Integration of extreme value statistics and Bayesian estimation for early forecasting of aftershock shaking: application to main shock–aftershock sequences in inland Japan

SUMMARY Extreme value statistics (EVS) is commonly used to model rare, extreme events such as natural disasters. This study proposes a method that integrates EVS and Bayesian estimation to enable the early forecasting of aftershock-induced ground shaking. The method is applied to continuous seismograms recorded immediately after a large earthquake. The proposed method is based on several key assumptions: the Gutenberg–Richter (G–R) and Omori–Utsu laws, as well as the proportionality between earthquake magnitude and the logarithmic maximum amplitude. Based on these assumptions, two metrics were computed at each seismic station: the exceedance probability of the maximum amplitude (EPMA) and the number of threshold value exceedances (EPNUM). While EPMA follows a long-tailed Fréchet distribution, with uncertainty spanning at least an order of magnitude, EPNUM follows a short-tailed Poisson distribution, with uncertainty typically varying by a factor of two. The performance of the proposed method was evaluated across three different types of aftershock sequences in Japan. The practical forecasting capability was demonstrated within 1 hr of the main shock and was effective up to 7 d. Compared to conventional methods that rely on incomplete earthquake catalogues, the proposed approach demonstrated faster and more robust results. While the median forecast of maximum amplitude tended to be overestimated, possibly due to the potential nonlinear relationship between magnitude and logarithmic maximum amplitude, the forecast for the number of felt earthquakes did not show such bias. Because the proposed method is based on single-station processing, it can be applied in regions without a dense seismograph network or real-time earthquake monitoring system, as long as continuous ground motion data are available at the target site.