Forecasting Aftershock Activity: 4. Estimating the Maximum Magnitude of Future Aftershocks

Abstract

In this paper, we consider the problem of forecasting the magnitude of the strongest aftershock starting from a certain instant of time in the future. This problem is topical since the strong aftershocks that occur later against a background of less frequently repeating shocks are less expected and thus pose an independent hazard. At the same time, the magnitudes of the strongest aftershocks decrease with time after the main shock. The purpose of accurately forecasting them is to minimize the underestimation or overestimation of the magnitude of future risks. In this study, the aftershock process is represented by the superposition of the Gutenberg–Richter and Omori–Utsu laws whose parameters are estimated by the Bayess method using the data on the aftershocks that have already occurred up to a given time point and the a priori information about the probable values of the parameters. This significantly improves the forecast compared to the estimates that are based on the magnitude of the main shock alone. The quality of forecasting is estimated relative to Båth’s dynamic law with the use of two independent criteria. The first criterion is based on the similarity estimates, and the second, on the error diagram.