Физика ЗемлиФизика Земли0002-3337The Russian Academy of Sciences1343210.31857/S0002-33372019415-32Research ArticleForecasting aftershock activity: 4. Estimating the maximum magnitude of future aftershocksBaranovS. V.bars.vl@gmail.comPavlenkoV. A.pavlenko.vasily@gmail.comShebalinP. N.shebalin@mitp.ruInstitute of Earthquake Prediction Theory and Mathematical Geophysics,Russian Academy of SciencesKola Branch, Federal Research Center “Geophysical Survey of Russian Academy of Sciences”Schmidt Institute of Physics of the Earth, Russian Academy of Sciences200620194153214062019Copyright © 2019, Russian academy of sciences2019<p style="text-align: justify;">In this paper, we consider the problem of forecasting the magnitude of the future, starting from a certain instant of time, strongest aftershock. This problem is topical since the later strong aftershocks occur against the background of the 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 accurate forecasting 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 GutenbergRichter and OmoriUtsu laws whose parameters are estimated by the Bayess method using the data on the aftershocks that have already occurred 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 the Bths dynamic law with the use of two independent criteria. 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