Forecasting strong subsequent events in the Italian territory: a National and Regional application for NESTOREv1.0

doi:10.21203/rs.3.rs-3936647/v1

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Forecasting strong subsequent events in the Italian territory: a National and Regional application for NESTOREv1.0

https://doi.org/10.21203/rs.3.rs-3936647/v1

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published 04 Oct, 2024

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The Italian territory is one of the most seismically active areas in Europe, where Strong Subsequent Events (SSEs), in combination with the strong mainshock effects, can lead to the collapse of already weakened buildings and to further loss of lives. In the last few years, the machine learning-based algorithm NESTORE (Next STrOng Related Earthquake) [Gentili and Di Giovambattista 2017, 2020, 2022, Gentili et al. 2023, Anyfadi et al. 2023] was proposed and used to forecast clusters in which the mainshock is followed by a SSE of similar magnitude. Recently, a first new version of a MATLAB package based on this algorithm (NESTOREv1.0) has been developed to improve SSE forecasting for research purpose and on-line sharing (Gentili et al. 2023). In our analysis, we considered both a nationwide and a regional approach for Italy, by studying the seismicity recorded over the last 40 years in two areas covering most of the Italian territory and northeastern Italy, respectively. In both approaches, using two dedicated catalogs, we trained NESTOREv1.0 on the clusters occurring approximately in the first 30 years of catalogues and we evaluated its performance on the last 10 years. The results showed that 1 day after the mainshock occurrence the rate of correct SSE forecasting is larger than 85% in both areas, supporting the application of NESTOREv1.0 in the Italian territory. Furthermore, by training the software on the entire period available for the two catalogs, we obtained good results in terms of near-real-time class forecasting for clusters recorded from 2021 onward.

machine learning

aftershock forecasting

statistical seismology

seismic risk mitigation

strong subsequent earthquake

Italian seismicity

Italy is a region with high seismicity due to the collision process between the African and Eurasian plates. In the last century, Italy has been hit by 8 earthquakes with a magnitude greater than 6.5 (Rovida et al. 2020, 2022), causing more than 120,000 victims. For most of the strong events that have occurred in Italy recently, a Strong Subsequent Event (SSE) with a comparable or higher magnitude was observed. These include M 6.1 1968 Belice (Monaco et al. 1996), M_w 6.4 1976 Friuli (Console 1976), M_S 6.9 1980 Irpinia (Bernard and Zollo 1989), M_w 5.9 1984 Val Comino (Milano and Di Giovambattista 2011), M_w 5.7 1997 Umbria-Marche (Di Giovambattista and Tyupkin 2000), M_w 6.1 2009 L’Aquila (Di Luccio et al. 2010), M_w 5.9 2012 Emilia (Ventura and Di Giovambattista 2013) and M_w 6.5 2016 Amatrice earthquake (Gentili et al. 2017). This behaviour can be related to the complexity of the fault systems (Gentili and Di Giovambattista 2017) and the Coulomb stress transfer on the fault corresponding to the mainshock or neighbouring earthquakes (Catalli et al. 2008). Compared to the effects of a strong mainshock, SSEs can lead to the collapse of already damaged structures and a further increase in the number of fatalities. Furthermore, they can have severe impacts on our globalised society and cause high economic losses. Therefore, forecasting of an SSE is of strategic importance to reduce the seismic risk during the occurrence of a seismic sequence (Gentili and Di Giovambattista 2017). In recent years, several methods have been proposed for California, Taiwan, Japan and Italy to forecast a SSE with a similar magnitude of the main strong earthquake. They focus on a pure Epidemic-Type Aftershock Sequence model (ETAS, Shcherbakov et al. 2019; Zhuang et al. 2002, 2004, 2005, 2008; Zhuang and Ogata 2006), the Omori-Utsu law of sequence (Shcherbakov 2014; Shcherbakov et al. 2018), its b-value trend (Shcherbakov and Turcotte 2004; Helmstetter and Sornette 2003; Gulia and Wiemer 2019, 2021), its mainshock characteristics (Persh and Houston 2004; Rodríguez-Pérez and Zúñiga 2016; Tahir et al. 2012; Gentili and Di Giovambattista 2017) and the seismicity associated with its aftershocks (Vorobieva and Panza 1993; Vorobieva 1999; Gentili and Di Giovambattista 2017, 2020, 2022). In particular, Gentili and Di Giovambattista (2017) proposed the machine learning-based algorithm NESTORE (Next STrOng Related Earthquake), which calculates seismicity parameters (features) at different time intervals after a first strong earthquake and provides the forecasting of a strong aftershock. Being DM the difference in magnitude between the first strong earthquake and its strongest aftershock in a sequence, it distinguishes the cases where DM ≤ 1 (type A) from the others (type B) and provides a probability that an ongoing seismic cluster is of type A. First versions of the algorithm have been successfully applied to seismicity in California and Italy (Gentili and Di Giovambattista 2017, 2020, 2022). Recently, a new and online released version of NESTORE (NESTOREv1.0) was made available on GitHub (Gentili et al. 2023).

In this paper we present the application of NESTOREv1.0 to Italian seismicity by considering both a nationwide and a regional approach. For this purpose, we used the data recorded in the last 40 years by the national seismic network of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) and the regional network of the Istituto Nazionale di Oceanografia e Geofisica Sperimentale - OGS. Specifically, for both approaches, we trained the program and evaluated its performance using data up to 2020 and then simulated its use in near-real-time mode using data after 2020.

In general, a regional approach is able to better identify particular characteristics of seismicity of a given region than a national approach. On the other hand, the number of available clusters in a regional approach can be very small compared to a national approach, which leads to a low significance of the analysis results. However, the high density of the OGS network in north-eastern Italy allowed us to lower the value of the minimum magnitude for the first strong earthquake used at the national level, resulting in a similar number of database clusters for both approaches.

This section gives a brief overview of the tectonic characteristics of the different regions of Italy: 1) the Alps, 2) the northern Apennines and the Po Valley, 3) the central and southern Apennines and 4) the Calabrian Arc and the Ionian Sea.

2.1. Alps

Seismic activity in the Alps mainly takes place in the upper crust, with the south-eastern and western regions of the Alps showing higher concentrations of seismic activity than the central Alps. According to Kiratzi and Papazachos (1995), Becker (2000) and Vannucci et al. (2004), the Eastern Alps exhibit active compression normal to the mountain belt, while the Western Alps exhibit extension perpendicular to the trend of the mountain belt, as noted by Fréchet (1978), Mathey et al. (2021) and Montone et al. (2004). In the last five decades, the Eastern Alps have been hit by two major earthquakes: the1976 M_L 6.5 Friuli earthquake, and the 1998 M_L 5.6 Kobarid earthquake (Gentili and Franceschina 2011). In contrast, no earthquake with a magnitude larger than 6 was recorded in the Western Alps during the same period.

2.2. Northern Apennines and Po Plain

Northern Apennines Neogene-Quaternary northeast-verging belt developed during the Euro-African convergence and involved the westward subduction of the Adriatic lithosphere (Alvarez 1972; Doglioni 1991). During convergence, the rollback of the W-subducting Adriatic plate triggered the eastward migration of thrust fronts and foredeep basins. The youngest of these basins is the Po Valley. The Northern Apennines thrust fronts' tectonic activity is supported by (a) historical and instrumental seismicity (CPTI, 2004; CSTI 1.0, 2001; Castello et al. 2006), the latter being characterized by reverse focal solutions (Pondrelli et al. 2006), (b) geological and geomorphological evidence of faulting and folding of recent deposits at the surface (Vannoli et al. 2004; Boccaletti et al. 2011) and (c) subsurface geophysical profiles showing very recent growth strata developed across buried anticlines (e.g.: Scrocca et al. 2007). The seismic activity in this region is characterized by shallow and moderate-depth earthquakes.

2.3. Central and Southern Apennines

It is assumed that the Apennines were formed by the combined effect of the opening of the Tyrrhenian Sea, the eastward movement of a compressive front and the retreat of the lithospheric plate beneath the Italian peninsula. The Apennines are subject to frequent seismic activity, with earthquakes generally occurring at a depth of 10–15 km (Italian Seismological Instrumental and Parametric Database, ISIDe Working Group 2007). The presence and movement of fluids in the Earth's crust can influence the stress and strength of fault zones, leading to changes in seismic activity. Active NW-SE striking normal faults separate the CO₂-releasing western region, originating from the mantle, from the non-degassing eastern area. Recent studies have identified an anomalous region of more than 100 mW m² with significant heat flow values over Tuscany and Lazio (up to 400 mW m²) (Della Vedova et al. 2001; Di Luccio et al. 2022).

2.4. Calabrian Arc and Ionian Sea

The region of the Calabrian Arc and the Ionian Sea, where the African and Eurasian plates collide, has a complex seismotectonic setting characterized by active fault systems, volcanic activity and earthquakes. The most important factor influencing seismotectonic activity in this area is the subduction of the African plate beneath the Eurasian plate. This subduction process leads to a wide range of earthquakes, including frequent quakes of varying magnitude, both onshore and offshore, from micro-earthquakes to severe earthquakes having magnitude larger than 7. Earthquakes in the Calabrian Arc vary greatly in depth, ranging from a few kilometers to over 400 kilometers. The predominant mechanism observed in this area is strike-slip faulting, which is associated with the subduction process and reveals an extensional style of deformation both in the direction parallel and perpendicular to the arc (Frepoli and Amato 2000).

To evaluate the national approach of NESTOREv1.0, we examined the seismicity recorded by INGV stations since 1980. In particular, we used the Lolli and Gasperini (2006) and “Italian Seismological Instrumental and Parametric Data-Base” [ISIDe, ISIDe Working Group (2007), http://iside.rm.ingv.it/iside/] catalogs, covering respectively the periods 1980–2004 and 2005–2020 (Fig. 1a). The first results from the integration of three catalogs, namely the “Catalogo Strumentale dei Terremoti Italiani” (CSTI, CSTI Working Group Version 1.1), which covers the period 1981–1996, the “Catalogo della Sismicità Italiana” (CSI), which covers the period 1997–2002 (Castello et al. 2006) and the Italian Seismic Bulletin (http://bollettinosismico.rm.ingv.it/), which covers the period 2003 to the end of 2004. The M_L of the merged catalogue was estimated by orthogonal regression to be compatible with the ISIDe data (Lolli and Gasperini 2006). Most of these data come from the Italian Telemetered Seismic Network (ITSN), whose waveforms were recorded from 1980 to 1984 with analog instruments and later with digital systems. This network was reinforced after the M_S 6.9 1980 Irpinia earthquake (Boschi et al. 1990; Barba et al. 1995; Marchetti et al. 2004) and currently comprises more than 470 stations (Fig. 1a).

To investigate the regional use of NESTOREv1.0 on Italian territory, we have analysed the seismicity in an area covering the northeast of Italy. This area is monitored by both the regional OGS and the national INGV seismic network. The OGS network has been operational since May 6, 1977 and, except for a short period when it was not operational (December 4, 1990-May 21, 1991), provides a seismic bulletin for the Friuli Venezia Giulia region and surrounding areas, which we refer to as the OGS bulletin for simplicity (Snidarcig et al. 2020; Friuli Venezia Giulia Seismometric Network Bulletin 2020; http://www.crs.ogs.it/bollettino_new/). During the operational period of the OGS network, the temporal improvement of instruments and data acquisition and analysis systems, the increase of installed seismic stations and the sharing of data with other nearby seismic networks led to a lowering of the detection threshold for earthquakes in north-eastern Italy and to an extension of the monitored area to the east and west (Gentili et al. 2011; Peruzza et al. 2015; Bragato et al. 2021). The OGS network currently consists of 43 seismic stations (Bragato et al. 2021).

Figure 1b shows the OGS Bulletin data between 1977 and 2020 and the distribution of the OGS network. Figure 2 shows the comparison between the number of events detected by the OGS and INGV networks in the period 1980–2020 within a rectangular study area for north-eastern Italy considered by Gentili and Di Giovambattista (2020). The longitude interval of this area is 11°-14° before 2008 and 11°-14.5° after 2008, while the latitude interval does not change over time and is 45.6°-46.75°. Due to the higher density within the area, the number of earthquakes recorded by the OGS network is always greater than that of the INGV network, as recorded in the adopted catalogues. This result can be easily explained by comparing Fig. 1 of Marchetti et al. (2004) with Fig. 2b of Peruzza et al. (2015). Figure S1 shows the local magnitudes provided by the INGV and OGS networks for the common events in the same period. The reference magnitude of the OGS catalogue is the duration magnitude M_D, and to avoid both the incorrect estimation of the Gutenberg-Richter law (Bragato and Tento 2005; Gentili et al. 2011) and to align the magnitude type with the national scale, we used the conversion law of Gentili et al. (2011) to transform them in M_L.

Figure S1 also shows the orthogonal regression of the data for M_L≥1.7 for the two catalogues OGS and INGV compared to the 1:1 line. Even if the difference between the two lines is small (maximum difference 0.1), the dispersion of the data is large; for this reason, we prefer not to merge the two catalogues and have decided to use the OGS catalogue provided by its network in the 1977–2020 period as part of the application at regional level.

For our analysis, we used the MATLAB-based toolbox NESTOREv1.0 (Gentili et al. 2023) to evaluate the ability to forecast a SSE on Italian territory after a first strong earthquake that has a magnitude value equal or larger than a fixed threshold M_th. In the following, we refer to the latter event as the First Strong Event (FSE) or operative mainshock and indicate its magnitude as M_FSE. NESTOREv1.0 is a machine learning algorithm freely available on Github (see Gentili et al. 2023 for more details) and consists of four modules that were used in this study. These are the cluster identification, training, testing and near-real-time classification modules of NESTOREv1.0. The flowchart of how the four NESTOREv1.0 modules work is shown in Fig. 3. Using the cluster identification module, NESTOREv1.0 identified clusters from an initial seismic catalogue using a window-based method (Gardner and Knopoff 1974; Uhrhammer 1986; Kagan 2002; Lolli and Gasperini 2003; Gentili and Bressan 2008; Gentili and Di Giovambattista 2020). Then, we divided the cluster database into two parts: the first part we used for training and the second part for testing to avoid bias in the estimation of the performances in case of overfitting. In the training procedure, NESTOREv1.0 measured a set of seismic parameters (features) at increasing time interval T_i on clusters from the occurrence of the FSE to learn to distinguish between type A and type B cluster populations using thresholds. In the test procedure, these threshold values were compared with the feature values measured in the same intervals, and an overall Bayesian probability of type A P(A) was calculated for each cluster by combining the class selection of all features. For both test and training processing, we opted for an initial period of 6 hours in order to have sufficient data for the analysis and to limit the effect of the increase in completeness magnitude (M_c) at the beginning of the cluster. According to Gentili et al. (2023), if the number of events was at least 80, the M_c of each cluster was calculated using the maximum curvature method (MAXC) adding 0.2. Otherwise, we assumed a M_c value equal to a default value M_cDEF. In the near-real-time classification procedure, we derived a probability that an ongoing cluster is type A using both the training information and the test procedure approach. A more detailed description of the features used in the analysis (Table S1), the statistical parameters used in the evaluation of the threshold performances (Accuracy, Informedness, Precision, Recall, Good Interval Range) and the functioning of the four NESTOREv1.0 modules can be found in Section S1 of the Supplementary Material.

After the first version of the "NESTORE" algorithm (Gentili and Di Giovambattista 2017, 2020), already applied in Italy, several changes were made in the following years, making it more robust and transferable in different regions and improving the performance evaluation. These are:

We used a minumum M_FSE equal to M_c + 2 (Gentili and Di Giovambattista 2022) for the clusters instead of M_c+ 3 in the previous versions of the algorithm in order to maintain the reliability of the results and obtain more data for the analysis.

We used a Bayesian method to merge and combine independent classifiers (Gentili and Di Giovambattista 2020), which allows to weight the classifiers of a single feature depending on their hit and false alarm rate and to deal with the typical imbalances between A and B classes.

We have assumed a common starting time based on the equation of Helmstetter et al. (2006), which considers an increase in M_c due to the superposition of waveforms after the FSE (Gentili and Di Giovambattista 2022).

We improved the reliability of the cluster class definition by excluding the cases in which the DM is between 0.8 and 1.2 from the analysis to take into account the uncertainty of the magnitude estimation.

We ended the analysis for A-type clusters with the time of the first aftershock with a magnitude ≥ M_FSE-1 instead of the time of the strongest aftershock.

We improved the estimation of training performance by using an independent database instead of a Leave One Out (LOO) method for the same training database.

The main innovation in this work is the application of the near-real-time classification module to Italy, which allows the forecasting of A-type during seismic crises.

5.1. Cluster Identification and Analysis Region Definition

Following Gentili and Di Giovambattista (2017), we identified clusters through a window-based approach using Uhrhammer (1986) and Lolli and Gasperini (2003), as presented in Section S2 of the Supplementary Material. Thanks to point 1 in Section 4, with reference to the work of Gentili and Di Giovambattista (2017), we were able to lower the threshold for the minimum magnitude of the FSEs (M_th) from 4.5 M_L to 4 M_L. The analysis region was selected in two steps: First, we excluded off-shore areas to avoid clusters with high location errors due to poor azimuthal seismic station coverage. We also excluded the Etna area and events deeper than 30 km to avoid events related to the volcanic or subduction regime in the southern Tyrrhenian Sea (Lanzano et al. 2019). We did not exclude the Vesuvius area as we did not have volcanic clusters in the region; the margins of the northern Italian area need to be less precisely defined due to data sharing with seismic networks of different countries. Even if Sardinia is located on Italian territory, its seismicity is too low to be considered in this analysis. Figure 4a shows the first selection boundaries in red together with the location of the FSE epicenters of the 47 detected clusters within the region. Type A clusters (red circles in Fig. 4a) account for 30% of the total number of clusters. In agreement with Gentili and Di Giovambattista (2017), we found that the central Apennines are dominated by A-type clusters (Fig. 4a). In addition, the B-type population is dominant in the northern Italian area and widespread in the southern Italian regions. According to Section 4, the A-type clusters of L’Aquila (2009), Emilia (2012) and Central Italy (2016) were not included in the analysis because a strong aftershock with magnitude or equal than M_FSE-1 occurs before the 6 hours following the FSE. In a future implementation of the algorithm, we plan to change this limitation by shortening the time interval between the FSE and the first strong aftershock. The second step in the region selection was to understand if there was a region of anomalous seismicity that should not be analyzed along with the others. The methodology of NESTOREv1.0 assumes that a type A cluster is more productive in terms of events and energy than a type B cluster. To obtain a first check of the validity of our model on the Italian territory, we applied the training and testing modules to the entire 1980–2020 cluster catalog, assuming a M_cDEF of 2.5, in agreement with Schorlemmer et al. (2010).

Figure 4b shows that NESTOREv1.0 achieves a correct cluster classification in 81% of the cases 6 hours after the occurrence of the FSE. We found that 5 incorrectly forecasted clusters (56% of the misclassifications) are located in a zone in the northwestern Apennines, which includes the areas of Mugello, Garfagnana, Lunigiana (Tuscany) and the southwestern part of the Emilia-Romagna region. This region, outlined in purple in Figs. 4a-4b, is mainly populated by type B clusters which exhibit anomalous seismic productivity in terms of the number of events and the amount of seismic energy released in a short time (Fig. 4b). This particular behaviour, which is discussed in Section 5.2, suggests that a separate training procedure would be more appropriate for this region. Since the clusters of this area are almost exclusively type B, which are of the order of ten, we decided not to include this area in the following national-level analysis. We then defined a national area for Italy without the previous anomalous area (ITA) and named the corresponding cluster catalogue C_ITA. It is important to note that we selected the purple region based on the available clusters. Some evidence of smaller sequences suggests that the selected region may be larger, but this will be the subject of future more detailed independent work on the characteristics of seismicity in Italy.

5.2. The anomalous area of the North Central Apennines

A possible explanation for the anomalous behaviour of the previously discovered area can be derived from its geological and structural complexity, as evidenced by several studies in the region. The shallow layer of this region seems to be a transitional region between the extensional-transtensional behaviour in the Tyrrhenian domain and the compressional behaviour in the Adriatic domain (Carmignani and Kligfield 1990; Barchi et al. 1998; Frepoli and Amato 1997, 2000; Montone et al. 1999; Carminati et al. 1998; Doglioni 1991; Doglioni et al. 1999; Negredo et al. 1997; Eva et al. 2005). Several studies have suggested that in this region the NNEward movement of the crustal block of the Adria plate and its rotation with respect to the European plate around a point on the Alpine chain has caused the process of extension into the Tyrrhenian domain (Bassi et al. 1997; Anderson and Jackson 1987; Ward 1994; Devoti et al. 2002, Eva et al. 2005). Eva et al. (2005) found that the region is characterized by transtensional stress in the first 30 km depth and transpressive stress in the deeper layers. Barani et al. (2010) hypothesized that the rotation of the Adria and the gravitational settling of the area are related to the high values of strain rates measured in the northern Apennines and especially in the Etrurian Fault System. Bonini et al. (2016) observed a large rate of seismic energy during strong earthquakes, which is attributed to a Coulomb stress coupling between the normal faults of the axial sector of the northern Apennines and thrust fronts outside it. In the studied area, Di Luccio et al. (2022), interpreting the CO₂ distribution in the Apennines, found that CO₂-rich fluids in the crust regulate both seismicity and the evolution of the most intense sequences in the Apennine region. Furthermore, using tomographic anomaly analyzes, they found that areas with lower S-wave velocity anomaly (ΔV_S) values coincide with areas of higher CO₂ outgassing in Tuscany. According to the authors, the presence of such areas of high heat flow would explain the low seismicity that characterizes the area. Considering the variation distribution of the ratio between P-wave and S-wave velocity V_P/V_S obtained by Di Luccio et al. (2022) at 8 kilometers depth, a depth close to the mean value of the anomalous clusters, we found that almost all these events are close to zones of zero anomaly for ΔV_S and Δ(V_P/V_S), which represent zones of rapid transition for the Vs velocity. Similar behavior has been observed in the Parkfield area of the San Andreas Fault, where the area characterized by strong V_P/V_S gradients is characterized by a stronger faulting tendency and consequently greater seismic activity (Agostinetti et al. 2022). Such areas, characterized by rapid material changes and subject to supra-hydrostatic conditions, could be prone to dynamic ruptures (Agostinetti et al. 2022). Based on these observations, we hypothesize that the high seismicity of the anomalous clusters could have its origin in rigid structures close to fluid-rich areas exposed to both the particular tectonic stress conditions of the area and the overpressure due to crustal fluids. A more in-depth analysis of the area in terms of cluster behavior will be investigated in the future with more extensive data sets.

5.3 Application to Italy

In machine learning applications, the available data is split into two separate data sets to obtain reliable training and performance evaluation: the first is used to train the algorithm, the second to verify performance. The percentage of data used in each dataset is variable. Some studies suggest that the best model performance is achieved when the training and testing databases account for 70% and 30% of the original dataset, respectively (Liu et al. 2019); other authors concluded that the percentage of data corresponding to the training database can be as high as 80% (Gholamy et al. 2018) or between 50% and 70% (Xu and Goodacre 2018). In this paper, we considered a ratio of 3 to 1 for the time periods corresponding to the training and test catalogues, respectively, at both national and regional levels. In particular, we split C_ITA into two parts, training the algorithm for the first 30 years (C_ITA_train) and testing the results on the clusters of the last 10 years (C_ITA_test). Due to the higher number of available clusters in more recent times, which is a consequence of the better coverage of the network and the lower M_c, 63% of the clusters were used in the training analysis, while the remaining 37% were used in the test procedure. The spatial distribution of the two databases along the ITA area is shown in Figs. 5a and 5b.

5.3.1 Training for ITA area

Figure 5a shows the distribution of C_ITA_train clusters, consisting of a set of 24 clusters occurring on the Italian territory between 1980 and 2009. During training, for each time interval and applying a LOO method to each feature classifier separately, NESTOREv1.0 estimates the performances of each classifier based on a set of performance evaluators. Features whose classifier fails the test with all evaluators for a time interval are not used for classification in that time interval. Figures 6a and 6b show two of these evaluators: Accuracy and Informedness (Powers 2011; Gentili and Di Giovambattista 2017; Gentili et al. 2023). The blue area corresponds to the region where NESTOREv1.0 considers the performance unreliable for the evaluator. Each symbol corresponds to a different classifier and indicates in which interval the threshold performance is good (ΔT_G). Figure 6 shows that no feature provides reliable performance for T_i greater than one day. This is related to the temporal occurrence of the first strong aftershock with M ≥ M_FSE-1 for A-type clusters in the training database. In almost 43% of the cases, these earthquakes occur before the second day after the FSE, resulting in poorer statistics for the calculation of thresholds for longer time intervals.

Figure 6c shows the Receiving Operating Characteristics (ROC, Egan 1975; Sweets et al. 2000; Fawcett 2006; Gentili and Di Giovambattista 2017; Gentili et al. 2023) graph, which was determined using the LOO method for threshold values 6 hours after the FSE. Compared to the results of Gentili and Di Giovambattista (2017), we observe a better performance for all features at 6 hours of observation, while at 1 day (Fig. 6d) we observe an improvement in terms of False Positive Rate and a decrease in terms of Recall (True Positive Rate). However, due to the changes described in session 4, a larger number of additional features are available, which improves the robustness of the algorithm. The values of the feature thresholds found for C_ITA_train are listed in Table S2 in section S3 of the Supplementary Material.

5.3.2 Testing for ITA area

We applied the testing procedure of NESTOREv1.0 to C_ITA_test, which consists of 14 clusters and is divided into 6 A-type and 8 B-type cases. These clusters correspond to the period 2010–2020 and their spatial distribution is shown in Fig. 5b. Figure S2a shows the Bayesian probability that a cluster belongs to the A-type as a function of the analysis periods T_i corresponding to C_ITA_test. In particular, after the first 6 hours after the FSE, 79% of the clusters are correctly classified, and the percentage of successful forecasting increases to 86% after the first day (Figures S2a-7). Indeed, the M_L 4.4 cluster that occurred in Sicily in 2011 was classified as B-type due to the initial lack of aftershocks with a magnitude of 2.4 M_L or more before one day and correctly forecasted as A-type afterwards.

The Recall-Precision graph after 6 hours shows that all type A forecastings are correct (i.e. no false alarm) and that 50% of type A clusters are recognized by almost all features and their Bayesian combination (Figure S3). The latter percentage increases to 67% 1 day after the FSE, due to the change in classification of the M_L 4.4 (2011) Sicily cluster (Fig. 8a). In addition, the ROC diagram shows a zero value for the false positive rate after one day (Fig. 8b), indicating that the B-type clusters are all correctly classified. This performance does not change in the following periods (see Fig. S2a). The two misclassifications (Fig. 7) correspond to the A-type clusters M_L 4.2 (2017) Central Italy and M_L 4.7 (2018) Molise, both characterized by the absence of aftershocks between the FSE and the SSE. In the first case, we speculate that the high seismicity in the Central Italy region since August 2016 has led to an anomalous behavior of the subsequent clusters, which cannot be considered isolated. As for the second case, due to the low density of seismic stations in the Molise region, M_c cannot be guaranteed for the entire duration of the cluster; a more detailed analysis of the seismicity of the 2018 Molise cluster, which is beyond the scope of this article, will be the subject of a future article in preparation.

6.1 Cluster Identification Analysis

According to Gentili and Di Giovambattista (2020), the OGS bulletin has a M_c smaller than that of the national INGV network in correspondence with northeastern Italy. This finding made it possible to lower M_th in the first application of the NESTORE method in Northeast Italy (Gentili and Di Giovambattista 2020). In our analysis at the regional level, we considered the same time-dependent area, mainly covering north-eastern Italy (hereafter NEI), using the OGS bulletin in the period 1977–2020. Similar to the ITA area, only FSEs with a depth of less than 30 km were considered. Following Gentili and Di Giovambattista (2020), we assumed a M_cDEF of 2.0 before 1994 and of 1.5 in the following years, set M_th for NEI at 3.7 and used the relationships proposed by the authors for the identification of clusters in space and time based on Gentili and Bressan (2008) (see section S2 in the Supplementary Material). We obtained a catalogue of 32 clusters for NEI (C_NEI), of which 8 belonged to the A-type (Fig. 9). In contrast to ITA, the spatial distribution of the A-type population does not appear to be concentrated in specific areas, while the eastern part is dominated by B-type clusters.

6.2. Training procedure and application for NEI

In the case of C_NEI, we chose almost the same temporal split as for C_ITA by considering data between 1977 and 2009 as the training catalogue (C_NEI_train) and between 2010 and 2020 as the test catalogue (C_NEI_test). In particular, since we found that the M_L 3.8 1999 Kobarid (Slovenia) A-type cluster has anomalous seismic properties compared to the other data from C_NEI, probably due to its proximity to an earlier cluster with a strong main earthquake in the same area, we did not include this cluster in the C_NEI_train training database. Figures 10a and 10b show the spatial distribution of C_NEI_train and C_NEI_test, respectively. In this case, 42% of the C_NEI clusters are used for the training of NESTOREv1.0 and the remaining 58% for the test procedure. Even if this temporal division of the database differs somewhat from that given by Xu and Goodacre (2018), it makes it possible to limit the imbalance between A and B typologies in the two datasets.

6.2.1 Training for NEI area

In the NESTOREv1.0 training for the NEI regional area, we analysed 13 clusters consisting of 4 A-type and 9 B-type clusters (Fig. 10a). According to the Accuracy values obtained for C_NEI_train, the thresholds correctly identify the cluster typology in more than 75% of the cases. This percentage is 77% for N₂ and S and 92% for V_m and Z after the first 6 hours (Fig. 11a). At this period, the Informedness values of the features show that the rate of correct identification of type A clusters is between 53% and 75% (Fig. 11b). 12 hours after the FSE, Accuracy and Informedness are both 1, showing that most features correctly identify all clusters of C_NEI_train (Figs. 11a and 11b). As in the case of C_ITA_train, 50% of the type A clusters were found to have the SSE before the first 18 hours after the FSE. This means that the periods corresponding to the good interval time are always less than 1 day. As for the previous national case, the thresholds cannot be compared with those of Gentili and Di Giovambattista (2020) due to the changes in section 4. The determined thresholds are listed in Table S3 in the Supplementary Material. Comparing the ROC diagram obtained after 6 hours (Fig. 11c) with the results of Gentili and Di Giovambattista (2020), the estimated performances during the training procedure are better, but this could be related to the exclusion of the 1999 Kobarid outlier from the training set. Comparing the results of C_ITA_train with those of C_NEI_train, we find that the percentage of A-type clusters correctly identified for NEI with all features is similar to that of ITA. Conversely, for type B misclassification (False Positive Rate, FPR), the percentage for NEI is slightly higher than for ITA for some features (Fig. 11c).

6.2.2 Testing for NEI area

The test catalogue for NEI (C_NEI_test) consists of 18 clusters, which are shown in Fig. 10b. 40% of the C_NEI_test clusters are located in eastern Slovenia and belong to the B-type class. The 3 A-type clusters of C_NEI_test occurred in the Veneto region and in the north-central part of Friuli. Figures S2b and 12 show that the 6-hour forecast of NESTOREv1.0 for C_NEI_test is correct in 94% of the cases. The only misclassification in this period concerns the M_L 3.7 (2015) Valdobbiadene earthquake, which corresponds to an anomalous A-type cluster (Fig. 12). After the FSE of magnitude M_L 3.7 on May 12, no aftershocks with a magnitude greater than M_L 1.6 were detected before the SSE (M_L 3.6) on May 15. Since the Valdobbiadene earthquake is located in an area for which there was no training, the incorrect forecasting could be due to differences between the local seismicity and the Friulian-Slovenian seismicity. The Precision-Recall and ROC plots show that 6 hours after the FSE, 67% of the A-type clusters are correctly identified by N₂, S, Q, the simple and the Bayesian combination of feature probabilities (Figs. 13a-13b). Similar to the C_ITA_test, the ROC plot shows that all B-type cases are correctly identified (Fig. 13b). This finding was to be expected due to the large population of type B clusters in C_NEI_train.

To better explore both the properties of feature thresholds for national and regional areas and to evaluate the performance of the near-real-time classification module of NESTOREv1.0 on ITA and NEI, we used the entire C_ITA and C_NEI catalogues. As described in section S5.1 of the Supplementary Material, we first checked the temporal stability of the feature thresholds for the Italian territory and their possible dependence on the 1980–1990 period, when the national network was characterised by a poorer performance in terms of M_c, location and magnitude calculation. We found that the thresholds for all features are stable in time to a first approximation, except in the case of S and Z (Figures S4-S5). To use the refined thresholds for the near-real-time procedure in both the ITA and NEI areas, we performed an autotest for the two areas and excluded the clusters of C_ITA and C_NEI that were outliers in at least one period T_i. The resulting refined catalogues were named C_ITA_R and C_NEI_R and were used to perform a second training and obtain new thresholds for ITA and NEI (Tables S4 and S5 in the Supplementary Material). This last process is described in more detail in section S5.2 of the Supplementary Material. Taking the period T_i=6 hours, an interval in which the performance results of both C_ITA_test and C_NEI_test are significant, it was found that the ITA thresholds (Table S4) are two or three times higher than the NEI thresholds (Table S5) for all available features. This result seems to indicate that the characteristics of NEI seismicity differ from those of ITA seismicity in the early stages of cluster occurrence. In particular, NEI appears to be characterised by lower productivity in terms of number of events, source area and energy than those measured at the national scale. Further details on this observation can be found in section S5.2 of the Supplementary Material. In order to use a refined training corresponding to the longest possible time period, we decided to use the training corresponding to C_ITA_R and C_NEI_R for the near-real-time application to ITA and NEI described in the following section.

To obtain a first simulation of NESTOREv1.0's ability to classify a cluster in the hours immediately following the occurrence of its FSE, we evaluated the performance of the near-real-time module in both the ITA and NEI area. Since the first period of feature calculation of NESTOREv1.0 is currently 6 hours after the occurrence of the FSE, the forecasting of an SSE is limited to those clusters that do not have an event with a magnitude M ≥ M_FSE-1 in the first 6 hours after the FSE. Subsequently, 5 clusters for the ITA area and 2 clusters for the NEI area were analyzed, corresponding to the available cases with M_FSE≥4 and M_FSE≥3.7 in the case of ITA and NEI, respectively. As the final forecasting period, we chose the one corresponding to the best threshold performance obtained for the C_ITA_test and the C_NEI_test, which corresponds to one day after the FSE in the case of ITA and 6 hours after the FSE in the case of NEI. We have shown in Fig. 14a the type of clusters analyzed and in Fig. 14b the performance of NESTOREv1.0 corresponding to the last forecasting period.

8.1 Application to ITA

For the ITA area, we considered the M_L 4.4 Gambettola (type A), M_L 4.6 Montagano (type B), M_L 4.4 Catania (type B), M_L 4.2 Ceneselli (type A) clusters that occurred in 2023 using INGV data (http://terremoti.ingv.it/) (Fig. 14). In addition, we included in the analysis the B-type cluster corresponding to the M_L 3.9 Moltelparo event, whose M_FSE value was reported as 4.0 in the first week after the FSE (Fig. 14). In such a case, we can test the classification in near-real-time, even when the magnitude of the FSE fluctuates around the given M_th threshold.

In the case of the Gambettola cluster (northern Italy), the FSE with magnitude M_L 4.1 occurred at 10:45:41 UTC on January 26, 2023, followed by the SSE at 05:32:51 on January 28 with the same magnitude value. In the first six hours, there are four events with a magnitude of M_L 2.1 or more, and the voting of the S, Z, V_m, Q and N₂ features after six hours is of type A with a probability P(A) equal to 1. In the following periods, the additional A-type voting of SLCum, QLCum at 12 hours and SLCum2, QLCum2 at 18 hours after the FSE leads to a Bayesian probability of type A P(A) equal to 1 (Figure S6) and then to a correct classification of the cluster for all periods considered (Fig. 14c).

The Montagano B-type cluster is characterised by a FSE of M_L 4.6 that occurred on 28 March 2023 at 21:52:42 UTC. The earthquake was clearly felt in the Molise region (central Italy) and neighbouring regions, and the strongest aftershock occurred the following day with a M_L of 2.6 at a time interval of just over 6 hours. The latter event turns out to be the only aftershock analysed by NESTOREv1.0 that leads to a zero P(A) probability for S, Z, Q, V_m, N₂ at 6 hours and for SLCum at 12 hours (Figure S7). The resulting Bayesian probability that the cluster is type A is correctly equal to 0 from 6 hours to one day after the FSE (Fig. 14d).

The third case analysed concerns a B-type cluster whose FSE had an epicentre about 10 km southeast of the coast of Catania (southern Italy) on April 21, 2023 with M_L 4.4. This event, which was about 17 km deep, was widely resonant in the south-eastern part of Sicily and was followed by only two events with M_L below 2. Since there is therefore no event with a magnitude greater than M_FSE-2, all the features vote for type B from 6 hours to 1 day. It follows that, as in the previous case, the classification of the cluster based on the Bayesian method is correctly type B for all increasing periods from the FSE occurrence onwards.

The fourth case analyzed is the type A cluster, whose FSE with M_L 4.2 occurred on October 28, 2023 in the southern part of the Veneto region and was followed three days later by an event of the same magnitude. No event with a magnitude greater than 2.1 occurred in the time window between these events. Consequently, the features and their Bayesian combination result in a P(A) = 0 for each time period leading to a misclassification of the cluster.

The last case corresponds to the type B cluster in Montelparo (Marche region) having a FSE that occurred on November 14, 2023. Its estimated magnitude value was M_L 4.0 in the first two weeks and M_L 3.9 thereafter. In the first six hours after the FSE, an event with M_L greater than 2 occurs, and at 6 hours the P(A) values provided by N₂, V_m, Z, Q are equal to 0 and are inherited in the following periods. Even if another event with M_L>2.0 occurs after the 6 hours and the features S, SLCum to SLCum2 vote for a cluster of type A, the resulting Bayesian probability P(A) is equal to 0 up to one day, which leads to a correct classification of the cluster.

8.2 Application to NEI

In the case of NEI, we analysed in near-real-time the M_L 3.9 Zuglio A-type cluster (2021) and the M_L 4.5 Klana B-type cluster (2023) using the data from the OGS network and bulletin (http://www.crs.inogs.it/bollettino_new/). In both cases, a report was sent to the head of the OGS Seismological Research Centre (CRS).

The first cluster occurred about 80 km northwest of Udine town. The FSE occurred on October 21, 2021 (M_L 3.9) and its SSE (M_L 3.0) occurred almost a day apart. Two aftershocks were recorded between these events, one with a magnitude of M_L 2.1 and another with a magnitude of M_L 1.1, which occurred two and five hours after the FSE respectively. The first of them was considered in the NESTOREv1.0 analysis, which correctly provides a Bayesian probability P(A) for the cluster equal to 1 after 6 hours. In particular, the features S, Q and N₂ vote for a cluster A with a P(A) = 1 in the case of S and Q and P(A) = 0.8 in the case of N₂.

The second case considered refers to a type B cluster whose FSE with a M_L of 4.5 occurred on July 29, 2023 in Klana (Croatia) near the border between Croatia and Slovenia. This event, which was felt in Croatia, Slovenia and north-eastern Italy, was followed by several aftershocks, the strongest of which had a M_L of 2.4. As there were no events with a magnitude greater than 2.5, the available N₂, S and Q features at 6 hours gave a P(A) = 0, resulting in a correct classification of the cluster in near-real-time.

8.3 Final remarks

Although our analysis provides a correct near-real-time estimate of the cluster type for the most intense clusters that occurred in ITA and NEI after 2020 (Fig. 14b), it should be noted that our methodology is currently not applicable for periods of less than 6 hours after the occurrence of the FSE. In the future, the possibility of further shortening this minimum period will be investigated in order to also obtain information for clusters where the next strong event occurs in the first hours after the FSE. It should also be noted that for a reliable evaluation of the performance of the near-real-time module of NESTOREv1.0, it is necessary to test the algorithm on a much larger independent database of clusters than the one considered so far. However, the first results of the analysis seem promising when it comes to informing the population or civil protection about the occurrence of a SSE in order to reduce the seismic risk.

In this paper we have shown the results of applying the new machine learning package NESTOREv1.0 (Gentili et al. 2023) to the seismicity data of Italy recorded by the INGV and OGS networks in the last 40 years. Compared to the previous version of the algorithm already applied in Italy (Gentili and Di Giovambattista 2017, 2020), NESTOREv1.0 allowed us to improve forecasting of A-type clusters in terms of 1) required M_c and feature calculation, 2) the definition of clusters and their class, 3) the estimation of training performances and, more interestingly, 4) the use of a specific module to forecast the typology of an ongoing cluster.

The analysis was performed with all four modules of NESTOREv1.0, both with a national and a regional approach. In the case of the regional approach, we compared the number of events recorded by the INGV and OGS networks in NEI during the period 1980–2020 and concluded that the OGS bulletin is the more appropriate dataset for both local seismicity analysis and M_th reduction compared to the national approach. In the national analysis, preliminary training and testing with the same INGV database for the period 1980–2020 allowed us to discover an area of type B anomalous clusters in the northwestern Apennines that were not observed in previous studies. These clusters show a remarkable frequency of events after the FSE. As several studies have shown, this area seems to be characterized by several geophysical factors such as heterogeneous stress distribution at depth, high strain rate, Coulomb stress coupling between faults and CO₂ degassing (Eva et al. 2005; Barani et al. 2010; Bonini et al. 2016; Di Luccio et al. 2022), which could explain the particular seismic behavior. For the remaining national territory, lowering M_th respect to Gentili and Di Giovambattista (2017), we obtained 38 clusters in the period 1980–2020 for the INGV catalog. In the regional approach, exploiting the higher density of the OGS network in Northeast Italy, using the same M_th of Gentili and Di Giovambattista (2020), we extracted 32 clusters in the period 1977–2020 for the OGS catalog. First, we trained the algorithm with the period 1980–2009 for the analysis at the national level and with the period 1977–2009 for the analysis at the regional level. This training analysis shows that the maximum reliability period for the thresholds is different for the two areas (18 hours for NEI and 1 day for ITA), which can be explained by the shorter time interval between the SSE and the FSE in the case of NEI compared to ITA. We found that for both approaches, the Accuracy and Informedness of the thresholds are greater than 0.85 and 0.6, respectively, for most of the features. In particular, in the case of the national approach, the feature N₂, which is based on the number of aftershocks, has the best performance, while the feature QLCum, which is based on the variation of cumulative energy, has the worst performance. We evaluated the performance of the training by testing the algorithm for the period 2010–2020 for both approaches. The results show that NESTOREv1.0 provides the 94% of correct forecasting of the cluster type in the case of NEI six hours after the main earthquake and 86% of correct forecasting in the case of ITA one day after the operative mainshock. In the previous periods, the percentage of correct classification of the A-type (Recall) is slightly less than 70%. With the aim of obtaining robust and reliable information to forecast the cluster type for sequences occurring after 2020 in ITA and NEI, we trained the algorithm on the entire available period of the C_ITA and C_NEI catalogs. In the case of the national approach, we made sure that the poor coverage of the Italian seismic network in the period 1980–1990 does not significantly affect the thresholds of the features. To obtain refined thresholds for both areas, we performed training for ITA and NEI for the periods 1980–2020 and 1977–2020, respectively, excluding the outlier clusters (B-type clusters with high seismicity and A-type clusters with low seismicity). Using these thresholds, we performed a near-real-time classification analysis for seven clusters that occurred between 2021 and 2023 in the ITA and NEI areas recorded by INGV and the OGS data, respectively. We found that 86% of the clusters were already correctly classified 6 hours after the FSE, in good agreement with the testing results. The good performance of NESTOREv1.0 on test and near-real-time databases for both the nationwide and regional approach encourages us to use the algorithm in the future for the forecasting of strong aftershocks on Italian territory. Furthermore, analyzing the new algorithm on a larger training dataset would lead to an even more reliable forecasting for civil protection to mitigate seismic risk during a series of earthquakes.

Funding

Funded by a grant from the Italian Ministry of Foreign Affairs and International Cooperation

Author Contributions

All authors contributed to the study conception and design. Material preparation, data collection and data preparation were done by Piero Brondi and Stefania Gentili. The methodology has been developed by Stefania Gentili and Rita Di Giovambattista and its corresponding software by Stefania Gentili and Piero Brondi. The funding acquisition was managed by Stefania Gentili. Analysis were performed by Piero Brondi and Stefania Gentili. The first draft of the manuscript was written by Piero Brondi with the contribution of Stefania Gentili and Rita Di Giovambattista. Stefania Gentili and Rita Di Giovambattista reviewed and edited the previous versions of the manuscript. All authors read and approved the final manuscript.

Acknowledgments

We wish to thank Giuseppe Falcone for the data and Elena Eva for the useful discussion on the anomalous North Central Italy area.

Data Availability

The NESTOREv1.0 toolbox is available for free download from GitHub at the address https://github.com/StefaniaGentili/NESTORE and the reproducibility package is available on Zenodo https://zenodo.org/account/settings/github/repository/StefaniaGentili/NESTORE.

The catalogues used in this paper for the national approach are the Lolli and Gasperini (2006) database downloaded from the authors' anonymous ftp site: ftp://ibogfs.df.unibo.it/lolli/aft2005/italycat6004.dat (last accessed on 9 August 2006), the “Italian Seismological Instrumental and Parametric Data-Base” (ISIDe, ISIDe Working Group, 2007) available at http://iside.rm.ingv.it/iside/ (last accessed on 3 October 2022), and INGV database available at https://terremoti.ingv.it/ (last accessed on 3 January 2024). The catalogue used for the regional approach is the OGS bulletin available at http://www.crs.ogs.it/bollettino_new/ (Snidarcig et al. 2020) and https://rts.crs.inogs.it/ (last accessed 20 September 2023).

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Forecasting strong subsequent events in the Italian territory: a National and Regional application for NESTOREv1.0

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Abstract

Figures

1. Introduction

2. Seismotectonic framework

2.1. Alps

2.2. Northern Apennines and Po Plain

2.3. Central and Southern Apennines

2.4. Calabrian Arc and Ionian Sea

3. Data

4. Methodology: NESTOREv1.0

5. Nationwide Application of NESTOREv1.0 for Italy

5.1. Cluster Identification and Analysis Region Definition

5.2. The anomalous area of the North Central Apennines

5.3 Application to Italy

5.3.1 Training for ITA area

5.3.2 Testing for ITA area

6. Regional scale Application of NESTOREv1.0 on North East Italy

6.1 Cluster Identification Analysis

6.2. Training procedure and application for NEI

6.2.1 Training for NEI area

6.2.2 Testing for NEI area

7. Thresholds characteristics for Italian Territory

8. Near-Real-Time analysis for Italian Territory

8.1 Application to ITA

8.2 Application to NEI

8.3 Final remarks

Conclusions

Declarations

Funding

Author Contributions

Acknowledgments

Data Availability

References

Supplementary Files

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