1 Introduction

The seismological community is investing in development and application of stochastic models for forecasting the space–time distribution of earthquakes conditional on the seismic history at the time of the probabilistic evaluation: e.g., epidemic type aftershock sequence or ETAS (Ogata 1988, 1998) and short-term earthquake probability or STEP (Gerstenberger et al. 2005) models. The common assumption is that each event of a seismic sequence can trigger new events causing an alteration of the seismicity in the area where it strikes; i.e., no physical differences are assumed among foreshocks, mainshocks and aftershocks (Jordan et al. 2011). Coupling this kind of models with real-time data acquired from monitoring seismic networks, the resulting systems can constantly provide operational earthquake forecasting (OEF). In Italy, an OEF prototype (OEF-Italy) of the national institute of geophysics and volcanology (INGV) is currently under testing in order to evaluate whether it is suitable to provide information about the short-term seismic hazard to the Italian civil protection system (Marzocchi et al. 2014).

In fact, the output of OEF can be useful for risk management if the rates of events above a magnitude threshold of interest may be used as an input for probabilistic assessment of seismic losses (e.g., Marzocchi et al. 2015). A procedure to do so, that is converting outputs of OEF into loss-related measures in a probabilistically consistent manner, has been recently developed and defined as operational earthquake loss forecasting (OELF; Iervolino et al. 2015a). A prototype system for OELF, called MANTIS-K, is also currently under experimentation in Italy. It starts from the weekly earthquake rates continuously provided (i.e., daily or after an event 3.5+ in magnitude) by OEF-Italy, and combines them with exposure data (at the scale of municipality) and models about seismic vulnerability of the building stock, to compute weekly expected values of seismic loss metrics after each OEF rates release.

Validation of expected losses requires a large amount of observed data, certainly unavailable in the case of MANTIS-K at this point. In fact, validation is out of the scope of this paper; however, referring to past seismic sequences, a critical analysis of the results provided by the system, during seismic sequences that raised risk management issues, may be useful. It may help understanding whether OELF, in the analysed cases, would have been a useful additional instrument for short-term risk management. Moreover, the retrospective analyses herein presented allow describing the type of information provided by MANTIS-K and recognizing common features, if any, among the losses forecasted during three sequences, which are quite different from the seismological perspective.

As it regards the structure of the paper, even if details can be found in Iervolino et al. (2015a), the main equations and implemented models of MANTIS-K are summarised first. Subsequently, the three selected Italian seismic sequences are presented. They are those with the largest magnitude events occurred in Italy from 2004 to 2014 (excluding those offshore) and are named as L’Aquila (2009), Emilia (2012) and Garfagnana (2013). For each sequence, a general description is provided and the evolution of the earthquake rates forecasted by OEF-Italy, for each day in a selected period, is presented. Then, the daily-updated loss indices, forecasted by MANTIS-K for the area of the sequence, are shown; i.e., the expected values of fatalities, unusable buildings, and displaced residents, in the time-horizon of 1 week after each OEF data release. These indices are computed referring to four groups of municipalities characterised by increasing distance from the epicentre of the mainshock of the sequence. The work is concluded by a comparison of the OELF results among the sequences and a discussion with respect to the observed losses.

2 MANTIS-K system for operational earthquake loss forecasting in Italy

If data from a seismic sensor network, monitoring a given region, are available at each time instant t, that is, the seismic history, H(t), is known, then OEF models provide an estimation of future seismicity. More specifically, according to OEF, the territory is divided into elementary areas which are identified by pairs of coordinates {x, y}. Each area is considered as a point-like seismic source to which OEF assigns an expected number of generated earthquakes above a magnitude of interest per unit-time; i.e., the seismic rate. Such a rate, λ[t, x, y|H(t)], depending on the recorded seismic history, varies with t.

In Italy, an OEF system is operating (Marzocchi et al. 2014). It is based on the country-wide seismic network of INGV and provides, for a grid of about 9000 point-like seismic sources covering the whole Italian territory and sea, the seismic rates updated at least once a day and every time an earthquake of local magnitude (M L ) equal or larger than 3.5 occurs. These rates are the forecasted mean number of ML 4.0+ events produced by each point source in a time-horizon of 1 week. The probability density function of the magnitude of the events, f M (m) in the following, is assumed to be derived from a Gutenberg–Richter-type relationship (Gutenberg and Richter 1944), with unbounded maximum magnitude and b-value equal to one. This is common to all the point sources, that is, differences among the sources derive only from the seismic rates.

Although a prototypal version of the system has started working on the 7th of April 2009 (Marzocchi and Lombardi 2009), the complete Italian seismic catalogue from April 2005 to June 2014 has been analysed offline by the OEF-Italy system and the seismic rates for the whole grid of point sources have been computed at 00:00 of each day. A database collecting all the results for the analysed period (about 3300 days) has been provided to the authors (Warner Marzocchi, personal communication, July, 2014) and has been used for the analyses presented in the following.

An example of the seismic rates provided by OEF-Italy system is reported in Fig. 1 for illustrative purpose. The picture, arbitrarily, refers to the OEF-Italy results computed at 00:00 of the 6th of April 2009.

Fig. 1
figure 1

Map of expected number of ML 4+ events in the week following 00:00 of 06/04/09, estimated through OEF-Italy

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In Iervolino et al. (2015a), it has been demonstrated that, starting from the rates resulting from the OEF-Italy system, it is possible to derive indices of seismic losses via a probabilistically sound procedure. The latter involves models used in the classical probabilistic seismic hazard analysis (PSHA; e.g., McGuire 2004), and is consistent with the performance-based earthquake engineering (Cornell and Krawinkler 2000) framework. While the interested reader should refer to the given reference for details, such a procedure for OELF is summarised here for the sake of readability of the results of the study. In fact, the equation and the models required are recalled, as well as the data and models used for Italy.

2.1 Hazard (shaking intensity)

Starting from the weekly seismic rates from OEF-Italy described above, λ[t, x, y|H(t)], associated to each point-like seismic source in Italy, MANTIS-K associates probabilities of shaking intensity in terms of macroseismic (MS) intensity. This is because the vulnerability models considered (to follow) are function of MS.

Prediction equations allow estimating the probability of a specific MS intensity at the generic site, identified by the couple of coordinates {w, z}, conditional on the occurrence of an earthquake of known magnitude, M, at a given point-like seismic source; i.e., P[MS = ms|m, R(x, y, w, z)], being R(x, y, w, z) the source-to-site distance. The chosen prediction equation for macroseismic intensity is that of Pasolini et al. (2008) that identified intensity as defined by the Mercalli–Cancani–Sieberg (MCS) scale (Sieberg 1931). The model applies to the [0, 220 km] interval of the distance,Footnote 1 and between V and XII of intensity.

2.2 Vulnerability

Structural vulnerability is accounted for in MANTIS-K via a damage probability matrix (DPM) that, according to the definition of Whitman et al. (1973) and Braga et al. (1982), provides the probability of observing a damage state (ds) to a building of a given structural typology (k), given a value of intensity, ms, at the site; i.e., P[DS (k) = ds|ms]. The DPM considered is based on Italian observational data (Zuccaro and Cacace 2009; Iervolino et al. 2014a). It accounts for four different vulnerability classes in which the Italian building stock is divided, from A to D (the same as indicated in European Macroseismic Scale EMS 98), and six damage levels (D0—no damage, D1—slight damage, D2—moderate damage, D3—heavy damage, D4—very heavy damage, D5 collapse).

Another model used is, for the k-th structural typology and conditional on damage state, the probability for an occupant to suffer casualties, P[Cas (k)|ds]. Casualty probabilities, conditional on structural damage and vulnerability class, are those of Zuccaro and Cacace (2011). Such a model refers to two types of casualties; i.e., (1) fatalities and (2) injuries (someone requiring hospital treatment is considered as injured).

2.3 Exposure

In Italy, the elementary units for which dwelling building exposure data are made publicly available from the population census are municipalities. For this reason, all computations performed by MANTIS-K refer to the municipality level and to dwelling buildings only: the centroid of each municipality area is the {w, z} point used for computing the source-to-site distance, and in which all exposed assets in the municipality are supposed to be concentrated. For each municipality, exposure in terms of buildings is the number of buildings of k-th typology, \(N_{b}^{(k)}.\) The number of residents living in the k-th building typology, \(N_{p}^{(k)},\) is a measure of exposure in terms of residents. Both kinds of data are derived from the National census of 2001 (Zuccaro et al. 2012). Note that these exposure measures depend on the municipality, that is on {w, z}; however, the coordinates are dropped for simplicity in the symbols.

2.4 Losses

Assuming that the stochastic process of events causing damage to the building at the site is approximated, in the short time interval (Δt), by a homogeneous Poisson process, the expected number of casualties (fatalities or injuries) in the considered {w, z} municipality, E[N Cas,(t,t+Δt)|H(t)], can be computed via Eq. (1). According to Zuccaro et al. (2012), casualty and injury assessments are carried out considering that 65 % of the total population is exposed at the time of occurrence of the earthquake, which justifies 0.65 in the equation.

$$\begin{aligned} & E\left[ {N_{{Cas,\left( {t,t + \Delta t} \right)}} \left| {H\left( t \right)} \right.} \right] \approx \Delta t \cdot \sum\limits_{k} {0.65 \cdot N_{p}^{\left( k \right)} \cdot \iint\limits_{x,y} {\lambda \left[ {t,x,y\left| {H\left( t \right)} \right.} \right] \cdot }\sum\limits_{ds} {P\left[ {Cas^{\left( k \right)} \left| {ds} \right.} \right] \cdot } } \\ & \quad \cdot \sum\limits_{ms} {P\left[ {DS^{\left( k \right)} = ds\left| {ms} \right.} \right] \cdot } \int\limits_{m} {P\left[ {MS = ms\left| {m,R\left( {x,y,w,z} \right)} \right.} \right] \cdot f_{M} \left( m \right) \cdot dm \cdot dx \cdot dy} \\ \end{aligned}$$
(1)

Zuccaro and Cacace (2011) also provide the probability of a building to be unusable for a given damage state, P[Unus|ds]. Such a probability, which does not depend on the structural typology, is 1 for damage state D4 and D5, whereas it is 0.5 for buildings in D3, and it is 0 for lower damage levels. Thus, the expected number of unusable buildings in one time unit, E[N Unus,(t,t+Δt)|H(t)], can be computed via Eq. (2).

$$\begin{aligned} & E\left[ {N_{{Unus,\left( {t,t + \Delta t} \right)}} \left| {H\left( t \right)} \right.} \right] \approx \Delta t \cdot \sum\limits_{k} {N_{b}^{\left( k \right)} \cdot \iint\limits_{x,y} {\lambda \left[ {t,x,y\left| {H\left( t \right)} \right.} \right] \cdot }\sum\limits_{ds} {P\left[ {Unus\left| {ds} \right.} \right] \cdot } } \\ & \quad \cdot \sum\limits_{ms} {P\left[ {DS^{\left( k \right)} = ds\left| {ms} \right.} \right] \cdot } \int\limits_{m} {P\left[ {MS = ms\left| {m,R\left( {x,y,w,z} \right)} \right.} \right] \cdot f_{M} \left( m \right) \cdot dm \cdot dx \cdot dy} \\ \end{aligned}$$
(2)

Replacing the number of buildings, \(N_{b}^{(k)}\), with the number of residents, \(N_{p}^{(k)}\), the expected number of displaced residents may also be computed. Indeed, all the residents living in an unusable building are considered as shelter-seeking.

To give a sense of the results MANTIS-K provides with these models and data, Fig. 2 shows, for each municipality, the expected values of: (a) unusable and (b) collapsed buildings (values are per 100 buildings), and the expected value of (c) injuries and (d) fatalities (both per 100 residents), on the basis of the OEF-Italy data of Fig. 1. Indeed, these results are the losses forecasted for the week after the OEF rates’ release (00:00 on 06/04/09), and the same weekly horizon will be maintained for all results shown in the following sections of the paper.

Fig. 2
figure 2

Illustrative example of MANTIS-K outputs: maps of the expected values of a unusable and b collapsed buildings (per 100 municipality buildings), and the expected values of c injuries and d fatalities per 100 municipality residents. These results are computed using the OEF-Italy data of Fig. 1 as the input. Therefore they refer to the week after 00:00 of 06/04/09

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The previous equations may be considered as site-specific risk measures as they apply to municipalities; however, they can be summed over an area of interest to compute total expected losses.

3 Considered Italian seismic sequences

From 2004 to 2014 more than two-hundred M 4.0+ events occurred in Italy (i.e., in a geographic area identified by 35.0–48.0°N latitude and 6.0–19.0°E longitude).Footnote 2 Epicentral locations of these events are plotted in Fig. 3; the size of each circle is proportional to the magnitude and the colour relates to the date of the event. Earthquakes with the largest magnitude identify three seismic sequences named L’Aquila, Emilia and Garfagnana, due to the areas where they occurred (identified in the same figure). For each sequence, the epicentre of the largest magnitude event (i.e., the mainshock) is indicated as a star; these points are referred to as the centres of the corresponding seismic sequence hereafter.

Fig. 3
figure 3

Epicentres of M 4+ seismic events occurred from 01/01/04 to 31/12/14 and geographic areas considered for the three sequences analysed

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L’Aquila and Emilia sequences were characterised by significant losses in terms of structural damages and fatalities. The same did not happened in Garfagnana; however, during this sequence, the Italian civil protection system was in state of attention for the possible occurrence of damaging events, after a MW 5.1 earthquake. For this reason, the Garfagnana seismic sequence has been considered in the context of this study.

The retrospective analysis of each sequence consisted of the computation of the expected losses for the week following each day for which forecasted seismicity was available by OEF-Italy. In the following, each seismic sequence is presented first and the rates computed by OEF-Italy are reported as a function of time and summed up over the point-like sources within 30 km from the centre of the sequence, to get a sense of the forecasted seismicity in the area. Then, the evolution of some indices of seismic losses from MANTIS-K are reported and compared among sequences. Finally, a discussion with respect to the observed consequences is given.

The considered risk metrics, computed by MANTIS-K for each municipality, are the expected values in 1 week of: (1) fatalities and (2) displaced residents, (3) unusable and (4) collapsed dwelling buildings. Results are reported as the expected value of total loss within four areas identified by the maximum distance (10, 30, 50 and 70 km) from the epicentre of the mainshockFootnote 3; see Fig. 4b. For the sake of presentation, arbitrarily, a time window spanning 3 months before and 1 year after the mainshock is considered.

Fig. 4
figure 4

Geographic representation of the mainshock epicentre together with a the grid of the point-like seismic sources according to OEF-Italy and b the centroids of municipalities within 70 km from the epicentre

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3.1 L’Aquila 2009

The main event of L’Aquila sequence, moment magnitude (MW) 6.1, struck on the 6th of April 2009; it produced a maximum observed peak ground acceleration (PGA) equal to 644 cm/s2 (e.g., Chioccarelli et al. 2009; Dolce and Di Bucci 2015). In the area identified by 41.8–42.8°N latitude and 12.6–14.1°E longitude (red square in Fig. 1), a single M 4+ event occurred before the mainshock since the 1st of January 2009, that is, the MW 4.0 on the 30th of March 2009. In the same area and period, there were 29 M 2.5+ events and 10 M 3.0+. On the other hand, the aftershock sequence was characterised by 8 M 4.5+ earthquakes, reported in Table 1 (along with mainshock data), and more than 300 events M 2.5+ in the 24 h after the mainshock.

Table 1 M 4.5+ aftershocks in a geographic area within latitude 41.8°–42.8° and longitude 12.6°–14.1° (mainshock in bold)
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The geographic area affected by the sequence is reported in Fig. 4a, b; both panels show boundaries of municipalities and the mainshock epicentre (represented by a star). Figure 4a displays the grid of point-like seismic sources, the OEF-Italy system assigns earthquake rates to. Figure 4b reports the centroids of each municipality for which loss indices are computed together with contours of the distance from the epicentre of the mainshock, R.

In order to provide a synthetic representation of the forecasted seismicity during the whole sequence, the values of seismic rates provided by OEF-Italy, for each point-like source within 30 km from the epicentre of the mainshock (see Fig. 4a), are summed up and plotted in Fig. 5 as a function of the day in which rates were released by the INGV system. In the same figure, the dates of occurrence of all MW 4.2+ events are also reported with dotted vertical lines. It is to note that the event rates during the seismic crisis are two orders of magnitude larger than those computed at the beginning of 2009. It is also to underline that the maximum is on the day after the mainshock of the sequence; this is a feature of the OEF-Italy system according to which the rates peak right after the maximum seismic moment release (Marzocchi and Lombardi 2009). Similarly, a significant increment of forecasted rates can be identified after all the strong events of the sequence. In fact, although discussion of pro and cons of OEF is out of the scope of this paper, it has to be anticipated that trend of the seismic loss estimates from the MANTIS-K system reflect the trend in time of OEF-Italy rates.

Fig. 5
figure 5

Sum of the following week’s (with respect to the date in the abscissa) rates of M 4+ events within 30 km from the centre of the sequence, and dates of M 4.2+ events occurred in the area of Fig. 1 (see also Table 1 for date of each event). In the picture, M refers to moment magnitude MW

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Figure 6a shows the evolution of the expected number of total fatalities, for municipalities within 10, 30, 50 and 70 km from the epicentre of the mainshock (see Fig. 4 for the identification of such municipalities).

Fig. 6
figure 6

Expected number of a fatalities and b displaced residents in the week following the date in the abscissa, summed over all municipalities within 10, 30, 50 and 70 km from the centre of the sequence

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At the beginning of 2009 the expected value of fatalities in 1 week is lower than one for the whole area considered around the centre of the sequence (i.e., about 0.22 for R < 70 km on 01/01/2009). Five days before the mainshock, the trend of loss shows some increments (due to the MW 4.0 event on the 30th of March) and the expected fatalities for the week after 06/04/09 are about 0.64 within 70 km. Results change right after the mainshock, when the expected number of total fatalities becomes larger than one; i.e., 3.7, 6.5, 11.1 and 15.5 for radii of 10, 30, 50 and 70 km, respectively.Footnote 4 One year after the mainshock, the maximum value of the expected number of fatalities is around 0.4 that is comparable with the reported value computed at the beginning of 2009; i.e., the sequence seems have come to an end.

Figure 6b shows the expected number of total displaced residents. The maximum value is equal to 1452.5 within 70 km from the epicentre of the mainshock (940.1, 493.4 and 259.8 for radii in descending order).

3.2 Emilia 2012

The prominent magnitude event of the sequence, the mainshock, is the MW 5.8 occurred on the 20th of May 2012 (see also Iervolino et al. 2012). The aftershock sequence, until the end of May 2013, and in the box identified by 44.5–45.5°N latitude and 10.5–12.0°E longitude (see also Fig. 1), includes 13 M 4.5+ events reported in Table 2 (data from ISIDe, last accessed 20/07/15). The (first) mainshock and the MW 5.6 event on the 29th of May (sometimes referred to as second mainshock; e.g., Dolce and Di Bucci 2015) were felt in the whole Northern Italy. (Dates in Table 2 show a difference with respect to the case of L’Aquila. Indeed, most of the largest magnitude events occurred few hours after the two mainshocks.) The recorded largest (corrected) horizontal PGAs are about 259 and 495 cm/s2 for the 5.8 and 5.6 MW event, respectively.Footnote 5

Table 2 M 4.5+ earthquake in a geographic area within latitude 44.5°–45.5° and longitude 10.5°–12.0° (mainshocks in bold)
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Following the first strong event, on the 22nd of May, the Italian government declared the emergency for the provinces of Modena, Ferrara, Bologna and Mantova. On the 30th of May, after the MW 5.6 event, the state of emergency was extended to the provinces of Reggio Emilia and Rovigo.

Similarly to L’Aquila, Fig. 7a shows the point-like seismic sources in the area of interest, identifying those within 30 km from the epicentre of the mainshock; Fig. 7b displays the centroids of municipalities within the four boundaries presented results refer to; i.e., radii lower than 10, 30, 50 and 70 km.

Fig. 7
figure 7

Geographic representation of the mainshock epicentre together with a the grid of the point-like seismic sources according to OEF-Italy and b the centroids of municipalities within 70 km from the epicentre

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The distribution in time of the main aftershocks, clustered in the few days after the mainshock, is reflected by the evolution of forecasted seismic rates (Fig. 8) that has a regular trend decreasing with the increasing time after the MW 5.6 event. It is to note that maximum forecasted seismicity corresponds to the day after the second mainshock that has, in fact, a magnitude lower than the first one.

Fig. 8
figure 8

Sum of the following week’s (with respect to the date in the abscissa) rates of M 4+ events within 30 km from the centre of the sequence, and dates of main events occurred in the area

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Figure 9 shows the expected values of fatalities and unusable buildings in the time interval of Fig. 8. Expected number of fatalities for the week after 00:00 of 20/05/12 (i.e., right before the mainshock) are 0.1, 0.5, 0.9 and 1.2 for the municipalities within radii of 10, 30, 50 and 70 km from the centre, respectively. The same estimates right after the mainshock (i.e., for the week after 21/05/12) become 2.6, 12.3, 23.8 and 29.7, respectively. For the week after 29/05/12, values are about 1.1, 4.8, 8.9 and 11.1 and become 2.5, 16.0, 31.2 and 39.5, after the MW 5.6. In the same period, the largest numbers of expected unusable buildings are 36.9, 232.9, 471.9 and 639.0.

Fig. 9
figure 9

Expected number of a fatalities and b unusable buildings in the week following the date in the abscissa, summed over all municipalities within 10, 30, 50 and 70 km from the centre of the sequence

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3.3 Garfagnana 2013

The mainshock of this sequence was the MW 5.1 on the 21st of June 2013 and, consistent with previous cases, the considered time window extends to about 1 year after this date. However, on the 25th of January 2013, a MW 4.8 struck in the same area (identified in Fig. 1; 43.5–44.5°N and 9.5–11.0°E). Thus, available data were analysed starting from about 3 months before this event; i.e., from the 1st of November 2012.

From November 2012 to the mainshock, 20 M 2.5+ earthquakes stroke in the area; among these events, 6 had magnitude equal to or larger than 3.0, and 1 larger than 4.0 (the one of MW 4.8). In the 24 h after the mainshock, 12 earthquakes occurred in the area, all with magnitude between 3 and 4. The subsequent event with M equal to 4.5 occurred on the 30th of June 2013. Table 3 shows the five events with M equal to or larger than four in the considered area and time interval.

Table 3 M 4.0+ earthquake in a geographic area within latitude 43.5°–44.5° and longitude 9.5°–11.0° (mainshock in bold)
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During the sequence, someone claimed similarities with respect to seismic events preceding L’Aquila mainshock (authors are not aware of scientific studies supporting such a similarity). In fact, the sequence focalised the attention of mass media and the worries of residents, and the Italian civil protection department was constantly in state of attention.Footnote 6

The point-like seismic sources within 30 km from the epicentre of the mainshock are reported in Fig. 10a while centroids of municipalities and boundaries of interest are shown in Fig. 10b. The evolution of the sum OEF rates within 30 km from the epicentre of the mainshock is clearly affected by the two largest magnitude events as reported in Fig. 11a.

Fig. 10
figure 10

Geographic representation of the mainshock epicentre together with a the grid of the point-like seismic sources according to OEF-Italy and b the centroids of municipalities within 70 km from the epicentre

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Fig. 11
figure 11

a Sum of the following week’s (with respect to the date in the abscissa) rates of M 4+ events within 30 km from the centre of the sequence, and dates of main events occurred in the area; b weekly expected number of fatalities summed over all municipalities within 10, 30, 50 and 70 km from the centre of the sequence

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Expected values of fatalities are reported in Fig. 11b. For the week after 25th of January 2013, loss estimates are lower than one (0.2 within 70 km form the centre of the sequence). For the week after 26/01/13, the same estimation becomes about 1.4 and decreases in the subsequent days with a regular path. A peculiar trend can be identified in the 6 days before the mainshock: about 0.3 is the expected number of fatalities within 70 km for the week after 21/06/13 (i.e., right before the mainshock), and it becomes 4.1 for the week after the day of the mainshock.

3.4 Sequences’ comparison

Figure 12 shows, for the three analysed sequences, (a) the sum of the weekly rates of M 4+ events within 70 km from the centre of the shock and (b) the weekly expected fatalities in the same areas. In the figure, for the sake of comparison, the days of the mainshocks are coincident and the chosen time window goes from 100 days before to 50 days after the mainshock.

Fig. 12
figure 12

a Sum of the following week’s (with respect to the time in the abscissa) rates of M 4+ events within 70 km from the centre of each sequence; b weekly expected number of fatalities within 70 km from the centre of each sequence

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The comparison between Fig. 12a, b underlines, once again, that the results of MANTIS-K are more informative than those of OEF, because it accounts not only for hazard but also for vulnerability and exposure. Indeed, in the whole considered time-window before the mainshock, seismic rates for L’Aquila are larger than those for Garfagnana and Emilia (in this latter case the rates are the lowest). Conversely, the expected fatalities for L’Aquila and Garfagnana are comparable, while the largest are associated to the Emilia sequence.Footnote 7 Similarly, after the mainshock, the seismicity rates for L’Aquila and Emilia are comparable, and both higher than Garfagnana. On the other hand, the expected losses for Emilia are significantly higher than those expected in L’Aquila, and the expected losses in Garfagnana are lower than those of the other sequences. Considering only the 7 days before the mainshock, it is also interesting to note that L’Aquila shows some increment of expected losses with respect to previous weeks, while the Emilia shows significant expected loss variations only since the day before the mainshock, Fig. 12b. This trend can be also identified in terms of seismic rates (Fig. 12a).

3.5 Observed losses and the meaning of OELF results

In this section the consequences observed in the analysed earthquakes are reported (see Dolce and Di Bucci 2015, for details). Indeed, it is believed appropriate to discuss the losses produced in the seismic sequences to better understand the intrinsic meaning of OELF and the current features and/or limitations of MANTIS-K.

For what concerns L’Aquila, 308 total fatalities were counted. Approximately 34,000 buildings failed or resulted unusable, at least 1500 residents were injured and more than 65,000 were temporarily displaced. During the Emilia sequence the number of dwelling buildings declared unusable after a survey was in the order of 15,000. Fatalities reported are 26, 7 of which are due to the mainshock on the 20th of May, and 19 to the second event on the 29th of May. Finally, in the Garfagnana sequence, no significant damage or injuries were observed.

Even if OELF provides losses’ predictions, there is a number of reasons why direct comparison of the observed consequences with the results of OELF, if not inappropriate, requires at least particular caution. First of all, OELF provides weekly expected values. In statistical terms, the expected value is the limit of the arithmetic mean over a virtually infinite number of nominally equivalent trials. In this respect, the observed losses are individual realizations only, which do not allow validation (see also Iervolino 2013, for a discussion of similar issues). It is also to note that OELF, by nature of the OEF models providing the input rates, provides the largest expected losses only after the strongest event of the sequence, while a significant portion of the consequences observed is due to the main events (e.g., in the L’Aquila case).

In addition to this basic discussion of the meaning of OELF, it has to be recalled that at this stage there are some features/limitations of MANTIS-K, which are relevant to the analysis of the observed losses. For example, most of the fatalities occurred during the Emilia sequence were in industrial buildings and not in residential buildings, which are those at the basis of damage vulnerability matrices and exposure data. Moreover, it is to also underline that MANTIS-K does not account for damage accumulation. Although it is something feasible to consider, it is not yet implemented, while it may be relevant to sequences with multiple potentially-damaging events, such as the Emilia one. In these cases, the vulnerability of the building stock varies during the sequence (e.g., Iervolino et al. 2014b, 2015b). Finally, also exposure may vary singificantly in a sequence featuring at least one damaging event, due to precautionary evacuations; e.g., L’Aquila. Also this issue could be accounted for in the MANTIS-K approach, yet it is something not yet in place.

4 Conclusions

The study focused on a retrospective analysis of three Italian seismic sequences through the recently developed MANTIS-K system for short-term earthquake loss forecasting. Indeed, seismicity rates estimated by the OEF-Italy system are the input data for MANTIS-K that, performing a probabilistic analysis, is able to convert them into weekly estimates of seismic losses (e.g., expected values of fatalities, displaced residents, and damaged buildings), using vulnerability and exposure data and models at the municipality scale for Italy.

The seismic sequences, chosen for the critical analysis of OELF, are L’Aquila (2009), Emilia (2012) and Garfagnana (2013), which include the main earthquakes occurred in Italy from 2004 to 2014. For each sequence, risk measures for areas characterised by different values of radius from the mainshock epicentre (10, 30, 50 and 70 km) were considered. It was observed that the trends of forecasted losses are, as expected, strongly influenced by OEF input data. In particular, due to the features of the OEF-Italy system, the largest increments of the expected losses are always right after the maximum seismic moment release (i.e., for the week after the largest events in the sequence).

A discussion of the observed losses allowed to discuss the meaning of the OELF predictions as well as the current features and/or limitations of the MANTIS-K system. In fact, the statistical interpretation of the expected loss was recalled. Moreover, the cases of the L’Aquila and the Emilia sequences allowed to point out that during seismic sequence with one or more damaging events, damage accumulation in the building stock and precautionary evacuations, may lead to short-term variations of vulnerability and exposure that may affect the expected losses, yet are not accounted for at this stage. Finally, MANTIS-K relies on dwelling building exposure, not suitable to reflect peculiar structural typologies, which may also affect the losses, as observed, for example, with precast industrial buildings in the Emilia sequence.

Even with the discussed issues and limitations, it is believed that OELF implemented in the MANTIS-K system is a step in the direction of rational decision making for risk management during seismic sequences due to its quantitative approach, and it is certainly more informative than OEF alone.