The monitoring of statistical network properties could be useful for the
short-term hazard assessment of the occurrence of mainshocks in the presence
of foreshocks. Using successive connections between events acquired from the
earthquake catalog of the Istituto Nazionale di Geofisica e Vulcanologia
(INGV) for the case of the L'Aquila (Italy) mainshock (

Seismicity is a 3-D complex process evolving in the heterogeneous space, time and size domains. Since the birth of the science of seismology about 130 years ago, the underlying statistical properties of seismicity have attracted increasingly great interest (see, e.g., a review in Utsu, 2002), enhancing our understanding of the complex physical mechanisms that cause earthquakes. Over the years, several models have been proposed for the description of seismicity. For example, the random walk model (Lomnitz, 1974) was introduced to describe on-clustered background seismicity. However, space–time earthquake clusters deviate significantly from randomness. In fact, the pioneering work of Omori (1894), extended later by others (e.g., Utsu, 1962a, b; Utsu et al., 1995), revealed the strong clustered nature of aftershock sequences following large mainshocks. Aftershocks decay with time in a power-law mode, the so-called Omori law. However, as the decay of aftershocks very often deviates from the simple power law, the statistical model of epidemic-type aftershock sequences (ETAS) was introduced (Ogata, 1998) to describe the complex pattern of aftershocks' time distribution (Zhuang, 2012). On the other hand, a physical approach based on the rate and state model of fault friction was also introduced (Dieterich, 1994).

On some occasions, short-term foreshocks preceding mainshocks by hours, days or up to a few months were reported. It was found that the number of foreshocks generally increases with the inverse of time (Mogi, 1962, 1963a, b; Papazachos, 1975; Kagan and Knopoff, 1978; Jones and Molnar, 1979; Hainzl et al., 1999; Main, 2000; Papadopoulos et al., 2010). Therefore, foreshocks may provide time-dependent information that may lead to a more robust estimation of the probability of the occurrence of future strong mainshocks (e.g., Agnew and Jones, 1991). However, some mainshocks are preceded by foreshocks, while others are not. Long-term accelerating foreshock activity has also been described (for a thorough review, see Mignan, 2011). A very early case in the Hellenic arc was studied by Papadopoulos (1988), while models for the long-term accelerating seismicity were further developed by others (e.g., Bufe and Varnes, 1993). A recent revision of these models has been proposed in order to cope with some previous limitations (De Santis et al., 2015). Another major type of space–time seismicity cluster, termed earthquake swarm, is characterized by a gradual rise and fall in seismic moment release, but it is lacking a foreshocks–mainshock–aftershocks pattern (e.g., Yamashita, 1998; Hainzl, 2004; Hauksson et al., 2013). Although seismic swarms are abundant in volcanic and geothermal fields as well as in areas of induced seismicity, caused by fluid injection, mining or gas recovery, they are not unusual in purely tectonic settings.

Over the last years, complex network theory has provided a new insight and perspective in analyzing seismicity patterns (Abe and Suzuki, 2004, 2007; Baiesi and Paczuski, 2004, 2005; Barrat et al., 2008; Daskalaki et al., 2014). This line of research is motivated by the concept of self-organized criticality (Bak, 1996), which models structural phase transitions from random to scale-free spatial correlations between seismic events (e.g., Sammis and Sornette, 2002). However, the generalization and reliability of the outcomes of this relatively new approach remain an open question. Within this framework the so-called visibility graph (VG) method maps time series into networks or graphs, which converts dynamical properties of time series into topological properties of networks, and can identify possible precursory signatures (Telesca et al., 2012, 2015).

In this paper, we exploited the tools of complex network theory to identify
potential spatio-temporal foreshock patterns that could add value to
short-term earthquake forecasting or hazard assessment. We focused on the
case of the shallow, strong (

Epicentral distribution of earthquakes in the area of L'Aquila for the time interval extending from 1 January 2006 to 6 April 2009. The focal mechanism of the L'Aquila mainshock (star) was calculated by INGV. Note the dense concentration of foreshock epicenters close to the mainshock epicenter in the last 10 days preceding the mainshock occurrence, which indicates that foreshocks moved towards the mainshock nucleation area.

We chose to study the L'Aquila seismic sequence since the mainshock was preceded by abundant foreshocks (Papadopoulos et al., 2010; De Santis et al., 2011), thus allowing us to test topological metrics, which are in use in complex network theory. Such metrics are potential tools for the investigation of short-term precursory seismicity patterns. The aim is to show whether and how the exploitation of network theory metrics can independently add value to short-term seismic hazard assessment in the presence of foreshocks. Therefore, before the implementation of selected topological metrics, in Sect. 2 we examined further the seismicity patterns that preceded the L'Aquila mainshock by mainly focusing on statistics of the foreshock sequence in space, time and size (magnitude) domains.

Here, we adopted the term “seismic hazard assessment” referring to
“forecasting”/“hindcasting” (Evison, 1999; Bormann, 2011), i.e., a
warning that a mainshock would probably happen within a specific region in
the short term, instead of the term “prediction”, which contains a much
stronger statement that a mainshock will deterministically happen. In this
sense, earthquake forecasts are prospective probabilistic statements
specifying the likelihood that target events will occur in space–time
subdomains. In a time-dependent forecast, the probabilities

Long-term seismicity analysis showed that the L'Aquila mainshock was preceded
by seismic quiescence prevailing for about 40–50 years, and thus very likely
filled in a seismic gap (Barani and Eva, 2011). It was also suggested that
the earthquake was hindcasted from a fault-based earthquake rupture model
(Peruzza et al., 2011). During the 2 years before the event, no anomalous
strainmeter signal larger than a few tens of nanostrains was visible, but
during the last few days, there was evidence of dilatancy of saturated rock
over the earthquake causative fault, perhaps related to the presence of
foreshocks (Amoruso and Crescentini, 2010). However, around a year before the
mainshock, possible effects due to fluid migration were found from magnetic
data analyses (Cianchini et al., 2012). The non-extensivity parameter

In the short term, the mainshock was preceded by a foreshock sequence that
developed in two main stages (Papadopoulos et al., 2010). That is, a
posteriori analysis of the INGV catalog data
(

We examined further the seismicity evolution in the time–space–size domains
before the L'Aquila mainshock as illustrated in Fig. 2. The earthquake
catalog of INGV
(

Time–space–size evolution of the L'Aquila foreshock sequence based
on the INGV earthquake catalog.

Figure 2a shows the cumulative number of earthquake events within a circle of
radius of 30 km from the L'Aquila mainshock epicenter. The dramatic increase
in the seismicity rate in about the last 3 months before the mainshock of 6
April 2009 is evident. Particularly, in the last 10 days, the seismicity rate
increased at significance level 99 % according to the

ACC and SW indices global statistical network measures from
1 January 2008 to 30 June 2009. Computations
were performed in the space window centered at the mainshock epicenter
(42.42

As in Fig. 3 for computations performed with radius

With the increase in the seismicity rate in the last 10 days, that is, during
the strong foreshock stage, the mean distance of foreshock epicenters from
the mainshock epicenter decreased, being about 7 km (Fig. 2b). The time
evolution of the parameter

Building on previous efforts (Abe and Suzuki, 2004, 2007; Baiesi and Paczuski, 2004, 2005; Barrat et al., 2008; Daskalaki et al., 2014), exploiting the arsenal of complex networks, we were able to independently investigate statistically significant changes in the underlying seismic network topology marked about 2 months before the mainshock. Our analysis was based on the earthquake catalog of INGV.

We discretized the area under study (Fig. 1) into square cells with a side of
0.1

Betweenness centrality (BC) computations in the space window
centered at the mainshock epicenter (42.42

As in Fig. 5 for a space window with radius

In order to detect statistically significant changes between the measures obtained from the emergent seismic networks and the ones resulting from consistent random network realizations, the following procedure was applied. Within each sliding window, we constructed an ensemble of 500 realizations of consistent random networks, i.e., random networks with the same number of nodes and with connectivity probability equal to the average degree (see Appendix A for a definition) of the emerged seismic network divided by the number of nodes (Newman, 2003; Albert and Barabasi, 2002). For each of the 500 random network realizations, we computed the statistical measures mentioned above. We adopted as statistically significant the values that were above 95 % or below 5 % of the distributions calculated from the random networks.

In order to test the robustness of the outcomes of the analysis, we
constructed networks using different values of sliding window lengths and
shift steps as well as different sizes of centered or off-centered, with
respect to the mainshock epicenter (42.42

For our illustrations, we show the results obtained using a sliding window
with a shift step of either constant time of 1 day or of constant number of
events

For larger space windows of

However, an important question that naturally emerges is the following: is it
possible to “forecast” the spatial location of a probable large earthquake
from the identification of phase changes that have arisen in the topology of
the underlying emerged networks? To respond to such a crucial question, we
computed the BC for each node, trying to identify hubs that could serve as
potential epicenter locators. Figures 5 and 6 show snapshots of the BC map
for the space window of

In order to test whether these results were sensitive to the selection of the
center of the space window used for the construction of the network, we
repeated the analysis using off-the-epicenter-centered space windows.
Off-the-epicenter analysis was also employed, resulting in equivalent
outcomes. In Fig. 8, we depict the BC map for the space window with radius

The mean degree of the seismic network (blue line) as computed using sliding windows with the constant time shift of 1 day. Red and green lines represent statistically significant levels of 95 and 5 %, respectively, as obtained from an ensemble of equivalent random networks (see the description in the methods section).

BC computations in the space window centered at 42.00

Snapshots of seismic networks overlaid on the BC contours for

The drastic increase in the seismicity rate is a common feature in
foreshocks, swarms and aftershocks. Therefore, such seismicity clusters are
traditionally considered retrospective designations: they can only be
identified as such after an earthquake sequence has been completed (Jordan et
al., 2011) given that certain criteria for the discrimination of foreshocks
from other types of space–time seismicity clusters are needed (Ogata, 1998).
Although this is in general true, the retrospective analysis of the 2009
L'Aquila foreshock sequence showed that in a scheme of regular, daily
statistical seismicity evaluation, the ongoing state of weak foreshock
activity would be detectable about 1 or 2 months before the mainshock
(Papadopoulos et al., 2010). Then, the strong foreshock signal, being evident
in the space, time and size domains, could be detectable a few days before
the mainshock. The presence of foreshocks, as states of elevated seismicity
with respect to background seismicity level, could also be suggested by
independent approaches, such as Poisson hidden Markov models (Orfanogiannaki
et al., 2014). The spatial organizations of foreshocks as a tool for
forecasting mainshocks has been positively examined (Papadopoulos et al.,
2010; Lippiello et al., 2012; see also results in Sect. 2). In the size
domain, the drop in the

Compared to the above studies, our analysis provides an alternative way to describe the spatio-temporal precursory seismicity changes. Thus, it is worth mentioning that our method succeeded in determining the mark of onset of significant changes in seisimicity when also considering an off-epicenter analysis (Fig. 8). Based on the BC measure, the identification of the spatial location of the epicenter 2 months before the main event was also possible.

One of the advantages of complex network theory is that networks may be used to identify efficiently, within the nonlinear dynamics theory framework, phase transitions that mark the onset of big changes in the underlying seismicity. The wealth of statistical measures of the reconstructed network activity (such as the small-worldness, path length, local and global clustering coefficient, betweenness centrality) offers many different views and tools for characterizing the underlying varying topology. We showed that key topological measures of the emerged seismic network constitute an independent tool for hazard assessment of the occurrence of the mainshock in the short run. In this sense, the proposed approach looks promising, as it could identify (retrospectively as all other methods until now) quite efficiently, about 2 months before the mainshock, the location of the mainshock epicenter. Interestingly, in the a posteriori analysis of the 2009 L'Aquila seismic sequence, the betweenness centrality and its cumulative expression started to pinpoint the nucleation area of the forthcoming strong earthquake 2 months before its occurrence (see also De Santis et al., 2015).

Nevertheless, the detection of a seismicity anomaly in space and time by
topological measures does not provide evidence of the seismicity style
beforehand: it is designated only retrospectively. In fact, the foreshock
style of seismicity becomes obvious only with the a posteriori knowledge that
the anomaly concluded with a strong mainshock. Such knowledge, however, could
be obtained from classic statistics beforehand on the basis of the 3-D
space–time–size seismicity analysis. Furthermore, the role of the parameter

Hence, in view of the statistical and geophysical significance of

Utilizing complex network theory, we showed that key topological measures, such as the average clustering coefficient (ACC), small-world index (SW) and the betweenness centrality (BC), could serve as potential indices for short-term seismic hazard assessment. Of particular interest is the detection of forthcoming mainshocks in the presence of foreshocks.

In the case of foreshocks that preceded the L'Aquila (Italy) mainshock
(

The proposed approach is promising regarding the identification of spatio-temporal patterns related to the underlying seismicity, and thus could potentially serve as an alternative and/or complement to well-established traditional statistical methods for short-term, time-dependent hazard assessment of earthquakes.

This is a contribution of research project EARTHWARN of the Institute of Geodynamics, National Observatory of Athens. Edited by: L. Telesca Reviewed by: A. De Santis and R. V. Donner