The seismicity of the Central Apennines (Italy) studied by means of a physics-based earthquake simulator

The seismicity of the Central Apennines (Italy) studied by means of a physics-based earthquake... Abstract The application of a physics-based earthquake simulation algorithm to the Central Apennines, where the 2016–2017 seismic sequence occurred, allowed the compilation of a synthetic seismic catalogue lasting 100 kyr, and containing more than 500 000 M ≥ 4.0 events, without limitations in terms of completeness, homogeneity and time duration. This simulator is based on an algorithm constrained by several faulting and source parameters. The seismogenic model upon which we applied the simulator code, was derived from the Database of Individual Seismogenic Sources including all the fault systems that are recognized in the Central Apennines. The application of our simulation algorithm provides typical features in time, space and magnitude behaviour of the seismicity, which are comparable with the observations. These features include long-term periodicity and a realistic earthquake magnitude distribution. The statistical distribution of earthquakes with M ≥ 6.0 on single faults exhibits a fairly clear pseudo-periodic behaviour, with a coefficient of variation Cv of the order of 0.4–0.8. We found in our synthetic catalogue a clear trend of long-term acceleration of seismic activity preceding M ≥ 6.0 earthquakes and quiescence following those earthquakes. Lastly, as an example of a possible use of synthetic catalogues, an attenuation law was applied to all the events reported in the synthetic catalogue for the production of maps showing the exceedance probability of given values of peak acceleration in the investigated territory. Numerical modelling, Earthquake hazards, Earthquake interaction, forecasting, and prediction, Seismicity and tectonics, Statistical seismology 1 INTRODUCTION The characteristic earthquake hypothesis is the basis of time-dependent modeling of earthquake recurrence on major faults, using the renewal process methodology. However, the complex situation of real fault systems may lead to a more chaotic and (almost) unpredictable behaviour, often referred to as a manifestation of self-organized criticality. In spite of the popularity achieved in the past decades, the characteristic earthquake hypothesis is not strongly supported by observational data (see Kagan et al. 2012). Few faults have long historical or palaeoseismic records of individually dated ruptures, and when data and parameter uncertainties are allowed for, the form of the recurrence distribution is difficult to establish. This is the case of the Central Apennines, for which strong earthquakes are documented since the 11th century, but the seismic catalogue can be considered complete for magnitudes ≥ 6.0 only for the last five centuries, during which not more than one characteristic earthquake is reported for most individual faults. As a matter of fact, the time elapsed between successive earthquakes on a particular fault segment in Italy is thought to be on the order of one or more millennia and therefore their probability of occurrence in the period covered by historical records is low or very low (e.g. Valensise & Pantosti 2001). The seismic activity of the Central Apennines reported in the Parametric Catalog of the Italian Earthquakes (CPTI15; Rovida et al. 2016) evidences 14 strong events with magnitudes that span from 6.0 to 7.1, since 1500 AD to 2014. From 2014 to date, three earthquakes having Mw ≥ 6.0 occurred in the region (ISIDe Working Group 2016; Table 1). Note that the historical catalogue covers a relatively short time period with respect to the long interevent time between strong events. Table 1. Mw ≥ 6.0 events of the Central Apennines since 1500 AD with their epicentral coordinates, intensity and magnitude. Year  Month  Day  Epicentral area  Lat (°)  Lon (°)  Io  Mw  1599  11  6  Valnerina  42.724  13.021  9  6.07  1639  10  7  Moti della Laga  42.639  13.261  9-10  6.21  1703  1  14  Valnerina  42.708  13.071  11  6.92  1703  2  2  Aquilano  42.434  13.292  10  6.67  1706  11  3  Maiella  42.076  14.080  10-11  6.84  1730  5  12  Valnerina  42.753  13.120  9  6.04  1741  4  24  Fabrianese  43.425  13.005  9  6.17  1747  4  17  Appennino umbro-marchigiano  43.204  12.769  9  6.05  1751  7  27  Appennino umbro-marchigiano  43.225  12.739  10  6.38  1799  7  28  Appennino marchigiano  43.193  13.151  9  6.18  1832  1  13  Valle Umbra  42.980  12.605  10  6.43  1915  1  13  Marsica  42.014  13.530  11  7.08  1997  9  26  Appennino umbro-marchigiano  43.014  12.853  8-9  5.97  2009  4  6  Aquilano  42.309  13.510  9-10  6.29  2016  8  24  Appennino centrale  42.70  13.23  10a  6.20  2016  10  26  Appennino centrale  42.91  13.13  9b  6.10  2016  10  30  Appennino centrale  42.83  13.11  10b  6.50  Year  Month  Day  Epicentral area  Lat (°)  Lon (°)  Io  Mw  1599  11  6  Valnerina  42.724  13.021  9  6.07  1639  10  7  Moti della Laga  42.639  13.261  9-10  6.21  1703  1  14  Valnerina  42.708  13.071  11  6.92  1703  2  2  Aquilano  42.434  13.292  10  6.67  1706  11  3  Maiella  42.076  14.080  10-11  6.84  1730  5  12  Valnerina  42.753  13.120  9  6.04  1741  4  24  Fabrianese  43.425  13.005  9  6.17  1747  4  17  Appennino umbro-marchigiano  43.204  12.769  9  6.05  1751  7  27  Appennino umbro-marchigiano  43.225  12.739  10  6.38  1799  7  28  Appennino marchigiano  43.193  13.151  9  6.18  1832  1  13  Valle Umbra  42.980  12.605  10  6.43  1915  1  13  Marsica  42.014  13.530  11  7.08  1997  9  26  Appennino umbro-marchigiano  43.014  12.853  8-9  5.97  2009  4  6  Aquilano  42.309  13.510  9-10  6.29  2016  8  24  Appennino centrale  42.70  13.23  10a  6.20  2016  10  26  Appennino centrale  42.91  13.13  9b  6.10  2016  10  30  Appennino centrale  42.83  13.11  10b  6.50  Notes: Data from CPTI15 (Rovida et al. 2016) and, for the last three recent earthquakes, ISIDe Working Group (2016). Io is in MCS scale. aGalli et al. (2016). bTertulliani & Azzaro (2016). View Large Earthquake simulators can overcome the limitations that real catalogues suffer in terms of completeness, homogeneity and time duration, providing data that can be used for the evaluation of different models of the seismogenic processes (Wilson et al. 2017). Earthquake simulators can provide in these cases interesting information based on features of fault geometry and its kinematics in order to use them in the renewal models. This concept was adopted by Tullis (2012) for earthquakes simulators in California using the long-term slip rate on seismogenic sources without taking into account rheological parameters. In this study, we applied a physics-based earthquake simulator for producing a long-term synthetic catalogue lasting 100 kyr and containing more than 500 000 events 4.0 ≤ M ≤ 7.0 magnitude, considering fault systems derived from the Database of Individual Seismogenic Sources (DISS; DISS Working Group 2015). 2 SEISMOGENIC SOURCES MODEL OF THE CENTRAL APENNINES Historical and instrumental earthquake catalogues show that Central Apennines have been struck by numerous earthquakes, ranging from sparse seismicity up to Mw 7.1 events, for example, the 1915 January 13 earthquake (Fig. 1 and Table 1). The 1915 event is to date the largest event to have occurred since 1500 AD in the study area, and is certainly one of the strongest earthquakes reported in the Italian historical and instrumental catalogues. Most of the major earthquakes are concentrated along the main axis of Central Apennines, but also the piedmont and coastal area have been locus of isolated large earthquakes (Fig. 1). Figure 1. View largeDownload slide Seismotectonic setting of the Central Apennines showing the projections on the ground surface of the CSSs of DISS 3.2.0 (in grey; DISS Working Group 2015). The boxes are the projection onto the ground surface of the SFSs and their colours denote their kinematics (see Frohlich diagram). The epicentres of the CPTI15 earthquakes with M 5.5+ are shown by red squares and the M 6+ earthquakes are labeled with the year of occurrence (Table 1; Rovida et al. 2016). The events of the 2016–2017 seismic sequence with M 5.5+ are shown by red stars; 1: 2016 August 24, Mw 6.2; 2: 2016 October 26, Mw 6.1; 3: 2016 October 30, Mw 6.5 and 4: 2017 January 18, Mw 5.6 (ISIDe Working Group 2016). Figure 1. View largeDownload slide Seismotectonic setting of the Central Apennines showing the projections on the ground surface of the CSSs of DISS 3.2.0 (in grey; DISS Working Group 2015). The boxes are the projection onto the ground surface of the SFSs and their colours denote their kinematics (see Frohlich diagram). The epicentres of the CPTI15 earthquakes with M 5.5+ are shown by red squares and the M 6+ earthquakes are labeled with the year of occurrence (Table 1; Rovida et al. 2016). The events of the 2016–2017 seismic sequence with M 5.5+ are shown by red stars; 1: 2016 August 24, Mw 6.2; 2: 2016 October 26, Mw 6.1; 3: 2016 October 30, Mw 6.5 and 4: 2017 January 18, Mw 5.6 (ISIDe Working Group 2016). The structural architecture of Central Apennines is dominated by ENE-verging arc-shaped folds and thrusts that developed through progressive migration of the contractional process. The earthquakes have hit the area east of the thrust belt testifying that these geodynamic processes which led to the shortening of the Apennines fold and thrust system are still active. Therefore, the major frontal thrusts located between the mountain chain and the Adriatic coast are thought to be active and responsible for some earthquakes of the region (e.g. Vannoli et al. 2015). The earthquakes located between the piedmont and the Adriatic coastline can be relatively deep (15–30 km depth range). In this case, they are thought to be caused by the deep-seated E-W trending shear zones that affect the Apulian foreland beneath the Apennines thrust belt (e.g. Kastelic et al. 2013). The extension trends nearly parallel to the former contractional axis, and favoured the development of normal faults that have either downthrown the back limb of the pre-existing, large thrust systems, or have somehow disrupted the landscape that resulted from the palaeogeographic domains and the contractional phases (e.g. Vezzani & Ghisetti 1998). The extensional fault systems straddles the crest of the Central Apennines, and are responsible for the 2016–2017 seismic sequence (including four earthquakes of magnitude equal to or larger than 5.5), and for a large number of strong earthquakes that struck the area (Fig. 1). Therefore, the seismogenic model of the Central Apennines consists of extensional, compressional and strike-slip sources located between the mountain chain and the Adriatic coast. For further details about the seismotectonic framework and the characterization of most of the seismogenic sources included in this model the reader can refer to Kastelic et al. (2013) for the sources belonging to the compressional fronts of the Central Apennines and offshore domains, and Vannoli et al. (2012) for the sources belonging to the extensional domain of the Apennines. The seismogenic model upon which we applied the simulator code, was derived from the DISS, version 3.2.0 (DISS Working Group 2015; http://diss.rm.ingv.it/diss/). The DISS supplies a unified view of seismogenic processes in Central Apennines by building on basic physical constraints concerning rates of crustal deformation, on the continuity of deformation belts and on the spatial relationships between adjacent faults (Basili et al. 2008). One of the main core objects of the DISS are the Composite Seismogenic Sources (CSS), fully parametrized crustal fault systems, believed to be capable of producing M ≥ 5.5 earthquakes. This category of sources was conceived to achieve completeness of the record of potential earthquake sources. The CSSs are based on regional surface and subsurface geological data that are exploited well beyond the identification of active faults. They are characterized by geometric and kinematics parameters and the maximum value of earthquake magnitude in the moment magnitude scale. Every parameter (including magnitude) is qualified according to the type of analyses that were done to determine it. Table 2 in Basili et al. (2008) shows the principal types of data and methods used in DISS to determine the parameters of the seismogenic sources. Five different methods are listed for the parameter ‘Magnitude’. Table 2. Parameters of the Simplified Fault Systems (SFSs) adopted in this study ID  Name  Lat (°N)  Lon (°E)  D (km)  S (°)  Dip (°)  R (°)  L (km)  W (km)  S-R (mm yr−1)  SFS01  Città diCastello-Spoleto  42.6418  12.8171  0.5  329  33  270  100  13.8  0.55  SFS02  Leonessa-Posta  42.4776  13.0369  0.5  314  33  270  22  13.8  0.55  SFS03  Cittaducale-Barrea  42.4098  13.0284  1  133  53  270  100  17.9  0.9  SFS04  Borbona-Goriano Sicoli  42.5539  13.1559  2  134  50  270  73  15  0.55  SFS05  Cocullo-Aremogna  42.0877  13.8071  2  143  50  270  40.5  15  0.55  SFS06  Gubbio  43.414  12.4442  2  131  20  270  26  11.8  0.55  SFS07  Colfiorito-Cittareale  43.2603  12.7436  2.5  148  45  270  80  16.2  0.55  SFS08  Campotosto  42.6443  13.2693  2.5  138  45  270  24  16.2  0.55  SFS09  Barisciano-Sulmona  42.4339  13.4536  1  134  53  270  64  16  0.55  SFS10  Sassoferrato-Fabriano  43.5428  12.7298  12  125  38  90  28  16.2  0.3  SFS11  Camerino-Montefortino  43.3565  13.0711  12  153  38  90  54.9  16.2  0.3  SFS12  Montegallo-Cusciano  42.913  13.3843  12  142  38  90  41  16.2  0.3  SFS13  Caramanico Terme-Palena  42.2489  13.9977  8  137  25  90  53  21  0.3  SFS14  Orsogna-Archi  42.3008  14.1942  3  131  30  90  29  10  0.3  SFS15  Macerata-Canzano  43.602  13.5187  3  160  40  90  88.2  9.3  0.3  SFS16  San Clemente-Pietranico  42.6418  13.8797  3  167  40  90  36.2  9.3  0.3  SFS17  Ancona-Sirolo  43.6535  13.5211  3  139  38  90  16.5  5.7  1.2  SFS18  Numana-Civitanova Marche  43.5274  13.6653  3  158  38  90  25  5.7  1.2  SFS19  Conero offshore NW  43.7077  13.596  1.5  136  33  90  17  9.2  0.7  SFS20  Conero offshore SE  43.5768  13.7571  1.5  153  33  90  11  9.2  0.7  SFS21  Porto Sant’Elpidio offshore  43.891  13.8072  3  148  40  95  22  5.5  0.3  SFS22  Pedaso offshore-Rosciano  43.2045  13.9616  3  175  40  95  101  5.5  0.3  SFS23  Ortolano-Montesilvano  42.524  13.3558  11  92  80  200  82  9  0.3  SFS24  Tocco da Casauria-Tremiti  42.2432  13.8043  11  95  80  200  154  9  0.3  ID  Name  Lat (°N)  Lon (°E)  D (km)  S (°)  Dip (°)  R (°)  L (km)  W (km)  S-R (mm yr−1)  SFS01  Città diCastello-Spoleto  42.6418  12.8171  0.5  329  33  270  100  13.8  0.55  SFS02  Leonessa-Posta  42.4776  13.0369  0.5  314  33  270  22  13.8  0.55  SFS03  Cittaducale-Barrea  42.4098  13.0284  1  133  53  270  100  17.9  0.9  SFS04  Borbona-Goriano Sicoli  42.5539  13.1559  2  134  50  270  73  15  0.55  SFS05  Cocullo-Aremogna  42.0877  13.8071  2  143  50  270  40.5  15  0.55  SFS06  Gubbio  43.414  12.4442  2  131  20  270  26  11.8  0.55  SFS07  Colfiorito-Cittareale  43.2603  12.7436  2.5  148  45  270  80  16.2  0.55  SFS08  Campotosto  42.6443  13.2693  2.5  138  45  270  24  16.2  0.55  SFS09  Barisciano-Sulmona  42.4339  13.4536  1  134  53  270  64  16  0.55  SFS10  Sassoferrato-Fabriano  43.5428  12.7298  12  125  38  90  28  16.2  0.3  SFS11  Camerino-Montefortino  43.3565  13.0711  12  153  38  90  54.9  16.2  0.3  SFS12  Montegallo-Cusciano  42.913  13.3843  12  142  38  90  41  16.2  0.3  SFS13  Caramanico Terme-Palena  42.2489  13.9977  8  137  25  90  53  21  0.3  SFS14  Orsogna-Archi  42.3008  14.1942  3  131  30  90  29  10  0.3  SFS15  Macerata-Canzano  43.602  13.5187  3  160  40  90  88.2  9.3  0.3  SFS16  San Clemente-Pietranico  42.6418  13.8797  3  167  40  90  36.2  9.3  0.3  SFS17  Ancona-Sirolo  43.6535  13.5211  3  139  38  90  16.5  5.7  1.2  SFS18  Numana-Civitanova Marche  43.5274  13.6653  3  158  38  90  25  5.7  1.2  SFS19  Conero offshore NW  43.7077  13.596  1.5  136  33  90  17  9.2  0.7  SFS20  Conero offshore SE  43.5768  13.7571  1.5  153  33  90  11  9.2  0.7  SFS21  Porto Sant’Elpidio offshore  43.891  13.8072  3  148  40  95  22  5.5  0.3  SFS22  Pedaso offshore-Rosciano  43.2045  13.9616  3  175  40  95  101  5.5  0.3  SFS23  Ortolano-Montesilvano  42.524  13.3558  11  92  80  200  82  9  0.3  SFS24  Tocco da Casauria-Tremiti  42.2432  13.8043  11  95  80  200  154  9  0.3  Notes: Geometric coordinates refer to the upper left edge of the SFS. D: the depth of the upper edge of the SFS from the sea level; S: the value of the strike angle; Dip: the value of the dip angle; R: the value of the rake angle; L: the SFS length measured along its strike; W: the SFS width measured along its dip and SR: the value of the slip rate on the SFS. View Large We converted the 15 CSSs identified in the Central Apennines into 24 Simplified Fault Systems (SFS), new sources specifically developed for this study (Fig. 1). The SFSs are rectangular fault systems consistent with the parameters supplied for the CSSs. As a matter of fact, each SFS is characterized by 1: the strike of that segment; 2: the average dip; 3: the average rake; 4: the depth intervals; 5: the length of that segment; 6: the maximum width obtained with average dip down to maximum depth and finally, 7: the slip rate value of the respective CSS (Fig. 1 and Table 2). Table 2 reports the list and the parameters of the 24 SFSs recognized in the Central Apennines (Fig. 1). 3 ALGORITHM OF THE SIMULATOR CODE The algorithm on which this simulator is based is described in detail by Console et al. (2015, 2017). Here, we recall that this algorithm is constrained by several physical elements as: The geometry, kinematics and average slip rate for every fault system. The process of rupture growth and termination, leading to a self-organized earthquake magnitude distribution. Interaction between earthquakes, including small-magnitude events. The seismogenic system is modeled by rectangular fault systems (SFS; Table 2), each of which is composed by many square cells of the same size. Each cell is initially given a stress chosen from a random distribution. The stress on each cell is increased in time by the tectonic loading computed from a given slip rate, the value of which is uniform on each segment. Some heuristic rules are adopted for nucleating and stopping a rupture: A cell can nucleate a rupture if the stress reaches a value that exceeds its strength. After nucleation, the effective strength on the cells neighbouring the already ruptured cells is reduced by a constant value multiplied by the square root of the number of already ruptured cells, as a proxy of weakening mechanism; the free parameter introduced to produce such weakening effect is called hereafter strength-reduction coefficient (S-R; Console et al. 2017); this parameter has a similar role of the η  free parameter in the Virtual Quake simulator developed for California (Schultz et al. 2017). The S-R is not allowed to increase further if the ruptured area exceeds a given number of times the square of the width of the rupturing fault system, discouraging rupture propagation over very long distances; the free parameter introduced to produce such effect is called hereafter aspect-ratio coefficient (A-R; Console et al. 2017). At each ruptured cell, the stress is decreased by a constant stress drop (e.g. 3 MPa), and the slip on the ruptured cell is estimated proportionally to the square root of the already ruptured cells. When a cell ruptures the stress on all the surrounding cells is changed by a value equal to the Coulomb stress change physically computed by the seismic moment of the ruptured cell, the distance between the causative and receiving cells and their respective source mechanism. A rupture stops when there are not cells in the search area where the stress exceeds the effective strength. A cell can rupture more than once in the same event. Events nucleated in one fault system are allowed to expand into neighbouring fault systems, applying the (1)–(3) rules, if they are separated by less than a given maximum distance (e.g. 10 km). In this way, different fault systems are treated as a unique fault system by the algorithm. As already stated, in the rupture process of an earthquake, the simulation algorithm allows a cell to rupture more than once. This may happen if at the initial stage of the rupture of a big earthquake a cell ruptures releasing a constant stress drop, but with a moderate slip. When, subsequently, the rupture grows, the next rupturing cells transfer positive Coulomb stress change to the previously ruptured cells, recharging them and allowing them to exceed again the threshold strength (which is decreasing as the rupture area expands). So, for the final estimate of the seismic moment of an earthquake generated by the simulation process, the single seismic moment released by each ruptured cell is considered and their total is computed. The average slip is then computed from the total seismic moment and the total ruptured area. This simulation algorithm has been refined in time, by the production of more complex and efficient versions of the computer code. Let us recall, for instance, that the main improvement of the algorithm between the version adopted by Console et al. (2017) and the previous one introduced by Console et al. (2015) was a more efficient way of searching successive ruptures, avoiding the procedure based on a huge number of very short time steps. This is reflected in the flow chart of the two respective algorithms (Fig. 1, Console et al. 2015, and Fig. 1, Console et al. 2017). A new feature in the algorithm of the present simulator code with respect to the previous version (Console et al. 2017) consists in the after-slip process: a fraction of the total slip computed for a ruptured cell is released with a time delay after the origin time of the earthquake. Two free parameters control the generation of aftershocks by the simulator. They are used to assign the fraction of coseismic slip released by the after-slip process and the characteristic time of the decaying Omori-like power law and must be interactively assigned by the user. Typically, simulation parameters are adjusted so that natural earthquake sequences are matched in their scaling properties (Wilson et al. 2017). In this respect, the role of the S-R and A-R parameters in our simulation algorithm has been previously analysed and described by Console et al. (2017). 4 APPLICATION OF THE EARTHQUAKE SIMULATOR TO THE CENTRAL APENNINES The 24 rectangular SFSs that represent the Central Apennines seismogenic structures reported in Table 2 were discretized in cells of 1.0 km × 1.0 km. The smallest magnitude generated by an earthquake rupturing a single cell is approximately 4.0. The time spanned by the synthetic catalogue was 100 kyr, excluding a warm up period of 20 kyr introduced to lead the system to a standby status, independent of the initial stress randomly assigned to every cell. In our simulation, an event of given magnitude produced by the simulation algorithm could have ruptured only part of a single SFS, or encompass more than one SFS, without any constrain imposed by the size of the SFS where the nucleation is started. After having carried out a series of trials with different choices of the free parameters, we chose the combination of S-R = 0.2 and A-R = 2 in order to obtain a good match between the magnitude distributions of the synthetic and the real catalogues (see Console et al. 2017). The application of the earthquake simulation algorithm to the SFSs of the Central Apennines produced a homogeneous and complete seismic catalogue containing more than 500 000 M ≥ 4.0 events, with a time duration of 100 kyr. The results of the simulation process for single SFS are given in Table 3, where the source kinematics, the source area, the seismic moment annual rate, the number of M ≥ 4.0 and 6.0 earthquakes, and the maximum magnitude, respectively, are reported. It must be noted the total number of M ≥ 6.0 earthquakes contained in the synthetic catalogue is much smaller than the sum of the earthquakes reported in column 6 of Table 3, as numerous events are multiple segment ruptures. Note also that the maximum magnitudes are often the same for neighbouring SFSs (e.g. SFS01, SFS02 and SFS03) because the largest magnitude is referred to a unique earthquake that ruptured more than one SFS together. Table 3. Main features of the synthetic catalogue of 100 kyr obtained by the simulator for the SFSs of the Central Apennines. ID  Rake  Area (km2)  Mo/year (Nm yr−1)  Number of synthetic events M ≥ 4.0  Number of synthetic events M ≥ 6.0  Synthetic Max M  CSS Max M  SFS01  N  1380  2.3E+16  24 824  256  7.15  6.2  SFS02  N  304  5.0E+15  6761  176  7.15  6.2  SFS03  N  1790  4.8E+16  60 773  374  7.15  6.7  SFS04  N  1095  1.8E+16  18 731  283  7.18  6.5  SFS05  N  608  1.0E+16  11 354  153  7.18  6.5  SFS06  N  307  5.1E+15  7456  131  6.96  6.0  SFS07  N  1296  2.1E+16  26 411  266  7.18  6.5  SFS08  N  389  6.4E+15  9580  218  7.18  6.5  SFS09  N  1024  1.7E+16  19 332  281  7.18  6.4  SFS10  R  454  4.1E+15  4780  59  6.97  6.2  SFS11  R  890  8.0E+15  8649  116  6.97  6.2  SFS12  R  664  6.0E+15  7554  92  6.97  6.2  SFS13  R  1113  1.0E+16  11 825  181  6.83  6.8  SFS14  R  290  2.6E+15  3781  148  6.83  5.6  SFS15  R  820  7.4E+15  10 107  382  6.66  5.9  SFS16  R  337  3.0E+15  4004  148  7.05  5.9  SFS17  R  94  3.4E+15  7720  289  6.55  5.8  SFS18  R  143  5.1E+15  10 404  317  6.55  5.8  SFS19  R  156  3.3E+15  6273  204  6.55  5.9  SFS20  R  101  2.1E+15  4368  172  6.55  5.9  SFS21  R  121  1.1E+15  2739  0  5.93  5.5  SFS22  R  556  5.0E+15  5686  196  6.76  5.5  SFS23  SS  738  6.6E+15  11 858  301  7.08  5.7  SFS24  SS  1386  1.2E+16  23 800  353  6.83  6.0  ID  Rake  Area (km2)  Mo/year (Nm yr−1)  Number of synthetic events M ≥ 4.0  Number of synthetic events M ≥ 6.0  Synthetic Max M  CSS Max M  SFS01  N  1380  2.3E+16  24 824  256  7.15  6.2  SFS02  N  304  5.0E+15  6761  176  7.15  6.2  SFS03  N  1790  4.8E+16  60 773  374  7.15  6.7  SFS04  N  1095  1.8E+16  18 731  283  7.18  6.5  SFS05  N  608  1.0E+16  11 354  153  7.18  6.5  SFS06  N  307  5.1E+15  7456  131  6.96  6.0  SFS07  N  1296  2.1E+16  26 411  266  7.18  6.5  SFS08  N  389  6.4E+15  9580  218  7.18  6.5  SFS09  N  1024  1.7E+16  19 332  281  7.18  6.4  SFS10  R  454  4.1E+15  4780  59  6.97  6.2  SFS11  R  890  8.0E+15  8649  116  6.97  6.2  SFS12  R  664  6.0E+15  7554  92  6.97  6.2  SFS13  R  1113  1.0E+16  11 825  181  6.83  6.8  SFS14  R  290  2.6E+15  3781  148  6.83  5.6  SFS15  R  820  7.4E+15  10 107  382  6.66  5.9  SFS16  R  337  3.0E+15  4004  148  7.05  5.9  SFS17  R  94  3.4E+15  7720  289  6.55  5.8  SFS18  R  143  5.1E+15  10 404  317  6.55  5.8  SFS19  R  156  3.3E+15  6273  204  6.55  5.9  SFS20  R  101  2.1E+15  4368  172  6.55  5.9  SFS21  R  121  1.1E+15  2739  0  5.93  5.5  SFS22  R  556  5.0E+15  5686  196  6.76  5.5  SFS23  SS  738  6.6E+15  11 858  301  7.08  5.7  SFS24  SS  1386  1.2E+16  23 800  353  6.83  6.0  Notes: N: normal faulting; R: reverse faulting and SS: strike-slip faulting. View Large As can be seen in Table 3, the annual moment rate on each SFS, obtained by multiplying the source area by its slip rate and by the constant shear modulus (assumed equal to 30 GPa), is approximately proportional to the number of M ≥ 4.0 earthquakes, for all the normal and some reverse SFSs. The ratio between the number of M ≥ 4.0 earthquakes and the seismic rate is higher by nearly 50 per cent for five of the reverse sources (SFS17-18-19-20-21) and the two strike-slip sources (SFS23-24). The proportionality is less clear for M ≥ 6.0 earthquakes. In fact, in many cases an SFS of small area can be associated with the same strong earthquake with one or more neighbouring source, and so being assigned many more M ≥ 6.0 events than could be the case if that SFS worked independently of the others. The last column of Table 3 contains also, for each SFS, the maximum magnitudes attributed to the respective fault system (CSS) in the DISS 3.2.0. The comparison between the largest magnitudes obtained from the simulation process for 100 kyr and the DISS maximum magnitudes shows that the former magnitudes are larger than the latter ones by an order of 0.7 magnitude units or more. The explanation of this mismatch is attributed to the fact that the simulator allows ruptures to cover the whole area of a single SFS, and even overcome the border among SFSs. On the contrary, the maximum magnitudes guessed by the DISS compilers are mainly based on (1) the largest magnitude of associated historical/instrumental earthquake(s), and/or (2) the scaling relationships between magnitude and fault size (Wells & Coppersmith 1994), where the fault length and/or the width are derived from geological and/or seismological data, but are generally smaller than the entire SFS to which they belong. As explained in the previous section, in the simulated rupture process, the same cell can participate in a rupture more than once. To show how this circumstance really happened in our application of the simulator to the fault systems, for the 10 largest earthquakes contained in the first 10 000 yr of the synthetic catalogue, we report in Table 4 the number of cells that have ruptured once or more than once in the specific event. The results of this analysis are interesting, as it appears that for some events most cells had only single ruptures, while in other cases multiple ruptures of the same cells are common. Table 4. Number of repeated ruptures of the same cells for the 10 largest events of the first 10 000 yr of the synthetic catalogue. Year  Mw  Number of ruptures/1 time  Number of ruptures/2 times  Number of ruptures/3 times  Number of ruptures/4 times  Number of ruptures/5 times  Number of ruptures/6 times  Number of ruptured cells  Number of total ruptures  Number of nucleation SFS  Number of ruptured SFS  482  6.97  1383  23  1  0  0  0  1407  1432  03  03  1622  6.95  1282  31  0  0  0  0  1313  1344  03  03  3932  6.96  672  229  119  0  0  0  1020  1487  03  01,02,03  6620  6.97  1358  21  0  0  0  0  1379  1400  03  03  7068  6.99  358  270  222  12  0  0  862  1612  11  10,11,12  7680  7.04  1695  31  1  0  0  0  1727  1760  03  03  8212  6.99  868  194  173  1  0  0  1236  1779  01  01,02,04,06  8808  7.05  1729  31  1  0  0  0  1761  1794  03  03  9492  7.11  358  322  182  136  63  10  1071  2467  05  01,02,04,05,08,09  9838  6.99  1419  30  1  0  0  0  1450  1482  03  03  Year  Mw  Number of ruptures/1 time  Number of ruptures/2 times  Number of ruptures/3 times  Number of ruptures/4 times  Number of ruptures/5 times  Number of ruptures/6 times  Number of ruptured cells  Number of total ruptures  Number of nucleation SFS  Number of ruptured SFS  482  6.97  1383  23  1  0  0  0  1407  1432  03  03  1622  6.95  1282  31  0  0  0  0  1313  1344  03  03  3932  6.96  672  229  119  0  0  0  1020  1487  03  01,02,03  6620  6.97  1358  21  0  0  0  0  1379  1400  03  03  7068  6.99  358  270  222  12  0  0  862  1612  11  10,11,12  7680  7.04  1695  31  1  0  0  0  1727  1760  03  03  8212  6.99  868  194  173  1  0  0  1236  1779  01  01,02,04,06  8808  7.05  1729  31  1  0  0  0  1761  1794  03  03  9492  7.11  358  322  182  136  63  10  1071  2467  05  01,02,04,05,08,09  9838  6.99  1419  30  1  0  0  0  1450  1482  03  03  Notes: Year: year of the synthetic earthquake; Mw: magnitude of the synthetic earthquake; number of ruptures/x times: number of times that the same cell breaks during the synthetic earthquake; number of ruptured cells: number of different cells ruptured during the synthetic earthquake; number of total ruptures: total number of ruptures during the synthetic earthquake; number of nucleation SFS: SFSXX containing the nucleation cell and number of ruptured SFS: SFSXX(s) responsible for the large synthetic earthquake. View Large We show in Fig. 2, the cumulative magnitude–frequency plot of the synthetic 100 000 yr catalogue compared with the plots of the CPTI15 catalogue obtained for three different threshold magnitudes with their respective completeness intervals. Figure 2. View largeDownload slide Cumulative frequency–magnitude distribution of the earthquakes in the synthetic catalogue, compared with those obtained from CPTI15 for the magnitude thresholds and the time intervals during which they are assumed complete. Figure 2. View largeDownload slide Cumulative frequency–magnitude distribution of the earthquakes in the synthetic catalogue, compared with those obtained from CPTI15 for the magnitude thresholds and the time intervals during which they are assumed complete. The comparison reported in Fig. 2 shows a substantial similarity between the synthetic catalogue and the real data in the magnitude range 4.0 ≤ M ≤ 6.5. This could be expected because the A-R and S-R free parameters were calibrated to obtain such resemblance and the slip rate assigned to the seismic sources constrains the total seismic moment released by the whole system of SFSs. however, a slight underestimation of the simulator with respect to the real catalogues appears in the magnitude range 4.5 ≤ M ≤ 6.0. This can be put in connection with the b-value variations of the synthetic catalogue along the whole magnitude range, as a b-value larger than 1.0 is noted for M ≤ 5.5, and smaller than 1.0 for 5.5 ≤ M ≤ 6.5. Some discrepancy between the synthetic and the CPTI15 catalogues can be also observed in the high magnitude range (M ≥ 6.4). In this magnitude range, the shape of the magnitude distribution of the two longer completeness time intervals is dominated by the occurrence of few very large events. In particular, the CPTI15 catalogue starting in 1871 contains only one earthquake of M ≥ 6.4, that is, the Mw 7.1 1915 Marsica earthquake. The limited number of events and the large uncertainty in magnitude estimations of the historical catalogue does not allow a robust comparison with the simulator's results, a problem already faced and analysed in detail by Wilson et al. (2017). In conclusion, although the comparison between the seismicity produced by the simulator and the observed data for evaluating the obtained results could be useful for the validation of the simulator algorithm and the assessment of its free parameters, it is not a simple problem. The five century of completeness for the M 6+ earthquakes may not be long enough to encompass the recurrence time of characteristic earthquakes on single SFS. Moreover, as already remarked, a single earthquake could have ruptured only a part of a single segment for moderate magnitudes, or have propagated to more than one segment for the larger magnitudes, in agreement with the assumption made in our simulation algorithm. In order to carry out a statistical analysis on the number of ruptured SFSs contributing to a single earthquake and their recurrence intervals, some quantitative, even if somehow arbitrary, definitions are necessary to assign a specific earthquake to one or more SFSs. For a more in-depth analysis of this issue, we refer to the discussion made by Field (2015) addressing the ‘recurrence of what?’ question. In our analysis, the following criteria were adopted: The minimum equivalent magnitude for a ruptured group of cells is 6.0. Initially the earthquake is assigned to the SFS containing the nucleation cell of the earthquake. If the number of cells ruptured by the earthquake in one of the other SFSs is larger than 150 or this SFS has atleast 60 per cent of ruptured cells, then this segment can also be included in the same earthquake. In this way, we counted through the whole 100 kyr synthetic catalogue the number of times that a given fault segment was present in any M ≥ 6.0 earthquake alone (1898 times) or jointly with other segments (505 times). In a unique case, six SFSs ruptured all together in one single very large earthquake. In order to assess whether the earthquake occurrence time on single segments in the synthetic catalogue behaves as a Poisson process or not, we carried out a statistical analysis of the interevent times for the entire 100 kyr simulation. For this purpose, Fig. 3 displays for each of three selected fault systems (SFS03, SFS04 and SFS07), the recurrence time distribution for the M ≥ 6.0 events to which they were assigned, as previously described. Table 5 shows the statistical parameters obtained by the whole procedure for each source: the average recurrence time for M ≥ 6.0, Tr, the Poisson probability that the segment might rupture in 50 yr at a rate of 1/Tr, P50, the standard deviation of the recurrence times, σ, and the coefficient of variation, Cv. The last column of Table 5 reports also the date and the magnitude of the latest historical earthquake assigned to every SFS, when this information is available. Figure 3. View largeDownload slide Interevent time distribution from a simulation of 100 000 yr of seismic activity across the Central Apennines, for three selected fault systems. The time-dependent 50 yr occurrence probability of an M6+ earthquake on the Colfiorito-Cittareale fault system, under a renewal BPT model, could be estimated before the 2016 August 24 earthquake as 13 per cent. Figure 3. View largeDownload slide Interevent time distribution from a simulation of 100 000 yr of seismic activity across the Central Apennines, for three selected fault systems. The time-dependent 50 yr occurrence probability of an M6+ earthquake on the Colfiorito-Cittareale fault system, under a renewal BPT model, could be estimated before the 2016 August 24 earthquake as 13 per cent. Table 5. Statistical parameters of the synthetic catalogue for each SFS (see the text for explanations). ID  Tr (M ≥ 6.0) (yr)  P50 (%)  σ (yr)  Cv  Latest largest EQ  SFS01  493.5  9.6  339.9  0.69  1832, Mw 6.4  SFS02  1206.7  4.1  517.8  0.43  1298, Mw 6.3  SFS03  283.1  16.2  206.5  0.73  1915, Mw 7.1  SFS04  555.9  8.6  341.9  0.61  2009, Mw 6.3  SFS05  944.6  5.2  447.2  0.47  No data  SFS06  997.0  4.9  305.6  0.31  1984, Mw 5.6  SFS07  517.8  9.2  330.1  0.64  2016, Mw 6.5  SFS08  971.0  5.0  547.6  0.56  1639, Mw 6.2  SFS09  657.2  7.3  364.8  0.56  1461, Mw 6.5  SFS10  1905.8  2.6  800.1  0.42  1741, Mw 6.2  SFS11  1077.2  4.5  681.7  0.63  1799, Mw 6.2  SFS12  1448.3  3.4  660.4  0.46  No data  SFS13  832.1  5.8  498.9  0.60  1706, Mw 6.8  SFS14  2105.4  2.3  1187.3  0.56  No data  SFS15  776.6  6.2  565.7  0.73  1943, Mw 5.7  SFS16  1330.2  3.7  539.2  0.41  No data  SFS17  643.4  7.5  571.8  0.89  1269, Mw 5.6  SFS18  611.8  7.8  531.3  0.87  No data  SFS19  947.5  5.1  552.6  0.58  1690, Mw 5.6  SFS20  1019.9  4.8  655.7  0.64  No data  SFS21  –  0.0  –  –  No data  SFS22  825.0  5.9  451.4  0.55  No data  SFS23  917.1  5.3  553.7  0.60  1950, Mw 5.7  SFS24  419.5  11.2  289.2  0.69  No data  ID  Tr (M ≥ 6.0) (yr)  P50 (%)  σ (yr)  Cv  Latest largest EQ  SFS01  493.5  9.6  339.9  0.69  1832, Mw 6.4  SFS02  1206.7  4.1  517.8  0.43  1298, Mw 6.3  SFS03  283.1  16.2  206.5  0.73  1915, Mw 7.1  SFS04  555.9  8.6  341.9  0.61  2009, Mw 6.3  SFS05  944.6  5.2  447.2  0.47  No data  SFS06  997.0  4.9  305.6  0.31  1984, Mw 5.6  SFS07  517.8  9.2  330.1  0.64  2016, Mw 6.5  SFS08  971.0  5.0  547.6  0.56  1639, Mw 6.2  SFS09  657.2  7.3  364.8  0.56  1461, Mw 6.5  SFS10  1905.8  2.6  800.1  0.42  1741, Mw 6.2  SFS11  1077.2  4.5  681.7  0.63  1799, Mw 6.2  SFS12  1448.3  3.4  660.4  0.46  No data  SFS13  832.1  5.8  498.9  0.60  1706, Mw 6.8  SFS14  2105.4  2.3  1187.3  0.56  No data  SFS15  776.6  6.2  565.7  0.73  1943, Mw 5.7  SFS16  1330.2  3.7  539.2  0.41  No data  SFS17  643.4  7.5  571.8  0.89  1269, Mw 5.6  SFS18  611.8  7.8  531.3  0.87  No data  SFS19  947.5  5.1  552.6  0.58  1690, Mw 5.6  SFS20  1019.9  4.8  655.7  0.64  No data  SFS21  –  0.0  –  –  No data  SFS22  825.0  5.9  451.4  0.55  No data  SFS23  917.1  5.3  553.7  0.60  1950, Mw 5.7  SFS24  419.5  11.2  289.2  0.69  No data  View Large Both Tables 3 and 5 show, as expected, that the most active segments are those characterized by larger size and/or higher slip rate (see Table 2 for the parameters), such as SFS01, SFS03 and SFS24, characterized by recurrence times of 300–500 yr. The simulation also shows that, especially for the less active segments (SFS10, SFS12 and SFS14), interevent times of several thousands of years are possible. The coefficient of variation Cv is typically close to 0.6, which would be associated to a moderate periodicity of the seismicity. As an exercise made upon these results, we computed the time-dependent 50 yr occurrence probability of an M ≥ 6.0 earthquake on the SFS07 Colfiorito-Cittareale, where the 2016 August–October seismic sequence really occurred, how it could have been estimated at the beginning of 2016, under a renewal Brownian passage time (BPT) model. This probability, conditioned by a time of 313 yr elapsed since the last ‘characteristic’ earthquake occurred in 1703 (Table 1), could be calculated as equal to 13.0 per cent from the SFS03 recurrence distribution. Conversely, under a time-independent Poisson model, this probability, obtained from a recurrence time Tr = 518 yr, would be only 9.2 per cent (Table 5). Another temporal feature of the synthetic catalogue obtained from our simulation algorithm was explored by analysing the statistical distribution of the time by which an event of any magnitude can precede or follow an earthquake of M ≥ 6.0. This study was aimed to assess the existence in the synthetic catalogues of some kind of time-dependent occurrence rate as a long-term precursor of strong earthquakes. The analysis was carried out by a stacking technique on the synthetic catalogue. For each event of M ≥ 6.0, the catalogue has been scanned for the 1000 yr preceding and the 1000 yr following such event, dividing this time period in bins of 10 yr. The events occurred in each time bin of this time period have been counted regardless of their location and magnitude. The procedure has been repeated for all M ≥ 6.0 earthquakes and the numbers of events found in each bin have been counted together. The results give the total number of M4+ earthquakes preceding and following an M6+ earthquake in each bin of 10 yr in the time period considered. These results are displayed in Fig. 4(a). This figure shows an outstanding trend of acceleration of seismic activity in a 400 yr period before the strong earthquakes, as well as a sort of quiescence with a slow recovering to the normality after such earthquakes. This feature can be compared with the result obtained through a similar analysis, reported by Console et al. (2017) for the Calabria region. In that case, the seismic rate acceleration was noted for only 200 yr, while the recovering to the normal rate was significantly slower. Such difference between the two cases could be explained by a combination of factors, like a different magnitude threshold chosen for the analysis (M4.5 in the Calabria study), a different slip rate of some of the sources in the two regions, and mainly the existence of long extensional and compressional parallel SFSs in the Central Apennine region (Fig. 1). This feature, which is not observable in Calabria, can produce a different mechanism of positive or negative stress transfer among SFSs in case of large magnitude earthquakes. Figure 4. View largeDownload slide Stacked number of M4+ earthquakes preceding and following an M6+ earthquake, obtained from the 100 000 yr simulation in a long-term (a; top) and short-term (b; bottom) timescale, respectively. The long-term plot shows acceleration before and quiescence after the strong event. The short-term plot shows the occurrence of aftershocks in the two months after the strong earthquake. Figure 4. View largeDownload slide Stacked number of M4+ earthquakes preceding and following an M6+ earthquake, obtained from the 100 000 yr simulation in a long-term (a; top) and short-term (b; bottom) timescale, respectively. The long-term plot shows acceleration before and quiescence after the strong event. The short-term plot shows the occurrence of aftershocks in the two months after the strong earthquake. The acceleration of seismic moment release before strong earthquakes is a well-known phenomenon reported in literature as a possible earthquake precursor but generally observed over shorter timescales (see e.g. De Santis et al. 2015, and references therein). It would be interesting to compare this result with something happening in nature if historical catalogues covering a comparable time length of hundreds of years were available, which is not the case for moderate magnitude events (see e.g. Wilson et al. 2017). In a preliminary way, we could guess that this is a result of the stress transfer on faults from prior events becoming an increasingly important fraction of the total stress compared with tectonic loading over time. As to the quiescence after M6+ earthquakes, any stress release model would exhibit such behaviour, but rarely, if ever, over 400 yr. The 1906 San Francisco earthquake has a stress shadow of a century or so, for instance (Parsons 2002). The longer quiescence period found in our simulations for Central Apennines with respect to California can be justified by the difference of the slip rate by an order of magnitude over the major fault systems of the two regions. In fact, the slip rate on single sources is the factor that controls the timescale of the seismicity generated by our simulator. As a simple consequence, if we only changed the slip rate of our geological model of Central Apennines, we would obtain an identical catalogue of earthquakes, but with a time duration inversely proportional to the slip rate given in input to the model. Considering the case of short-term interaction, Fig. 4(b) shows the result of a similar stacking technique carried out for a time interval of ±0.5 yr. In this case, the total time spanned before and after the M6+ earthquakes is one year and the time bins are 0.01 yr (about 3.65 d) long. The sudden raise of seismic activity soon after an earthquake of M ≥ 6.0 testifies the presence of a feature resembling that of aftershock production, modeled through the inclusion of an after-slip process in the simulation algorithm. Note that the seismic activity few months after the main shocks in average goes back to values lower than those existing few months before the same main shocks. 5 THE SIMULATED CATALOGUE APPLIED TO TIME INDEPENDENT SEISMIC HAZARD ASSESSMENT In order to test the potential application of our simulations to seismic hazard assessment, we adopted a simple ground motion prediction equations (GMPE) model, and applied the Cornell (1968) method to the M ≥ 4.5, 100 000 yr simulated catalogue. The peak acceleration (PGA) at a dense grid of points covering the territory of the Central Apennines was estimated for each earthquake of the catalogue through a typical attenuation law (Sabetta-Pugliese 1987):   \begin{eqnarray*} \log ({\rm{PGA}}) &=& - 1.562 + 0.306M - \log ( {\sqrt {{d^2} + {{5.8}^2}} } )\nonumber \\ && +\, 0.169{S_1} + 0.169{S_2} \pm 0.173 \end{eqnarray*} (1)where M is the earthquake magnitude, d is the epicentral distance and S1 and S2 are parameters taking into account the soil dynamic features at the site. At each node of the grid, we obtained the distribution of the number of times that a given PGA was exceeded in 100 000 yr, and repeating it for many PGA values, we obtained the value of PGA characterized by a probability of exceedance of 10 per cent in 50 yr (Fig. 5). Figure 5. View largeDownload slide Map of PGA characterized by a probability of exceedance of 50 per cent in 50 yr, inferred from the 100 000 yr synthetic catalogue of the Central Apennines. Figure 5. View largeDownload slide Map of PGA characterized by a probability of exceedance of 50 per cent in 50 yr, inferred from the 100 000 yr synthetic catalogue of the Central Apennines. 6 DISCUSSION The application of our physics-based simulation algorithm to the fault systems of the Central Apennines has allowed the compilation of synthetic seismic catalogue lasting 100 kyr for M ≥ 4.0. This catalogue contains more than 500 000 earthquakes whose magnitude distribution and time–space features resemble those of the observed seismicity, but without the limitations that real catalogues suffer in terms of completeness and time duration. In this section, we consider items of our study that deserve particular attention and some more detailed discussion. 6.1 The role of specific parameters of the simulation model The real catalogue of Central Apennines, reports 17 earthquakes with M ≥ 6.0 after 1500 (Table 1), and the catalogue obtained from the simulation contains 2403 M ≥ 6.0 events in 100 kyr. The respective occurrence rate of M ≥ 6.0 earthquakes is 0.035 events per year from the historical records and 0.024 events per year for the simulation. We have already stated in Sections 3 and 4 that simulation parameters are typically adjusted so that natural earthquake sequences are matched in their scaling properties (Wilson et al. 2017). This implies that the user must have a good knowledge of the effect of each single parameter. The role of the S-R and A-R parameters in our simulation algorithm was already analysed by Console et al. (2015, figs 5a–c; 2017, figs 6a and b). A similar analysis has been carried out also in this study, with the application of the simulator to the seismicity of Central Apennines. Figure 6. View largeDownload slide (a) Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 1 km × 1 km, a stress reduction (S-R) coefficient equal to 0.4 and different values of the aspect-ratio (A-R) coefficient. (b) As in A, using an A-R coefficient equal to 2 and various values of the stress reduction (S-R) coefficient. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. Figure 6. View largeDownload slide (a) Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 1 km × 1 km, a stress reduction (S-R) coefficient equal to 0.4 and different values of the aspect-ratio (A-R) coefficient. (b) As in A, using an A-R coefficient equal to 2 and various values of the stress reduction (S-R) coefficient. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. As shown in Fig. 6(a), the A-R parameter (the parameter that allows the growth of ruptures towards larger portions of a fault), has effect only on the large magnitude range of the magnitude distribution (M ≥ 6.0). This figure shows the magnitude distribution of the synthetic catalogues obtained changing A-R from 2 to 16 for a constant value of S-R equal to 0.4. The larger A-R is, the larger is the maximum magnitude of the synthetic catalogue, but smaller is the number of earthquakes with 6.0 ≤ M ≤ 7.0. Having small influence on the magnitude distribution of small magnitude earthquakes, the A-R parameter has also a little effect on the b-value, which in our tests ranges from 1.25 (A-R = 2) to 1.33 (A-R = 16). The role of the S-R parameter is reducing the fault strength and favouring the expansion of nucleated ruptures, as a sort of dynamic weakening effect. Fig. 6(b) reports the magnitude distribution of synthetic catalogues obtained maintaining a constant value of A-R = 2 and changing S-R from 0.2 to 0.6. It can be easily noted that the effect of the S-R parameter is specifically referred to the ratio between the number of moderate magnitude events (4.0 ≤ M ≤ 6.0) and the number of larger magnitudes, with a significant impact on the b-value of the magnitude distribution. As a matter of fact, the b-value of the synthetic catalogues decreases from 1.29 (S-R = 0.2) to 0.78 (S-R = 0.6). We can conclude that the results obtained in this analysis, as to the role of both the A-R and S-R parameters on the magnitude distributions of the synthetic catalogues confirm the similar analyses carried out in previous papers by Console et al. (2015, 2017). Figs 6(a) and (b) give also a comparison of the occurrence rate distribution of the synthetic catalogues with that of two real catalogues, respectively CPTI15 (1950–2013, M ≥ 4.0) and CPTI15 (1500–2017, M ≥ 6.0). A visual inspection of these figures supports our choice described in Section 3 for small values of both the S-R and A-R parameters, such as S-R = 0.2–0.4 and A-R = 2–4. Increasing the free parameters beyond these values produces larger discrepancies with the exhibited by all our synthetic catalogues with respect to the real ones can be justified by the lack of moderate size faults in our model consisting of only 24 main faults. 6.2 Modeling smaller magnitude earthquakes by the simulator As already said at the beginning of Section 4, the minimum magnitude of the earthquakes of the synthetic catalogues, having adopted a model with cells of 1.0 km × 1.0 km size and a stress drop of 3.0 MPa, is 4.0 (or more precisely 3.98). This is not a limit of the methodology but just a practical consequence of the computer time necessary for running a simulation based on a given number of cells and lasting a given number of years. For instance, each of the simulations of 100 kyr described above required several tens of hours of computer time on an inexpensive PC. In order to test the simulator for producing a catalogue containing smaller magnitude events, we adopted a model with the same 24 SFSs of Fig. 1 and a discretization in cells of 0.5 km × 0.5 km. This implies a minimum magnitude of the synthetic catalogue equal to 3.4 (or more precisely 3.38). The results of this test are shown in Fig. 7 for two synthetic catalogues lasting 10 000 yr, with a choice of S-R = 0.2 and 0.4, and A-R = 2 and 4, respectively. Also in this plot, we have added the magnitude–frequency distribution of two real catalogues (CPTI15 1950–2013 and CPTI15 1500–2017) for sake of comparison. Figure 7. View largeDownload slide Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 0.5 km × 0.5 km, and two different combinations of the parameters S-R and A-R. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. Figure 7. View largeDownload slide Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 0.5 km × 0.5 km, and two different combinations of the parameters S-R and A-R. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. 6.3 Comparison of the synthetic and real catalogue for the largest magnitudes Let us focus our attention on the SFS03 Cittaducale-Barrea source, the one containing the strongest historical earthquake of the whole region (the 1915 Mw 7.1 Marsica earthquake; Table 1), as well as the one with a large slip rate (Table 2) and a short recurrence time (Table 5). We see in Fig. 1 that three M ≥ 5.5 earthquakes, but no other M ≥ 6.0 earthquakes are reported for this SFS. Referring to SFS03, the 100 kyr synthetic catalogue contains 374 M ≥ 6.0 earthquakes and 9 M ≥ 7.0 earthquakes, with a 7.15 maximum magnitude. Therefore, the simulation algorithm would give an expectation of about one earthquake in 10 000 yr of magnitude class 7 on the SFS03 source. This simple computation leads us to consider the 1915 Mw 7.1 Marsica earthquake an extremely rare phenomenon, unlikely to recur on the same fault system in the next several thousands of years. Another interpretation of this circumstance could be that the Mw 7.1 magnitude reported in CPTI15 is overestimated. This interpretation appears consistent also with the maximum magnitude value of 6.7 assigned by the DISS 3.2.0 compilers to this particular source. The presence of the Mw 7.1 Marsica earthquake in the CPTI15 historical catalogue is the main reason of the discrepancy between the cumulative magnitude distribution of the CPTI15 data and those obtained by the 100 kyr simulation for the whole Central Apennines region, especially for the observations with M ≥ 5.0 starting in 1871 (Fig. 2). However, taking into account the uncertainties shown by the error bars of Fig. 2, this discrepancy is not quite significant. Moreover, in light of the discussion about the singularity of the 1915 earthquake, made above, this discrepancy can be also justified by the relatively short length of the catalogue with respect to the recurrence time of large events, and uncertainty characterizing their magnitude. Another interesting piece of information is given by the last column of Table 5. Here, we see that for only 15 out of 24 SFSs, the date of the latest strong event is known. Moreover, we can note that 10 of these 15 earthquakes occurred after 1700 AD and only two are older than 500 yr, while the average recurrence time obtained from the synthetic catalogue is typically larger than 500 yr except for only two cases. Unless we believe that most of the SFSs in the Central Apennines have released their energy in a relatively short time window of 3–4 centuries, this is a strong evidence of the lack of information available in the historical earthquake catalogue for the region considered in this study, discouraging the use of historical catalogues for a statistical earthquake rate assessment. 6.4 Fault segmentation and geographical extension of ruptures for the largest magnitude earthquakes One of the main purposes of our application of the simulator to the seismicity of the Central Apennines area was testing whether fault segmentation and characteristic earthquake hypothesis are or are not necessary conditions for modeling in reasonable way earthquake patterns observed in real historical records. To show how the unsegmented model of SFS used in our simulation can generate realistic seismicity patterns that can be compared with the real seismicity observed in the most recent centuries, we analysed the complete history of simulated ruptures in a period of 10 kyr along three SFS linked together, along a nearly straight line. For this exercise, we extracted, from a synthetic catalogue of 10 kyr obtained for the complete set of 24 SFSs, the earthquakes occurring on a fault system including SFS07, SFS08 and SFS09 with a total length of about 170 km (Fig. 1). The simulator algorithm is not conditioned by the subpartition of this structure in three SFSs because their minimum relative distance is shorter than 10 km, and ruptures are allowed to propagate from one to another in a unique event. In Fig. 8, excluding the events with magnitude smaller than 6.0, all the larger earthquakes are represented colouring the cells of 1 km × 1 km ruptured in each of them. Each panel from the top to the bottom of the picture shows the events occurred in separate time windows of 300 yr with different colours for each earthquake in the same time window. The colours represent the order by which the events enucleated in each panel of 300 yr, from blue to yellow and red, respectively. Multiple ruptures on the same cell in a unique earthquake are represented by darker tones of their respective colours. Figure 8. View largeDownload slide Map of ruptures for M ≥ 6.0 earthquakes on the joint set of SFS07, SFS08 and SFS09 in 33 time windows of 300 yr represented from top to bottom. The 170-km-long fault system is displayed in each panel from left to right moving from NW to SE (Fig. 1). On any panel, the blue, yellow and red colours represent the temporal order of earthquake occurrence, and the darker tone of the respective colours represent the amount of slip on multiply ruptured cells. Figure 8. View largeDownload slide Map of ruptures for M ≥ 6.0 earthquakes on the joint set of SFS07, SFS08 and SFS09 in 33 time windows of 300 yr represented from top to bottom. The 170-km-long fault system is displayed in each panel from left to right moving from NW to SE (Fig. 1). On any panel, the blue, yellow and red colours represent the temporal order of earthquake occurrence, and the darker tone of the respective colours represent the amount of slip on multiply ruptured cells. By examining Fig. 8, we can note that only three 300 yr periods of 33 were lacking any M ≥ 6.0 earthquake, while only two of the other periods contain three earthquakes of such magnitude. There is a clear trend for earthquakes not to occupy the same rupture areas in the same time window, or in consecutive time windows, while they are mostly separated from each other by more than 300 yr of several time windows. During the whole test of 10 000 yr, every portion of the 170 km long fault system was occupied by at least 6–7 ruptures in distinct earthquakes, and none of them was left empty. This is consistent with the recurrence time of 500–1000 yr characterizing the three SFSs considered in this test. From the results of the exercise discussed in this subsection (see Fig. 8), we can infer that the segmentation scheme mainly based on historical records of earthquakes occurred during the latest centuries could have likely been conditioned by the particular pattern of ruptures exhibited by a group of SFS in this relatively recent time window. A detailed analysis was carried out on the 10 strongest earthquakes in the 10 kyr catalogue reported in Table 4, examining to which single or multiple SFS(s) these earthquakes can be assigned: Extensional fault systems are responsible of 9 of these 10 strongest earthquakes. SFS03, responsible of the strongest earthquake of the historical and simulated catalogues (Mw 7.1) is the source that was activated most often in the 10 kyr simulation (70 per cent of times), in agreement with the observed seismicity. SFS03 is ruptured singularly in 90 per cent of the cases, without activating other neighbouring sources. The other sources responsible of the 10 strongest earthquakes in 10 kyr (SFS01, SFS05 and SFS11) never ruptured alone, but always jointly with the closest SFSs, along both the strike and the geometrically normal directions. Moving further to consider the occurrence time pattern of the simulated catalogue, we have already introduced Table 5 showing that, for most single SFS, strong earthquakes of M ≥ 6.0 exhibit an interevent time distribution characterized by a fairly pseudo-periodic behaviour. Fig. 4(a) also shows that, in the Central Apennines region as a whole, moderate magnitude earthquakes have a higher probability of occurrence during the period of 400 yr preceding strong earthquakes than during the same period of 400 yr following them. It is a challenging issue to compare this particular feature exhibited by the synthetic catalogue with real observations. In fact, the duration of the period of completeness for earthquakes with M ≥ 4.0, as those for which Fig. 4 was prepared, is only 64 yr, by far too short for assessing the existence of a cyclic process lasting hundreds of years. However, from Fig. 4, we can receive a warning, that is not to trust the assessment of earthquake rates based on historical data only, as such assessment could be biased by long-term seismicity changes that occur on specific groups of SFSs, depending on the particular status of those SFSs in their respective multicentury earthquake cycle. 6.5 Clustering versus random behaviour of the simulated catalogue Here, we want to remark that the occurrence times of M ≥ 6.0 earthquakes obtained from the simulator do not exhibit any clear clustering trend. To show it, we have analysed the number of M ≥ 6.0 synthetic events contained in consecutive time intervals of fixed length (Table 6). Table 6. Number of times that a different number of M ≥ 6.0 earthquakes are reported in consecutive time windows of the 100 kyr synthetic catalogue (S) compared with the expected number of times computed under the Poisson time-independent hypothesis (P), for different time window lengths. Number of events  Time window length    10 yr  20 yr  50 yr  100 yr  250 yr    S  P  S  P  S  P  S  P  S  P  0  7833  7863.9  3056  3092.0  568  593.4  71  90.45  0  0.98  1  1938  1889.7  1539  1486.0  756  721.0  223  217.3  7  5.91  2  209  227.0  352  357.1  442  438.0  264  261.1  11  17.76  3  15  18.19  45  57.21  179  177.3  223  209.1  25  35.56  4  0  1.09  6  6.87  45  53.88  142  125.6  54  53.41  5    0.05  0  0.66  8  13.09  58  60.39  69  64.17  6    0.00    0.05  1  2.65  10  24.19  71  64.25  7          0  0.46  8  8.30  67  55.14  8            0.07  0  2.49  56  41.41  9            0.01  1  0.67  18  27.64  10            0.00  0  0.16  15  16.60  11                0.03  4  9.07  12                0.01  1  4.54  13                0.00  1  2.10  14                  1  0.90  15                  0  0.36  16                    0.14  17                    0.05  18                    0.02  19                    0.01  20                    0.00  P(χ2)  0.52  0.29  0.32  0.14  0.13  Number of events  Time window length    10 yr  20 yr  50 yr  100 yr  250 yr    S  P  S  P  S  P  S  P  S  P  0  7833  7863.9  3056  3092.0  568  593.4  71  90.45  0  0.98  1  1938  1889.7  1539  1486.0  756  721.0  223  217.3  7  5.91  2  209  227.0  352  357.1  442  438.0  264  261.1  11  17.76  3  15  18.19  45  57.21  179  177.3  223  209.1  25  35.56  4  0  1.09  6  6.87  45  53.88  142  125.6  54  53.41  5    0.05  0  0.66  8  13.09  58  60.39  69  64.17  6    0.00    0.05  1  2.65  10  24.19  71  64.25  7          0  0.46  8  8.30  67  55.14  8            0.07  0  2.49  56  41.41  9            0.01  1  0.67  18  27.64  10            0.00  0  0.16  15  16.60  11                0.03  4  9.07  12                0.01  1  4.54  13                0.00  1  2.10  14                  1  0.90  15                  0  0.36  16                    0.14  17                    0.05  18                    0.02  19                    0.01  20                    0.00  P(χ2)  0.52  0.29  0.32  0.14  0.13  View Large As it can be easily seen, the comparison between the simulations and the Poisson time-independent model, as shown in Table 6, demonstrates a clear similarity of the two distributions, as far as the Central Apennines area is considered all together. This can be explained by the relatively large number of 24 SFSs, which, besides a certain degree of interaction, produce a random sequence of occurrence times. By a more careful comparison of the simulated and theoretical values, it can be noted that, for time windows of 100 and 250 yr, the values obtained from the simulations in the central part of the distributions are a little larger than those expected from the Poisson model. It means that, for these two time window lengths, the events tend to occur a little more frequently in pseudo-periodical manner than in completely random way. However, the last line of Table 6, where the p-values of the χ2 test are reported, proves that the null time-independent hypothesis cannot be rejected with a confidence level larger than 90 per cent for any of the examined time window lengths. In contrast with the features of the synthetic catalogue resulting from the above-mentioned analysis, it is widely recognized that the actual M6+ seismicity in the Central Apennines exhibits strong clustering properties. For instance, in the time up to and including the 2016 sequence of M6+ events in our study area, there are five events in ∼19 yr, four events in ∼7.5 yr and three events in ∼0.18 yr. The probabilities of these happening in a Poisson process with a rate of 0.02403 events per year are 1.16 × 10−4, 3.94 × 10−5 and 1.44 × 10−8, respectively. We can argue that our simulation's SFS specific Tr and Cv, are reliable and therefore they can be useful for a long-term seismic hazard estimation (e.g. Fig. 5). However, the results of the analysis reported in Table 6 show that the simulator does not accurately capture the conditional probabilities of a large event anywhere in the system given that another large event has occurred somewhere in the system recently. Concerning the short and very short-term behaviour, we have shown in Fig. 4(b) that a simple algorithm introduced in the most recent version of the simulator applied in this study, which we call ‘after-slip’effect, can produce an increase of the seismic rate soon after a strong earthquake. This algorithm mimics in some respect the well-known aftershock phenomenon observed in the real seismicity. However, a simple examination of Fig. 4(b) shows that the stacked rate of events in the first day after an earthquake of M6+ does not exceed by more than a factor of 10 times the average rate before such earthquakes. To analyse this circumstance in more detail, we have computed the average number of events of magnitude M4+ following any earthquake of magnitude M6+ within six months after their occurrence time and 100 km of distance from their epicentre. This computation, done on the synthetic catalogue characterized by the couple of parameters S-R = 0.2 and A-R = 2 and an after-slip ratio equal to 0.2, leads to an average number of aftershocks equal to 1.64. The same kind of computation, carried out on the catalogue obtained from a discretization of 0.5 km × 0.5 km (and a smallest magnitude of 3.4) and the same model parameters results in an average number of aftershocks equal to 10.7. The number of aftershocks contained in our synthetic catalogues is smaller by at least an order of magnitude than the number of aftershocks of similar magnitude threshold observed in the Central Apennine after the events of M6+ during the seismic sequence of 2016 August–October (Table 1). The results of this analysis show that our after-slip algorithm does not totally capture the aftershock phenomenon observed on real data. We argue that this poor result could be ascribed to the lack of small secondary faults surrounding the main faults in our simplified geological model. Another comparison with real data was done with the average difference between the main shock magnitude and the magnitude of the largest aftershock, commonly retained approximately equal to 1.2 according to the so-called Bath's law (Vere Jones 1969). Such difference was found respectively equal to 2.29 and 2.97 magnitude units with the two above-mentioned synthetic catalogues. These results are clearly indicative of the fact that most of the aftershocks contained in our synthetic catalogues are represented by events of very small magnitude rupturing a small number of cells. 6.6 The seismic hazard map and its comparison with existing seismic hazard assessment in Central Italy It could be interesting to make a comparison of the results shown in Section 5 with those obtained in previous assessments. For instance, this comparison can be done with the National Seismic Hazard Map in annex to the Ordinance of the President of the Council of Ministers issued on 2003 March 30 (updated until 2015). This map is currently used for applications in new building design overall the Italian territory, expressed in terms of maximum PGA with a probability of exceedance of 10 per cent in 50 yr on stiff soil (http://zonesismiche.mi.ingv.it/documenti/mappa_opcm3519.pdf.). The comparison shows substantial similarity for the exceedance probability of 0.2 g PGA overall the Central Apennine area. However, the scattered pattern resembling the structure of the SFSs clearly visible in Fig. 5 is not represented in the National Seismic Hazard Map. In particular, the national map does not show the spot of high values connected to SFS17, SFS18, SFS19 and SFS20, in the northern part of the map of Fig. 5. The high values of exceedance probability for 0.2 g PGA in 50 yr for the four sources located southeast of Ancona (Figs 1 and 5) are probably due to the high values of the slip rates of those sources (Table 2). These slip rates values were assessed for the Plio-Pleistocene with great accuracy by Maesano et al. (2013) through an analysis of seismic lines. If this discrepancy is just an effect of having overestimated the slip rate of those sources in our model, or if it is an underestimation of hazard in the present national map, is a very difficult question that deserves further studies. 7 CONCLUSIONS In this study, we have applied a newly developed physics-based earthquake simulation algorithm to build a synthetic catalogue of earthquakes, the epicentres of which cover the whole seismic region of Central Apennines. The spatial distribution of the simulated seismicity is constrained by the geometrical parameters of the seismogenic model of Central Apennines derived from the DISS. The total seismic moment released by the earthquakes of the synthetic s is very much constrained by the value of slip rate assumed for each fault system, a critical ingredient of the simulation algorithm. The relative simplicity of our algorithm has allowed simulations lasting 10 000 yr or 100 000 yr, and containing hundreds of thousands earthquakes with a smallest magnitude, respectively, equal to 3.4 or 4.0. The main conclusions that can be drawn from the results of this study, carried out by the employment of a physics-based simulation technique to the seismicity of the Central Apennines fault systems, are the following. The frequency–magnitude distribution of the simulated seismicity is rather consistent with observations in the intermediate magnitudes range (4.0 ≤ M ≤ 6.5), with a b-value slightly larger than 1.0 for small magnitudes (4.0 ≤ M ≤ 5.5) and slightly smaller than 1.0 for higher magnitudes (5.5 ≤ M ≤ 6.5). The frequency–magnitude distribution is clearly tapered for M ≥ 6.5. The long period of simulations allowed us to obtain the statistical distribution of repeat times—an indispensable component for any time-dependent seismic hazard assessment, which is lacking in the real historical observations. The statistical distribution of interevent times for earthquakes with M ≥ 6.0 on single segments exhibits a moderate pseudo-periodic behaviour, with a coefficient of variation Cv of the order of 0.4–0.8. The space–time behaviour of earthquake ruptures on the fault systems produced by the simulator shows that segmentation is not needed to model long-term seismicity patterns. We have found in our synthetic catalogue a clear trend of acceleration of seismic activity in the 400 yr preceding M ≥ 6.0 earthquakes and quiescence in a period of the same order of magnitude following those earthquakes, which leads to infer a possible cyclic earthquake rate variation with a duration of some centuries. The phenomenon of short-term interaction and aftershocks, dealt with the introduction of an after-slip process in our algorithm, is not adequately represented in our synthetic catalogues and deserves further consideration. An exercise of potential use of the simulator as a tool for time-independent statistical hazard assessment was carried out by the application of a simple GMPE model to all the events contained in the synthetic catalogue lasting 100 kyr for the Central Apennines. Even if this study was aimed to explore methodological aspects and potential capabilities of new-generation simulator algorithms, the initial results shown in this paper encourage further investigations about the application of simulators in support to other methodologies of time-independent and time-dependent seismic hazard assessment in Italy. 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Seismol. , 5( 3), 287– 306. https://doi.org/10.1023/A:1011463223440 Google Scholar CrossRef Search ADS   Vannoli P., Burrato P., Fracassi U., Valensise G., 2012. A fresh look at the seismotectonics of the Abruzzi (Central Apennines) following the 6 April 2009 L’Aquila earthquake (Mw 6.3), Ital. J. Geosci. , 131( 3), 309– 329. Vannoli P., Vannucci G., Bernardi F., Palombo B., Ferrari G., 2015. The source of the 30 October 1930, Mw 5.8, Senigallia (central Italy) earthquake: a convergent solution from instrumental, macroseismic and geological data, Bull. seism. Soc. Am. , 105( 3), 1548– 1561. https://doi.org/10.1785/0120140263 Google Scholar CrossRef Search ADS   Vere-Jones D., 1969. A note on the statistical interpretation of Bath's Law, Bull.seism. Soc. Am. , 59( 4), 1535– 1541. Vezzani L., Ghisetti F., 1998. Cartageologicadell’Abruzzo. Scale 1:100,000, S.EL.CA., Firenze. Wells D.L., Coppersmith K.J., 1994. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. seism. Soc. Am. , 84, 974– 1002. Wilson J.M., Yoder M.R., Rundle J.B., Turcotte D.L., Schultz K.W., 2017. Spatial evaluation and verification of earthquake simulators, Pure appl. Geophys. , 174, 2279– 2293. https://doi.org/10.1007/s00024-016-1385-x Google Scholar CrossRef Search ADS   © The Author(s) 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

The seismicity of the Central Apennines (Italy) studied by means of a physics-based earthquake simulator

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Abstract

Abstract The application of a physics-based earthquake simulation algorithm to the Central Apennines, where the 2016–2017 seismic sequence occurred, allowed the compilation of a synthetic seismic catalogue lasting 100 kyr, and containing more than 500 000 M ≥ 4.0 events, without limitations in terms of completeness, homogeneity and time duration. This simulator is based on an algorithm constrained by several faulting and source parameters. The seismogenic model upon which we applied the simulator code, was derived from the Database of Individual Seismogenic Sources including all the fault systems that are recognized in the Central Apennines. The application of our simulation algorithm provides typical features in time, space and magnitude behaviour of the seismicity, which are comparable with the observations. These features include long-term periodicity and a realistic earthquake magnitude distribution. The statistical distribution of earthquakes with M ≥ 6.0 on single faults exhibits a fairly clear pseudo-periodic behaviour, with a coefficient of variation Cv of the order of 0.4–0.8. We found in our synthetic catalogue a clear trend of long-term acceleration of seismic activity preceding M ≥ 6.0 earthquakes and quiescence following those earthquakes. Lastly, as an example of a possible use of synthetic catalogues, an attenuation law was applied to all the events reported in the synthetic catalogue for the production of maps showing the exceedance probability of given values of peak acceleration in the investigated territory. Numerical modelling, Earthquake hazards, Earthquake interaction, forecasting, and prediction, Seismicity and tectonics, Statistical seismology 1 INTRODUCTION The characteristic earthquake hypothesis is the basis of time-dependent modeling of earthquake recurrence on major faults, using the renewal process methodology. However, the complex situation of real fault systems may lead to a more chaotic and (almost) unpredictable behaviour, often referred to as a manifestation of self-organized criticality. In spite of the popularity achieved in the past decades, the characteristic earthquake hypothesis is not strongly supported by observational data (see Kagan et al. 2012). Few faults have long historical or palaeoseismic records of individually dated ruptures, and when data and parameter uncertainties are allowed for, the form of the recurrence distribution is difficult to establish. This is the case of the Central Apennines, for which strong earthquakes are documented since the 11th century, but the seismic catalogue can be considered complete for magnitudes ≥ 6.0 only for the last five centuries, during which not more than one characteristic earthquake is reported for most individual faults. As a matter of fact, the time elapsed between successive earthquakes on a particular fault segment in Italy is thought to be on the order of one or more millennia and therefore their probability of occurrence in the period covered by historical records is low or very low (e.g. Valensise & Pantosti 2001). The seismic activity of the Central Apennines reported in the Parametric Catalog of the Italian Earthquakes (CPTI15; Rovida et al. 2016) evidences 14 strong events with magnitudes that span from 6.0 to 7.1, since 1500 AD to 2014. From 2014 to date, three earthquakes having Mw ≥ 6.0 occurred in the region (ISIDe Working Group 2016; Table 1). Note that the historical catalogue covers a relatively short time period with respect to the long interevent time between strong events. Table 1. Mw ≥ 6.0 events of the Central Apennines since 1500 AD with their epicentral coordinates, intensity and magnitude. Year  Month  Day  Epicentral area  Lat (°)  Lon (°)  Io  Mw  1599  11  6  Valnerina  42.724  13.021  9  6.07  1639  10  7  Moti della Laga  42.639  13.261  9-10  6.21  1703  1  14  Valnerina  42.708  13.071  11  6.92  1703  2  2  Aquilano  42.434  13.292  10  6.67  1706  11  3  Maiella  42.076  14.080  10-11  6.84  1730  5  12  Valnerina  42.753  13.120  9  6.04  1741  4  24  Fabrianese  43.425  13.005  9  6.17  1747  4  17  Appennino umbro-marchigiano  43.204  12.769  9  6.05  1751  7  27  Appennino umbro-marchigiano  43.225  12.739  10  6.38  1799  7  28  Appennino marchigiano  43.193  13.151  9  6.18  1832  1  13  Valle Umbra  42.980  12.605  10  6.43  1915  1  13  Marsica  42.014  13.530  11  7.08  1997  9  26  Appennino umbro-marchigiano  43.014  12.853  8-9  5.97  2009  4  6  Aquilano  42.309  13.510  9-10  6.29  2016  8  24  Appennino centrale  42.70  13.23  10a  6.20  2016  10  26  Appennino centrale  42.91  13.13  9b  6.10  2016  10  30  Appennino centrale  42.83  13.11  10b  6.50  Year  Month  Day  Epicentral area  Lat (°)  Lon (°)  Io  Mw  1599  11  6  Valnerina  42.724  13.021  9  6.07  1639  10  7  Moti della Laga  42.639  13.261  9-10  6.21  1703  1  14  Valnerina  42.708  13.071  11  6.92  1703  2  2  Aquilano  42.434  13.292  10  6.67  1706  11  3  Maiella  42.076  14.080  10-11  6.84  1730  5  12  Valnerina  42.753  13.120  9  6.04  1741  4  24  Fabrianese  43.425  13.005  9  6.17  1747  4  17  Appennino umbro-marchigiano  43.204  12.769  9  6.05  1751  7  27  Appennino umbro-marchigiano  43.225  12.739  10  6.38  1799  7  28  Appennino marchigiano  43.193  13.151  9  6.18  1832  1  13  Valle Umbra  42.980  12.605  10  6.43  1915  1  13  Marsica  42.014  13.530  11  7.08  1997  9  26  Appennino umbro-marchigiano  43.014  12.853  8-9  5.97  2009  4  6  Aquilano  42.309  13.510  9-10  6.29  2016  8  24  Appennino centrale  42.70  13.23  10a  6.20  2016  10  26  Appennino centrale  42.91  13.13  9b  6.10  2016  10  30  Appennino centrale  42.83  13.11  10b  6.50  Notes: Data from CPTI15 (Rovida et al. 2016) and, for the last three recent earthquakes, ISIDe Working Group (2016). Io is in MCS scale. aGalli et al. (2016). bTertulliani & Azzaro (2016). View Large Earthquake simulators can overcome the limitations that real catalogues suffer in terms of completeness, homogeneity and time duration, providing data that can be used for the evaluation of different models of the seismogenic processes (Wilson et al. 2017). Earthquake simulators can provide in these cases interesting information based on features of fault geometry and its kinematics in order to use them in the renewal models. This concept was adopted by Tullis (2012) for earthquakes simulators in California using the long-term slip rate on seismogenic sources without taking into account rheological parameters. In this study, we applied a physics-based earthquake simulator for producing a long-term synthetic catalogue lasting 100 kyr and containing more than 500 000 events 4.0 ≤ M ≤ 7.0 magnitude, considering fault systems derived from the Database of Individual Seismogenic Sources (DISS; DISS Working Group 2015). 2 SEISMOGENIC SOURCES MODEL OF THE CENTRAL APENNINES Historical and instrumental earthquake catalogues show that Central Apennines have been struck by numerous earthquakes, ranging from sparse seismicity up to Mw 7.1 events, for example, the 1915 January 13 earthquake (Fig. 1 and Table 1). The 1915 event is to date the largest event to have occurred since 1500 AD in the study area, and is certainly one of the strongest earthquakes reported in the Italian historical and instrumental catalogues. Most of the major earthquakes are concentrated along the main axis of Central Apennines, but also the piedmont and coastal area have been locus of isolated large earthquakes (Fig. 1). Figure 1. View largeDownload slide Seismotectonic setting of the Central Apennines showing the projections on the ground surface of the CSSs of DISS 3.2.0 (in grey; DISS Working Group 2015). The boxes are the projection onto the ground surface of the SFSs and their colours denote their kinematics (see Frohlich diagram). The epicentres of the CPTI15 earthquakes with M 5.5+ are shown by red squares and the M 6+ earthquakes are labeled with the year of occurrence (Table 1; Rovida et al. 2016). The events of the 2016–2017 seismic sequence with M 5.5+ are shown by red stars; 1: 2016 August 24, Mw 6.2; 2: 2016 October 26, Mw 6.1; 3: 2016 October 30, Mw 6.5 and 4: 2017 January 18, Mw 5.6 (ISIDe Working Group 2016). Figure 1. View largeDownload slide Seismotectonic setting of the Central Apennines showing the projections on the ground surface of the CSSs of DISS 3.2.0 (in grey; DISS Working Group 2015). The boxes are the projection onto the ground surface of the SFSs and their colours denote their kinematics (see Frohlich diagram). The epicentres of the CPTI15 earthquakes with M 5.5+ are shown by red squares and the M 6+ earthquakes are labeled with the year of occurrence (Table 1; Rovida et al. 2016). The events of the 2016–2017 seismic sequence with M 5.5+ are shown by red stars; 1: 2016 August 24, Mw 6.2; 2: 2016 October 26, Mw 6.1; 3: 2016 October 30, Mw 6.5 and 4: 2017 January 18, Mw 5.6 (ISIDe Working Group 2016). The structural architecture of Central Apennines is dominated by ENE-verging arc-shaped folds and thrusts that developed through progressive migration of the contractional process. The earthquakes have hit the area east of the thrust belt testifying that these geodynamic processes which led to the shortening of the Apennines fold and thrust system are still active. Therefore, the major frontal thrusts located between the mountain chain and the Adriatic coast are thought to be active and responsible for some earthquakes of the region (e.g. Vannoli et al. 2015). The earthquakes located between the piedmont and the Adriatic coastline can be relatively deep (15–30 km depth range). In this case, they are thought to be caused by the deep-seated E-W trending shear zones that affect the Apulian foreland beneath the Apennines thrust belt (e.g. Kastelic et al. 2013). The extension trends nearly parallel to the former contractional axis, and favoured the development of normal faults that have either downthrown the back limb of the pre-existing, large thrust systems, or have somehow disrupted the landscape that resulted from the palaeogeographic domains and the contractional phases (e.g. Vezzani & Ghisetti 1998). The extensional fault systems straddles the crest of the Central Apennines, and are responsible for the 2016–2017 seismic sequence (including four earthquakes of magnitude equal to or larger than 5.5), and for a large number of strong earthquakes that struck the area (Fig. 1). Therefore, the seismogenic model of the Central Apennines consists of extensional, compressional and strike-slip sources located between the mountain chain and the Adriatic coast. For further details about the seismotectonic framework and the characterization of most of the seismogenic sources included in this model the reader can refer to Kastelic et al. (2013) for the sources belonging to the compressional fronts of the Central Apennines and offshore domains, and Vannoli et al. (2012) for the sources belonging to the extensional domain of the Apennines. The seismogenic model upon which we applied the simulator code, was derived from the DISS, version 3.2.0 (DISS Working Group 2015; http://diss.rm.ingv.it/diss/). The DISS supplies a unified view of seismogenic processes in Central Apennines by building on basic physical constraints concerning rates of crustal deformation, on the continuity of deformation belts and on the spatial relationships between adjacent faults (Basili et al. 2008). One of the main core objects of the DISS are the Composite Seismogenic Sources (CSS), fully parametrized crustal fault systems, believed to be capable of producing M ≥ 5.5 earthquakes. This category of sources was conceived to achieve completeness of the record of potential earthquake sources. The CSSs are based on regional surface and subsurface geological data that are exploited well beyond the identification of active faults. They are characterized by geometric and kinematics parameters and the maximum value of earthquake magnitude in the moment magnitude scale. Every parameter (including magnitude) is qualified according to the type of analyses that were done to determine it. Table 2 in Basili et al. (2008) shows the principal types of data and methods used in DISS to determine the parameters of the seismogenic sources. Five different methods are listed for the parameter ‘Magnitude’. Table 2. Parameters of the Simplified Fault Systems (SFSs) adopted in this study ID  Name  Lat (°N)  Lon (°E)  D (km)  S (°)  Dip (°)  R (°)  L (km)  W (km)  S-R (mm yr−1)  SFS01  Città diCastello-Spoleto  42.6418  12.8171  0.5  329  33  270  100  13.8  0.55  SFS02  Leonessa-Posta  42.4776  13.0369  0.5  314  33  270  22  13.8  0.55  SFS03  Cittaducale-Barrea  42.4098  13.0284  1  133  53  270  100  17.9  0.9  SFS04  Borbona-Goriano Sicoli  42.5539  13.1559  2  134  50  270  73  15  0.55  SFS05  Cocullo-Aremogna  42.0877  13.8071  2  143  50  270  40.5  15  0.55  SFS06  Gubbio  43.414  12.4442  2  131  20  270  26  11.8  0.55  SFS07  Colfiorito-Cittareale  43.2603  12.7436  2.5  148  45  270  80  16.2  0.55  SFS08  Campotosto  42.6443  13.2693  2.5  138  45  270  24  16.2  0.55  SFS09  Barisciano-Sulmona  42.4339  13.4536  1  134  53  270  64  16  0.55  SFS10  Sassoferrato-Fabriano  43.5428  12.7298  12  125  38  90  28  16.2  0.3  SFS11  Camerino-Montefortino  43.3565  13.0711  12  153  38  90  54.9  16.2  0.3  SFS12  Montegallo-Cusciano  42.913  13.3843  12  142  38  90  41  16.2  0.3  SFS13  Caramanico Terme-Palena  42.2489  13.9977  8  137  25  90  53  21  0.3  SFS14  Orsogna-Archi  42.3008  14.1942  3  131  30  90  29  10  0.3  SFS15  Macerata-Canzano  43.602  13.5187  3  160  40  90  88.2  9.3  0.3  SFS16  San Clemente-Pietranico  42.6418  13.8797  3  167  40  90  36.2  9.3  0.3  SFS17  Ancona-Sirolo  43.6535  13.5211  3  139  38  90  16.5  5.7  1.2  SFS18  Numana-Civitanova Marche  43.5274  13.6653  3  158  38  90  25  5.7  1.2  SFS19  Conero offshore NW  43.7077  13.596  1.5  136  33  90  17  9.2  0.7  SFS20  Conero offshore SE  43.5768  13.7571  1.5  153  33  90  11  9.2  0.7  SFS21  Porto Sant’Elpidio offshore  43.891  13.8072  3  148  40  95  22  5.5  0.3  SFS22  Pedaso offshore-Rosciano  43.2045  13.9616  3  175  40  95  101  5.5  0.3  SFS23  Ortolano-Montesilvano  42.524  13.3558  11  92  80  200  82  9  0.3  SFS24  Tocco da Casauria-Tremiti  42.2432  13.8043  11  95  80  200  154  9  0.3  ID  Name  Lat (°N)  Lon (°E)  D (km)  S (°)  Dip (°)  R (°)  L (km)  W (km)  S-R (mm yr−1)  SFS01  Città diCastello-Spoleto  42.6418  12.8171  0.5  329  33  270  100  13.8  0.55  SFS02  Leonessa-Posta  42.4776  13.0369  0.5  314  33  270  22  13.8  0.55  SFS03  Cittaducale-Barrea  42.4098  13.0284  1  133  53  270  100  17.9  0.9  SFS04  Borbona-Goriano Sicoli  42.5539  13.1559  2  134  50  270  73  15  0.55  SFS05  Cocullo-Aremogna  42.0877  13.8071  2  143  50  270  40.5  15  0.55  SFS06  Gubbio  43.414  12.4442  2  131  20  270  26  11.8  0.55  SFS07  Colfiorito-Cittareale  43.2603  12.7436  2.5  148  45  270  80  16.2  0.55  SFS08  Campotosto  42.6443  13.2693  2.5  138  45  270  24  16.2  0.55  SFS09  Barisciano-Sulmona  42.4339  13.4536  1  134  53  270  64  16  0.55  SFS10  Sassoferrato-Fabriano  43.5428  12.7298  12  125  38  90  28  16.2  0.3  SFS11  Camerino-Montefortino  43.3565  13.0711  12  153  38  90  54.9  16.2  0.3  SFS12  Montegallo-Cusciano  42.913  13.3843  12  142  38  90  41  16.2  0.3  SFS13  Caramanico Terme-Palena  42.2489  13.9977  8  137  25  90  53  21  0.3  SFS14  Orsogna-Archi  42.3008  14.1942  3  131  30  90  29  10  0.3  SFS15  Macerata-Canzano  43.602  13.5187  3  160  40  90  88.2  9.3  0.3  SFS16  San Clemente-Pietranico  42.6418  13.8797  3  167  40  90  36.2  9.3  0.3  SFS17  Ancona-Sirolo  43.6535  13.5211  3  139  38  90  16.5  5.7  1.2  SFS18  Numana-Civitanova Marche  43.5274  13.6653  3  158  38  90  25  5.7  1.2  SFS19  Conero offshore NW  43.7077  13.596  1.5  136  33  90  17  9.2  0.7  SFS20  Conero offshore SE  43.5768  13.7571  1.5  153  33  90  11  9.2  0.7  SFS21  Porto Sant’Elpidio offshore  43.891  13.8072  3  148  40  95  22  5.5  0.3  SFS22  Pedaso offshore-Rosciano  43.2045  13.9616  3  175  40  95  101  5.5  0.3  SFS23  Ortolano-Montesilvano  42.524  13.3558  11  92  80  200  82  9  0.3  SFS24  Tocco da Casauria-Tremiti  42.2432  13.8043  11  95  80  200  154  9  0.3  Notes: Geometric coordinates refer to the upper left edge of the SFS. D: the depth of the upper edge of the SFS from the sea level; S: the value of the strike angle; Dip: the value of the dip angle; R: the value of the rake angle; L: the SFS length measured along its strike; W: the SFS width measured along its dip and SR: the value of the slip rate on the SFS. View Large We converted the 15 CSSs identified in the Central Apennines into 24 Simplified Fault Systems (SFS), new sources specifically developed for this study (Fig. 1). The SFSs are rectangular fault systems consistent with the parameters supplied for the CSSs. As a matter of fact, each SFS is characterized by 1: the strike of that segment; 2: the average dip; 3: the average rake; 4: the depth intervals; 5: the length of that segment; 6: the maximum width obtained with average dip down to maximum depth and finally, 7: the slip rate value of the respective CSS (Fig. 1 and Table 2). Table 2 reports the list and the parameters of the 24 SFSs recognized in the Central Apennines (Fig. 1). 3 ALGORITHM OF THE SIMULATOR CODE The algorithm on which this simulator is based is described in detail by Console et al. (2015, 2017). Here, we recall that this algorithm is constrained by several physical elements as: The geometry, kinematics and average slip rate for every fault system. The process of rupture growth and termination, leading to a self-organized earthquake magnitude distribution. Interaction between earthquakes, including small-magnitude events. The seismogenic system is modeled by rectangular fault systems (SFS; Table 2), each of which is composed by many square cells of the same size. Each cell is initially given a stress chosen from a random distribution. The stress on each cell is increased in time by the tectonic loading computed from a given slip rate, the value of which is uniform on each segment. Some heuristic rules are adopted for nucleating and stopping a rupture: A cell can nucleate a rupture if the stress reaches a value that exceeds its strength. After nucleation, the effective strength on the cells neighbouring the already ruptured cells is reduced by a constant value multiplied by the square root of the number of already ruptured cells, as a proxy of weakening mechanism; the free parameter introduced to produce such weakening effect is called hereafter strength-reduction coefficient (S-R; Console et al. 2017); this parameter has a similar role of the η  free parameter in the Virtual Quake simulator developed for California (Schultz et al. 2017). The S-R is not allowed to increase further if the ruptured area exceeds a given number of times the square of the width of the rupturing fault system, discouraging rupture propagation over very long distances; the free parameter introduced to produce such effect is called hereafter aspect-ratio coefficient (A-R; Console et al. 2017). At each ruptured cell, the stress is decreased by a constant stress drop (e.g. 3 MPa), and the slip on the ruptured cell is estimated proportionally to the square root of the already ruptured cells. When a cell ruptures the stress on all the surrounding cells is changed by a value equal to the Coulomb stress change physically computed by the seismic moment of the ruptured cell, the distance between the causative and receiving cells and their respective source mechanism. A rupture stops when there are not cells in the search area where the stress exceeds the effective strength. A cell can rupture more than once in the same event. Events nucleated in one fault system are allowed to expand into neighbouring fault systems, applying the (1)–(3) rules, if they are separated by less than a given maximum distance (e.g. 10 km). In this way, different fault systems are treated as a unique fault system by the algorithm. As already stated, in the rupture process of an earthquake, the simulation algorithm allows a cell to rupture more than once. This may happen if at the initial stage of the rupture of a big earthquake a cell ruptures releasing a constant stress drop, but with a moderate slip. When, subsequently, the rupture grows, the next rupturing cells transfer positive Coulomb stress change to the previously ruptured cells, recharging them and allowing them to exceed again the threshold strength (which is decreasing as the rupture area expands). So, for the final estimate of the seismic moment of an earthquake generated by the simulation process, the single seismic moment released by each ruptured cell is considered and their total is computed. The average slip is then computed from the total seismic moment and the total ruptured area. This simulation algorithm has been refined in time, by the production of more complex and efficient versions of the computer code. Let us recall, for instance, that the main improvement of the algorithm between the version adopted by Console et al. (2017) and the previous one introduced by Console et al. (2015) was a more efficient way of searching successive ruptures, avoiding the procedure based on a huge number of very short time steps. This is reflected in the flow chart of the two respective algorithms (Fig. 1, Console et al. 2015, and Fig. 1, Console et al. 2017). A new feature in the algorithm of the present simulator code with respect to the previous version (Console et al. 2017) consists in the after-slip process: a fraction of the total slip computed for a ruptured cell is released with a time delay after the origin time of the earthquake. Two free parameters control the generation of aftershocks by the simulator. They are used to assign the fraction of coseismic slip released by the after-slip process and the characteristic time of the decaying Omori-like power law and must be interactively assigned by the user. Typically, simulation parameters are adjusted so that natural earthquake sequences are matched in their scaling properties (Wilson et al. 2017). In this respect, the role of the S-R and A-R parameters in our simulation algorithm has been previously analysed and described by Console et al. (2017). 4 APPLICATION OF THE EARTHQUAKE SIMULATOR TO THE CENTRAL APENNINES The 24 rectangular SFSs that represent the Central Apennines seismogenic structures reported in Table 2 were discretized in cells of 1.0 km × 1.0 km. The smallest magnitude generated by an earthquake rupturing a single cell is approximately 4.0. The time spanned by the synthetic catalogue was 100 kyr, excluding a warm up period of 20 kyr introduced to lead the system to a standby status, independent of the initial stress randomly assigned to every cell. In our simulation, an event of given magnitude produced by the simulation algorithm could have ruptured only part of a single SFS, or encompass more than one SFS, without any constrain imposed by the size of the SFS where the nucleation is started. After having carried out a series of trials with different choices of the free parameters, we chose the combination of S-R = 0.2 and A-R = 2 in order to obtain a good match between the magnitude distributions of the synthetic and the real catalogues (see Console et al. 2017). The application of the earthquake simulation algorithm to the SFSs of the Central Apennines produced a homogeneous and complete seismic catalogue containing more than 500 000 M ≥ 4.0 events, with a time duration of 100 kyr. The results of the simulation process for single SFS are given in Table 3, where the source kinematics, the source area, the seismic moment annual rate, the number of M ≥ 4.0 and 6.0 earthquakes, and the maximum magnitude, respectively, are reported. It must be noted the total number of M ≥ 6.0 earthquakes contained in the synthetic catalogue is much smaller than the sum of the earthquakes reported in column 6 of Table 3, as numerous events are multiple segment ruptures. Note also that the maximum magnitudes are often the same for neighbouring SFSs (e.g. SFS01, SFS02 and SFS03) because the largest magnitude is referred to a unique earthquake that ruptured more than one SFS together. Table 3. Main features of the synthetic catalogue of 100 kyr obtained by the simulator for the SFSs of the Central Apennines. ID  Rake  Area (km2)  Mo/year (Nm yr−1)  Number of synthetic events M ≥ 4.0  Number of synthetic events M ≥ 6.0  Synthetic Max M  CSS Max M  SFS01  N  1380  2.3E+16  24 824  256  7.15  6.2  SFS02  N  304  5.0E+15  6761  176  7.15  6.2  SFS03  N  1790  4.8E+16  60 773  374  7.15  6.7  SFS04  N  1095  1.8E+16  18 731  283  7.18  6.5  SFS05  N  608  1.0E+16  11 354  153  7.18  6.5  SFS06  N  307  5.1E+15  7456  131  6.96  6.0  SFS07  N  1296  2.1E+16  26 411  266  7.18  6.5  SFS08  N  389  6.4E+15  9580  218  7.18  6.5  SFS09  N  1024  1.7E+16  19 332  281  7.18  6.4  SFS10  R  454  4.1E+15  4780  59  6.97  6.2  SFS11  R  890  8.0E+15  8649  116  6.97  6.2  SFS12  R  664  6.0E+15  7554  92  6.97  6.2  SFS13  R  1113  1.0E+16  11 825  181  6.83  6.8  SFS14  R  290  2.6E+15  3781  148  6.83  5.6  SFS15  R  820  7.4E+15  10 107  382  6.66  5.9  SFS16  R  337  3.0E+15  4004  148  7.05  5.9  SFS17  R  94  3.4E+15  7720  289  6.55  5.8  SFS18  R  143  5.1E+15  10 404  317  6.55  5.8  SFS19  R  156  3.3E+15  6273  204  6.55  5.9  SFS20  R  101  2.1E+15  4368  172  6.55  5.9  SFS21  R  121  1.1E+15  2739  0  5.93  5.5  SFS22  R  556  5.0E+15  5686  196  6.76  5.5  SFS23  SS  738  6.6E+15  11 858  301  7.08  5.7  SFS24  SS  1386  1.2E+16  23 800  353  6.83  6.0  ID  Rake  Area (km2)  Mo/year (Nm yr−1)  Number of synthetic events M ≥ 4.0  Number of synthetic events M ≥ 6.0  Synthetic Max M  CSS Max M  SFS01  N  1380  2.3E+16  24 824  256  7.15  6.2  SFS02  N  304  5.0E+15  6761  176  7.15  6.2  SFS03  N  1790  4.8E+16  60 773  374  7.15  6.7  SFS04  N  1095  1.8E+16  18 731  283  7.18  6.5  SFS05  N  608  1.0E+16  11 354  153  7.18  6.5  SFS06  N  307  5.1E+15  7456  131  6.96  6.0  SFS07  N  1296  2.1E+16  26 411  266  7.18  6.5  SFS08  N  389  6.4E+15  9580  218  7.18  6.5  SFS09  N  1024  1.7E+16  19 332  281  7.18  6.4  SFS10  R  454  4.1E+15  4780  59  6.97  6.2  SFS11  R  890  8.0E+15  8649  116  6.97  6.2  SFS12  R  664  6.0E+15  7554  92  6.97  6.2  SFS13  R  1113  1.0E+16  11 825  181  6.83  6.8  SFS14  R  290  2.6E+15  3781  148  6.83  5.6  SFS15  R  820  7.4E+15  10 107  382  6.66  5.9  SFS16  R  337  3.0E+15  4004  148  7.05  5.9  SFS17  R  94  3.4E+15  7720  289  6.55  5.8  SFS18  R  143  5.1E+15  10 404  317  6.55  5.8  SFS19  R  156  3.3E+15  6273  204  6.55  5.9  SFS20  R  101  2.1E+15  4368  172  6.55  5.9  SFS21  R  121  1.1E+15  2739  0  5.93  5.5  SFS22  R  556  5.0E+15  5686  196  6.76  5.5  SFS23  SS  738  6.6E+15  11 858  301  7.08  5.7  SFS24  SS  1386  1.2E+16  23 800  353  6.83  6.0  Notes: N: normal faulting; R: reverse faulting and SS: strike-slip faulting. View Large As can be seen in Table 3, the annual moment rate on each SFS, obtained by multiplying the source area by its slip rate and by the constant shear modulus (assumed equal to 30 GPa), is approximately proportional to the number of M ≥ 4.0 earthquakes, for all the normal and some reverse SFSs. The ratio between the number of M ≥ 4.0 earthquakes and the seismic rate is higher by nearly 50 per cent for five of the reverse sources (SFS17-18-19-20-21) and the two strike-slip sources (SFS23-24). The proportionality is less clear for M ≥ 6.0 earthquakes. In fact, in many cases an SFS of small area can be associated with the same strong earthquake with one or more neighbouring source, and so being assigned many more M ≥ 6.0 events than could be the case if that SFS worked independently of the others. The last column of Table 3 contains also, for each SFS, the maximum magnitudes attributed to the respective fault system (CSS) in the DISS 3.2.0. The comparison between the largest magnitudes obtained from the simulation process for 100 kyr and the DISS maximum magnitudes shows that the former magnitudes are larger than the latter ones by an order of 0.7 magnitude units or more. The explanation of this mismatch is attributed to the fact that the simulator allows ruptures to cover the whole area of a single SFS, and even overcome the border among SFSs. On the contrary, the maximum magnitudes guessed by the DISS compilers are mainly based on (1) the largest magnitude of associated historical/instrumental earthquake(s), and/or (2) the scaling relationships between magnitude and fault size (Wells & Coppersmith 1994), where the fault length and/or the width are derived from geological and/or seismological data, but are generally smaller than the entire SFS to which they belong. As explained in the previous section, in the simulated rupture process, the same cell can participate in a rupture more than once. To show how this circumstance really happened in our application of the simulator to the fault systems, for the 10 largest earthquakes contained in the first 10 000 yr of the synthetic catalogue, we report in Table 4 the number of cells that have ruptured once or more than once in the specific event. The results of this analysis are interesting, as it appears that for some events most cells had only single ruptures, while in other cases multiple ruptures of the same cells are common. Table 4. Number of repeated ruptures of the same cells for the 10 largest events of the first 10 000 yr of the synthetic catalogue. Year  Mw  Number of ruptures/1 time  Number of ruptures/2 times  Number of ruptures/3 times  Number of ruptures/4 times  Number of ruptures/5 times  Number of ruptures/6 times  Number of ruptured cells  Number of total ruptures  Number of nucleation SFS  Number of ruptured SFS  482  6.97  1383  23  1  0  0  0  1407  1432  03  03  1622  6.95  1282  31  0  0  0  0  1313  1344  03  03  3932  6.96  672  229  119  0  0  0  1020  1487  03  01,02,03  6620  6.97  1358  21  0  0  0  0  1379  1400  03  03  7068  6.99  358  270  222  12  0  0  862  1612  11  10,11,12  7680  7.04  1695  31  1  0  0  0  1727  1760  03  03  8212  6.99  868  194  173  1  0  0  1236  1779  01  01,02,04,06  8808  7.05  1729  31  1  0  0  0  1761  1794  03  03  9492  7.11  358  322  182  136  63  10  1071  2467  05  01,02,04,05,08,09  9838  6.99  1419  30  1  0  0  0  1450  1482  03  03  Year  Mw  Number of ruptures/1 time  Number of ruptures/2 times  Number of ruptures/3 times  Number of ruptures/4 times  Number of ruptures/5 times  Number of ruptures/6 times  Number of ruptured cells  Number of total ruptures  Number of nucleation SFS  Number of ruptured SFS  482  6.97  1383  23  1  0  0  0  1407  1432  03  03  1622  6.95  1282  31  0  0  0  0  1313  1344  03  03  3932  6.96  672  229  119  0  0  0  1020  1487  03  01,02,03  6620  6.97  1358  21  0  0  0  0  1379  1400  03  03  7068  6.99  358  270  222  12  0  0  862  1612  11  10,11,12  7680  7.04  1695  31  1  0  0  0  1727  1760  03  03  8212  6.99  868  194  173  1  0  0  1236  1779  01  01,02,04,06  8808  7.05  1729  31  1  0  0  0  1761  1794  03  03  9492  7.11  358  322  182  136  63  10  1071  2467  05  01,02,04,05,08,09  9838  6.99  1419  30  1  0  0  0  1450  1482  03  03  Notes: Year: year of the synthetic earthquake; Mw: magnitude of the synthetic earthquake; number of ruptures/x times: number of times that the same cell breaks during the synthetic earthquake; number of ruptured cells: number of different cells ruptured during the synthetic earthquake; number of total ruptures: total number of ruptures during the synthetic earthquake; number of nucleation SFS: SFSXX containing the nucleation cell and number of ruptured SFS: SFSXX(s) responsible for the large synthetic earthquake. View Large We show in Fig. 2, the cumulative magnitude–frequency plot of the synthetic 100 000 yr catalogue compared with the plots of the CPTI15 catalogue obtained for three different threshold magnitudes with their respective completeness intervals. Figure 2. View largeDownload slide Cumulative frequency–magnitude distribution of the earthquakes in the synthetic catalogue, compared with those obtained from CPTI15 for the magnitude thresholds and the time intervals during which they are assumed complete. Figure 2. View largeDownload slide Cumulative frequency–magnitude distribution of the earthquakes in the synthetic catalogue, compared with those obtained from CPTI15 for the magnitude thresholds and the time intervals during which they are assumed complete. The comparison reported in Fig. 2 shows a substantial similarity between the synthetic catalogue and the real data in the magnitude range 4.0 ≤ M ≤ 6.5. This could be expected because the A-R and S-R free parameters were calibrated to obtain such resemblance and the slip rate assigned to the seismic sources constrains the total seismic moment released by the whole system of SFSs. however, a slight underestimation of the simulator with respect to the real catalogues appears in the magnitude range 4.5 ≤ M ≤ 6.0. This can be put in connection with the b-value variations of the synthetic catalogue along the whole magnitude range, as a b-value larger than 1.0 is noted for M ≤ 5.5, and smaller than 1.0 for 5.5 ≤ M ≤ 6.5. Some discrepancy between the synthetic and the CPTI15 catalogues can be also observed in the high magnitude range (M ≥ 6.4). In this magnitude range, the shape of the magnitude distribution of the two longer completeness time intervals is dominated by the occurrence of few very large events. In particular, the CPTI15 catalogue starting in 1871 contains only one earthquake of M ≥ 6.4, that is, the Mw 7.1 1915 Marsica earthquake. The limited number of events and the large uncertainty in magnitude estimations of the historical catalogue does not allow a robust comparison with the simulator's results, a problem already faced and analysed in detail by Wilson et al. (2017). In conclusion, although the comparison between the seismicity produced by the simulator and the observed data for evaluating the obtained results could be useful for the validation of the simulator algorithm and the assessment of its free parameters, it is not a simple problem. The five century of completeness for the M 6+ earthquakes may not be long enough to encompass the recurrence time of characteristic earthquakes on single SFS. Moreover, as already remarked, a single earthquake could have ruptured only a part of a single segment for moderate magnitudes, or have propagated to more than one segment for the larger magnitudes, in agreement with the assumption made in our simulation algorithm. In order to carry out a statistical analysis on the number of ruptured SFSs contributing to a single earthquake and their recurrence intervals, some quantitative, even if somehow arbitrary, definitions are necessary to assign a specific earthquake to one or more SFSs. For a more in-depth analysis of this issue, we refer to the discussion made by Field (2015) addressing the ‘recurrence of what?’ question. In our analysis, the following criteria were adopted: The minimum equivalent magnitude for a ruptured group of cells is 6.0. Initially the earthquake is assigned to the SFS containing the nucleation cell of the earthquake. If the number of cells ruptured by the earthquake in one of the other SFSs is larger than 150 or this SFS has atleast 60 per cent of ruptured cells, then this segment can also be included in the same earthquake. In this way, we counted through the whole 100 kyr synthetic catalogue the number of times that a given fault segment was present in any M ≥ 6.0 earthquake alone (1898 times) or jointly with other segments (505 times). In a unique case, six SFSs ruptured all together in one single very large earthquake. In order to assess whether the earthquake occurrence time on single segments in the synthetic catalogue behaves as a Poisson process or not, we carried out a statistical analysis of the interevent times for the entire 100 kyr simulation. For this purpose, Fig. 3 displays for each of three selected fault systems (SFS03, SFS04 and SFS07), the recurrence time distribution for the M ≥ 6.0 events to which they were assigned, as previously described. Table 5 shows the statistical parameters obtained by the whole procedure for each source: the average recurrence time for M ≥ 6.0, Tr, the Poisson probability that the segment might rupture in 50 yr at a rate of 1/Tr, P50, the standard deviation of the recurrence times, σ, and the coefficient of variation, Cv. The last column of Table 5 reports also the date and the magnitude of the latest historical earthquake assigned to every SFS, when this information is available. Figure 3. View largeDownload slide Interevent time distribution from a simulation of 100 000 yr of seismic activity across the Central Apennines, for three selected fault systems. The time-dependent 50 yr occurrence probability of an M6+ earthquake on the Colfiorito-Cittareale fault system, under a renewal BPT model, could be estimated before the 2016 August 24 earthquake as 13 per cent. Figure 3. View largeDownload slide Interevent time distribution from a simulation of 100 000 yr of seismic activity across the Central Apennines, for three selected fault systems. The time-dependent 50 yr occurrence probability of an M6+ earthquake on the Colfiorito-Cittareale fault system, under a renewal BPT model, could be estimated before the 2016 August 24 earthquake as 13 per cent. Table 5. Statistical parameters of the synthetic catalogue for each SFS (see the text for explanations). ID  Tr (M ≥ 6.0) (yr)  P50 (%)  σ (yr)  Cv  Latest largest EQ  SFS01  493.5  9.6  339.9  0.69  1832, Mw 6.4  SFS02  1206.7  4.1  517.8  0.43  1298, Mw 6.3  SFS03  283.1  16.2  206.5  0.73  1915, Mw 7.1  SFS04  555.9  8.6  341.9  0.61  2009, Mw 6.3  SFS05  944.6  5.2  447.2  0.47  No data  SFS06  997.0  4.9  305.6  0.31  1984, Mw 5.6  SFS07  517.8  9.2  330.1  0.64  2016, Mw 6.5  SFS08  971.0  5.0  547.6  0.56  1639, Mw 6.2  SFS09  657.2  7.3  364.8  0.56  1461, Mw 6.5  SFS10  1905.8  2.6  800.1  0.42  1741, Mw 6.2  SFS11  1077.2  4.5  681.7  0.63  1799, Mw 6.2  SFS12  1448.3  3.4  660.4  0.46  No data  SFS13  832.1  5.8  498.9  0.60  1706, Mw 6.8  SFS14  2105.4  2.3  1187.3  0.56  No data  SFS15  776.6  6.2  565.7  0.73  1943, Mw 5.7  SFS16  1330.2  3.7  539.2  0.41  No data  SFS17  643.4  7.5  571.8  0.89  1269, Mw 5.6  SFS18  611.8  7.8  531.3  0.87  No data  SFS19  947.5  5.1  552.6  0.58  1690, Mw 5.6  SFS20  1019.9  4.8  655.7  0.64  No data  SFS21  –  0.0  –  –  No data  SFS22  825.0  5.9  451.4  0.55  No data  SFS23  917.1  5.3  553.7  0.60  1950, Mw 5.7  SFS24  419.5  11.2  289.2  0.69  No data  ID  Tr (M ≥ 6.0) (yr)  P50 (%)  σ (yr)  Cv  Latest largest EQ  SFS01  493.5  9.6  339.9  0.69  1832, Mw 6.4  SFS02  1206.7  4.1  517.8  0.43  1298, Mw 6.3  SFS03  283.1  16.2  206.5  0.73  1915, Mw 7.1  SFS04  555.9  8.6  341.9  0.61  2009, Mw 6.3  SFS05  944.6  5.2  447.2  0.47  No data  SFS06  997.0  4.9  305.6  0.31  1984, Mw 5.6  SFS07  517.8  9.2  330.1  0.64  2016, Mw 6.5  SFS08  971.0  5.0  547.6  0.56  1639, Mw 6.2  SFS09  657.2  7.3  364.8  0.56  1461, Mw 6.5  SFS10  1905.8  2.6  800.1  0.42  1741, Mw 6.2  SFS11  1077.2  4.5  681.7  0.63  1799, Mw 6.2  SFS12  1448.3  3.4  660.4  0.46  No data  SFS13  832.1  5.8  498.9  0.60  1706, Mw 6.8  SFS14  2105.4  2.3  1187.3  0.56  No data  SFS15  776.6  6.2  565.7  0.73  1943, Mw 5.7  SFS16  1330.2  3.7  539.2  0.41  No data  SFS17  643.4  7.5  571.8  0.89  1269, Mw 5.6  SFS18  611.8  7.8  531.3  0.87  No data  SFS19  947.5  5.1  552.6  0.58  1690, Mw 5.6  SFS20  1019.9  4.8  655.7  0.64  No data  SFS21  –  0.0  –  –  No data  SFS22  825.0  5.9  451.4  0.55  No data  SFS23  917.1  5.3  553.7  0.60  1950, Mw 5.7  SFS24  419.5  11.2  289.2  0.69  No data  View Large Both Tables 3 and 5 show, as expected, that the most active segments are those characterized by larger size and/or higher slip rate (see Table 2 for the parameters), such as SFS01, SFS03 and SFS24, characterized by recurrence times of 300–500 yr. The simulation also shows that, especially for the less active segments (SFS10, SFS12 and SFS14), interevent times of several thousands of years are possible. The coefficient of variation Cv is typically close to 0.6, which would be associated to a moderate periodicity of the seismicity. As an exercise made upon these results, we computed the time-dependent 50 yr occurrence probability of an M ≥ 6.0 earthquake on the SFS07 Colfiorito-Cittareale, where the 2016 August–October seismic sequence really occurred, how it could have been estimated at the beginning of 2016, under a renewal Brownian passage time (BPT) model. This probability, conditioned by a time of 313 yr elapsed since the last ‘characteristic’ earthquake occurred in 1703 (Table 1), could be calculated as equal to 13.0 per cent from the SFS03 recurrence distribution. Conversely, under a time-independent Poisson model, this probability, obtained from a recurrence time Tr = 518 yr, would be only 9.2 per cent (Table 5). Another temporal feature of the synthetic catalogue obtained from our simulation algorithm was explored by analysing the statistical distribution of the time by which an event of any magnitude can precede or follow an earthquake of M ≥ 6.0. This study was aimed to assess the existence in the synthetic catalogues of some kind of time-dependent occurrence rate as a long-term precursor of strong earthquakes. The analysis was carried out by a stacking technique on the synthetic catalogue. For each event of M ≥ 6.0, the catalogue has been scanned for the 1000 yr preceding and the 1000 yr following such event, dividing this time period in bins of 10 yr. The events occurred in each time bin of this time period have been counted regardless of their location and magnitude. The procedure has been repeated for all M ≥ 6.0 earthquakes and the numbers of events found in each bin have been counted together. The results give the total number of M4+ earthquakes preceding and following an M6+ earthquake in each bin of 10 yr in the time period considered. These results are displayed in Fig. 4(a). This figure shows an outstanding trend of acceleration of seismic activity in a 400 yr period before the strong earthquakes, as well as a sort of quiescence with a slow recovering to the normality after such earthquakes. This feature can be compared with the result obtained through a similar analysis, reported by Console et al. (2017) for the Calabria region. In that case, the seismic rate acceleration was noted for only 200 yr, while the recovering to the normal rate was significantly slower. Such difference between the two cases could be explained by a combination of factors, like a different magnitude threshold chosen for the analysis (M4.5 in the Calabria study), a different slip rate of some of the sources in the two regions, and mainly the existence of long extensional and compressional parallel SFSs in the Central Apennine region (Fig. 1). This feature, which is not observable in Calabria, can produce a different mechanism of positive or negative stress transfer among SFSs in case of large magnitude earthquakes. Figure 4. View largeDownload slide Stacked number of M4+ earthquakes preceding and following an M6+ earthquake, obtained from the 100 000 yr simulation in a long-term (a; top) and short-term (b; bottom) timescale, respectively. The long-term plot shows acceleration before and quiescence after the strong event. The short-term plot shows the occurrence of aftershocks in the two months after the strong earthquake. Figure 4. View largeDownload slide Stacked number of M4+ earthquakes preceding and following an M6+ earthquake, obtained from the 100 000 yr simulation in a long-term (a; top) and short-term (b; bottom) timescale, respectively. The long-term plot shows acceleration before and quiescence after the strong event. The short-term plot shows the occurrence of aftershocks in the two months after the strong earthquake. The acceleration of seismic moment release before strong earthquakes is a well-known phenomenon reported in literature as a possible earthquake precursor but generally observed over shorter timescales (see e.g. De Santis et al. 2015, and references therein). It would be interesting to compare this result with something happening in nature if historical catalogues covering a comparable time length of hundreds of years were available, which is not the case for moderate magnitude events (see e.g. Wilson et al. 2017). In a preliminary way, we could guess that this is a result of the stress transfer on faults from prior events becoming an increasingly important fraction of the total stress compared with tectonic loading over time. As to the quiescence after M6+ earthquakes, any stress release model would exhibit such behaviour, but rarely, if ever, over 400 yr. The 1906 San Francisco earthquake has a stress shadow of a century or so, for instance (Parsons 2002). The longer quiescence period found in our simulations for Central Apennines with respect to California can be justified by the difference of the slip rate by an order of magnitude over the major fault systems of the two regions. In fact, the slip rate on single sources is the factor that controls the timescale of the seismicity generated by our simulator. As a simple consequence, if we only changed the slip rate of our geological model of Central Apennines, we would obtain an identical catalogue of earthquakes, but with a time duration inversely proportional to the slip rate given in input to the model. Considering the case of short-term interaction, Fig. 4(b) shows the result of a similar stacking technique carried out for a time interval of ±0.5 yr. In this case, the total time spanned before and after the M6+ earthquakes is one year and the time bins are 0.01 yr (about 3.65 d) long. The sudden raise of seismic activity soon after an earthquake of M ≥ 6.0 testifies the presence of a feature resembling that of aftershock production, modeled through the inclusion of an after-slip process in the simulation algorithm. Note that the seismic activity few months after the main shocks in average goes back to values lower than those existing few months before the same main shocks. 5 THE SIMULATED CATALOGUE APPLIED TO TIME INDEPENDENT SEISMIC HAZARD ASSESSMENT In order to test the potential application of our simulations to seismic hazard assessment, we adopted a simple ground motion prediction equations (GMPE) model, and applied the Cornell (1968) method to the M ≥ 4.5, 100 000 yr simulated catalogue. The peak acceleration (PGA) at a dense grid of points covering the territory of the Central Apennines was estimated for each earthquake of the catalogue through a typical attenuation law (Sabetta-Pugliese 1987):   \begin{eqnarray*} \log ({\rm{PGA}}) &=& - 1.562 + 0.306M - \log ( {\sqrt {{d^2} + {{5.8}^2}} } )\nonumber \\ && +\, 0.169{S_1} + 0.169{S_2} \pm 0.173 \end{eqnarray*} (1)where M is the earthquake magnitude, d is the epicentral distance and S1 and S2 are parameters taking into account the soil dynamic features at the site. At each node of the grid, we obtained the distribution of the number of times that a given PGA was exceeded in 100 000 yr, and repeating it for many PGA values, we obtained the value of PGA characterized by a probability of exceedance of 10 per cent in 50 yr (Fig. 5). Figure 5. View largeDownload slide Map of PGA characterized by a probability of exceedance of 50 per cent in 50 yr, inferred from the 100 000 yr synthetic catalogue of the Central Apennines. Figure 5. View largeDownload slide Map of PGA characterized by a probability of exceedance of 50 per cent in 50 yr, inferred from the 100 000 yr synthetic catalogue of the Central Apennines. 6 DISCUSSION The application of our physics-based simulation algorithm to the fault systems of the Central Apennines has allowed the compilation of synthetic seismic catalogue lasting 100 kyr for M ≥ 4.0. This catalogue contains more than 500 000 earthquakes whose magnitude distribution and time–space features resemble those of the observed seismicity, but without the limitations that real catalogues suffer in terms of completeness and time duration. In this section, we consider items of our study that deserve particular attention and some more detailed discussion. 6.1 The role of specific parameters of the simulation model The real catalogue of Central Apennines, reports 17 earthquakes with M ≥ 6.0 after 1500 (Table 1), and the catalogue obtained from the simulation contains 2403 M ≥ 6.0 events in 100 kyr. The respective occurrence rate of M ≥ 6.0 earthquakes is 0.035 events per year from the historical records and 0.024 events per year for the simulation. We have already stated in Sections 3 and 4 that simulation parameters are typically adjusted so that natural earthquake sequences are matched in their scaling properties (Wilson et al. 2017). This implies that the user must have a good knowledge of the effect of each single parameter. The role of the S-R and A-R parameters in our simulation algorithm was already analysed by Console et al. (2015, figs 5a–c; 2017, figs 6a and b). A similar analysis has been carried out also in this study, with the application of the simulator to the seismicity of Central Apennines. Figure 6. View largeDownload slide (a) Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 1 km × 1 km, a stress reduction (S-R) coefficient equal to 0.4 and different values of the aspect-ratio (A-R) coefficient. (b) As in A, using an A-R coefficient equal to 2 and various values of the stress reduction (S-R) coefficient. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. Figure 6. View largeDownload slide (a) Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 1 km × 1 km, a stress reduction (S-R) coefficient equal to 0.4 and different values of the aspect-ratio (A-R) coefficient. (b) As in A, using an A-R coefficient equal to 2 and various values of the stress reduction (S-R) coefficient. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. As shown in Fig. 6(a), the A-R parameter (the parameter that allows the growth of ruptures towards larger portions of a fault), has effect only on the large magnitude range of the magnitude distribution (M ≥ 6.0). This figure shows the magnitude distribution of the synthetic catalogues obtained changing A-R from 2 to 16 for a constant value of S-R equal to 0.4. The larger A-R is, the larger is the maximum magnitude of the synthetic catalogue, but smaller is the number of earthquakes with 6.0 ≤ M ≤ 7.0. Having small influence on the magnitude distribution of small magnitude earthquakes, the A-R parameter has also a little effect on the b-value, which in our tests ranges from 1.25 (A-R = 2) to 1.33 (A-R = 16). The role of the S-R parameter is reducing the fault strength and favouring the expansion of nucleated ruptures, as a sort of dynamic weakening effect. Fig. 6(b) reports the magnitude distribution of synthetic catalogues obtained maintaining a constant value of A-R = 2 and changing S-R from 0.2 to 0.6. It can be easily noted that the effect of the S-R parameter is specifically referred to the ratio between the number of moderate magnitude events (4.0 ≤ M ≤ 6.0) and the number of larger magnitudes, with a significant impact on the b-value of the magnitude distribution. As a matter of fact, the b-value of the synthetic catalogues decreases from 1.29 (S-R = 0.2) to 0.78 (S-R = 0.6). We can conclude that the results obtained in this analysis, as to the role of both the A-R and S-R parameters on the magnitude distributions of the synthetic catalogues confirm the similar analyses carried out in previous papers by Console et al. (2015, 2017). Figs 6(a) and (b) give also a comparison of the occurrence rate distribution of the synthetic catalogues with that of two real catalogues, respectively CPTI15 (1950–2013, M ≥ 4.0) and CPTI15 (1500–2017, M ≥ 6.0). A visual inspection of these figures supports our choice described in Section 3 for small values of both the S-R and A-R parameters, such as S-R = 0.2–0.4 and A-R = 2–4. Increasing the free parameters beyond these values produces larger discrepancies with the exhibited by all our synthetic catalogues with respect to the real ones can be justified by the lack of moderate size faults in our model consisting of only 24 main faults. 6.2 Modeling smaller magnitude earthquakes by the simulator As already said at the beginning of Section 4, the minimum magnitude of the earthquakes of the synthetic catalogues, having adopted a model with cells of 1.0 km × 1.0 km size and a stress drop of 3.0 MPa, is 4.0 (or more precisely 3.98). This is not a limit of the methodology but just a practical consequence of the computer time necessary for running a simulation based on a given number of cells and lasting a given number of years. For instance, each of the simulations of 100 kyr described above required several tens of hours of computer time on an inexpensive PC. In order to test the simulator for producing a catalogue containing smaller magnitude events, we adopted a model with the same 24 SFSs of Fig. 1 and a discretization in cells of 0.5 km × 0.5 km. This implies a minimum magnitude of the synthetic catalogue equal to 3.4 (or more precisely 3.38). The results of this test are shown in Fig. 7 for two synthetic catalogues lasting 10 000 yr, with a choice of S-R = 0.2 and 0.4, and A-R = 2 and 4, respectively. Also in this plot, we have added the magnitude–frequency distribution of two real catalogues (CPTI15 1950–2013 and CPTI15 1500–2017) for sake of comparison. Figure 7. View largeDownload slide Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 0.5 km × 0.5 km, and two different combinations of the parameters S-R and A-R. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. Figure 7. View largeDownload slide Magnitude–frequency distribution of the earthquakes in the synthetic catalogues obtained from the simulation algorithm described in the text using a discretization of 0.5 km × 0.5 km, and two different combinations of the parameters S-R and A-R. The coloured areas represent the observed magnitude distribution obtained for two sections of the CTPI15 catalogue. 6.3 Comparison of the synthetic and real catalogue for the largest magnitudes Let us focus our attention on the SFS03 Cittaducale-Barrea source, the one containing the strongest historical earthquake of the whole region (the 1915 Mw 7.1 Marsica earthquake; Table 1), as well as the one with a large slip rate (Table 2) and a short recurrence time (Table 5). We see in Fig. 1 that three M ≥ 5.5 earthquakes, but no other M ≥ 6.0 earthquakes are reported for this SFS. Referring to SFS03, the 100 kyr synthetic catalogue contains 374 M ≥ 6.0 earthquakes and 9 M ≥ 7.0 earthquakes, with a 7.15 maximum magnitude. Therefore, the simulation algorithm would give an expectation of about one earthquake in 10 000 yr of magnitude class 7 on the SFS03 source. This simple computation leads us to consider the 1915 Mw 7.1 Marsica earthquake an extremely rare phenomenon, unlikely to recur on the same fault system in the next several thousands of years. Another interpretation of this circumstance could be that the Mw 7.1 magnitude reported in CPTI15 is overestimated. This interpretation appears consistent also with the maximum magnitude value of 6.7 assigned by the DISS 3.2.0 compilers to this particular source. The presence of the Mw 7.1 Marsica earthquake in the CPTI15 historical catalogue is the main reason of the discrepancy between the cumulative magnitude distribution of the CPTI15 data and those obtained by the 100 kyr simulation for the whole Central Apennines region, especially for the observations with M ≥ 5.0 starting in 1871 (Fig. 2). However, taking into account the uncertainties shown by the error bars of Fig. 2, this discrepancy is not quite significant. Moreover, in light of the discussion about the singularity of the 1915 earthquake, made above, this discrepancy can be also justified by the relatively short length of the catalogue with respect to the recurrence time of large events, and uncertainty characterizing their magnitude. Another interesting piece of information is given by the last column of Table 5. Here, we see that for only 15 out of 24 SFSs, the date of the latest strong event is known. Moreover, we can note that 10 of these 15 earthquakes occurred after 1700 AD and only two are older than 500 yr, while the average recurrence time obtained from the synthetic catalogue is typically larger than 500 yr except for only two cases. Unless we believe that most of the SFSs in the Central Apennines have released their energy in a relatively short time window of 3–4 centuries, this is a strong evidence of the lack of information available in the historical earthquake catalogue for the region considered in this study, discouraging the use of historical catalogues for a statistical earthquake rate assessment. 6.4 Fault segmentation and geographical extension of ruptures for the largest magnitude earthquakes One of the main purposes of our application of the simulator to the seismicity of the Central Apennines area was testing whether fault segmentation and characteristic earthquake hypothesis are or are not necessary conditions for modeling in reasonable way earthquake patterns observed in real historical records. To show how the unsegmented model of SFS used in our simulation can generate realistic seismicity patterns that can be compared with the real seismicity observed in the most recent centuries, we analysed the complete history of simulated ruptures in a period of 10 kyr along three SFS linked together, along a nearly straight line. For this exercise, we extracted, from a synthetic catalogue of 10 kyr obtained for the complete set of 24 SFSs, the earthquakes occurring on a fault system including SFS07, SFS08 and SFS09 with a total length of about 170 km (Fig. 1). The simulator algorithm is not conditioned by the subpartition of this structure in three SFSs because their minimum relative distance is shorter than 10 km, and ruptures are allowed to propagate from one to another in a unique event. In Fig. 8, excluding the events with magnitude smaller than 6.0, all the larger earthquakes are represented colouring the cells of 1 km × 1 km ruptured in each of them. Each panel from the top to the bottom of the picture shows the events occurred in separate time windows of 300 yr with different colours for each earthquake in the same time window. The colours represent the order by which the events enucleated in each panel of 300 yr, from blue to yellow and red, respectively. Multiple ruptures on the same cell in a unique earthquake are represented by darker tones of their respective colours. Figure 8. View largeDownload slide Map of ruptures for M ≥ 6.0 earthquakes on the joint set of SFS07, SFS08 and SFS09 in 33 time windows of 300 yr represented from top to bottom. The 170-km-long fault system is displayed in each panel from left to right moving from NW to SE (Fig. 1). On any panel, the blue, yellow and red colours represent the temporal order of earthquake occurrence, and the darker tone of the respective colours represent the amount of slip on multiply ruptured cells. Figure 8. View largeDownload slide Map of ruptures for M ≥ 6.0 earthquakes on the joint set of SFS07, SFS08 and SFS09 in 33 time windows of 300 yr represented from top to bottom. The 170-km-long fault system is displayed in each panel from left to right moving from NW to SE (Fig. 1). On any panel, the blue, yellow and red colours represent the temporal order of earthquake occurrence, and the darker tone of the respective colours represent the amount of slip on multiply ruptured cells. By examining Fig. 8, we can note that only three 300 yr periods of 33 were lacking any M ≥ 6.0 earthquake, while only two of the other periods contain three earthquakes of such magnitude. There is a clear trend for earthquakes not to occupy the same rupture areas in the same time window, or in consecutive time windows, while they are mostly separated from each other by more than 300 yr of several time windows. During the whole test of 10 000 yr, every portion of the 170 km long fault system was occupied by at least 6–7 ruptures in distinct earthquakes, and none of them was left empty. This is consistent with the recurrence time of 500–1000 yr characterizing the three SFSs considered in this test. From the results of the exercise discussed in this subsection (see Fig. 8), we can infer that the segmentation scheme mainly based on historical records of earthquakes occurred during the latest centuries could have likely been conditioned by the particular pattern of ruptures exhibited by a group of SFS in this relatively recent time window. A detailed analysis was carried out on the 10 strongest earthquakes in the 10 kyr catalogue reported in Table 4, examining to which single or multiple SFS(s) these earthquakes can be assigned: Extensional fault systems are responsible of 9 of these 10 strongest earthquakes. SFS03, responsible of the strongest earthquake of the historical and simulated catalogues (Mw 7.1) is the source that was activated most often in the 10 kyr simulation (70 per cent of times), in agreement with the observed seismicity. SFS03 is ruptured singularly in 90 per cent of the cases, without activating other neighbouring sources. The other sources responsible of the 10 strongest earthquakes in 10 kyr (SFS01, SFS05 and SFS11) never ruptured alone, but always jointly with the closest SFSs, along both the strike and the geometrically normal directions. Moving further to consider the occurrence time pattern of the simulated catalogue, we have already introduced Table 5 showing that, for most single SFS, strong earthquakes of M ≥ 6.0 exhibit an interevent time distribution characterized by a fairly pseudo-periodic behaviour. Fig. 4(a) also shows that, in the Central Apennines region as a whole, moderate magnitude earthquakes have a higher probability of occurrence during the period of 400 yr preceding strong earthquakes than during the same period of 400 yr following them. It is a challenging issue to compare this particular feature exhibited by the synthetic catalogue with real observations. In fact, the duration of the period of completeness for earthquakes with M ≥ 4.0, as those for which Fig. 4 was prepared, is only 64 yr, by far too short for assessing the existence of a cyclic process lasting hundreds of years. However, from Fig. 4, we can receive a warning, that is not to trust the assessment of earthquake rates based on historical data only, as such assessment could be biased by long-term seismicity changes that occur on specific groups of SFSs, depending on the particular status of those SFSs in their respective multicentury earthquake cycle. 6.5 Clustering versus random behaviour of the simulated catalogue Here, we want to remark that the occurrence times of M ≥ 6.0 earthquakes obtained from the simulator do not exhibit any clear clustering trend. To show it, we have analysed the number of M ≥ 6.0 synthetic events contained in consecutive time intervals of fixed length (Table 6). Table 6. Number of times that a different number of M ≥ 6.0 earthquakes are reported in consecutive time windows of the 100 kyr synthetic catalogue (S) compared with the expected number of times computed under the Poisson time-independent hypothesis (P), for different time window lengths. Number of events  Time window length    10 yr  20 yr  50 yr  100 yr  250 yr    S  P  S  P  S  P  S  P  S  P  0  7833  7863.9  3056  3092.0  568  593.4  71  90.45  0  0.98  1  1938  1889.7  1539  1486.0  756  721.0  223  217.3  7  5.91  2  209  227.0  352  357.1  442  438.0  264  261.1  11  17.76  3  15  18.19  45  57.21  179  177.3  223  209.1  25  35.56  4  0  1.09  6  6.87  45  53.88  142  125.6  54  53.41  5    0.05  0  0.66  8  13.09  58  60.39  69  64.17  6    0.00    0.05  1  2.65  10  24.19  71  64.25  7          0  0.46  8  8.30  67  55.14  8            0.07  0  2.49  56  41.41  9            0.01  1  0.67  18  27.64  10            0.00  0  0.16  15  16.60  11                0.03  4  9.07  12                0.01  1  4.54  13                0.00  1  2.10  14                  1  0.90  15                  0  0.36  16                    0.14  17                    0.05  18                    0.02  19                    0.01  20                    0.00  P(χ2)  0.52  0.29  0.32  0.14  0.13  Number of events  Time window length    10 yr  20 yr  50 yr  100 yr  250 yr    S  P  S  P  S  P  S  P  S  P  0  7833  7863.9  3056  3092.0  568  593.4  71  90.45  0  0.98  1  1938  1889.7  1539  1486.0  756  721.0  223  217.3  7  5.91  2  209  227.0  352  357.1  442  438.0  264  261.1  11  17.76  3  15  18.19  45  57.21  179  177.3  223  209.1  25  35.56  4  0  1.09  6  6.87  45  53.88  142  125.6  54  53.41  5    0.05  0  0.66  8  13.09  58  60.39  69  64.17  6    0.00    0.05  1  2.65  10  24.19  71  64.25  7          0  0.46  8  8.30  67  55.14  8            0.07  0  2.49  56  41.41  9            0.01  1  0.67  18  27.64  10            0.00  0  0.16  15  16.60  11                0.03  4  9.07  12                0.01  1  4.54  13                0.00  1  2.10  14                  1  0.90  15                  0  0.36  16                    0.14  17                    0.05  18                    0.02  19                    0.01  20                    0.00  P(χ2)  0.52  0.29  0.32  0.14  0.13  View Large As it can be easily seen, the comparison between the simulations and the Poisson time-independent model, as shown in Table 6, demonstrates a clear similarity of the two distributions, as far as the Central Apennines area is considered all together. This can be explained by the relatively large number of 24 SFSs, which, besides a certain degree of interaction, produce a random sequence of occurrence times. By a more careful comparison of the simulated and theoretical values, it can be noted that, for time windows of 100 and 250 yr, the values obtained from the simulations in the central part of the distributions are a little larger than those expected from the Poisson model. It means that, for these two time window lengths, the events tend to occur a little more frequently in pseudo-periodical manner than in completely random way. However, the last line of Table 6, where the p-values of the χ2 test are reported, proves that the null time-independent hypothesis cannot be rejected with a confidence level larger than 90 per cent for any of the examined time window lengths. In contrast with the features of the synthetic catalogue resulting from the above-mentioned analysis, it is widely recognized that the actual M6+ seismicity in the Central Apennines exhibits strong clustering properties. For instance, in the time up to and including the 2016 sequence of M6+ events in our study area, there are five events in ∼19 yr, four events in ∼7.5 yr and three events in ∼0.18 yr. The probabilities of these happening in a Poisson process with a rate of 0.02403 events per year are 1.16 × 10−4, 3.94 × 10−5 and 1.44 × 10−8, respectively. We can argue that our simulation's SFS specific Tr and Cv, are reliable and therefore they can be useful for a long-term seismic hazard estimation (e.g. Fig. 5). However, the results of the analysis reported in Table 6 show that the simulator does not accurately capture the conditional probabilities of a large event anywhere in the system given that another large event has occurred somewhere in the system recently. Concerning the short and very short-term behaviour, we have shown in Fig. 4(b) that a simple algorithm introduced in the most recent version of the simulator applied in this study, which we call ‘after-slip’effect, can produce an increase of the seismic rate soon after a strong earthquake. This algorithm mimics in some respect the well-known aftershock phenomenon observed in the real seismicity. However, a simple examination of Fig. 4(b) shows that the stacked rate of events in the first day after an earthquake of M6+ does not exceed by more than a factor of 10 times the average rate before such earthquakes. To analyse this circumstance in more detail, we have computed the average number of events of magnitude M4+ following any earthquake of magnitude M6+ within six months after their occurrence time and 100 km of distance from their epicentre. This computation, done on the synthetic catalogue characterized by the couple of parameters S-R = 0.2 and A-R = 2 and an after-slip ratio equal to 0.2, leads to an average number of aftershocks equal to 1.64. The same kind of computation, carried out on the catalogue obtained from a discretization of 0.5 km × 0.5 km (and a smallest magnitude of 3.4) and the same model parameters results in an average number of aftershocks equal to 10.7. The number of aftershocks contained in our synthetic catalogues is smaller by at least an order of magnitude than the number of aftershocks of similar magnitude threshold observed in the Central Apennine after the events of M6+ during the seismic sequence of 2016 August–October (Table 1). The results of this analysis show that our after-slip algorithm does not totally capture the aftershock phenomenon observed on real data. We argue that this poor result could be ascribed to the lack of small secondary faults surrounding the main faults in our simplified geological model. Another comparison with real data was done with the average difference between the main shock magnitude and the magnitude of the largest aftershock, commonly retained approximately equal to 1.2 according to the so-called Bath's law (Vere Jones 1969). Such difference was found respectively equal to 2.29 and 2.97 magnitude units with the two above-mentioned synthetic catalogues. These results are clearly indicative of the fact that most of the aftershocks contained in our synthetic catalogues are represented by events of very small magnitude rupturing a small number of cells. 6.6 The seismic hazard map and its comparison with existing seismic hazard assessment in Central Italy It could be interesting to make a comparison of the results shown in Section 5 with those obtained in previous assessments. For instance, this comparison can be done with the National Seismic Hazard Map in annex to the Ordinance of the President of the Council of Ministers issued on 2003 March 30 (updated until 2015). This map is currently used for applications in new building design overall the Italian territory, expressed in terms of maximum PGA with a probability of exceedance of 10 per cent in 50 yr on stiff soil (http://zonesismiche.mi.ingv.it/documenti/mappa_opcm3519.pdf.). The comparison shows substantial similarity for the exceedance probability of 0.2 g PGA overall the Central Apennine area. However, the scattered pattern resembling the structure of the SFSs clearly visible in Fig. 5 is not represented in the National Seismic Hazard Map. In particular, the national map does not show the spot of high values connected to SFS17, SFS18, SFS19 and SFS20, in the northern part of the map of Fig. 5. The high values of exceedance probability for 0.2 g PGA in 50 yr for the four sources located southeast of Ancona (Figs 1 and 5) are probably due to the high values of the slip rates of those sources (Table 2). These slip rates values were assessed for the Plio-Pleistocene with great accuracy by Maesano et al. (2013) through an analysis of seismic lines. If this discrepancy is just an effect of having overestimated the slip rate of those sources in our model, or if it is an underestimation of hazard in the present national map, is a very difficult question that deserves further studies. 7 CONCLUSIONS In this study, we have applied a newly developed physics-based earthquake simulation algorithm to build a synthetic catalogue of earthquakes, the epicentres of which cover the whole seismic region of Central Apennines. The spatial distribution of the simulated seismicity is constrained by the geometrical parameters of the seismogenic model of Central Apennines derived from the DISS. The total seismic moment released by the earthquakes of the synthetic s is very much constrained by the value of slip rate assumed for each fault system, a critical ingredient of the simulation algorithm. The relative simplicity of our algorithm has allowed simulations lasting 10 000 yr or 100 000 yr, and containing hundreds of thousands earthquakes with a smallest magnitude, respectively, equal to 3.4 or 4.0. The main conclusions that can be drawn from the results of this study, carried out by the employment of a physics-based simulation technique to the seismicity of the Central Apennines fault systems, are the following. The frequency–magnitude distribution of the simulated seismicity is rather consistent with observations in the intermediate magnitudes range (4.0 ≤ M ≤ 6.5), with a b-value slightly larger than 1.0 for small magnitudes (4.0 ≤ M ≤ 5.5) and slightly smaller than 1.0 for higher magnitudes (5.5 ≤ M ≤ 6.5). The frequency–magnitude distribution is clearly tapered for M ≥ 6.5. The long period of simulations allowed us to obtain the statistical distribution of repeat times—an indispensable component for any time-dependent seismic hazard assessment, which is lacking in the real historical observations. The statistical distribution of interevent times for earthquakes with M ≥ 6.0 on single segments exhibits a moderate pseudo-periodic behaviour, with a coefficient of variation Cv of the order of 0.4–0.8. The space–time behaviour of earthquake ruptures on the fault systems produced by the simulator shows that segmentation is not needed to model long-term seismicity patterns. We have found in our synthetic catalogue a clear trend of acceleration of seismic activity in the 400 yr preceding M ≥ 6.0 earthquakes and quiescence in a period of the same order of magnitude following those earthquakes, which leads to infer a possible cyclic earthquake rate variation with a duration of some centuries. The phenomenon of short-term interaction and aftershocks, dealt with the introduction of an after-slip process in our algorithm, is not adequately represented in our synthetic catalogues and deserves further consideration. An exercise of potential use of the simulator as a tool for time-independent statistical hazard assessment was carried out by the application of a simple GMPE model to all the events contained in the synthetic catalogue lasting 100 kyr for the Central Apennines. Even if this study was aimed to explore methodological aspects and potential capabilities of new-generation simulator algorithms, the initial results shown in this paper encourage further investigations about the application of simulators in support to other methodologies of time-independent and time-dependent seismic hazard assessment in Italy. 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Geophysical Journal InternationalOxford University Press

Published: Feb 1, 2018

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