Abstract
The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.
Highlights
The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes
The Bayesian approach combined with extreme value statistics was used to analyze this problem by assuming that the occurrence of earthquakes can be approximated by a homogeneous Poisson process[2,24]
The Markov Chain Monte Carlo (MCMC) approach was used to sample the posterior distribution of the Epidemic Type Aftershock Sequence (ETAS) parameters, in order to estimate the rates of seismicity during short forecasting time intervals
Summary
The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. A closely related problem is the estimation of the absolute maximum magnitude of an earthquake for a given seismogenic zone[1,21,22,23] In this regard, the Bayesian approach combined with extreme value statistics was used to analyze this problem by assuming that the occurrence of earthquakes can be approximated by a homogeneous Poisson process[2,24]. The Bayesian methods were used to constrain the magnitudes of the largest expected aftershocks, where the earthquake rate was modeled by the Omori–Utsu law and the events were assumed to follow a non-homogeneous Poisson process[4,25] Those approaches do not fully incorporate the complicated triggering structure of earthquake sequences, which are important for shortterm earthquake forecasting. The parameters of the ETAS model were subjected to certain constraints in order to facilitate the sampling
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