Markov modulated Poisson processes for stochastic modelling of background seismicity

Declustering a seismic catalog is a relevant preliminary step in many applications, such as earthquake forecasting and seismic hazard assessment. Declustering aims at partitioning an earthquake catalog into background seismicity, which is supposed to reflect the steady tectonic loading, and clustered seismicity, which is formed by dependent events. We decluster two Italian earthquake catalogs by applying two different data-driven declustering algorithms, namely the nearest-neighbor method (Zaliapin and Ben-Zion, J. Geophys. Res., 2013) and the stochastic declustering method (Zhuang et al., J. Geophys. Res., 2004). We verify the general assumption according to which the temporal sequence of background seismicity is suitably modelled by the stationary Poisson model. Whenever the Poissonian hypothesis is rejected, we get evidence of certain heterogeneity in the background sequence, which leads us to rule out the Poisson process for background seismicity modeling in favor of the Markov Modulated Poisson Process (MMPP), which allows the Poisson seismicity rate to change over time according to a finite (unknown) number of Markovian states (Benali et al., Stoch. Environ. Res. Risk Assess., 2020). The MMPP model turns out suitable for identifying and quantifying heterogeneities in background seismicity, as well as for comparing them against the two considered declustering algorithms.