Early Forecast of Maximum Amplitude due to Aftershocks by Applying Extreme Value Statistics to a Single Continuous Seismogram

Abstract

ABSTRACT To evaluate the exceedance probability of maximum amplitude (EPMA) due to aftershocks, I developed a forecasting scheme based on the extreme value statistics applied to a single continuous seismogram of early aftershocks. By combining the general laws of aftershock activity (Gutenberg–Richter and Omori–Utsu laws) and a ground-motion prediction equation (including source, path, and site factors), I verified that the interval maximum amplitude of a continuous seismogram of aftershocks follows the non-stationary Frechet distribution (NFD), which is one of the extreme value distributions. The parameters of NFD are written explicitly from the parameters commonly used in seismology. By optimizing the NFD parameters through the maximum-likelihood method and using the maximum-likelihood estimates and their covariance values, I derived the EPMA due to aftershocks based on the Bayesian approach. The performance of the EPMA was examined by Monte Carlo simulations and real seismograms. The numerically generated maximum amplitude was predicted well from the EPMA, which was evident even in the period of intense seismicity in which many waveforms overlap in a seismogram. This performance was also robust for real seismograms of aftershocks for the 2008 Iwate–Miyagi Nairiku, Japan, earthquake. The maximum amplitudes observed for four days were mostly within the 10% and 90% EPMA curves issued within 3 hr of the mainshock. The proposed method does not need to evaluate source, path, and site factors because these factors are included in the estimated NFD parameters. Given that the proposed method allows single-station processing, a seismic “network” is not required. Therefore, the proposed algorithm will be easily implementable in a seismic observation system installed at important facilities. Also, the NFD parameters estimated robustly in the early lapse times may provide important knowledge regarding early aftershocks.