


According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock—this law has received much less attention due to its large uncertainty. Here, we mainly study the inverse Omori law based on a highly detailed Southern California earthquake catalog, which is complete for magnitudes mc≥1 or even lower. First, we develop a technique to identify mainshocks, foreshocks, and aftershocks. We then find, based on a statistical procedure we developed, that the rate of earthquakes is higher a few days prior to a mainshock. We find that this increase is much smaller for (a) a catalog with a magnitude threshold of mc=2.5 and (b) for the Epidemic-Type Aftershocks Sequence (ETAS) model catalogs, even when used with a small magnitude threshold (i.e., mc=1). We also analyze the rate of aftershocks after mainshocks and find that the Omori-Utsu law does not hold for many individual mainshocks and that it may be valid only statistically when considering many mainshocks together. Yet, the analysis of the ETAS model based on the Omori-Utsu law exhibits similar behavior as that of the real catalogs, indicating the validity of this law.

Original languageEnglish
Article number114261
JournalChaos, Solitons and Fractals
StatePublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s)


We thank the EU H2020 project RISE , the Israel Science Foundation (grant no. 189/19 ), the Israel Ministry of Energy , and the PAZY Foundation, Israel for financial support.

FundersFunder number
EU H2020
PAZY Foundation, Israel
Israel Science Foundation189/19
Ministry of Energy, Israel


    • ETAS
    • Earthquakes
    • Omori-utsu law
    • Statistics


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