第57回統計地震学セミナー / The 57th Statistical Seismology Seminar

Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In the studies of seismicity, aftershock sequences are observed after moderate to large main shocks. Empirical observations reveal that aftershocks obey power-law scaling with respect to their energies (seismic moments) which in magnitude domain can be modeled by the Gutenberg-Richter law.

The decay rate of aftershocks above a certain magnitude is typically inversely proportional to the time since the main shock and is approximated by the modified Omori law. The largest aftershocks in a sequence constitute significant hazard and can inflict additional damage to infrastructure that is already affected by the main shock. Therefore, the estimation of the magnitude of a possible largest aftershock in a sequence is of high importance. In this presentation, a Bayesian predictive distribution and the corresponding confidence intervals for the magnitude of the largest expected aftershock in a sequence are derived using the framework of Bayesian analysis and extreme value statistics. The analysis is applied to several well-known aftershock sequences world-wide to construct retrospectively the confidence intervals for the magnitude of the subsequent largest aftershock by using the statistics of early aftershocks in the sequences. In order to infer the physical mechanisms of triggering and time delays responsible for the occurrence of aftershocks, a nonlinear viscoelastic slider-block model is considered. It is shown that nonlinear viscoelasticity plays a critical role in the triggering of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks, which are observed in the studies of systems with relaxation dynamics, specifically, for earthquakes.