Prediction of aftershocks with GPR
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Uncovering the distribution of magnitudes and arrival times of aftershocks is a key to comprehend the characteristics of the sequence of earthquakes, which enables us to predict seismic activities and hazard assessments. However, identifying the number of aftershocks is very difficult due to contaminations of arriving seismic waves immediately after the main shock. To overcome the difficulty, we construct a likelihood based on the detected data incorporating a detection function to which the Gaussian process regression (GPR) is applied. The GPR is capable of estimating not only the parameter of the distribution of aftershocks together with the detection function, but also credible intervals for both of the parameters and the detection function. A property of both the Gaussian process and a distribution of aftershocks are exponential functions leads to an efficient Bayesian computational algorithm to estimate the hyperparameters. After the validations through numerical tests, the proposed method is retrospectively applied to the catalog data related to the 2004 Chuetsu earthquake towards early forecasting of the aftershocks. The result shows that the proposed method stably estimates the parameters of the distribution simultaneously their uncertainties even within three hours after the main shock.
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