Can We Forecast 1-Month Span Aftershock Activity from the First Day Data after the Main Shock?
Abstract:A large earthquake triggers persistent aftershock activity in and near the focal region. Thus, intermediate term forecasting of aftershocks at its earlier stage is important for mitigating seismic risks. A main difficulty for the early forecasting is the substantial incompleteness of early aftershock data. To deal with such incomplete data, we have developed a statistical model of the incomplete data, enabling us to obtain the immediate estimate of the forecasting models from incomplete data [1, 2]. Another difficulty for the intermediate term forecasting is that we have to determine the parameter values of the forecasting models with high accuracy, because even a small bias in the parameter values can lead to a significant bias of the forecasting in intermediate term. However such accurate estimation is quite difficult at the early stage, especially using the early and incomplete data. Here we present a Bayesian forecasting method by using the epidemic-type aftershock sequence (ETAS) model. The Bayesian forecasting considers not only the best parameter values such as the maximum likelihood estimates or maximum a posteriori estimates but also the estimation uncertainty of the parameter values. By analyzing aftershock sequences in Japan, we show the forecasting performances of the intermediate-term aftershocks can be significantly improved by considering the estimation uncertainty of the ETAS model . Furthermore, we discuss the impact of the modeling of the magnitude frequency distribution of detected aftershocks within a day span on the forecasting of large aftershocks.
 T. Omi, Y. Ogata, Y. Hirata and K. Aihara, "Forecasting large aftershocks within one day after the main shock", Scientific Reports 3, 2218 (2013).
 T. Omi, Y. Ogata, Y. Hirata and K. Aihara, "Estimating the ETAS model from an early aftershock sequence", Geophysical Research Letters 41, 850 (2014).
 T. Omi, Y. Ogata, Y. Hirata and K. Aihara, "Intermediate-term forecasting of aftershocks from an early aftershock sequence: Bayesian and ensemble forecasting approaches", (Submitted).