Scenario-based seismic hazard for horizontal and vertical ground motions in central Italy

Abstract

We propose an innovative methodology for seismic emergency planning and earthquake risk mitigation in central Italy by integrating three prototypal earthquake scenarios. The different scenarios derive maximum earthquake magnitudes from different input data. The first scenario utilizes local rheological, geological, and geophysical conditions; the second scenario considers the study area fault characteristics, while the third scenario relies on the cluster analysis of historical and instrumental earthquake records. The magnitudes and related uncertainties are combined using a conflation method to derive the expected ground motions for a grid of sites in central Italy. The resulting scenarios include peak ground acceleration and spectral ordinates, presented as maps and spectra for two selected localities. The vertical component of ground motion is also presented, because it is essential for accurately assessing the response of short-period structures. Our methodology complements the more classic seismic hazard analyses, offering additional insights for earthquake contingency planning and loss analysis. The proposed methodology is flexible; multiple models and ongoing advancements in scenario practice (near-field effects, vertical ground motion, and the choice of ground motion models) can be easily incorporated, increasing the effectiveness of seismic scenario modeling in seismic emergency planning and risk mitigation.

1 Introduction

The approach of an earthquake scenario is based on the occurrence of a potential future earthquake of a particular magnitude, location, and fault-rupture geometry that results in a certain shaking level. Scenarios are commonly used to better plan seismic risk mitigation (e.g., Earthquake Engineering Research Institute 2006) and in seismic urgent computing (Stallone et al. 2024). In the simplest form, a scenario provides a means to visualize the potential impacts of defined earthquakes on society and critical infrastructure (e.g., Bordoni et al. 2023; Zuccolo et al. 2011), aiding decision-makers in assessing specific impacts based on currently accepted scientific knowledge (including social, economic and environmental science) and engineering principles. In this sense, scenarios constitute the basis for applications targeting the analysis of liquefaction or landslide triggering. For example, Lee et al. (2008) proposed a methodology to use earthquake intensity as a landslide-triggering factor. Rodríguez-Peces et al. (2020) successfully tested many earthquake-induced landslide hazard maps against observing landslides triggered by the 2011 Lorca earthquake. The impact of earthquake scenarios and geotechnical parameters of landslides and reservoirs was recently analyzed by Kohler et al. (2023). The authors applied a numerical technique to model the landslide response to earthquakes. First, some recorded earthquake signals were used to validate the model for low-magnitude events. Then, they investigated more severe scenarios, obtaining negative rate effects in the shear zone, and a softening in the landslide mass was considered, which can cause a slope collapse and generate waves in the reservoir. Kohler et al. (2023) focused on the wide range of co-seismic displacement for different modeled scenarios. They emphasized the importance of adequately assessing rate effects in the shear zone, pointing out that investigating the highest potential scenarios is mandatory to properly establish the landslide movement and the height of the generated waves. In the case of Seismic Urgent Computing, time-sensitive simulations quickly assess the potential hazards of an earthquake immediately after it occurs. This information is crucial for local authorities and disaster risk managers to minimize casualties, coordinate rescue operations, and reduce financial losses.

Scenarios allow for testing response, relief, and recovery strategies, enhancing our understanding of community vulnerabilities, which often become apparent during catastrophic events. As an example, De Natale et al. (2019) estimated the number of victims for an earthquake scenario using the information on damaged and collapsed buildings compiled after the Mw = 4.26 (epicentral macroseismic intensity Io = 9–10) 1883 Ischia (Italy) earthquake. Despite advancements in building resilience compared to 1883, recent statistics still project highly catastrophic scenarios. Victims estimates range from several hundred to over 1300, underscoring the gravity of potential consequences. This study highlights the importance of scenario-based risk assessment for its mitigation. A scenario projects performance levels of buildings and structures under different design codes and policies, with the ultimate goal of reducing earthquake risk. In this sense, Calvi et al. (2021) proposed a method for determining the average expected annual loss, which considers both direct and indirect losses. The study shows indirect losses resulting from downtime/disruption could be more significant than the corresponding direct loss. For example, in the event of a building collapse, the most apparent form of indirect loss is the cost of relocating the occupants, which is in the same range as the cost for a total reconstruction in 730 days. Following the same approach, in the case of a bridge, the indirect losses of a 4-month interval of downtime are comparable to the entire cost of reconstruction.

In such an approach, scenarios allow us to evaluate the consequences of extreme and catastrophic earthquakes and support the decision-making process in the mitigative actions that could be taken. While a scenario is sometimes associated with “worst case” or “maximum magnitude” events, there are various approaches to building it, most developed for nuclear power plants or critical infrastructures. One example is given by the United States Nuclear Regulatory Commission Regulatory Guide procedure (U.S. Nuclear Regulatory Commission 2007), which involves a de-aggregation of the probabilistic seismic hazard into earthquake magnitudes and distances. The U.S. NRC Regulatory Guide procedure includes steps, such as (a) performing site-specific PSHA (a lower bound magnitude of 5.0 is recommended) and evaluating mean, median, and percentiles for peak ground acceleration and different frequencies; (b) evaluating ground motion levels for different spectral accelerations from the total median hazard and calculate the average of the ground motion level for different spectral acceleration pairs; (c) disaggregating results for the median annual probability of exceeding the ground motion levels for magnitude–distance bins; (d) determining the controlling earthquake; (e) and finally establishing the safe shutdown earthquakes response spectrum. The Japan Atomic Energy Research Institute developed a second disaggregation-based approach (Ishikawa and Kameda 1991). This procedure uses the source contribution factors to identify influential earthquake sources or fault(s) and determine one or more earthquake scenarios. Like these approaches, also Kastelic et al. (2016), Scotti et al. (2021) and Valentini et al. (2019), for example, calculate the source contribution factors for fault-based probabilistic seismic hazard models for different sites and input data.

In contrast, France follows a deterministic methodology outlined in the French Safety Rule (https://www.french-nuclear-safety.fr/asn-regulates/safety-rules) to evaluate the seismic input motion in the nuclear power plant framework. This approach, published in 1981 and revised in 2001, involves seven main steps: (i) seismotectonic zonation; (ii) estimating the characteristics of the historical and instrumental events that occurred in each zone, (iii) selecting one or more events, that produce the most penalizing effect (in term of intensity at the site), (iv) associating a safe shutdown earthquake with each maximum historically probable earthquake (increasing their magnitude by 0.5), (v) evaluating the seismic movement (mean acceleration response spectra), related to the safe shutdown earthquake, using the attenuation relationship developed by Berge-Thierry et al. (2004), (vi) assessing paleoseismic evidence if available, and (vii) compare the seismic motion with the safe shutdown earthquake motion.

Finally, the so-called neo-deterministic approach (Magrin et al. 2017; Panza and Bela 2020; Panza et al. 2021) is a further scenario-based modeling technique integrating the available knowledge on seismic source process, the propagation of earthquake waves, and their combined interactions with site conditions.

A specific scenario-based model responds to the parameterization of a few data; here, we propose an ensemble of models to capture epistemic uncertainty related to a single scenario. In particular, we focused on the magnitude estimation from three different approaches based on empirically derived estimates in the central Apennines (Italy) (Fig. 1). The magnitudes from all scenarios are then aggregated to produce an ensemble model, which is used to estimate the ground shaking for a grid of sites.

Fig. 1

Red polygon shows the location map of the study area. The cross section from Corsica to the Adriatic Sea in the lower panel, modified after (Carminati and Doglioni 2012), is slightly north of the investigated area. Most of the seismicity (black dots) is concentrated in the Apennines range, where extensional tectonics dominates, apart from local transfer strike–slip faults. The contraction is confined to the eastern side of the belt and in the Adriatic Sea. The seismicity illuminates the shallow downgoing of the Adriatic lithospheric slab (color figure online)

We opted for a grid-based approach in the present study, assuming that any part of the study area is defined as the zone where the largest shaking is expected (epicentral area). This choice derives from several lines of evidence: Petricca et al. (2021) scrutinized seismic ground motion of different earthquakes and determined that the most intense shaking occurs at InSAR-derived maximum ground deformation, where the vertical-to-horizontal PGA ratios are the highest. These findings are in line with the significant damages reported from previous events (Ambraseys and Douglas 2003; Iervolino et al. 2021; Petricca et al. 2021) and the greater strength of vertical and horizontal ground motions due to proximity to the source (Ambraseys and Douglas 2003). In detail, the maximum vertical spectral response can exceed the horizontal response at very short periods (0.15 s). However, this ratio diminishes rapidly as the period lengthens, stabilizing at around 0.5 for longer periods. To consider the impact of near-source and the vertical ground shaking response, we utilized the empirical Ground Motion Prediction Models (GMM) developed by Lanzano et al. (2020) and the vertical-to-horizontal response spectral amplitudes proposed by Ramadan et al. (2021), which includes an adjustment term to enhance the predictive capability in near-source scenarios. We apply the method to central Italy and provide maps and spectra presenting the percentiles of ground shaking. The proposed seismic hazard calculation technique suggests quantifying the most significant ground shaking within the epicentral area, which is the fundamental information for saving lives and reducing economic losses, especially for public infrastructures.

2 The seismotectonic setting of central Italy

The seismotectonic setting makes the Apennines chain in central Italy one of the most seismically active areas in Europe (Chiarabba et al. 2005), with the occurrence of four earthquake sequences Mw > 5.9 since 1997, Mw = 5.97 Colfiorito 1997–98, Mw = 6.29 L’Aquila 2009, Mw = 6.09 Emilia 2012, and Amatrice–Norcia 2016–17 (Rovida et al. 2020). Decades of works on surface geology and stratigraphy, the availability of an extensive dataset of seismic reflection profiles (e.g., Scrocca et al. 2003; Videpi Project 2009) and high-resolution seismic data (Chiarabba et al. 2009, 2014; Chiaraluce et al. 2003, 2017; Improta et al. 2019; Waldhauser et al. 2021) allow extensive understanding of the central Mediterranean geodynamics (e.g., Carminati and Doglioni 2012). From the Eocene–Oligocene to the present day, the central-northern Apennines have experienced two phases of eastward migrating deformation: an early compression with eastward-directed thrusting and a following extensional tectonic setting, with 4–6 km spaced normal faults cross-cutting previous thrusts and folds of the accretionary wedge (Doglioni 1991). Compressional tectonics is now active along the Adriatic coast and its offshore and the Po Plain, whereas active extension is located along the axial zone of the Apennines (e.g., Devoti et al. 2017; Montone and Mariucci 2016). Over 20 years of GNSS measurements show a general agreement between present-day observations with the stretching between the Tyrrhenian and Adriatic coastlines of about 4–5 mm/year (Carafa et al. 2020; Devoti et al. 2017) and the long-term geodynamics governed by the shear stresses applied at the base of the lithosphere (Carminati and Doglioni 2012; Barba et al. 2008; Carafa et al. 2015). Present-day compressional rates are 2–3 mm/year and distributed between the outermost Apennines and External Dinarides (Kastelic and Carafa 2012; Devoti et al. 2017).

The extension in the Apennines is accommodated by diffuse faulting in the brittle portion of the Apennines crust and viscous deformation at greater depths (> 10–15 km), being the brittle–ductile transition (BDT) shallowing toward the west, e.g., toward the Tyrrhenian side (Carafa et al. 2020). The partitioning of the upper-crustal long-term extension is split among SW-dipping Pleistocene extensional faults and inherited structures. In the past decades, several compilations of Pleistocene–Holocene active faults have been published (e.g., Carafa et al. 2022; Faure Walker et al. 2021 and references therein) mainly relying on their long-term geomorphic expression/structure/characteristics, such as half-graben intermontane basins, dislocated breccias, or cumulated offset since the Last Glacial Maximum. However, the reactivation of Mesozoic normal faults and Miocene–Pliocene thrusts cannot be excluded if favorably oriented in the current stress field (Porreca et al. 2020).

The outermost Apennines are currently undergoing compression accommodated by seismogenic faulting in the shallower 20–25 km along the Adriatic coast and offshore range (Petricca et al. 2019). De Nardis et al. (2022) and Lavecchia et al. (2007) have also studied the hierarchic structure of the compressional front, articulated in two significant arcs, the Padan–Adriatic (in central-northern Italy) and Sicilian–Ionian ones (in southern Italy), which are divided into a series of second-order arcs, with the Adriatic Basal Thrust that is part of the Padan–Adriatic one. Recently, Ferrarini et al. (2022) confirmed the late Quaternary active shortening hypothesis in the Abruzzo and Molise regions by exploiting a combined relief, fluvial network, and late Quaternary landform analysis to highlight evidence of uplift consistent with compressional tectonics. Their results show localized uplift along the Abruzzo Adriatic piedmont and its inner foothill sector, whereas no clear evidence of uplift was observed in the Molise region (Fig. 1). Rheological modeling of the study area showed a complex feature (Carafa and Barba 2011; Lavecchia et al. 2007). Moving from east to west, Carafa and Barba (2011) and Petricca et al. (2015) found a progressively shallower BDT transition in the crust and a sharp variation in the strength; the upper plate region showed a weak mantle, with a “crème brûlée”-like behavior, whereas the forearc showed higher strength, especially in the lithospheric mantle. Lavecchia et al. (2007) identified a rheological stratification of the lithosphere, which controls the location of the seismic activity at different depth intervals along the fault plane: 0–10 km, 15–25 km, and 35–45 km. The evidence of two geographically distinct depth ranges for the thrust-related seismicity has led to identifying two broad seismotectonic provinces (e.g., Lavecchia et al. 2007), each of relatively homogenous deformation, referred to as Shallow and Deep contractional provinces. According to the above description of the rheological stratification, the Shallow Province extends from the Adriatic Basal Thrust near-surface trace to 10 km depth. In contrast, the Deep Province extends from 15 to 25 km within the Apennine Foothills, as evidenced by the shallower part of the subducting Adriatic plate. In addition, the subordinate right-lateral fault system runs ca. E–W across the foreland in the western and southern part of the study area, as documented by focal mechanisms and local stress data (Pondrelli et al. 2020; Mariucci and Montone 2020).

3 Seismic source characterization

We used a grid-based modeling method to estimate the scenario magnitude. We set up a grid of points spaced by 0.1° × 0.1° in latitude and longitude (study area is ~ 210 km × 260 km). For each point, first, we model the magnitudes associated with three different prototypal scenarios based on our current understanding of rheology, seismotectonics, and earthquake occurrence in central Italy. Then, each scenario magnitude is assigned a uniform probability and weighting in the ensemble model. Finally, we use it to calculate distributions of expected ground motions for a list of sites corresponding to the same grid of points. The three scenarios are described below.

3.1 Modeled earthquake scenarios #1

Model #1 is based on the work of Petricca et al. (2022), which calculated the seismic brittle volume considering fault kinematics and rock rheology, particularly the brittle–ductile transition depth. They show that the rheology of a region gives hints on the volumes that can be mobilized during an earthquake, hence on the maximum magnitude and its hypocenter depth. In model #1, we created smooth surfaces from the scatter data (magnitudes and depths) of Petricca et al. (2022). The resulting magnitudes in the study area are ~ 6.3–~ 7 for thrust faulting, ~ 5.8–~ 7.3 for normal faulting, and ~ 6.6 for strike–slip faulting. The magnitude and kinematics of each point of the grid of model #1 are shown in Fig. 2 and given in Supplement A.

Fig. 2

Maps of magnitude estimations and kinematics for the three models. All values are given in Supplement A

3.2 Modeled earthquake scenarios #2

Based on available seismotectonic characterization of the study area (Lavecchia et al. 2007; Ferrarini et al. 2022; Visini et al. 2021), we map three major areas with different faulting characteristics from west to east: a western extensional area, a coastal compressional area, and an eastern compressional area. We also mapped a small area characterized by strike–slip faulting, located in the southernmost part of the study area (actually, it is only one point in the study area). The seismicity cutoff depth for the compressional area is delimited in the 15–25 km depth range in the coastal area and between 0 and 10 km for the easternmost part (De Nardis et al. 2022). We first compute the seismogenic thickness (Z) by calculating the difference between upper and lower seismogenic depths to determine the magnitude at each grid point. Then, using the fault dip angles provided by Petricca et al. (2022), we calculate the width (W) for a hypothetical fault rupturing the entire brittle layer with a dip angle (α):

$$W = \frac{Z}{\text{sin}(\alpha )}.$$

(1)

Considering the coefficients for the aspect ratio from Leonard (2010, 2012), according to the style-of-faulting of each grid point (C1 = 1.7 for dip–slip; C1 = 1.5 for strike–slip), we calculate the length and the area of each hypothetical fault:

$$L= {\left(\frac{W}{C1}\right)}^{1.5}.$$

(2)

Finally, we derive the magnitudes for dip–slip and strike–slip faulting classes, as Leonard (2010, 2012) defined in the area–magnitude relationship

$${m}_{w}=b\text{log}\left(LW\right)+a,$$

(3)

using b = 1, a = 4.0 for dip–slip and a = 3.99 for strike–slip and a standard deviation of 0.3 (after simplifying the one standard deviation range of a, which is 3.73–4.33).

The mean of the calculated magnitudes is 6.75 for thrust faulting, 6.7 for strike–slip faulting, and a range between 6.4 and 6.9 for normal faulting. Figure 2 shows the magnitudes and the kinematics of each point of model #2. Values are also given in Supplement A.

3.3 Modeled earthquake scenario #3

Model #3 is based on historical and instrumental earthquake records from the Catalogo Parametrico dei Terremoti Italiani (CPTI15; Rovida et al. 2020, 2022). According to Gerstenberger et al. (2020), we assume that future seismicity will be like the past one for the location, magnitude range, and rate. Several lines of evidence of plate tectonics verify this assumption well. Among the others, paleoseismological studies report repeated earthquakes for thousands of faults, and satellite geodesy certifies that crustal volumes close to the active faults along plate boundaries undergo the highest deformation rates.

To this aim, we first estimate the magnitude associated with each grid point by assigning all earthquakes with a distance lesser or equal to 5 km to each grid point. Next, we identify the earthquake with the highest magnitude from this subset of earthquakes. Successively, using tectonic parameters of points of the grid, such as seismogenic layer and kinematics, taken from model #2, we construct agglomerative clusters of the grid points, ensuring that each grid point is associated with a specific cluster. For each cluster, we identify the maximum observed magnitude among the highest magnitudes of the points of the cluster. We selected the most recent cases of multiple earthquakes having the same (highest) magnitude. With this approach, an earthquake could be associated with more than a cluster. However, this should be reasonably accepted considering the uncertainty in the earthquake location.

It is important to note that there could be discrepancies between a grid-based approach and the methodology of model #3. Specifically, associating earthquakes with a single cell without clustering could result in a scattered map, where each cell is represented by the highest magnitude earthquake whose epicenter is located within it. The methodology proposed here aims to address this issue inherent in gridding: cells adjacent to those with a significant earthquake, such as the Mw 7.1 epicenter of the 1915 earthquake, have the potential to experience similar seismic events given comparable tectonic and rheological conditions. However, it is also important to note that the volume affected by an Mw 7 event, for example, exceeds the dimensions of a single cell. In addition, earthquake catalogs like CPTI15 are subject to uncertainties in both epicentral location and magnitude estimation, which complicates direct assignment. Our approach considers these uncertainties by spreading potential maximum magnitudes derived from CPTI15 over larger zones that could realistically generate seismic events.

The magnitude of uncertainties in model#3 is derived from the CPITI15 catalog. The calculated magnitudes range between 5.3 and 6.8 for thrust faulting and 5.8 and 7.1 for normal faulting. No earthquake results were associated with the strike–slip regime, so we arbitrarily assigned a maximum magnitude of 6.0. Figure 2 shows the magnitudes and kinematics for the grid points in model #3. Values are also given in Supplement A.

4 Ensemble earthquake scenario

As the final step, we merge the three different prototypal scenarios in the ensemble model for ground shaking calculation. The grid-point magnitudes and uncertainties of the ensemble model are calculated with the "conflation" method (Hill and Miller 2011). The conflation is defined as the distribution determined by the normalized product of the probability density or probability mass functions.

As a first step, we generate the probability distribution functions (PDF) for the magnitudes of each model at every grid point, assuming a normal distribution, where the mean is the magnitude value and the standard deviation is the corresponding uncertainty. We here used a normal distribution as there are no specific descriptions of the PDF of earthquake magnitudes; however, the use of different PDF could be implemented in future studies. Standard deviations for the magnitudes of the three models derive from empirical regressions. For model #1, which may have asymmetrical uncertainty around the central value in the dataset calculated by Petricca et al. (2022), the standard deviation is computed as the average of the upper and lower values; for model #2, the uncertainty derives from the empirical regression of Leonard (2010, 2012) and; for model #3, the standard deviation is listed for each earthquake in the CPTI15 (Rovida et al. 2020, 2022). Then, we calculate the PDFs and the Truncated PDF (TPDF) at three standard deviations for each distribution. Figure 3 provides examples of TPDF for two points (PT1 and PT2) of the grid. We chose these two examples to illustrate both the differences among the magnitudes estimated by the three original models and how they are combined to obtain the final model for magnitude.

Fig. 3

Examples of magnitude distributions and conflation for two points of the grid

We calculate the magnitude of the ensemble model with the following approach: given the distributions P1, P2,.., Pn of the variable y, with densities f₁(y), f_2(y),…, f_n(y), respectively (e.g., normal or exponential distributions), then the conflation, according to Hill and Miller (2011), yields a density for a value x of y expressed as

$$f\left(x\right)= \frac{{f}_{1}(x){f}_{2}(x){\dots f}_{n}(x)}{{\int }_{-}^{\infty }{f}_{1}(y){f}_{2}(y){\dots f}_{n}(y)dy},$$

(4)

where the denominator is not 0 or infinite. In Fig. 3, for the two selected points, we show the conflation for two magnitude distributions; the magnitudes obtained for the ensemble model are shown in Fig. 4. To note, comparing Figs. 2 and 4, none of the three models is, a priori, the highest or lowest. For PT1, for example, one could argue that the magnitude observed in the CPTI is not representative of the maximum potential magnitude or, vice versa, that the rheological and geological information are not sufficiently accurate to best estimate the maximum magnitude. On the other hand, PT2 could suggest that the magnitude of CPTI is affected by an unknown positive bias. Actually, ensembling the three models aims to manage these (and other) features to find an average estimate (and uncertainty) of the magnitude.

Fig. 4

Map of magnitude estimations for the ensemble model. Values are relative to the peaks of the distributions obtained using the conflation. All values are given in supplement A

5 Seismic hazard calculation

To generate the ruptures associated with each grid point, we adopt the fault-source typology provided by the OpenQuake Engine (Pagani et al. 2014). Ruptures of scenario earthquakes are constrained in terms of fault planes, requiring information on their 3D geometry, the hypocenter location, and magnitude. To determine the fault plane dimension for each grid point, we follow these steps: (i) calculate the area of the fault plane using appropriate coefficients of the empirical relationships of Leonard (2010, 2012), which depend on the style-of-faulting; (ii) calculate a width of the fault plane assuming a square rupture (Wsq_rup); (iii) calculate the width (Wmax) for a hypothetical fault that would rupture the entire brittle layer; (iv) calculate the length of the fault plane using the area and the minimum between Wsq_rup and Wmax; (v) impose a maximum length to an arbitrary aspect ratio (length divided by the minimum between Wsq_rup and Wmax) of 10.

Once the dimensions are calculated, we place the finite fault plane in the three-dimensional space as follows: (vi) for each point of the grid, we calculated the hypocenter depth to be 2/3 of the bottom of the seismogenic layer calculated for model #2, used as reference model for the seismogenic thickness; (vii) to find the center of the fault trace at the top of the seismogenic layer, starting from the hypocenter coordinates (longitude, latitude, and depth of the grid point), we project the hypocenter upwards according to the dip angle from Petricca et al. (2022): 35° for reverse, 55° for normal and 90° for strike–slip faults; (viii) from this point, we calculate the uppermost two tips of the fault plane using the semi-length calculated at point (iv) and a fixed strike value. According to the orientation of the SHmax from Carafa and Barba (2013) and to a gross average of the strike faults in central Italy, we used a strike of 140° for normal and reverse and 105° for the strike–slip faults; (ix) finally, using the width (the minimum between Wsq_rup and Wmax) calculated at point (iv), we derive the lowermost two tips of the fault plane. The rupture plane is then fully defined by its four vertices. Rupture planes, hypocentral coordinates, and magnitudes are given in Supplement #A.

To model the ground shaking from each of these ruptures in terms of PGA (in units of g) and spectral ordinates up to 4 s, we use OpenQuake software (Pagani et al. 2014) and the ground motion prediction model (ITA18) of Lanzano et al. (2020). ITA18 revisited the model initially developed by Bindi et al. (2011) for shallow crustal earthquakes in Italy (ITA10). Despite its overall satisfactory performance, evidenced by ITA10 being among the three selected GMMs in MPS19 after rigorous statistical evaluations (Meletti et al. 2021; Lanzano et al. 2020), ITA10 is nowadays subject to several limitations due to the constrained dataset available during its calibration in 2009. For example, ITA10 has a maximum magnitude of Mw 6.9 and a maximum period of 2 s for the GMPEs. Lanzano et al. (2020) presented the recalibration of the GMM for Italy, by conducting a regression analysis on a significantly broader dataset consisting of 5607 records from 146 events and 1657 stations. This expanded dataset encompasses regional and extensively sampled global events, extending the magnitude range. Due to the limitations mentioned above of ITA10 and the enhancements achieved through ITA18, this last model demonstrates the potential to increase the predictive capabilities of Bindi et al. (2011), particularly concerning horizontal ground motion. ITA18 is calibrated across a moment magnitude range of 4.0–8.0, distance range of 0–200 km, and event depths shallower than 30 km for 36 periods ranging from 0.04 to 10 s, as well as PGA and PGV. All these characteristics fit the overall structure of the proposed scenario well. It is worth noting that this study primarily aims to establish a methodological framework for addressing the challenge of generating magnitudes for scenario-based earthquake-shaking fields, incorporating various methodologies to handle epistemic uncertainties in magnitude estimations and spectral acceleration profiles. While the proposed methodology can accommodate combinations of different GMMs, including non-ergodic ones, such considerations on the impact of different GMMs lie beyond the scope of this work.

All the calculations are referred to rock conditions (Vs30 = 800 m/s). Moreover, for each earthquake rupture scenario, we use the GMM with associated aleatory variabilities, generating a set of n-intensity measurements (with n = 1000), and randomly sampling acceleration values within ± 3 sigma from the median of the GMM. It is worth noting that the scenario-based approach does not require the probability of occurrence for a specific rupture. It only needs information to parameterize the location, geometry, magnitude, and style of faulting of the rupture. This procedure allows us to derive a distribution of the shaking values.

Figure 5 illustrates the workflow of this process. For each simulated set of ground shaking resulting from the combination of rupture-GMM at a point of the grid and for each spectral acceleration (S.A.), we calculate percentiles of the distribution (Fig. 5a). Then, given that multiple scenarios contribute to the hazard at a single locality (e.g., at the same site, we have a set of percentiles given by various ruptures-GMM), we envelop each percentile by taking the maximum intensity measure level (IML) value from the different ruptures at each grid point (Fig. 5b). For example, given a vector v of IML corresponding to the 84th percentiles of the distributions at a site, due to v ruptures, we map the maximum value of v at that site. This procedure can be repeated for all the percentiles, however, following Bordoni et al (2023) we focused on the 84th and 90th percentiles.

Fig. 5

This sketch illustrates the distribution of simulated ground motion from a a single rupture (red rectangle in the upper panel) and b from multiple ruptures (red and blue rectangles in the lower panel). Empirical cumulative distributions are shown in the two panels on the right. In case of multiple faults (red and blue curves), we compare the percentiles of each distribution obtained for each site and consider the maximum value. IML intensity measure level (color figure online)

The methods described above allow for evaluating horizontal ground motion components. As for the vertical component, according to the Italian Building Code (NTC2018 2018) and Eurocode 8 (EC8 2004), it is only considered in limited cases, such as for base-isolated structures and specific building components with large spans. Nevertheless, it has been observed that the vertical ground motion can be significantly greater than horizontal motion, especially in the near-source region of earthquakes, particularly at periods shorter than 0.3 s. This point can have a significant impact on short-period structures. The non-marginal impact of vertical ground motion has been evident in recent seismic events, such as the Po Plain earthquake in 2012 (Carydis et al. 2012) and the Central Italy seismic sequences in 2016 (Fiorentino et al. 2018), where specific stations recorded high ratios of vertical-to-horizontal (V.H.) response spectral accelerations at short periods, reaching approximately 3 and 8, respectively, or during the recent 2023 Turkey earthquake (Baltzopoulos et al. 2023). Neglecting the vertical component can lead to unsafe design evaluations for critical facilities like low-rise buildings, masonry constructions, and long-span bridges. Liberatore et al. (2019) have shown that cyclic variations in axial loads can cause repetitive reductions in friction force, resulting in extensive failures in structures with low cohesion. In addition, Di Michele et al. (2020) have shown that fluctuations in axial load also strongly affect the flexural and shear capacity of masonry walls, especially in near-source records of large-magnitude events. The detrimental effect of vertical ground motion has also been observed in reinforced concrete precast/frame structures and bridge structures. We have also determined the vertical ground motion based on the implications above.

Following Ramadan et al. (2021), we calculate V.H. response spectral acceleration ratios to scale the median horizontal accelerations predicted by the GMM of Lanzano et al. (2020). Additionally, based on the observations of the worldwide NEar-Source Strong motion dataset (NESS), as described by Sgobba et al. (2021) and Ramadan et al. (2021) calibrated a correction factor for the proposed V.H. ratios to improve predictions in the near-source region. The V.H. response spectral acceleration ratios are a function of magnitude, style-of-faulting, distance, and Vs30. Therefore, we compute V.H. response spectral acceleration ratios for each grid point for each scenario. Supplement #B reports the calculated median V.H. spectra for all scenario earthquakes in computing the vertical ground motion.

6 Results

We present PGA and S.A. maps based on scenario simulations for a grid of sites in central Italy. All the simulations, distributions, and percentiles are provided in Supplement #C. Here, we summarize our results in PGA and S.A. maps for the 84th and 90th percentiles of PGA, S.A. 0.1 s, and S.A. 1 s.

Figure 6 illustrates the horizontal component of ground motion measures. The horizontal component of PGA exceeds 0.8 g and ~ 1 g (respectively, for the 84th and 90th percentiles) in the central part of the region and ranges between 0.5–0.7 g and 0.6–0.9 g in the western region. Areas along the eastern coast display PGA values around 0.6–0.7 g and 0.8–0.9 g. For S.A. at 0.1 s, we calculate values of 1.8–1.9 g and from 1.8 up to > 2 g in the central part. Values range between 1.2 and 1.6 g and from 1.9 up to > 2 g in the western region. Areas along the eastern coast display S.A. at 0.1 s values around 1.5–1.7 g and from 1.7 up to > 2 g. For S.A. at 1 s, we calculate values in the range 0.7–1 g and 0.8–1 g in the central part and the range 0.3–0.4 g and 0.3–0.5 g in the western region. Areas along the eastern coast display values around 0.5–0.7 g and 0.6–0.8 g.

Fig. 6

Maps of the horizontal component of ground motion for the envelope of the 84th and 90th percentiles of distributions for PGA, S.A. 0.1 s, and S.A. 1 s

Applying the previously described procedure to estimate the V.H. ratio, Fig. 7 presents maps for the 84th and 90th percentiles of vertical ground motion for PGA, S.A. 0.1 s, and S.A. 1 s. PGA values on rock exceed 0.6 g and 0.7 (respectively, for the 84th and 90th percentiles) in the central part and range between 0.3–0.5 g and 0.4–0.6 g in the western region. Areas along the eastern coast show PGA values around 0.4–0.5 g and 0.5–0.7 g. For S.A. 0.1 s, we calculate values that reach 1.9 and > 2 g in the central part and range between 0.9–1.2 g and 1.2–1.4 g in the western region. Areas along the eastern coast exhibit PGA values in the 1.2–1.6 g range and from 1.5 up to > 2 g. For S.A. 1 s, we compute values that reach 0.5 g and 0.5 g in the central part and range between 0.2–0.3 g and 0.2–0.4 g in the western region. Areas along the eastern coast show values around 0.2–0.3 g and 0.2–0.4 g.

Fig. 7

Maps of the vertical component of ground motion for the envelope of the 84th and 90th percentiles of distributions for PGA, S.A. 0.1 s, and S.A. 1 s

In Fig. 8, we also present the spectra calculated for two sites: one located approximately in the center of the extensional area (L’Aquila) and one (Chieti) close to the coast, in the compressional domain (kinematics is shown in Fig. 2d). For both localities, we show the horizontal and vertical components of the simulated ground motion percentiles (84th and 90th). Figure 8c provides the V.H. ratio. Values of the V.H. ratio close to or higher than one are calculated for periods at around 0.1 s. In contrast, values larger than 0.6 are obtained for periods longer than 1.2 s for L’Aquila and 2 s for Chieti. These results agree with the observation of Ramadan et al. (2021), showing that, for short periods (less than 0.1 s), the V.H. ratios show a strong dependence on distance with higher values, up to nearly 1.5, for near-source sites (< 15 km). Furthermore, the V.H. ratio for Chieti is slightly larger than that for L’Aquila. This aspect can be related to the correction factor for the style of faulting that introduces a stronger correlation with the focal mechanism, with larger V.H. ratios for reverse and strike–slip compared to normal faulting.

Fig. 8

a, b Horizontal and vertical components of the hazard spectra resulting in the envelope of the 84th and 90th percentiles of distributions. c Ratio of the horizontal and vertical components of the hazard spectra resulting in the envelope of the 50th, 84th, and 90th percentiles of distributions

7 Discussion

In scenario-based SHA, the hazard level primarily depends on the combination of earthquake magnitude and distance that results in the highest ground motion intensity for a fixed value of ε (number of standard deviations), regardless of the event’s frequency of occurrence. ε is typically assigned a constant value (e.g., 0 for the median level or 1 for the 84th percentile level), without considering the scenario frequency of occurrence. The 84th and 90th percentile spectra may correspond to long return periods as seen in comparisons between scenario-based and PSHA PGA for the site of Sulmona, in central Italy, by Bordoni et al., (2023) and for the site of Melbourne by Somerville et al. (2015). Notably, even higher, albeit less probable, ground motions are possible due to the inherent random variability around the median value (epsilon). Consequently, the concept of a “deterministic” limit for ground motion intensity lacks a clear definition. To specify a “deterministic” ground motion level, a criterion, such as the number of standard deviations above the median value, would be necessary, but this would imply the potential for even greater values to exist. This uncertainty also applies to magnitude estimation, so our methodology is “scenario-based” rather than “deterministic”; it involves selecting a magnitude and a single ground motion scenario that cannot be definitively labeled as the “maximum possible” ground motion. Unlike previous studies (e.g., Somerville et al. 2015; Bordoni et al. 2023), our work mainly differs in the probability density functions used for the maximum magnitude to cover uncertainty in its estimate. This point allows the combination of multiple models of maximum magnitude to deal with the epistemic uncertainty.

We compared the PGA and S.A. calculated in this work with the ones observed in the last decades (from https://itaca.mi.ingv.it/, D’Amico et al. 2021) or inferred from older earthquakes in central Italy (from http://shakemap.ingv.it/shake4/) to show the advantages of the proposed methodology. For example, the October 30th 2016 Mw 6.6 earthquake returned PGA of about 0.9 g and S.A. at 0.3 s of about 2.3 g at the accelerometric station located on soil-A at Joiner–Boore distance Rjb of 0 km (epicentral distance Repi 10 km, Latitude 42.755°, Longitude 13.193°). At the nearest site of our grid to the station, we calculated PGA of 0.87 g and ~ 1 g and S.A. at 0.3 s of 2.2 g and 2.7 g, respectively, for the 84th and 90th percentile. As a further example, on January 13rd 1915 an earthquake with an estimated Mw ~ 7 struck central Italy, causing macroseismic intensity greater than the 10th degree of the Mercalli–Cancani–Sieberg scale. ShakeMap of this earthquake (the procedure is fully described by Michelini et al. 2020) shows PGA and S.A. at 0.3 s in the epicentral area of about 0.5–0.8 g and 1–1.5 g, respectively. Our model returns PGA of 0.86 g and ~ 1 g and S.A. at 0.3 s of 2.2 g and 2.8 g, respectively, for the 84th and 90th percentile. Both these comparisons show the reliability of our methodology. The richness of the Database Macrosismico Italiano (DBMI15) and the shakemaps database could allow a systematic and larger scale comparison among scenario-derived and observed macroseismic intensities at sites as recently done by Nekrasova et al. (2014) and Nekrasova et al. (2014) at the national scale for probabilistic and deterministic models. Recently, Cito et al. (2024) and D’Amico et al. (2024) also used shakemaps and macroseismic data to compare probabilistic models against observations. The work of D’Amico et al. (2024), in particular, highlighted the uncertainties in the conversion of PGA and S.A. in macroseismic intensities. Given the complexity of such comparisons and the importance of testing models against observations, we retain that this issue deserves an ad-hoc future study. Furthermore, as correctly suggested by Nekrasova et al. (2014), an oversimplified model computation of the minimum time interval required for reliable earthquake occurrence rate estimates, including the maximum expected magnitude, is at least in the order of 12,000 years. This required period implies a cautionary approach in using only the magnitude of CPTI for the earthquake scenario: in this sense, our approach allows comparison among various approaches and eventually application of a weighting scheme, different from the one here used, among the three scenarios. Some simplifications in modeling were made in the presented work regarding the number of simulated ruptures and complexity of the GMM logic tree. We have simulated accelerations from hundreds of ruptures of our final ensemble model treated as independent sources, and by comparing accelerations, we identified the most severe ones. However, exploring uncertainties in rupture parameters (such as focal depth, strike and dip of the source, aspect ratio, or hypocenter location) could significantly increase the number of ruptures by an order of magnitude. Then, to avoid being overwhelmed by the computational cost and related time-consuming processes, we tested a limited number of rupture orientations in tridimensional space. Moreover, not all uncertainties could have the same impact on the results; for example, aspect ratio and dip angle, given the density of the points on the grid, may have a negligible impact. We suggest that exploring more potential ruptures in some specific cases, like site-specific scenarios, critical infrastructure assessments, or regionally extended maps, is then demanded to fit the purpose of a specific study.

Additionally, the absolute and relative accelerations also depend on the GMM used. A logic tree including several GMMs, as Bordoni et al. (2023) proposed, can be applied. Moreover, recent fully non-ergodic GMMs, such as the one proposed by Sgobba et al. (2021) for the central Italy region, could be considered in future studies to reconstruct the ground motion pattern of past events and generate shaking scenarios with the proposed approach. The advantage of the Sgobba et al. (2021) model lies in its combination of a non-ergodic GMM with a spatial correlation model of the systematic residual terms, considering regional effects associated with sources, propagation paths, site response, and directivity effects.

However, besides the choice of GMM, we want to emphasize the importance of considering near-source conditions and the impact of the vertical component of accelerations, which have been modeled in our approach. Typically, seismic design actions for ordinary structures focus on horizontal ground motion components, represented by a design response spectrum. According to the Italian Building Code (NTC18 2018) and Eurocode 8 (EC8, 2004), the vertical component of the seismic action shall be considered in a minimal number of cases, such as base-isolated structures and selected building components (e.g., horizontal structural members with large spans). Nevertheless, it has been recognized that the vertical ground motion can be significantly larger than its horizontal component in the near-source region of earthquakes, particularly at periods less than about 0.3 s. The significant impact of vertical ground motion has been evident in recent seismic events, such as the Po Plain earthquake in 2012 (Carydis et al. 2012), the central Italy seismic sequences in 2016 (Fiorentino et al. 2018), and the recent 2023 Turkey earthquakes (Baltzopoulos et al. 2023). These events saw specific stations recording high ratios of vertical-to-horizontal (V.H.) response spectral accelerations at short periods, reaching approximately 3 and 8 for the Po Plain and central Italy earthquakes and approximately 1 for PGA during Turkey earthquakes (Baltzopoulos et al. 2023). This occurrence can have a notable impact on short-period structures, as shown, for example, in Liberatore et al. (2019), where cycles of increments of axial loads can induce repetitive reductions of friction force, leading to more extensive failures in structures with low cohesion. Petricca et al. (2021) have also discussed the impact of this effect in near-source conditions. The use of distributed sources (whose hypocentres are distributed over a grid of points) in combination with GMMs by Lanzano et al. (2020) and Ramadan et al. (2021), then makes our model particularly suitable for evaluating particular conditions in near-source field.

It is worth noting that our calculation was performed using rock conditions. For example, Brando et al. (2020) analyzed the seismic damage observed on masonry buildings of two historical centers following the 2016 central Italy earthquake sequence and interpreted damages in the light of 3rd level microzonation studies that helped to detect amplification phenomena due to the soil features. The two centers in Abruzzo are close; however, Brando et al. (2020) showed that different subsoil stratigraphic and topographic characteristics impact different damage patterns. Different damage levels correlated to the different spectral accelerations related to the different stratigraphic configurations. The presence of relevant amplification phenomena emphasized the higher damage levels that present higher frequencies in those areas of the historic centers with higher amplification factors.

Moreover, as shown, for example, by Herrero-Barbero et al. (2022) through physics-based scenario simulations, the combined effects of proximity to the rupture plane and the soil amplification can have a more significant impact on the PGA value than the earthquake magnitude itself. Herrero-Barbero et al. (2022) have shown that site amplification during an earthquake can be noticeable even at large distances, even when the calculated PGA on rock is less than 0.2 g. Therefore, the threat in some regions should not be neglected, even when they are far from the source of the maximum earthquake. Given the dimensions of our study area, its heterogeneous lithology (with the presence of carbonate, alluvial, unconsolidated clastic rocks, and beach deposits, see for example, Bucci et al. 2022), and the methodological purpose of our work, we did not perform soil-based scenarios. Considering Brando et al. (2020) and Herrero-Barbero et al. (2022), and following Bordoni et al. (2023), we suggest the use of site-dependent responses, which consider the dynamic properties of materials in the upper few meters and the anisotropies of the heterogeneous crust, as well as the non-linear response of soils during a large earthquake.

Providing realistic magnitude estimates for natural disaster scenarios is essential for emergency managers. Koschatzky et al. (2017) examined a series of realistic earthquake disaster scenarios for Melbourne (Australia). In response to requests from the end users, they considered three events with magnitudes of 5.5, 6, and 7, with the epicenter located between 7.5 and 9 km beneath Melbourne. These events were significantly larger than those historically recorded within the city and did not align with any known active faults. Nevertheless, as Koschatzky et al. (2017) described, such events are still theoretically possible, albeit with remote probabilities. Then, an essential aspect of any scenario-based hazard assessment is understanding (even if not directly used) the probability of magnitude occurrences.

Although the rate of occurrence is beyond the scope of scenario parameterization, it is essential to consider the implications of investigating maximum–magnitude events. To explore the recurrence rates, we selected magnitudes around the two localities of Chieti and L'Aquila within a 30 km radius. Using an earthquake catalog-independent activity rate model, we associated each magnitude with an exceedance annual rate. We used a geodetic-derived activity rate model (MG2) published by Visini et al. (2021) to achieve this. In detail, MG2 used data from GNSS interseismic horizontal velocities and stress azimuth data to determine both interseismic and long-term strain rates and velocities on a finite element grid using the NeoKinema code version 5.2 (Bird 2009; Bird and Carafa 2016). For each grid-point, we compared the magnitude–frequency distribution with the magnitude of the scenario and calculated the annual recurrence of each scenario. The magnitude–frequency distributions of these events are shown for Chieti and L’Aquila in Fig. 9. The calculated annual recurrence for each scenario suggests intervals ranging from approximately 1e⁻⁴ yr⁻¹ to 1e⁻⁵ yr⁻¹, which is in line with the observations of Nekrasova et al. (2014). Their Poisson probabilities of occurrence over periods of 50, 100, 500, and 1000 years are, respectively, 0.7%, 1.4%, 6. 7%, and 12.8% for Chieti 1.1%, 2.3%, 10.8%, and 20.4% for L’Aquila. While the probability values may not be the focus, it is essential to note that they could be much smaller in regions with lower deformation rates. Balancing the need to consider worst-case scenarios and the probability of their occurrence could be desirable for stakeholders. We suggest defining a threshold probability level depending on the site’s importance. For example, a user could define a minimum threshold level of 1% in 500 years for each scenario. Then, it would be possible to determine the corresponding magnitude by working backward from the magnitude estimated in the ensemble model. The uncertainties estimated using the conflation could also serve as a boundary for this research.

Fig. 9

On the top, the map shows log10 annual rates of exceedance of magnitudes computed with the ensemble model shown in Fig. 4. The magnitude frequency distributions obtained using the occurrence rates of the points inside the red circles are on the bottom (color figure online)

According to other authors (e.g., Bommer 2002; McGuire 2001; Robinson et al. 2018; Somerville et al. 2019), our method is not intended to supersede either probabilistic or determinist SHA, as no single analysis can suit all purposes. McGuire (2001) and Bommer (2002) recognized that seismic hazard assessment cannot adopt a one-size-fits-all approach. While a deterministic approach is commonly used for establishing the safe shutdown earthquake (SSE) for nuclear power plants or dams based on the maximum credible or maximum design earthquake (depending on the purpose of the project and following recommendations of ICOLD 2014), building project, contingency planning, and loss analysis prefer probabilistic approach, especially for loss analysis. The methodology chosen should align with the project’s specific nature and be calibrated according to the region’s seismic activity. The outcomes are the foundation for critical decision-making processes in seismic hazard or risk analysis. These decisions encompass choosing design or retrofit criteria, financial planning for earthquake-related losses (e.g., insurance levels), investments in resilient industrial systems, emergency response and post-earthquake recovery planning, and long-term recovery strategies. The applied methodology in each study should be chosen according to the nature of the project and calibrated to the seismicity of the region under study, including the quantity and quality of the data available to characterize the seismicity.

Seismic hazard assessment should continue to evolve, unfettered by almost ideological allegiance to particular approaches, with the understanding of earthquake processes. Such decisions could be best served with deterministic and probabilistic perspectives, and the best analyses are conducted knowing the decisions to be made. For example, Somerville et al. (2019), in the context of seismic hazard assessments for extreme consequence dams in Australia (ANCOLD, 2019, ANCOLD is the Australian National Committee on Large Dams), specify that the safety evaluation earthquake (SEE) should be determined by either the ground motions from the median maximum credible earthquake (MCE) on active faults or the 85th fractile of probabilistic ground motion with a 1e − 4 annual exceedance probability. The 85th fractile of the probabilistic SEE represents epistemic uncertainty, with only a 15% chance that the actual value exceeds it. On the other hand, the 84th percentile of the deterministic SEE accounts for random variability in response to spectral acceleration during the earthquake scenario, with a 16% chance of exceeding it in any given occurrence of the MCE earthquake.

The proposed methods could integrate classical approaches in motivating and supporting mitigation policies and programs through several key mechanisms: (a) supporting the case for mitigation by providing estimates of future disaster impacts (often paired with illustrative past earthquake damage) or even in seismic urgent computing; (b) communicating risk problems and potential solutions using discrete consequences meaningful to decision-makers, such as loss of life, housing damage, or infrastructure service outages; (c) developing relationships, trust, and capacity among professionals, decision-makers, and community members in the process of working together on scenarios; (d) improving conceptual understanding of risks among technical professionals; and (e) raising public awareness, which is necessary for political support of mitigation. Advancements that support these mechanisms will help improve scenario practice. For example, advancements in (a) and (b) include strategic planning methods that explore alternate futures based on different mitigation decisions and provide substantive ways to support decision-making in multi-hazard environments. Above all, scenarios need adequately funded, well-structured pathways to implementation, as mitigation actions rarely occur through simple dissemination of scenario results. Therefore, our work aligns with the research on scenario parameterization, which provides a crucial starting point for seismic emergency planning. The proposed methodology allows for adding new modules, models (e.g., magnitudes derived from disaggregation studies), and uncertainties to enhance the modeling process.

8 Conclusions

Our work presents a methodology for integrating various approaches for magnitude estimations in earthquake scenario modeling. While certain simplifications were made, such as hypocenter distributions and geometries of the ruptures, we acknowledge that additional parameters and uncertainties could be included to further enhance the accuracy of the results.

We emphasize the significance of considering near-source conditions and the impact of the vertical component of accelerations. The vertical ground motion in the proximity of seismic sources can be substantial, especially at short periods, and its consideration is essential for accurately assessing the response of short-period structures. Our methodology proposes a simplified method for modeling near-source conditions, considering the potential biases introduced by regional datasets dominated by far-field recordings.

The choice of applied GMM is crucial in determining the absolute and relative accelerations. A logic tree incorporating multiple GMMs, including recent non-ergodic models that consider regional effects, can be applied to improve the accuracy of ground motion predictions. Integrating these advancements with our proposed methodology can further refine the shaking scenarios.

We also emphasize the importance of understanding the probability of occurrence of magnitudes. While our scenario parameterization does not directly address the rate of occurrence, it is crucial to consider the implications of worst-case events and the associated recurrence intervals. Striking a balance between considering worst-case scenarios and their probability of occurrence is desirable, and defining a threshold probability level based on the site's importance can aid in decision-making. In conclusion, continued advancements in scenario practice, such as strategic planning methods and support for decision-making, will further enhance their effectiveness.