Can We Forecast 1-Month Span Aftershock Activity from the First Day Data after the Main Shock?

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 [3]. 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. [1] T. Omi, Y. Ogata, Y. Hirata and K. Aihara, "Forecasting large aftershocks within one day after the main shock", Scientific Reports 3, 2218 (2013). [2] T. Omi, Y. Ogata, Y. Hirata and K. Aihara, "Estimating the ETAS model from an early aftershock sequence", Geophysical Research Letters 41, 850 (2014). [3] 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).