Introduction

After a significant seismic event, the regional earthquake rate increases for days, months, or years1 over a distance comparable with the dimension of the source (aftershocks), or much further (up to thousands of kilometers) with fault failure implications on active structures critically stressed1,2,3,4. Hence, large earthquakes can trigger microseismicity or slow-slip events from intermediate to long distances depending on the local stress state and the size of the stress perturbation, which can broadly range from ~ 0.1 kPa to ~ 1MPa5. Triggered microseismicity has been well documented since the Landers earthquake (1992, MW 7.3) in correspondence to geothermal and volcanic sites and tectonically active areas mainly occurring at the edges of locked faults and deep basins6.

Remote earthquake triggering can directly depend on passing surface waves inducing deformation on fault zones, indirectly acting on frictional properties, or unlocking a fault by opening a fluid pressure valve2,7,8,9,10,11. On the other hand, the observations of these phenomena at large distances open the question of whether there is a direct connection between the main triggering event and observed seismic activity when earthquakes are delayed in time5,12. Dealing with delayed-dynamic triggering processes, it is frequently challenging to establish a conclusive argument that attributes the triggering solely to the transient dynamic wavefield.

It is well known that space-time earthquake clustering, observed in volcanic and active tectonic areas, can be favored by the seismic and aseismic transient local processes as fluid flow, fault creeps, or magma intrusion13. Moreover, in active tectonic areas, clustering can also be linked to slow slip events14,15 and show specific characteristics in durations (days, weeks, months), moment release (delayed from the onset of the clustering activity), and migration velocities (from 1 km/h to 1 km/day).

Understanding the physical processes underlying seismicity clustering, triggered after major earthquakes or other phenomena, is of fundamental importance for improving the knowledge on the stress redistribution required for fault failure and the degree of clock advances earthquakes in high seismic hazard areas.

This paper focuses on the seismicity following the 2009 L’Aquila earthquake (MW 6.3) in the southern sector of the central Apennines, a high-seismic-risk region undergoing tectonic extension (Fig. 1a).

Figure 1
figure 1

Instrumental and historical seismicity in the southern-central Italy tectonic framework (ArcMap, by ESRI, ArcMap/ArcGIS, v. 10.8, https://www.esri.com/en-us/home). (a) Extensional and contractional domains in southern-central Italy18 and major focal mechanisms (MW > 4.5) from19,20. (b) The density contour of the instrumental seismicity distribution (0 ≤ M ≤ 5.8) from 1981 to March 200921 and main seismic historical and instrumental events (MW ≥ 5.5) occurred in the study area before the L’Aquila seismic sequence (colored symbols as in the legend)22,23. The active fault patterns are from the QUIN database24,25 integrated with details from the geological map of Italy (scale 1:100.000 and 1:50.000) and from26. Blue lines represent the west-dipping normal faults, and the light blue colors show the northeast-dipping ones. (c) Density contour of seismicity distribution (0 ≤ M ≤ 6.3) and main seismic events that occurred in the study area after the L’Aquila seismic sequence (from 2009 to 2020). The magnitude of the Sora seismic event is from QRCMT16. (d) Histogram summarizing the frequency of instrumental seismicity before and after the L’Aquila seismic sequence in the study area (grey rectangle in panels b and c).

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Southward of the causative fault of the L’Aquila 2009 main event (e.g., Paganica fault), a general increase of the seismicity rate at some fault lengths (~ 60 km) is observed close to Sora town (grey rectangle Fig. 1b,c). This area is characterized by a low level of background seismicity that has increased fivefold from 2009 to 2013 (Fig. 1d) with cascading episodes of seismic clustering at an average depth of ~ 11–14 km that climaxed with deeper events on 16th of February 2013 (MWmax ~ 5, QRCMT16) at a depth of ~ 17–20 km17. The mainshock of the 2013 seismic activity represents the most energetic event of the last ~ 100 years (Fig. S1).

These episodes of seismic sequences and swarms occurring after the L’Aquila earthquake at different seismogenic depths raise questions about the remote triggering, the role of fluids, the tectonic control, and the thickness of the seismogenic layer of the extensional domain.

The primary objective of this paper is to elucidate the significance of the increase in seismicity and to gain insights into the genesis of the observed clusters of earthquakes. This is achieved by investigating the space-time evolution of the intense seismic activity, characterizing each seismic episode in terms of migration velocity and Vp/Vs ratio, and exploring the potential correlation of event distribution with local tectonic factors, including pre-existing fault geometry and kinematics influencing the multi-depth earthquake nucleation and distribution.

Furthermore, seismological analyses are conducted to study the swarms and the evolution of the Sora seismic sequence, aiming to define the relationships between the occurrence of the observed seismic activity and the distribution of static and dynamic stress transfer induced by the L’Aquila earthquake, as well as transient (e.g., fluid involvement) or tectonic phenomena.

Seismotectonic framework

Central Apennines in Italy is a high-seismic-risk area undergoing extensional tectonics (Fig. 1a) stretching at low rates of 3–4 mm/yr in the SW–NE direction27,28. This extensional belt is characterized by NNW-SSE to WNW-ESE striking normal to normal-oblique faults, Late Pliocene to Quaternary in age25. The overall system is composed of high-angle westward-dipping segments detaching on eastward-dipping low-angle basal planes29,30,31,32. The seismicity associated with this framework is mainly located at upper crustal depths (< 12–14 km)17 and is primarily controlled by tectonic processes. Locally, deeper normal events are observed along the extensional domain, such as the Matese seismic sequence of December 2013-January 2014 (MW 5.2, QRCMT16), that occurred at depths ranging from 10 to 25 km33,34,35 (Figs. 1a and S1a). The hypothesis of associating these deeper events with intrusive episodes of magmatic sources has been advanced by Di Luccio et al.36.

The focal mechanisms of the major earthquakes, including those of the deepest events, show an SW–NE trending nearly horizontal T-axes, also consistent with the long-term Quaternary stress field18,20,34 (Fig. 1a and S1a).

The area, affected by the increasing seismic activity after the L’Aquila 2009 earthquake, is in correspondence with inner fault alignments of the Apennines extensional domain37 (Figs. 1b,c and S1).

The seismic catalogs22,23 report that the southern-central Apennines experienced four significant events during the last ~ 700 years: the 1349 earthquake (Io X MCS, MW 6.8), 1654 (Io IX-X MCS, MW 6.3), 1915 (Io X-XI MCS, MW 7.1) and 1984 one (Io VIII MCS, MW 5.8) (Figs. 1b, S1b and S2a–c).

The Fucino-Marsicano-Barrea alignment (Fig. 1b) is highly seismogenic. The Fucino segment has been associated with the large and devasting earthquake in 1915 (MW 7.1), while the Barrea segment with the 1984 seismic event (MW 5.8)38. The latter was of lesser magnitude but also destructive. A consensus exists in the literature on the seismogenic behavior of this alignment and the individual seismic sources of these two earthquakes (Figs. 1b and S1b).

On the contrary, the Villavallelonga-Pescasseroli-San Donato Val Comino, the Balsorano-Posta Fibreno, and the Sora faults are still debated segments (Figs. 1b,c, and S1b). They represent faults mapped at the outcrop scale with well-exposed fault planes25,26,39,40,41,42,43, with few associated seismicity.

The source of the 1654 earthquake (Fig. S2a,b), reviewed by44 using the macroseismic field and coseismic effects, is associated with the Sora fault (Fig. 1b).

Finally, the 1349 event was a significant earthquake in a portion of the extensional domain considered a seismic gap by45 due to the significant moment release deficit in the last 500 years (Fig. S2a–c).

The study area (grey rectangle in Figs. 1b,c, and 2) is bordered eastward by the Fucino-Marsicano-Barrea SW-dipping alignment. It is crosscut by SW to WSW-dipping normal fault systems of Villavallelonga-Pescasseroli-San Donato Val Comino, as well as by the innermost right-stepping en-echelon Balsorano-Posta Fibreno sets and Sora fault. Westward, it is bound by the southern termination of Ernici NE to NNE-dipping fault systems. Over time, the area has experienced several moderate events with magnitude around M5-5.5 that occurred in the study area (1693, MW 5.2; 1771, MW 5.1; 1873, MW 5.4; 1874, MW 5.5; 1877, MW 5.2; 1901, MW 5.1; 1922, MW 5.2; 1927, MW 5.2 (Fig. S1b)22,26.

Figure 2
figure 2

The main characteristics of instrumental seismicity occurred in the study area from 1985 to 2020 (0 ≤ ML ≤ 4.8) as reported in the Italian Seismic Bulletin21. (a) Map distribution of seismic events (ArcMap, by ESRI, ArcMap/ArcGIS, v. 10.8, https://www.esri.com/en-us/home; ESRI, 2021). Light green dots represent earthquakes before 2009 and after 2013, while yellow-orange dots are the analyzed events. White circles with numbers from 1 to 10 refer to the focal mechanisms represented in panel (d). The black triangles represent two of the 7 permanent seismic stations used for enhancing the catalog. The complete configuration is shown in Fig. S3. (b) Beta Statistics computed for the study area since 1985 using a bin of 30 days and non-overlapping windows. (c) Depth distribution of earthquakes and the corresponding energy release. (d) Focal mechanisms of seismic events with ML ≥ 3.0 from48. The orange-bordered focal mechanism is related to the Sora earthquake.

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In contrast, a low level of seismicity rate characterizes the study area. A great effort to highlight the minor seismicity was made by experiments performed through temporary seismic networks46,47 and recently by48 that relocated the seismicity from 2009 to 2013 and computed a rich dataset of low-magnitude events and focal mechanisms (0 ≤ ML ≤ 4.8). The genesis of seismic events occurring in this internal sector of the Apennine’s extensional domain is still debated. In fact, in addition to tectonic loading, the presence of higher CO2 and heat flux values compared to the external sectors49,50 suggests that overpressurized CO2 reservoirs at upper crustal depths may contribute to seismicity in the study area.

Data and material

To perform a spatial-temporal analysis of the seismicity within the study area, we built a new seismic catalog having ~ 17,800 seismic events (− 1.3 ≤ ML ≤ 4.8) that occurred from 2009 to 2013 between the Fucino-Marsicano-Barrea SW-dipping alignment and the Ernici NE-NNE dipping fault systems (Figs. 1a and 2a). The enhanced seismic catalog was retrieved by using a template matching technique considering as templates the 856 relocated events of the Catalog of Absolute (nonlinear) 3D earthquake Locations17,51 with horizontal errors < 3 km and vertical errors < 4 km (Fig. 3).

Figure 3
figure 3

Main characteristics of the enhanced catalog. (a) Map showing the new catalog obtained using template matching technique and the spatial distribution of the main clusters CL-1-CL-3 and SO-1-SO-3 and minor clusters CL-4, CL-5 (ArcMap, by ESRI, ArcMap/ArcGIS, v. 10.8, https://www.esri.com/en-us/home; ESRI, 2021). (b) Temporal evolution of the analyzed seismicity for longitude. The colored rectangles indicate the clusters CL-1-CL-3 and SO-1-SO-3. (c) Gutenberg–Richter slope evaluated with the new catalog. The grey bars mark the completeness magnitude (Mc) of the old and new datasets. (d) Distribution of the nearest-neighbor distance for the analyzed seismic events computed with60 code. The plot displays the joint distribution of the re-scaled time and space components (T, R). Spatial and temporal occurrence of the analyzed seismic events.

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We collected the focal mechanism solutions of the events that occurred in the same time interval (2009 to 2013) from the relevant literature19,20,48.

Finally, the results of our analysis were opportunely integrated with geological information on active faults24,25,26,43 and the CO2 emissions50.

Results

General characteristics of instrumental seismicity

From 1985 to 2009, before the 6th of April L’Aquila mainshock (MW 6.3), the study area is characterized by a meager rate and sparse seismicity (~ 0.3 events/day) (Figs. 1c,d, and 2). After the L’Aquila mainshock, the activity rate increased five times up to the end of 2013. Such seismicity was characterized by about one thousand seismic events with ML < 4.0, except for the Sora earthquake (MW 5.0) that occurred on the 16th of February 2013.

This sharp temporary increase affects the study area with seismicity spatially distributed with well-identifiable localized clusters (Figs. 2 and 3).

The beta statistics analysis of the seismicity, which quantifies the seismicity rate changes52 (Fig. 2b), shows two increases in seismicity rates: one after 2005 and the other after 2009. The first variation is due to an improvement of the Italian National Seismic Network (Rete Sismica Nazionale, RSN)53 that produced a better-quality earthquake detection capability and lowered the earthquake catalog completeness threshold. The second one, and it is composed of at least four evident anomalies exceeding the average background rate by more than 20 standard deviations after the 6th of April 2009. Such anomalies were never observed before in the study area.

The frequency–depth histogram of the instrumental seismicity (1985–2020) depicts a bimodal pattern with maxima centered around 10 km and 14 km depths. Although the two peaks cannot be properly distinguished within the depth formal errors, this bimodal shape is widely observed along the Apennine chain in areas with outcropping normal faults and regional low-angle antithetic normal faults or basal detachments54,55,56,57. It is important to emphasize that, in this region, the base of the seismogenic layer deepens compared to observations in the central Apennines and is similar to those in southern Italy (e.g.,58,59). About 90% of the events occur at depths less than ∼14 km, while the remaining 10% occur at the lower crust depths (17–20 km). In the observed time interval, from an energy release point of view, we can see that the deepest events below the base of the seismogenic layer can have magnitudes comparable to or greater than the shallower ones (Fig. 2c).

The focal mechanisms of the minor events and the deep Sora earthquake show SSW–NNE to SW-NE T-trending axes compatible with the tectonic stress acting in the study area (Figs. 1a and 2d).

The new 2009–2013 seismic catalog

The waveform-based template matching technique allows us to augment the seismic catalog and enhance seismicity’s spatiotemporal evolution (Figs. 3 and S4).

Starting from ~ 856 templates, we obtain a significant increment of the output catalog of ~ 21 times (Fig. 3a,b). The new catalog comprises ~ 17,800 seismic events (− 1.3 ≤ ML ≤ 4.8) that occurred from 2009 to the end of 2013, containing multiplets and quasi-repeating events (Figs. 3b and S4). Figure 3b shows the newly detected earthquakes clustered multiple times. The high number of detections suggests the sensitivity of the template matching to multiple repeating over time seismic processes.

The enhanced catalog significantly improved the completeness magnitude, lowering Mc from 1.4 to 0 (Fig. 3c) and filling temporal gaps between the occurrence of larger ones.

The Zaliapin et al.60 declustering method applied to our catalog clearly shows that the distribution of time and space components (T, R) of the nearest-neighbor distance follows a prominently trimodal pattern, revealing the existence of three statistically distinct earthquake populations (background, clustered seismicity, multiplets and quasi-repeaters (Figs. 3d and S5). The results from the combination of waveform clustering are summarized in Figs. 3 and S4. This type of pattern is always observed when new detections are co-located with their templates, as discussed in61 (see Method section).

This approach allows us to separate background and clustered seismicity and highlights with different behaviors, foreshocks-mainshock-aftershock (FMA), and swarms or swarm-like sequences (S). We identify 8 clusters and deeply analyze six relevant episodes for a) duration, b) the number of earthquakes, and c) magnitudes. We call them CL-1-5 and SO-1-3 (Fig. 3). They are in three well-distinct epicentral positions: (1) south of the Villalonga locality (CL-1), (2) southward of Pescasseroli (CL-2 and CL-3 and two minor clusters CL-4 and CL-5) and (3) in the proximity of the Sora town (SO-1, SO-2, SO-3).

Temporal behavior

Starting from the enhanced catalog and its declustering, we could identify eight clusters from 2009 to 2013 in distinct space and time intervals, showing a complex temporal behavior (Fig. 3, Table S1).

CL-1 is the northernmost cluster that occurred on the 7th of April 2009, 34 h after the L’Aquila mainshock (MW 6.3). It comprises 2332 earthquakes, and its temporal activity is highly variable up to May 2012 (Fig. S5). The seismicity shows an intermittent behavior evolving in four main phases during 2009–2010 and nearly occupying the same volume (Fig. 3). The maximum magnitude of each phase ranges from 2.6 to 2.7, and their duration is dozens of days (12–64 days). Following62 classification, the cluster can be considered as foreshock-mainshock-aftershock (FMA) and pure swarm (S) behavior alternately during the four phases (Fig. 4a–d). Figure 4 clearly illustrates that microseismic sequences (CL-1, I-Phase, and III-Phase) characterized by prominent mainshocks are succeeded by more prolonged swarm activity involving approximately one thousand seismic events (CL-1, II-Phase, and IV-Phase).

Figure 4
figure 4

General characteristics of CL-1-CL-3 clusters. (a–f) Magnitude vs time distribution. The grey bands represent the completeness magnitude threshold (Mc = 0 in Fig. 3). (a’–f’) Coefficient variation of interevent times (COV). The colored bands indicate the degree of COV variation (thin band = low variation, thick band = high variation). (a’’–f’’) Maximum seismic moment, cumulative seismic moment ratio (MMR). Similar to COV, the colored bands highlight low (MMR < 0.25) and high (MMR > 0.75) MMR values.

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The coefficient of variation of interevent times (COV in Fig. 4a’–d’), representing the degree of clustering between consecutive seismic events, shows higher values corresponding to the occurrence of the most energetic events, consistently with what has been observed through the cumulative events over time (Fig. S6a), the COV trends are variable. During the first and third phases, they indicate higher temporal clustering at the beginning of the seismic episode. The second and the fourth phases are relatively constant, suggesting a steady pattern of seismic activity. On the contrary, the maximum-to-cumulative moment ratio (MMR in Fig. 4a”–d”) shows a simple trend for the first and third phases, with maximum values occurring at the beginning of the seismic activity in correspondence with the maximum magnitude while the second and the fourth phases show a complex pattern consistently with the magnitude distribution of the seismic episodes.

CL-2 and CL-3 mainly occurred in October 2009 and May 2011 (Figs. 3a and 4e,f). They appear to form a unique cluster but, they are well separated at depth, as described in section “3D tectonic control in seismic sequence evolution”.

CL-2 and CL-3 are composed of two phases that are difficult to separate over time. For this reason, in the text, we simply refer to CL-2 and CL-3. They exhibit a less complex temporal behavior than CL-1 (Figs. S5b and S6b) and comprise thousands of seismic events (~ 4000 and ~ 5000, respectively) with a maximum magnitude of ML 3.6 and 2.8, respectively. CL-2, overall, can be considered a swarm similar to CL-362. CL-2 coefficient variation of interevent times displays a distinct peak corresponding to higher magnitudes (Fig. 4e’,f’), showing a very high clustering of events with COV ~ 6. CL-3 shows low values over time (COV < 2). CL-2 and CL-3 maximum-to-cumulative moment ratios reveal complex patterns, with MMR reaching values beyond 0.75 (Fig. 4e’’,f’).

Unlike CL-1-CL3, SO-1-SO-2 occurred at deeper layers, occupying different volumes. The seismogenic depth boundary (Fig. S7) and the map distribution of epicenters (Fig. 3a) clearly show that, although partially temporal overlapping (Figs. 5a–c and S5c), SO-1-SO-3 cannot be considered a unique cluster, but three different seismic episodes.

Figure 5
figure 5

General characteristics of SO-1-SO-3 clusters. (a–c) Magnitude vs time distribution. (a’–c’). The grey bands represent the completeness magnitude threshold (Mc = 0 in Fig. 3). Coefficient variation of interevent times (COV). The colored bands indicate the degree of COV variation (thin band = low variation, thick band = high variation). (a’’–c’’) Maximum seismic moment, cumulative seismic moment ratio (MMR). Similar to COV, the colored bands highlight low (MMR < 0.25) and high (MMR > 0.75) MMR values.

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SO-1 is a foreshock-mainshock-aftershock (FMA) seismic sequence with a prominent mainshock (ML 4.8) occurring at ~ 17 km. The enhanced catalog contains 30 seismic events before the mainshock and allowed us to detail the foreshock sequence, highlighting a pre-seismic quiescence of approximately 13 h. Except for the main event, all the other earthquakes have a magnitude less than ~ ML 2. The coefficient of variation of interevent time shows high variability only in correspondence with the mainshock and low values for the remaining part of the sequence (Fig. 5a–a”).

SO-2 is located a few kilometers northeast of SO-1 and can also be considered a FMA seismic sequence. The main event (ML 3.2) occurred on the 23rd of February 2013, but it started on the 17th of February, only one day after the ML 4.8 earthquake. Similar to SO-1, the coefficient of variation of interevent time is higher in correspondence with the main event, and after that, it shows a quasi-flat trend (Fig. 5b’). The moment ratio trend is more complex due to some aftershocks with a magnitude of ~ ML 3.0 (Fig. 5b”).

SO-3 is located a few kilometers north of SO-1. It started in March 2013 and temporally overlapped with SO-2. The coefficient variation of interevent and the maximum-to-cumulative moment ratio time history of SO-3 do not show relevant trends with low values of COV and MMR (Fig. 5c–c”). The magnitude, COV, and MMR over time for all spatial clusters are represented in Fig. S5. The main parameters characterizing the identified clusters are summarized in Table S1.

Migration velocity, diffusivity, and Vp/Vs main characteristics

The four seismic phases of CL-1, classifiable as FMA, S, FMA, and S, migrate at an average velocity of 0.2–1 km/d, extending in an area of ~ 4 km (along strike) by ~ 2 km (along dip). The volume occupied by all CL-1 phases is the same. At the same time, the temporal evolution of CL-1 is not uniform (Phase I-IV in Figs. 4a–d and S6a), indicating that the architecture of the fault zone and the strength of heterogeneities is variable63.

For each cluster, we set the first event as a reference point, and we compute the distance of all the hypocentral locations to it. This allows us to observe, that the migration patterns of most of the analyzed seismicity grow monotonically with the square root of time according to the64 theoretical curve, thus suggesting that the seismicity might be driven by pore-pressure diffusion (Fig. 6). The retrieved hydraulic diffusivity D varies from 0.4 to 1.5 m2/s during the four seismic phases. The Vp/Vs ratio shows values ranging from 1.88 to 1.92 (Fig. 7), suggesting fluid-filled rocks following the observations made during the L’Aquila seismic sequence by65.

Figure 6
figure 6

Time evolution of the 2010–2013 CL-1-CL-3, SO-1-SO-3. Time evolution versus the temporal distance of seismicity from the first event of the cluster considered as the reference point. The grey bands represent the first 30% of seismic events relative to the overall duration. The dotted lines indicate the constant rate or velocity migration expressed in km/d. The black curves represent the interpolation of the data selected as the 90th percentile in each considered bin within 30% of the overall duration of the single cluster, assuming the homogeneous 3D diffusion model of64. The values of diffusivity along with their uncertainties are given in Table S2.

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Figure 7
figure 7

Modified Wadati diagram plots66 computed using P- and S-arrival times of the Italian Seismic Bulletin51. Black dashed lines represent the standard deviation of the orthogonal regression. The values of VP/VS along with their uncertainties are given in Table S2.

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As shown in the supplementary material (Fig. S6), during the four phases, it is possible to observe a predominant upward migration of seismicity from the base of the seismogenic layer, where the main events are also located.

CL-2 occurs about 3 months after the II phase of CL-1, while CL-3 is the last seismic episode associated with the CL group. The magnitude versus time and statistical indexes (Fig. 4e–f”) show that they are classifiable as swarms. The migration velocity is about 0.6–0.9 km/d, and the diffusivity is ~ 1.5 m2/s, evaluable only for CL-2 (Fig. 6). Differently from CL-1, CL-2 and CL-3 show one phase prevailing even if a further shorter phase is also identifiable in CL-2 pattern (Figs. 4, S5 and S6). The Vp/Vs ratios of CL-2 and CL-3 are similar and range from 1.88 to 1.89 (Fig. 7).

The main characteristics of the spatiotemporal evolution of SO-1-SO-3 are different from those described for CL-1-CL-3.

SO-1-SO-3 evolved during the time interval spanning from February to July 2013. On the 15th of February 2013, 30 foreshocks (MLmax 2.1) of the Sora main event (MW 5.0, SO-1, 16 February) occurred near Sora town at a depth range of 18–21 km (Figs. S7a”). With a high-velocity migration (5 km/d), the seismic front progressively upwards to ~ 17 km depth, where the mainshock enucleated (Fig. S6c). The evolution does not depict a diffusivity trend, and the Vp/Vs ratio reaches a very high value of ~ 2.

The day after, probably triggered by SO-1, SO-2 initiates to involve another volume, northeastward and shallower of SO-1. Like SO-1, the seismic front migrates upward with a velocity of 7 km/d at 12 km, showing an apparent high diffusivity behavior of 1.5 m2/s. The Vp/Vs ratio assumes the typical value of the central intra-Apennines areas47.

SO-3 starts in March, contemporary with SO-2 for almost one month. It is the shallowest cluster in the study area (~ 5–6 km, Fig. S7), and the space-time evolution shows a slow diffusivity trend of 0.4 m2/s. The Vp/Vs ratio is the lowest observed in this study.

3D fault models

The eight identified hypocentral clusters show differences not only in depth and seismological features but also in the shape of the hypocentral volume.

CL-1 is located approximately 60 km south of the main event of the L’Aquila seismic sequence, between the Villavallelonga and Balsorano active faults (Figs. 1 and 2). It comprises 2332 earthquakes occupying an elongated area, N-S striking, and ~ 4 km long. The 3D distribution of CL-1 well illuminates a high-angle, east-dipping volume, nonplanar surface. The seismicity migration depicts a surface that dips 63° toward the northeast (Fig. 8a) and seems to be associated with an antithetic fault of SW-dipping Villavallelonga’s northern segment.

Figure 8
figure 8

Section and map views of the reconstructed 3D models. Fault surfaces were built with the MOVE Suite software v. 2023 (Petroleum Experts Ltd) (a) 3D models and depth contour lines representing Villavallelonga and its antithetic faults, illuminated by CL-1, along with concurrent background seismicity (see Fig. 9d). (b) 3D models and depth contour lines depicting synthetic structures to the Villavallelonga-Pescasseroli alignment.

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The seismic activity of phases I-IV is well confined within a depth range of ~ 11–13 km (80% of seismic events, Fig. S7a–d), and the main event of each phase is located at depths of ~ 12–13 km (Fig. S6a–c). The coeval background seismicity partially illuminates the high-angle Villavallelonga normal fault. These observations are significant as seismicity has not been recorded over the instrumental times.

The focal mechanisms of the major events (ML ~ 2.6) (Fig. 4a–d) show strike-slip (left lateral) kinematics48 with an average T axis trending NNE-SSW (~ N25°) slightly counterclockwise rotated to the NE-SW average T axes of the pseudo-focal mechanism derived from geological data24,25 and the regional stress field of central Italy34. Cluster 1, with its four subclusters (phases I-IV), has a narrow and elongated sub-vertical shape.

CL-2-CL-5 are located ~ 10 km southeast of CL-1 between the Villavallelonga-Pescasseroli-San Donato V.C. and Posta Fibreno active faults (Figs. 2 and 3). On the map, CL-2 and CL-3 exhibit an elongated SW-NE shape, each spanning ~ 4 km. They have common extensional kinematics and are characterized by near planar hypocentral distribution (Fig. 8b). They are similar in shape and extent, all being small high-angle southwest-dipping extensional planar mesh (Fig. 9a–c). They are very close to each other (~ 2 km) and represent a set of SSW-dipping fault patches synthetic to the Pescasseroli-Villavallelonga southern segments. They deepened NNEward from a depth of 8 km, beneath CL-5, to a depth of 14 km, beneath CL-3. Specifically, a progressive deepening of seismicity is observed starting from CL-4 (8–10), CL-2 (9–12 km), CL-5 (12–13 km), CL-3 (12–15 km) (depth ranges represented in Fig. 9c, S6b and S7a’–b’). A low-angle N to NNE-dipping planar mesh interpolating the CL-2 to CL-5 bottom trace can be represented (Figs. 8b and 9c).

Figure 9
figure 9

Picture of the main results (faults map is represented with ArcMap, by ESRI, ArcMap/ArcGIS, v. 10.8, https://www.esri.com/en-us/home, fault surfaces and cross-section with the MOVE Suite software v. 2023, Petroleum Experts Ltd). (a) Active fault systems, CO2 measurements from50, evidence of magmatic rocks, and CL-1 and SO-3. The grey area represents the WNW-ESE deformation band reconstructed using CL-2 to CL-5 clusters, and the red and grey symbol on the right represents the point of view of the 3D fault models. The red lines represent the traces of the section in panel (d) and the view of the 3D model (panel c). (b) Zoom of the WNW-ESE deformation band explicitly indicating the depth contour lines of the 3D reconstruction as in Fig. 9c and the distribution of analyzed clusters. (c) The 3D models showing the seismicity at the hanging wall and footwall of the basal detachment. (d) SW-NE section view of the seismicity from 2009 to 2013 with trace shown in Fig. 9a. (e) Average focal mechanisms (Table S2) related to CL-1-CL-3 and SO-1-SO-3, computed considering Frepoli et al.48 data. Small circles plotted on the stereonets represent the T-axes of the single focal mechanisms, while black squares are the P, B, and T axes of the average ones.

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The focal mechanisms of the major events associated with CL-2 and CL-3 show normal kinematics, and as observed for CL-1, the average trend of T-axes (Fig. 9, Table S3) is ~ N35. There is a large dispersion of the T-axes of focal mechanisms in Fig. 9 (white dots in the stereograms), probably due to the trend changing (from NW–SE to WNW-ESE) of the Villavallelonga-Pescasseroli faults (Figs. 2 and 9a).

SO-1-SO-3 are located around Sora, about 7 km south of CL-1 and 5 km west of CL-2 and CL-3 (Fig. 3). The 3D distribution of SO-1 and SO-2 does not evidence fault planes but vertical strips confined beneath the NNW-dipping basal detachment of the overlying CL-2 to CL-5 clusters. This configuration could suggest seismicity due to natural fluid injection (Fig. 9a–c).

Differently, SO-3 started in March and was contemporary with SO-2 for almost one month. It was the shallowest cluster in the study area (~ 5–7 km, Fig. S7). The 3D seismicity representation helps us to associate this episode with an antithetic structure of the Balsorano normal fault (section view in Fig. 9d).

The focal mechanisms48 of the main seismic events of SO-1, SO-2, and SO-3 (Fig. 9e) show normal kinematics with average T-axes (N54, N51, N53, respectively) compatible with the regional stress field.

Discussion

From an earthquake process perspective, we investigate the spatiotemporal evolution of seismicity following the 2009 L’Aquila mainshock (MW 6.3) in a high-seismic-risk area of southern-central Italy located about 60 km south of L’Aquila town. Thanks to the template-matching approach, we enhance the temporal resolution of seismicity, lowering the completeness magnitude by unmasking hidden earthquakes. The geometric-kinematics and clustering characteristics here investigated allow us 1) to gain insight into the physical processes that occurred during the different stages of 2009–2013 seismic activity and 2) to contribute to better define the seismotectonic framework of an area characterized by extensional active faults. All the analyzed seismicity is highly controlled by fluid circulation at the upper and lower crust seismogenic layers, and multilayer extensional earthquakes characterize the study area.

Origin and Evolution of CL-1

The significant increment in seismic activity within the study region after the 2009 L’Aquila earthquake prompts an inquiry into the potential relation between the observed increase in seismicity and the mainshock of the L’Aquila seismic sequence.

Inferences of the L’Aquila earthquake on this sector of the Apennines were made by De Natale et al.,67. They highlighted the potentially anticipated reactivation of faults existing between the 1984 Barrea and the 2009 L’Aquila epicentral areas due to stress transfer from both earthquakes.

By analyzing the new catalog down to completeness magnitude (Mc = 0) and retrieving multiplets by template matching technique, we observe that CL-1 (I-Phase) occurs 34 h after the MW 6.3 seismic event of L’Aquila, at ~ 60 km, raising the question of probable delayed dynamic triggering. The delayed dynamic triggering is debated in the literature because seismicity is continuously produced in seismic active regions. Generally, the remote triggering delay can be ascribed to several potential mechanisms, including surface waves that circumnavigate the Earth multiple times, waves that perturb and alter the frictional properties within a fault zone, or a process in which seismic waves open a fluid pressure valve, leading to the unlocking of a fault2,8,68,69.

Moreover, Gomber and Johnson70 observe that, similarly to laboratory experiments, remote triggering could result from large dynamic deformation like the ones produced by strong directivity.

On this matter, Calderoni et al.,71 demonstrated that the earthquakes that occurred on the causative fault of the L’Aquila mainshock (i.e., Paganica fault in Fig. 1a) had strong unilateral directivity that largely affected the study area (Fig. S8a–b).

The seismic station nearest to CL-1 is Villavallelonga (VVLD), belonging to the National Seismic Network. The VVLD seismometer recorded a saturated seismic signal. In contrast, the nearest accelerometer, ORC, part of the Italian National Strong Motion Network72 (see Fig. S8a), located approximately 13 km northeast of CL-1, recorded a Peak Ground Velocity (PGV) exceeding the threshold identified by70 Fig. S8c. These authors suggest that areas undergoing large PGVs exceeding the values of the experimental curve, representing the scaling of dynamic deformations with the distance, could be susceptible to dynamic triggering.

These considerations, combined with the observation that the enhanced catalog ensures the absence of smaller or larger events responsible for primary triggering in the study area, make the delayed dynamic triggering effect a good candidate for explaining the genesis of CL-1. Specifically, the early CL-1 phase, comprising some hundred seismic events, intermittently promoted the other CL-phases, characterized by ~ 2000 earthquakes. This fluid circulation could promote the occurrence of other clusters (CL-2, CL-3) of seismicity (section “The role of fluid in triggering CL-2-CL-3 and SO-1-SO-2”).

The role of fluid in triggering CL-2-CL-3 and SO-1-SO-2

Recent seismological, geochemical, and hydrogeochemical literature illustrates how fluid circulation, originating from various sources within the crust or mantle in the Apennines, can potentially promote seismic events and exert influence over the entire seismic cycle41,73,74,75,76,77,78.

Our observations show that extensional earthquakes can occur at different seismogenic layers (Fig. 9), and the results support the hypothesis that fluids play an essential role in the processes controlling the cascade of the observed seismic episodes.

The presence of fluids is fully confirmed by direct measures of CO2 flux50. Three degassing sites classified as “very high flux” were found just in the proximity of the CL-2-CL-3 epicentral areas (green circles in Fig. 9a). Ciotoli et al.,79 measure an ongoing degassing of deep endogenic gases (Helium and Radon anomalies) along the Val Roveto Valley, North of Balsorano–Posta Fibreno fault system. Moreover, Smeraglia et al.,41 find insights into fluid circulation at the upper and lower crust by analyzing calcite-filled comb and slip parallel fractured veins on the Balsorano-Posta Fibreno faults alignment.

The high diffusivity values, resulting from our analysis, indicate that fluids could circulate through more fractured or permeable rocks at depths. In such conditions, seismogenic fault systems can represent a preferential pathway for fluid mobility80.

Based on these considerations, we suggest that the mainshock of the L’Aquila seismic sequence could have modified the frictional properties in the Villavallelonga fault zones (Fig. 8) or opened a fluid pressure valve2,7,68,69 sealed by mineral depositions or other chemical processes. High-pressure fluids could favor the occurrence of the CL-1 phases and the other intermittent phases until 2012 (Fig. S5) following the overpressure pulses migration upward along the fault as modeled by11. The fluid circulation, controlled by the major seismogenic faults, has promoted the delayed seismic activity of CL-2, CL-3, and other minor clusters in the crystalline basement.

The 3D position relative to the active fault alignments of Villavallelonga-San Donato Val Comino and Balsorano-Posta Fibreno and the depth range occupied by the hypocenters in the lower crust suggest that the genesis of SO-1 to SO-2 is different and independent from CL-1-CL-3. The spatial reconstruction of SO-1 bears similarity with the 3D geometry of the seismic sequence that occurred in 2013–2014, ~ 60 km southeast of SO-1 in the southern Matese region (MWmax 5.2) (Figs. 1a and S1a). This area, characterized by high attenuation values36,81, provides evidence that the triggering mechanisms of these earthquakes are associated with magmatic intrusion. Our findings concerning the spatiotemporal evolution, the high migration velocity, the Vp/Vs ratio, and the depth geometry indicate that SO-1 might be controlled by ascending mantle fluids possibly originating from degassing magmatic intrusions as observed in the study area41,50,79. Hints of volcanic processes (e.g., sparse magmatic outcrops) are present in proximity to the volcanic districts of the Ernici Mountains (Fig. 9a). The spectrograms of the main event (Fig. S9) show some signs but no clear evidence of the low-frequency content typical of similar earthquakes. However, we lack additional information to distinguish the triggering mechanisms definitively. In this scenario, we suggest that SO-2 and SO-3 can have been triggered in turn by SO-1.

3D tectonic control in seismic sequence evolution

Multiphase swarms and complex seismic sequences characterize the analyzed seismicity. This seismic activity involves multiple segments in a cascading mechanism, including synthetic and antithetic faults to major structures (Fig. 9a–e), and clusters (SO-1, SO-2) that are not directly correlated with tectonic structures and that show geometric warping along strike and dip.

Such a complex pattern, with interconnected multi-scale synthetic and antithetic faults, involves small-magnitude seismic events (ML < 4.8) but exhibits similarities with both the outcropping extensional structures of the Apennine fault systems and the spatiotemporal evolution of recent large earthquakes: Irpinia 1980, Colfiorito 1997, L’Aquila 2009, and Amatrice, Visso, and Norcia 2016–2017. These major events involve the failure of multiple critically stressed faults or fault segments, which, in turn, influence the duration and evolution of seismic activity.

Our results allow us to distinguish three cluster typologies concerning active faults:

Type 1—clusters on secondary structures antithetic to major faults, generally located close to the intersection with the main faults (i.e., CL-1, SO-3);

Type 2—clusters on major faults in specific positions, for example, close to the basal detachment or at synthetic fault intersections (i.e., CL-2-CL5);

Type 3—clusters not directly controlled by tectonics (i.e., SO-1, SO-2).

Type 1. CL-1 and SO-3 illuminated fault segments antithetical to the Villavallelonga and Balsorano faults, respectively (Fig. 9d). The two major faults were partially imaged through a synchronous mechanism of background seismicity. These observations further corroborate the pivotal role of antithetic faults in accommodating deformation and promoting interactions between antithetic and principal fault systems during seismic sequences, as observed in the 2016–2017 Central Italy seismic sequence57,82, in the foreshock sequence of the 2009 L’Aquila earthquake83,84,85,86 and during the Balsorano minor seismic sequence of 2019 (MWmax 4.6)87.

It is conceivable that the discontinuity associated with CL-1 resembles the Annifo segment of the Colfiorito sequence34. In that instance, the seismogenic N-S left-lateral fault inverted a pre-existing right-lateral structure formed during the Late Miocene-Pliocene compressional phase. Similarly, CL-1-related discontinuity could be originally a pre-existing right-lateral fault, subsequently reactivated with left-lateral shear within an extensional stress field. The affected volume, seemingly detaching along the southwest-dipping Villavallelonga fault, undergoes deformation characterized by a pure strike-slip regime with a nearly NNE-SSW oriented T-axis (see Fig. 9e). This strike-slip kinematics occur within the context of a purely regional extensional pattern.

Type 2. CL-2, CL-3, CL-4, and CL-5 nucleated on the lower portion of major WSW- to SSW-dipping Quaternary faults, extending upward for some kilometers from the intersection with the common basal detachment (Fig. 9c). The envelope of the base of the seismogenic layer of CL-2-CL-5 may be well interpolated by a planar surface dipping N-ward to NNE-ward with a dip angle of about 35° at depths from ~ 12 to ~ 15 km (Fig. 8). The spatial position of the reconstructed SSW-dipping parallel seismogenic patches (Fig. 9c) that are high-confined, and spaced a few kilometers perpendicular to the strike, suggest a leading role played by such N-dipping discontinuity. Following the reasoning of 88, we advance the hypothesis that such basal surface could have played essential role in driving seismicity. By undulating along-dip channels (e.g., tectonic mega groves), the natural fluid could be injected at the base of the fault zone, thus activating small portions of parallel antithetic structures.

A peculiarity of the 3D seismogenic fault mesh corresponding to these clusters (Fig. 9) is the length/width shape ratio, which is always < 1 due to a greater extent along the dip than along the length. This configuration supports the hypothesis that fluids naturally injected into the fault zone from below are diffused through dip-parallel channels while triggering earthquakes. This basal detachment surface can play the role of a transitory barrier or may be interpreted as a relevant tectonic structure connected with the Ernici NE to N-dipping extensional fault system (Fig. 9). In such a case, all the major SW- to SSW-dipping Quaternary normal faults of the study area would represent first-order antithetic splays to such a basement discontinuity. A similar geometric configuration is already highlighted from active and passive seismic data for the Eastern Sabini extensional fault system at the bottom of the Paganica fault system, responsible for the L’Aquila earthquake30, besides the well-known Altotiberina low-angle normal fault89.

Type 3. SO-1 and SO-2, as well as a very recent sequence that occurred in the same area in November 2023 (MLmax 2.8, depth 16 km), not considered in this study, are confined within the crystalline basement in the lower crust at the footwall of the NNE-dipping reconstructed discontinuity (Fig. 9c). These clusters do not appear to be controlled by a well-specific tectonic structure but rather by a mixture of sub-vertical channeling and pressure changes due to the ascent of mantle fluids or even melt. The spatiotemporal behavior and 3D reconstruction identify two in-space and time-close episodes of near-vertical strips of earthquakes rising from about 20 km up to 10 km (SO-1, SO-2). The overall 3D reconstruction (Fig. 9) allowed us to identify a deep seismogenic layer capable of generating earthquakes of significant magnitude for the area. These earthquakes are expressions of the regional extensional stress field and can produce additional seismicity in the Apennine area, independent from the main upper crust extensional system, increasing the seismic hazard of the study area.

Conclusions

The comprehensive analysis of dynamic seismic processes observed from 2009 to 2013, combined with geological data, enables us to characterize the typology of seismicity in a high seismic hazard area during an inter-seismic period and to reveal a previously unrecognized deformation zone. This zone spans 15 km in a WNW-ESE direction, that is lined up with the characteristic trends of the Pescasseroli and Sora faults (Fig. 9). Within this region, seismicity patterns depict a network of synthetic faults gradually converging along a 35° north-dipping plane, potentially serving as a permeability barrier or a low-angle normal fault associated with the Ernici fault systems.

Our analyses suggest that the north-dipping plane may be crucial in guiding mantle fluids in this region. These fluids enhance the seismic process, a conclusion backed by direct surface measurements from various studies41,50.

The reconstructed configuration indicates the existence of two overlapping extensional seismogenic domains. The first seismogenic layer extends from the outcropping faults to the crystalline basement, while the second layer stands in the lower crust. Consequently, earthquakes originating in this area can be correlated with the complex outcropping pattern of active faults and deeper earthquakes, such as the Sora seismic sequence. The second deeper seismogenic layer, capable of releasing moderate earthquakes (at least from what has been observed so far through historical and instrumental earthquakes), exacerbates the seismic scenarios in this high seismic hazard sector of the central Apennine.

We are confident that our findings offer valuable insights, marking a significant advancement in the field. They serve as a pivotal reference, steering upcoming research toward developing advanced seismotectonic models. These enhanced models will seamlessly incorporate tectonic data and seismic activity, comprehensively characterizing seismic processes.

Methods

Template matching

To enhance the seismic catalog of the earthquakes that occurred in the study area after the 2009 L’Aquila earthquake, we selected as templates the 856 relocated events of the Catalog of Absolute (nonlinear) 3D earthquake Locations (CLASS) 17,51 with horizontal errors < 3 km and vertical errors < 4 km (Fig. 3). Average horizontal and vertical errors are 0.5 and 1.5 km, respectively. RMS errors of the travel time residuals are less than 0.4 s and templates have an azimuthal gap less than 270°.

We use the open-source seismological package PyMPA77,90, which detects microseismicity from cross-correlation of continuous data and templates. PyMPA was used in previous applications, such as for processing recent seismic sequences in Italy84,91.

Template matching is applied to 4 years of continuous data recorded at 7 permanent three-component seismic stations (VVLD, INTR, LPEL, CERA, GUAR, POFI, PTQR) of the Italian National Seismic Network (Fig. S3) for searching hidden earthquakes that resemble well-located events. Continuous data are downsampled to 50 Hz and trimmed to 5 s starting 2.5 s before the theoretical S wave arrival, calculated using the velocity model derived from 47. The waveforms are also filtered from 3 to 15 Hz to enhance the signal-to-noise ratio of local earthquakes.

Templates are also evaluated by adopting Kurtosis-based tests92 to select an optimal signal-to-noise ratio, avoiding using blurred signals in the matching technique. Earthquake magnitudes for the enhanced catalog are calculated relative to the magnitude of master events, given in the original CLASS catalog, considering that the scalar moments of two events with similar waveforms scale as the amplitudes of their waveforms.

The location of the small events in the augmented catalog strictly depends on the quality of the input catalog locations and associated errors. Due to the high resolution of the starting catalog, we decided to keep the new detections co-located with the templates.

This choice of not relocating the new events is partly justified by the area dimensions, the seismic station inter-distance relative to the area under study, and the reduced number of earthquakes for which it is possible to obtain a more refined location. 93 and 94 demonstrated that only a small portion of events from template matching could be relocated (on average less than 20%). Moreover, relocation techniques based on limited frequency-band envelopes91 cannot improve the location of small-magnitude events when the network coverage is sparse. These considerations led us to collocate the new events at the respective template positions.

Data Analysis

Declustering

The first step in the cluster analysis is to apply the Zaliapin declustering method for separating background from clustered seismicity60.

The nearest-neighbor method computes the time-space distance between pairs of earthquakes. Rescaled time (T) and distance (R) between an event and its parent are normalized by the magnitude of the parent. The empirical distributions of the logarithm of the nearest-neighbor distance,\(log_{10} \eta^{*}\), and their components (T, R) are shown in Fig. 3d. It is worth noting that the co-location of new detections with their templates results in Rij becoming zero, leaving log(Tij) as the sole component for calculating the bidimensional spatiotemporal distance in the Zaliapin and Ben-Zion framework. This aspect leads to a trimodal pattern in the (T, R) plane that does not affect the declustering process. Combining the nearest neighbor method with the analysis of interevent times is effective for segregating events that are independent even if co-located, as shown in61.

After this, we can classify the most important clusters in swarms or seismic sequences as a function of their signature features.

In addition, we use the Gardner windowing method95 to separate different temporal phases.

Using the distribution of interevent times for spatially close events, we check if some multi-modality can suggest how to separate the related events from the independent ones. Results from this analysis, performed for some clusters, evidence that the problem does not affect our results. However, we notice that some events can be included in the same cluster, even if the cluster activity is off for some time and reactivates later. To overcome this problem, we rank clusters into sub-clusters or phases at similar positions using95 windowing.

Subsequently, all clusters and temporal phases within are classified into swarms, mainshock-aftershock, and foreshock-mainshock sequences following the criterion proposed by62. The mainshock is the strongest earthquake in a cluster, and all the previous seismic events are pre-shocks. All pre-shocks are set foreshocks when the magnitude gap between the largest pre-shock and the mainshock is greater than 0.5. Unlike, a swarm-like sequence has pre-shocks with similar magnitudes (the difference is smaller than 0.5).

Statistical indexes

To characterize the clustered seismicity, (1) we plot the magnitude versus time and classify the cluster as a swarm (S), foreshocks-mainshock-aftershocks (FMA), or mainshock-aftershocks (MA) considering the62 approach, we evaluate (2) the temporal evolution of the coefficient of variation of interevent times, and (3) the seismic moment ratio.

Coefficient of variation of interevent times

Studying the interevent times (τ) and their covariance (Cv) is very useful to quantify temporal clustering or the degree of periodicity in earthquake occurrence. Cv is the standard deviation of interevent times (σ) and the mean interevent time (μ) ratio. Periodic and quasi-periodic events have values of 0 < Cv < 1, random Poisson processes have Cv ~ 1, and temporally clustered earthquakes Cv > 196,97,98.

We compute Cv for each cluster using a sliding window. We repeat this computation considering six windows with lengths varying from 5 to 15% of the total events with an incremental step of 2%. For each window, we calculate the mean and standard deviation (σ) of the interevent time (τ) to determine the coefficient of variation. The final step is estimating the mean value and standard deviation of the coefficient of variation resulting from the six different windows.

Seismic moment ratio temporal evolution

The Seismic Moment Ratio evolution (SMR) over time99 defines the presence of main phases of seismicity in terms of the maximum release of energy. This index over time is significantly different for regular seismic sequences and swarms. SMR varies from 0 to 1, and values close to ~ 1 mean that the clustered seismicity has a seismic sequence behavior with a single dominating event.

As for the Cv, we evaluate SMR for each cluster using a sliding window, and we repeat this operation considering six different windows.

We preliminarily convert the magnitude of the events from ML to MW by using the relation proposed by100 for small earthquakes (\(M_{w} = \frac{2}{3}{ }M_{L} + C^{\prime}\)) and compute the seismic moment considering101 relationship \(\left( {M_{w} = \frac{2}{3}{ }log_{10} \left( {M_{0} } \right) - 6.07} \right)\).

Then, we calculate, for each window, the highest value of the seismic moment, the sum of the seismic moment of the events, and the ratio between these two parameters.

The final step is calculating the mean value and standard deviation of the ratio between the maximum seismic moment and the sum of the seismic moments of the events for the six, different windowing to obtain one single curve over time.

Migration velocities of the Seismicity and Vp/Vs ratio

The reconstruction of the migration velocities of the seismicity in space-time is particularly complex. It allows us to observe the presence of seismic fronts and calculate the average migration velocity to keep the mechanism of the genesis of seismic swarms.

We can determine in the seismic cluster and swarm activity a preferential direction of growth of the seismicity with different activity rates during the time. Following102, to compute the migration velocity and precisely the early stage of hypocenter migration, we:

  1. (1)

    Calculate the distance of the seismic events to the first seismic event;

  2. (2)

    Select the distance data as the 90th percentile in each considered bin falling within 30% of the overall duration of the single episode;

  3. (3)

    Compute the straight line’s angular coefficient connecting the first and the farthest event.

Moreover, we consider the events selected at point 2) and interpolate them by fitting the diffusion model proposed by64 over a regular grid of values.

3D model building

To build the 3D fault models, we consider the cluster hypocentral distribution and, where possible, apply the following multistep analysis.

(1–2) We select the earthquakes falling within the depth layer encompassing approximately 80% of seismic events, and we define an initial mesh by interpolating the selected hypocenters via the Inverse Distance Weight (IDW) method, employing a power inverse distance exponent value set at 0.5.

(3) We draw contour lines based on the initial mesh representing depth increments of 500 m.

(4) Then, we resample the depth contour lines at a consistent 500 m interval to achieve smoother lines.

We generate the final curvilinear mesh using either Delaunay Triangulation or Spline curves and apply them to the resampled contour lines.