Robust seismicity forecasting based on Bayesian parameter estimation for epidemiological spatio-temporal aftershock clustering models

Abstract

In the immediate aftermath of a strong earthquake and in the presence of an ongoing aftershock sequence, scientific advisories in terms of seismicity forecasts play quite a crucial role in emergency decision-making and risk mitigation. Epidemic Type Aftershock Sequence (ETAS) models are frequently used for forecasting the spatio-temporal evolution of seismicity in the short-term. We propose robust forecasting of seismicity based on ETAS model, by exploiting the link between Bayesian inference and Markov Chain Monte Carlo Simulation. The methodology considers the uncertainty not only in the model parameters, conditioned on the available catalogue of events occurred before the forecasting interval, but also the uncertainty in the sequence of events that are going to happen during the forecasting interval. We demonstrate the methodology by retrospective early forecasting of seismicity associated with the 2016 Amatrice seismic sequence activities in central Italy. We provide robust spatio-temporal short-term seismicity forecasts with various time intervals in the first few days elapsed after each of the three main events within the sequence, which can predict the seismicity within plus/minus two standard deviations from the mean estimate within the few hours elapsed after the main event.

Retrospective Operational Aftershock Forecasting for 2016 Amatrice-Norcia Seismic Sequence in Central Italy

“…Given a particular space-time model and a realization of the vector of model parameters , one can calculate a plausible value for the rate of occurrence denoted as (t,x,y,m|,seq,Ml). A robust estimate [16,18,19,23] of the average number of events in the spatial cell unit centered at (x,y) with magnitude greater than or equal to m in the forecasting interval [Tstart, Tend], and over the domain of the model parameters   can be calculated as:…”

“…In addition, several attempts are made for developing improved algorithms to attain maximum likelihood estimates of ETAS parameters [11][12][13]. Adaptive model parameter estimation based on the events in the ongoing sequence (e.g., calibrating the parameters of MO and ETAS models based on the ongoing catalogue by employing Bayesian parameter estimation [14][15][16][17][18]) has the advantage of both tuning a sequence-specific model, and also capturing possible time variations of the model parameters. As the original purpose of the present paper, we propose a fully simulation-based method to provide a robust estimate [16,18] for the spatial distribution of the events in a prescribed forecasting time interval after the main event.…”

“…Adaptive model parameter estimation based on the events in the ongoing sequence (e.g., calibrating the parameters of MO and ETAS models based on the ongoing catalogue by employing Bayesian parameter estimation [14][15][16][17][18]) has the advantage of both tuning a sequence-specific model, and also capturing possible time variations of the model parameters. As the original purpose of the present paper, we propose a fully simulation-based method to provide a robust estimate [16,18] for the spatial distribution of the events in a prescribed forecasting time interval after the main event. In the context of this robust estimate, the uncertainty in the ETAS model parameters is taken into account as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., registered events in the ongoing seismic sequence before the beginning of the forecasting interval).…”

“…In the context of this robust estimate, the uncertainty in the ETAS model parameters is taken into account as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., registered events in the ongoing seismic sequence before the beginning of the forecasting interval). The Markov Chain Monte Carlo (MCMC) simulation scheme [16][17][18][19] is used to sample directly from the posterior probability distribution for ETAS model parameters (i.e., conditioned on the registered events in the ongoing sequence). Moreover, this robust estimate also considers the sequence of events that is going to occur during the forecasting interval (and hence affect the seismicity in an epidemic type model like ETAS).…”

Long-Term Seismic Risk Assessment Considering the Triggered Aftershocks

“…The aftershock hazard is calculated by integrating the adopted ground-motion prediction equation over all possible aftershock magnitudes and distances within the desired aftershock zone (see [19,24,35] for more details). The aftershock zone considered herein is the one presented in [10,24], which is indicated as ZAS with cyan color in Figure 3(b).…”