When Is the Probability of a Large Earthquake Too Small?

Abstract

Classical probabilistic seismic-hazard models (Cornell, 1968), which typically refer to the homogeneous Poisson process for earthquake occurrence, are not able to model explicitly the space-time clustering of earthquakes. Clustering may be particularly evident in time windows of days and weeks (e.g., Kagan and Knopoff, 1987; Ogata, 1988), but it may be still appreciable in the medium term, because the time sequences to large earthquakes may last long (Kagan and Jackson, 1991; Parsons, 2002; Faenza et al., 2003; Marzocchi and Lombardi, 2008). The modeling of such a space–time clustering is an important subject of seismological research (Jordan et al., 2011). In fact, accounting for time–space clustering of earthquakes may provide additional information, not only to seismic-hazard assessment aimed at structural design (e.g., Iervolino et al., 2014; Marzocchi and Taroni, 2014), but also to short-term seismic risk management. The latter issue has been explored by the International Commission for Earthquake Forecasting, established after the L’Aquila earthquake in 2009, which paves the way to the so-called operational earthquake forecasting (OEF). As defined by Jordan et al. (2011), OEF comprises procedures for gathering and disseminating authoritative information about the time dependence of seismic hazards to help communities prepare for potentially destructive earthquakes. Notwithstanding some recent earthquake sequences showing the importance of tracking the time evolution of seismic hazard (e.g., as for the recent Canterbury sequence in New Zealand; Wein and Becker, 2013), currently OEF represents a controversial issue in seismology. Most critics are not focused on debating the scientific credibility of the models used to describe short-term earthquake clustering, but they dispute the usefulness (if not the potential danger) of the information they provide, in particular, the probability of a damaging event in a short time frame. According to OEF models available in the literature, the weekly probability of a large earthquake (e.g., of magnitude six or larger) is above a few percent only after another large event. During a seismic sequence of moderate events (e.g., of maximum magnitude less than five), the weekly probability of a large event may increase also by two to three orders of magnitude with respect to the background value, but almost always this probability remains below a few percent (Jordan et al., 2011). These figures sparked a debate among seismologists about the usefulness and danger of releasing information on the time evolution of short-term earthquake probability. A comprehensive discussion of all these issues can be found in Jordan et al. (2014) and Wang and Rogers (2014). In this article, we focus our attention on one particular aspect of this discussion. In particular, we put forward a different perspective that should replace the common practice of discussing when the probability of a large earthquake can be considered small. As a matter of fact, in a risk-informed decision framework, the variable of interest should be a probabilistically assessed loss (consequence) metric, for instance, the expected loss. A comparison of such a risk metric with some risk thresholds for individuals and/or for communities may help in understanding whether the risk is tolerable or not, and in choosing the optimal risk management decision. A step in this direction has been recently made by Iervolino et al. (2015), which introduces the operational earthquake loss forecasting (OELF) concept. Specifically, OELF translates short-term seismic hazard (OEF) into risk assessment (i.e., the weekly expected loss), using some specific metric, such as the expected number of collapsed buildings, displaced residents, injuries, and fatalities (see also van Stiphout et al., 2010; Zechar et al., 2014). Along these lines, in this article we analyze the evolutions of seismicity forecasts and consequent seismic risk for a seismic sequence that occurred in southern Italy in 2012 and featuring an ML 5.0 largest shock (the Pollino sequence hereafter). This sequence lasted for more than one year, and it was not associated with any destructive earthquake. In particular, the OEF seismicity rates and consequent OELF weekly estimates are evaluated as a function of time for a period spanning 2010–2013 to capture the full evolution of the sequence. Seismic risk metrics are compared with some reference risk values referring to other events from the literature.