Macroseismic intensity is used to classify the level of shaking caused by earthquakes based on qualitative observations of its effects on people, buildings, and the environment, using standardised intensity scales (e.g., MCS, Sieberg, 1932; MSK, Medvedev et al., 1964; EMS-98, Grünthal, 1998). Among these, the Mercalli–Cancani–Sieberg (MCS) scale and the European Macroseismic Scale 1998 (EMS-98) are the most widely adopted in Italy. These scales consist of twelve intensity degrees, each representing increasing severity of ground shaking based on observed effects. Macroseismic intensity is associated with a specific earthquake and site through geographic coordinates and constitutes a macroseismic Intensity Data Point (IDP).

Macroseismic observations are widely used in earthquake engineering applications for vulnerability modelling and for the calibration of Intensity Prediction Equations (hereafter, IPEs, e.g., Pasolini et al., 2008; Sørensen et al., 2009; Bindi et al., 2011; Rotondi et al., 2016; Gomez-Capera et al., 2024; Lolli et al., 2024), which estimate the expected macroseismic intensity at any site based on parameters such as epicentral distance and magnitude. Similarly, these data are used as input to develop Ground Motion to Intensity Conversion Equations for a specific region (GMICEs, e.g., Gomez-Capera et al., 2020; Oliveti et al., 2022), which relate ground motion Intensity Measures (IMs) to macroseismic intensities or vice versa. In this framework, macroseismic data are also used as a reference for reconstructing the ground shaking distribution of pre-instrumental events (e.g., Allen et al., 2008; Faenza et al., 2013; Oliveti et al., 2024; Gironelli et al., 2023; Munafò et al., 2024; Volatili et al., 2025). Moreover, the spatial distribution of IDPs (i.e., the macroseismic field) enables the estimation of key earthquake parameters such as epicentral location, magnitude, and depth (e.g., Gasperini and Ferrari, 1995, 2000; Bakun and Wentworth, 1997; Pettenati et al., 1999; Gasperini et al., 1999, 2010; Provost and Scotti, 2020; Sbarra et al., 2019, 2023).

The physical dimensions and orientation of seismogenic sources associated with large historical events can also be inferred from the spatial distribution of IDPs. For Italy, apart from the quantitative approach proposed by Gasperini et al. (1999), which estimates source orientation and dimensions from the spatial distribution of intensity data points (IDPs), the association between historical earthquakes and their seismogenic sources is generally based on qualitative interpretations (e.g., Albini and Rovida, 2010; Galli et al., 2010; Galli and Pallone, 2019). The Database of Italian Seismogenic Sources (DISS; Basili et al., 2008; DISS Working Group, 2025) provides hypotheses on the association between potential seismogenic sources and historical earthquakes reconstructed from geological and macroseismological data.

A few recent studies focus on individual earthquakes, comparing shaking scenarios generated by known fault ruptures with the macroseismic evidence of major historical events (e.g., Visini et al., 2009; Sgobba and Pacor, 2023; Munafò et al., 2024). The limitation of the existing studies is the lack of a validation with both macroseismic observations and geological constraints, and the analysis is restricted to individual earthquakes without proposing a standardised approach that can be systematically applied to an entire catalogue of historical events. In contrast, we propose a methodological workflow that can be systematically applied to investigate all the Italian past events, independently of their size.

In Italy, IDPs are collected and organised in the Italian Macroseismic Database (Database Macrosismico Italiano – DBMI15; Locati et al., 2022), to provide a homogeneous dataset for assessing earthquake parameters and compiling the Italian Parametric Earthquake Catalogue (Catalogo Parametrico dei Terremoti Italiani – CPTI15; Rovida et al., 2020, 2022). In the CPTI15 catalogue, the parameterization of historical events is based on the intensity dataset selected among those archived in the Italian Archive of Historical Earthquake Data (ASMI; Rovida et al., 2017, 2025) according to quality criteria such as: (i) the completeness and spatial distribution of IDPs; (ii) the methodological robustness of the original study; and (iii) the reliability of the event interpretation (Locati et al., 2022). Given the extensive availability of high-quality macroseismic data in Italy, this study leverages these records to implement a comprehensive workflow for historical seismic source identification. This workflow includes a pre-processing step followed by three stages: (i) reconstruction of seismogenic sources; (ii) ground shaking simulations; and (iii) validation through residual analysis. The pre-processing step detects possible outliers in macroseismic intensity distributions to better constrain the reconstruction of earthquake seismogenic sources.

The complete workflow is tested on three instrumental earthquakes with different characteristics to explore the overall applicability of the method. These events are the 1984 Monti della Meta (Mw 5.8), the 1989 Prealpi Vicentine (Mw 4.85), and the 2008 Parmense (Mw 5.36) earthquakes. Subsequently, the approach is applied to a historical earthquake, the 3 June 1781 Cagli earthquake (Central Apennines). For this event, seismogenic sources are reconstructed from two alternative, but plausible and reliable, macroseismic fields: the intensity distribution in DBMI15 (Monachesi, 1987) and the dataset from Guidoboni et al. (2018). This allows a quantitative evaluation of the impact of different datasets in terms of earthquake parameterisation and source geometries.

The results of this study emphasise that the proposed workflow, including the initial pre-processing of macroseismic fields, can be a useful tool for reconstructing seismogenic sources consistent with macroseismic data and for generating realistic shaking scenarios, especially for past events.

In the CPTI15 catalogue, the parametrisation of historical earthquakes is performed using the Boxer code (Gasperini et al., 1999, 2010), which is applied to the macroseismic field, hereinafter referred to as the preferred dataset, provided in DBMI15. Specifically, macroseismic epicentres and magnitudes are estimated using the “Method 0” implemented in Boxer. This approach determines the epicentral location as the barycentre of the sites experiencing the highest intensities, and the magnitude is inferred as the average of the magnitude estimates, for each intensity class, computed from the area of the circular isoseismal with radius equivalent to the average epicentre-to-site distance for that intensity level. These magnitude values are calculated with the IPE by Sibol et al. (1987), which also considers epicentral intensity. The final magnitude is then obtained as a weighted trimmed mean of the independent estimates derived from all intensity classes (see Gasperini et al., 2010, for further details). This parametrisation strongly depends on the quantity and spatial distribution of the input macroseismic data. In this work, a set of 191 earthquakes was selected from CPTI15 as a test dataset, with moment magnitudes (Mw) ranging between 5.5 and 7.0, occurring in the period 1117–2017 (Fig. 1a). This magnitude threshold was chosen to focus on events associated with seismogenic sources capable of generating substantial ground shaking. The events selection was based on the following criteria: (i) at least three associated IDPs, to exclude poorly constrained macroseismic fields; (ii) inland epicentres, as offshore events typically produce asymmetric intensity distributions; and (iii) events occurred in areas where the seismogenic layer is shallower than 35 km, consistent with the applicability range of the adopted IPE (Gomez-Capera et al., 2024), which is calibrated for shallow crustal earthquakes. Overall, the final dataset comprises 31 656 macroseismic observations, forming the basis for the subsequent analysis.

Only a subset of 24 recent events has instrumental estimates of epicentre and magnitude, available in the CPTI15 or in ASMI; these events therefore provide a benchmark for testing the methodology (Fig. 1a).

Before applying the methodology, we note that the input dataset may include outliers, i.e., intensity observations that are anomalously high or low with respect to the expected attenuation pattern. To address this issue, a pre-processing step was implemented to identify and remove such outliers using the IPE proposed by Gomez-Capera et al. (2024). Intensity data exceeding three standard deviations of the model (3σ ≈ 2.25 intensity units) are classified as outliers and discarded, and the resulting macroseismic dataset is considered (hereinafter referred to as the revised dataset). We adopted a 3σ criterion to ensure a conservative filtering of macroseismic observations, aimed at identifying only the largest discrepancies between observed and those predicted by the model, while minimising the exclusion of potentially reliable intensity data. This choice also considers the inherent uncertainty associated with macroseismic intensity, i.e. one intensity degree, and related to its ordinal nature. The outlier removal is necessary since the best-fitting fault is identified through the analysis of residuals between observed and predicted intensity values (based on the median predictions of the adopted model). In this context, the presence of outliers in the macroseismic dataset may systematically bias the residual distribution and, consequently, the inferred fault geometry.

To ensure the overall consistency of our procedure, we recompute earthquake parameters of the analysed earthquake with the Boxer code, with the same settings as in CPTI15 (described in Rovida et al., 2020), starting from the revised dataset. First, we tested the results of this pre-processing by computing the earthquake parameters both including and excluding the identified outliers. For the subset of 24 events with instrumental parameters, the difference between macroseismic and instrumental magnitudes is -0.12 for the preferred dataset and -0.13 for the revised dataset. Differences between macroseismic and instrumental epicentral locations are, on average, negligible.

The same analysis, performed on the full dataset of 191 earthquakes, shows that the two epicentral estimates are generally consistent, with an average difference of approximately 3 km. The comparison between magnitudes from the preferred and revised macroseismic fields shows a mean decrease of 0.15 magnitude units, within the uncertainty range of the Boxer estimates (e.g., 0.26 for pre-1900 events). These results align with Antonucci et al. (2025), who demonstrated that randomly varying intensities in the macroseismic fields of DBMI15 by ±1 intensity degree, Boxer locations remain very stable with locations within 10 km in 83 % of cases and magnitude differences within ±0.3 units in 87 % of the cases. However, significant variations in earthquake location and magnitude estimates (e.g., > 20 km and > 0.3 magnitude units) may lead to markedly different constraints on both the spatial position and the extent of the causative rupture. With this perspective, the pre-processing proves particularly effective in identifying macroseismic fields that require closer scrutiny or, in some cases, exclusion from the analysis. For completeness, Table S1 in the Supplement summarises the comprehensive details for each selected event and the results of the comparisons between solutions for the entire dataset.

The earthquakes that occurred on 25 December 1222, 4 September 1293, and 5 May 1990 show the largest epicentral shifts of approximately 20, 30, and 43 km, respectively. The 1222 and 1293 events are characterised by very few and uncertain macroseismic effects distributed over wide areas, maximum intensities documented at considerable distances from the inferred source, and large azimuthal gaps.

We consider the 1990 Potenza earthquake as a clear example of how IDPs identified as outliers can lead to a large epicentral shift (43 km). Similarly, we consider the well-documented 24 August 2016 Amatrice earthquake, characterised by well-constrained instrumental parameters and a documented seismogenic source (Tinti et al., 2016; DISS Working Group, 2025).

The 5 May 1990 Potenza earthquake struck the Southern Apennines with a Mw 5.8 from the Global Centroid Moment Tensor (GCMT; Dziewonski et al., 1981; Ekström et al., 2012; http://www.globalcmt.org/CMTsearch.html, last access: 10 September 2026). The Revised Bulletin of the International Seismological Centre (ISC, 2025, http://www.isc.ac.uk, last access: 10 September 2026) locates the epicentre slightly north of Potenza at [40.756° N, 15.843° E] and the Italian Seismic Bulletin (Bollettino Sismico Italiano, BSI; http://bollettinosismico.rm.ingv.it/, last access: 10 September 2026) at [40.682° N, 15.848° E], while the CPTI15 adopts the location at [40.738° N, 15.741° E] of the previous version of the ISC Bulletin (Fig. 2c). These differences in instrumental locations, compared with more recent events, are likely due to the limited density and heterogeneous configuration of the Italian National Seismic Network at the time of the 1990 event, which was still under development and only partially digitalised. The Boxer method, applied to the macroseismic field from DBMI15 (Gasparini et al., 1991b; Fig. 2a), estimates the epicentral location and magnitude as [40.710° N, 15.299° E] and Mw 5.37, respectively. These solutions do not match any of the available instrumental locations, and for this reason it is not included in CPTI15. The pre-processing identified 116 intensity outliers within the macroseismic field (Fig. 2b). Specifically, positive residuals exceeding 3 standard deviations were concentrated in the Neapolitan area, very far from the instrumental locations, in correspondence with the highest intensity values (I = 6–7 and 7). According to Antonucci et al. (2026), these IDPs were overestimated due to the cumulative damage caused by the 23 November 1980 earthquake (https://emidius.mi.ingv.it/CPTI15-DBMI15/eq/19801123_1834_000, last access: 10 September 2026). Negative residuals were identified at large distances from the epicentre, particularly in southern Abruzzo, Molise, and Calabria regions (Fig. 1b). After removing these outliers, the recalculated macroseismic epicentre [40.591° N, 15.785° E] shows a significant improvement, reducing the misfit with the CPTI15-ISC2016 instrumental location from 37.3 km to only 16.7 km, relocating the epicentre near the city of Potenza (Fig. 2c). The recalculated macroseismic magnitude (Mw 5.4) is significantly lower than the instrumental one but higher than the Mw 5.19 estimated by Antonucci et al. (2026).

A second example is the 24 August 2016 Amatrice earthquake, the triggering event of the Central Italy seismic sequence. The event was located by the BSI at [42.698° N, 13.233° E]. Different moment magnitude estimates are available: Mw 6.2 from the Regional Centroid Moment Tensor (RCMT; Pondrelli, 2002; Pondrelli et al., 2002) and GCMT, and Mw 6.0 from the Time Domain Moment Tensor (TDMT INGV; Scognamiglio et al., 2006, http://terremoti.ingv.it/, last access: 10 September 2026). The adopted macroseismic field in DBMI15, derived from the field survey described in Rossi et al. (2019; ROSAL019), consists of 221 IDPs with intensities ranging from I = 2–3 up to I ≥ 9 in the EMS-98 scale (Fig. 3a). From this macroseismic field the Boxer epicentral location and magnitude estimates are [42.683° N, 13.277° E] and Mw 6.46, as reported in CPTI15. The pre-processing identified 8 intensity outliers: two with positive residuals and six with negative ones (Fig. 3b). After removing these outliers, the recalculated macroseismic epicentre is [42.658° N, 13.288° E]. Both macroseismic epicentres are consistent with the BSI instrumental location, differing by just 3.9 and 6 km, respectively. This slight shift is related to the removal of the IDP at Pescara del Tronto (I = 10), where the observed damage was amplified due to the location on pre-existing landslide deposits. Conversely, an improvement is observed in the magnitude estimate: the recalculated value (Mw 6.26) is notably lower and more consistent with the instrumental ones. This difference in magnitude has significant implications for the reconstruction of the seismic source, since a magnitude of Mw 6.46 would imply a rupture area of approximately 270 km², which is inconsistent with the portion of the fault system activated during the mainshock, and with structural-geological data and DInSAR modelling (∼ 180 km²; Lavecchia et al., 2016), as well as with the observed rupture length of 20–25 km (Chiaraluce et al., 2017).

This section describes the integrated methodological workflow for seismogenic source reconstruction, which follows the initial pre-processing step and consists of three stages, as summarised in Fig. 4. In stage 1, we estimated earthquake parameters using the Boxer code (Gasperini et al., 1999, 2010) based on the revised macroseismic fields, and in stage 2, we used these parameters to reconstruct the seismogenic sources. Fault dimensions (length and width) are calibrated according to the scaling relationships by Wells and Coppersmith (1994). Although these empirical relations are widely adopted, source dimensions are indirectly inferred from estimated macroseismic magnitudes and may be affected by the intrinsic variability of the scaling relationships. In addition, for each source geometry, we defined credible parameters (e.g., strike, dip, rake, focal depth, and rupture vertices) by integrating data from several authoritative repositories: the Italian Seismic Bulletin (BSI; BSI Working Group, 2015), the Catalogue of Absolute Locations (CLASS; Latorre et al., 2022, 2023), the Engineering Strong-Motion Database (ESM; Luzi et al., 2020), the DISS database (Basili et al., 2008; DISS Working Group, 2025, version 3.3.1), and the ITaly HAzard from CApable faults catalogue (ITHACA Working Group, 2019).

The 3D source geometries are modelled as rectangular planes centred on the hypocentre. We simulate ground shaking including site effects using the ITA18 Ground Motion Model (GMM; Lanzano et al., 2019) by hypothesising variable hypocentral depths and considering the rupture distance (Rrup) as the source-to-site metrics. The resulting ground motion parameters (peak ground acceleration, PGA, and peak ground velocity, PGV), expressed in log₁₀ units, are then converted into intensity values using two distinct GMICEs: Gomez-Capera et al. (2020; GOM20) and Oliveti et al. (2022; OLI22).

While both equations generally align with the observed data, the quadratic formulations of OLI22 equations tend to exhibit a flattening effect of the regression curves for PGV greater than 5 cm s⁻¹ and PGA larger than 100 cm s⁻²,which may lead to a systematic underestimation of the highest macroseismic degrees than GOM20 (see Figs. 6 and 7 in Oliveti et al., 2022).

To identify the “best-fitting” seismogenic source (stage 3), we perform residual analyses of observed and predicted intensities (or PGA/PGV values when accelerometric recordings are available). Specifically, we compute the residuals for intensities derived from PGV, as this measure correlates most effectively with damage distribution and macroseismic intensity (Akkar and Özen, 2005; Munafò et al., 2024; Tang et al., 2019; Gomez-Capera et al., 2020). Finally, the best-fitting source is the one that minimises the mean of the residuals (Between-Event, BE) and their root-mean-square error (RMSE). Thresholds of ±0.5 for the BE and 1 for the RMSE are identified in intensity units to consider a source as reliable. These thresholds are chosen to maintain an acceptable comparison between observed and predicted intensity values and considering the intrinsic uncertainty of macroseismic intensity data (±1 intensity degree). A BE error of ±0.5 represents a conservative criterion, corresponding to a maximum discrepancy of only half an intensity degree compared to the observed value.

This approach allows us to generate multiple shaking scenarios and evaluate their consistency against three key benchmarks: (i) the observed macroseismic field; (ii) recorded instrumental data (when available); and (iii) geological evidence.

In Italy, a few methodological approaches have been proposed over the last decades for the reconstruction of historical earthquake sources. Such previous studies include the pioneering work of Gasperini et al. (1999) which presents the first attempt to infer source geometry directly from the spatial distribution of macroseismic observations, demonstrating that the elongation of the intensity field contains valuable information on source orientation and dimensions. Nevertheless, the methodology relies on simplifying assumptions. In particular, the orientation of the inferred source geometry is estimated from the azimuthal distribution of the highest intensity observations using a circular mean, providing a strike between 0 and 180° without resolving the fault dip direction. In addition, a fixed dip angle of 45° is assumed for all the seismogenic boxes, regardless of the geological characteristics of the candidate seismogenic structures.

Visini et al. (2009) demonstrated the potential of combining ground motion simulations with macroseismic data to evaluate competing seismogenic hypotheses for the 1693 Sicilian earthquake. Their approach evaluates a set of predefined fault models through synthetic ground motion simulations and statistical comparison with the observed intensities. Nevertheless, the geometry of the analysed sources is assumed a priori from previously proposed tectonic models, rather than being derived from the earthquake magnitude. Furthermore, the conversion between simulated ground motion parameters and macroseismic intensity relied on empirical relations not calibrated on Italian earthquakes.

More recently, Sgobba and Pacor (2023) proposed a non-ergodic empirical framework for reconstructing shaking scenarios of historical earthquakes, accounting for source, path and site effects specifically of Central Italy, by incorporating spatially variable source, propagation and site corrections. However, the approach requires the earthquake magnitude and fault geometry (i.e., fault vertices, strike and rupture dimensions) to be defined a priori. Consequently, its applicability depends on the availability of an independently constrained seismogenic source, making it particularly suitable for well-characterised historical earthquakes but less appropriate when the source itself remains uncertain.

Nevertheless, a common limitation of these studies is the absence of standardised metrics for source validation. This study aims to fill this gap by proposing an integrated and reproducible workflow that combines geological constraints, empirical fault-scaling relationships, regionally calibrated intensity-to-ground-motion conversions, and ground motion simulations. Candidate seismogenic sources are objectively ranked through quantitative statistical metrics, including between-event (BE) residuals and RMSE values, allowing the identification of the best-fitting source according to predefined thresholds.

This approach integrates an initial pre-processing stage for the identification and removal of potential outliers, followed by three main stages: (i) earthquake parameter estimation using the Boxer code, (ii) seismogenic source reconstruction and ground-motion simulation, and (iii) validation of the inferred source geometries through residual analysis (see Sect. 3) and comparison with geologic lineaments.

The pre-processing procedure aims at identifying macroseismic fields that require closer scrutiny or, in some cases, exclusion from the analysis. Although the presence of some possible over- or underestimated intensity value does not significantly change the macroseismic location and magnitude obtained with the adopted Boxer method, it may significantly affect the analysis of the residuals and, consequently, the interpretation of the geometry and dimensions of the seismogenic source.

The application of the proposed workflow to the selected instrumental earthquakes shows that macroseismic-derived parameters can provide realistic seismogenic source geometries that are mostly consistent with those derived from instrumental solutions. The validation has been performed for a wide magnitude range and with the aid of accelerometric recordings and mapped geological structures (e.g., 1984 Monti della Meta, 1989 Prealpi Vicentine, and 2008 Parmense earthquakes). The reliability of these results is confirmed by the fact that the residual values (BE and RMSE) obtained from accelerometric data align closely with the standard deviation (σ) of the adopted ITA18 GMM by Lanzano et al. (2019).

The application of the proposed workflow to the 1781 Cagli earthquake allows to select between alternative macroseismic fields for discriminating the best-fitting seismogenic source. Two alternative and reliable intensity datasets (Monachesi, 1987; Guidoboni et al., 2018) were simulated with four source hypotheses. The comparison of the residuals obtained from the simulations of the two datasets indicates that the seismogenic sources based on parameters derived from the CFTI5med dataset provide a better fit to the observed data in terms of BE_I and RMSE_I values.

The results further suggest that shaking scenarios simulated with a lower magnitude estimate (i.e., Mw 6.33) could be more consistent with this event. This implies that the coherence between intensity data points (IDPs), earthquake parameters, source geometry, and ground motion simulations can lead to a more comprehensive reconstruction of both the earthquake effects and the causative fault.

Based on the findings of this study, the workflow can be systematically applied to reconstruct the seismogenic sources of the strongest Italian historical earthquakes (Mw ≥ 5.5) reported in CPTI15-DBMI15, and for which consistent intensity distributions are available.