The northern Apennines, which defines the divide between the Tyrrhenian and Adriatic Sea, extends from Liguria to Latium forming a large arc convex towards ENE. The intermediate portion of this orogenic belt constitutes the Tuscan-Emilian-Romagna Apennines (Figure 1).

NE of the Apennines, relief gradually slopes towards the Po Plain and Adriatic coast, through the hilly Frignano, Romagna and Montefeltro belts (Figure 1). Towards the south-west, within the Apennine arc concavity, morphology is

more varied. There prominent ridges, mostly NW-SE-oriented, interrupt broad flat or hilly depressions. The maximum topographic elevation occurs in the north-western portion of the Apennines, from Mt. Orsaro to Corno alle Scale (Figure 1). In particular, Mt. Cimone has the maximum altitude of the whole northern Apennines (2165 meters above sea level). The Apuan Alps reach 1 - 2 km a.s.l. Significant height also has Mt. Falterona (1654 m a.s.l.) and Mt. Fumaiolo (1268 m), which house the sources of the Arno and Tiber river respectively. SE of these mountains, the Umbrian-Marche Apennines begins, with Mt. Nerone (1525 m a.s.l.) and Mt. Catria (1701 m).

The Tuscan territory extends from the Tuscan-Emilian-Romagna Apennine arc to the northern Tyrrhenian Sea. To the south, the border with Latium is marked by Quaternary volcanoes (Mts. Volsini in Figure 1). The Tuscan relief is diversified but not very accentuated. In the innermost sector, Mt. Amiata rises up to 1734 m a.s.l. Only a few of the other reliefs listed in Figure 1 exceed 1 km height, mostly in the Colline Metallifere. However, the morphological contrast between ridges and depressions is quite sharp; often it corresponds to important changes in surface geology and structural setting.

The depressions correspond to marine and continental sedimentary basins, developed from the upper Miocene (about 10 million years ago [10] ) upon a substrate already deformed by the Alpine-Apennine orogeny [11]. The basin age decreases from the Tyrrhenian coast towards the Apennine belt [12]. Therefore the most eastern (intramontane) basins developed in Pleistocene (Lunigiana, Garfagnana, Mugello, Casentino, Valtiberina in Tuscany; Gubbio, Deruta-Todi and Foligno-Spoleto in Umbria, see Figure 1). In the more ancient, western basins, the thickness of the Upper Miocene-Pliocene filling may exceed 2 km (e.g., Viareggio, Elsa and Radicofani in Figure 1 [13] ). Although both the basins and bounding ridges are generally NW-SE oriented, there exist NE-SW, transversal depressions such as Albegna, Cecina, Cornia, Grosseto and Valdarno inferiore (Figure 1).

The tectono-stratigraphic units outcropping in the ridges are much older (Paleozoic-lower Miocene) than basin filling. These units have been deformed during the Alpine-Apennine orogeny and often bear traces of a regional metamorphism [14]. The oldest formations of the Tuscan sedimentary cover outcrop in the so-called Middle Tuscan Ridge, formed by the Apuan Alps, Mt. Pisano, Iano, Montagnola Senese, part of the Colline Metallifere, Mt. Leoni, Uccellina Mts. and Argentario (Figure 1).

Ridges in western Tuscany were also affected by the Pliocene-Quaternary magmatism, as well as in northern Latium (Roccastrada, Amiata Mt.; Volsini, Cimini, Sabatini and Tolfa Mts. in Figure 1 [15] ).

The seismic activity of the above features is not correlated with their age in a simple way. Most of the strong earthquakes (M_W ≥ 5.5) occurred in the intramontane basins (Figure 1). Lunigiana and Garfagnana were hit by 6 strong shocks in 1481 A.D., 1740, 1834, 1837 and 1920 (September 6 and 7). Two historical events are located in Mugello (1542 and 1919). Finally, Valtiberina suffered 5 major shocks (1352, 1389, 1458, 1789 and 1917).

However, at least 5 strong earthquakes hit ridges and basins of inner Tuscany (Figure 1): Colline Metallifere (1414), Valdarno superiore (1558), Tora-Fine (1846), Chianti/Pesa/Florence (1895) and Montecarlo (1914). Due to closeness with Tuscany, we could also consider the Orvieto (1276) and Volsini Mts. (1695) shocks (Figure 1). This fact suggests that the active deformation of Tuscany is not confined to recent intramontane basins.

On the other hand, some parts of Tuscany appear to be almost aseismic: Casentino, Chiana, Era, Valdarno inferiore and the vast zone extending from Mt. Amiata to Elba Island [6]. Finally, it is worth noting that for a century no strong earthquake has occurred in the study area (1920 Garfagnana, M_W = 6.53).

In the study area, crustal thickness increases from about 20 km below Elba Island to 22 - 26 km in central Tuscany. The Moho depth reaches 50 km beneath the northern Apennine arc, then it decreases to 26 - 30 km near the Adriatic coast [16].

Geophysical survey allowed us to shed light on the architecture of this part of the Apennines [17] [18] [19] [20] [21]. It is a typical thrust-and-fold belt, formed by the progressive stacking of crustal slices. Regional, SW dipping overthrusts make the contact between the slices. They cut the sedimentary cover, dissect the metamorphic basement and perhaps prosecute in the underlying upper mantle as shear zones [20] [21] [22].

The study area belongs to the western edge of the Adriatic plate, whose deformation began in the lower Miocene with the development of eastward migrating thrust belt-foredeep systems [23] [24] After the opening of the northern Tyrrhenian basin in the late Miocene [25], the compressional regime involved an increasingly large area of the Adriatic foreland. Moreover, the related foredeeps were incorporated in the eastward migrating Apennine belt.

Two conflicting interpretations of the study area have emerged over time. The first interpretation provides that since middle Miocene, inner Tuscany was affected by an extensional stress regime. It generated a horst-and-graben (often semigraben) system, corresponding to the ridges and basins indicated in Figure 1 [8] [26] - [38]. Until the lower Pliocene, extension would have occurred by low-angle normal faults (detachments). The subsequent deformation was instead produced by high-angle normal faults, which bound the present depressions [8]. Figure 2 shows the main normal faults reported by the above works.

The alternative interpretation implies that compressional deformation dominated the study area until perhaps the middle Pleistocene [9] [40] - [52]. Indeed, the above Authors recognize the effect of normal faulting from the late Quaternary only. In this context, thrusts and reverse faults would have controlled the development of antiformal folds, corresponding to the ridges shown in Figure 1. The depressions developed as synform or thrust-top basins. Figure 3 shows the main reverse faults, thrusts and folds axes reported in the above works.

The aforementioned debate may seem irrelevant to the analysis of seismogenic processes, as it concerns past (pre-Holocene) tectonic phases. However, the gap between the two interpretations may cause serious ambiguity in mapping of tectonic features. For example, the boundary between the Mt. Cetona ridge and Chiana basin is reported as an east-dipping normal fault (VC in Figure 2 [53] ), or as a west-dipping thrust (CC in Figure 3 [9] ).

In both the above interpretations, most tectonic features are NW-SE directed (Figure 2 and Figure 3). However, some NE-SW features have been suggested also. Such lineaments (e.g., Al and GP in Figure 2) would explain the interruption in the continuity of the sedimentary basins. However, these transverse fault systems are often inferred by stratigraphic and structural considerations, rather than by direct field mapping [13]. More evidence on these features is reported along the northern Apennine arc [54].

An example of the Tuscan transverse structures is the dextral strike-slip fault system located just north of Valtiberina basin (PSS in Figure 2), which however is much older than the basin itself [55].

Recently, some sinistral, transverse fault systems have been described in central Tuscany (Am, Ar, Ca, Rp, St and Vi in Figure 2). These fractures are very recent and probably active, because they are associated with growing travertine deposits [53] [56] - [61] suggest that the western sector of the Larderello geothermal field (LGF in Figure 1) is a pull-apart basin bounded by NE-SW sinistral strike-slip faults. Similar transverse faults have been described in the Pleistocene volcanoes of northern Latium (Ci, Lt and Tf in Figure 2 [62] ). [63] recognize the Mt. Amiata strike-slip fault (Am in Figure 2), but they attribute it a dextral kinematics.

Although the faults and folds shown in Figure 2 and Figure 3 are often prominent morphotectonic features, they do not necessarily represent active structure or seismogenic sources. Indeed, the identification of active and capable faults [64] faces several difficulties. As regards Tuscany, it should be considered in its initial phase [63].

Two important uplift episodes affected the study area since the Upper Miocene. The first episode (middle-late Pliocene) led to the emersion of marine basins, such as Siena and Radicofani in southern Tuscany [65] [66]. The second episode has started in the middle Pleistocene with uplift rates of 1 - 2 mm/year. It affected both the northern Apennine arc [67] [68] [69] [70] and inner Tuscany [37] [71] [72]. As Quaternary uplift is possibly linked with active tectonics, Figure 2 indicates the most uplifted zones according to the above works.

In some cases, surface uplift can be a consequence of the emplacement in the crust of plutons and magma chambers [73]. This mechanism has been adopted to explain the current elevation of the Pliocene marine deposits of southern Tuscany, sometimes many hundreds of meters asl [34] [65] [74] [75] However, Pliocene-Quaternary magmatism has affected southern Tuscany only [15], so it cannot be invoked for the other uplifted zones. For example, both the Chianti Mts. and the adjacent Siena and Valdarno superiore basins (Figure 1 and Figure 2) have undergone a substantial Quaternary uplift [76]. Likewise, in north-western Tuscany the Apuan Alps acquired their rugged morphology in the Quaternary only [77]. In addition, conspicuous uplift and exhumation rates are estimated both north-west and south-east of the Mugello basin, as well as in the Romagna Apennines [31] [70] [78].

Any interpretation of the active tectonics of the study area must take in due account the evidence of recent uplift, at both the local and regional level.

Current compilations of active and seismogenic faults [79] [80] pay little attention to the study area. After the pioneering work of [81], only in recent years the identification of active faults in Tuscany renewed. In particular, the intramontane basins have been investigated: Casentino, Garfagnana, Lunigiana, Mugello, Pistoia-Prato-Florence and Valtiberina (Figure 1 and Figure 2) [48] [49] [82] [83] [84] [85] [86]. [70] looked for active faults in the Tuscan-Emilian-Romagna Apennines. Inner Tuscany has received much less attention so far [56] [58] [63] [87]. This may be due to the fact that the most recent strong earthquakes have hit the outer, intramontane basins (Figure 1).

The active structures identified (more often suggested) by the above studies usually are normal faults (Figure 2). Active reverse faults and folds are instead reported in the Tuscan-Emilia-Romagna Apennines (e.g. CdP in Figure 3).

So far, none of the active faults proposed in the literature has revealed its seismogenic nature, because the last strong earthquake occurred in the study area dates back to a century ago (1920 Garfagnana, Figure 1). In fact, confirming such nature needs accurate detection of the seismic fractures induced by a strong earthquake (usually M_W ≥ 6). This actually happened for the Mt. Vettore-Laga Mts. normal fault system after the October, 30 2016 Norcia earthquake (M_W = 6.6 [88] [89] [90] ). On the other hand, the surface distribution of the coseismic fractures is often difficult to reconstruct when many individual fault segments are involved, as usually happens for normal faulting [91] [92] [93] [94] [95].

In absence of coseismic deformation, the seismogenic nature of a fault remains largely speculative. Field researchers working in active tectonics often overlook the distinction between coseismic and aseismic slip of outcropping faults. Several aseismic faults are known, including the Hayward fault in California and the Ismetpasa segment of the North Anatolian fault in Turkey [96] [97]. However, the documentation is scarce for the Italian region [98]. Moreover, discrimination between seismic and aseismic slip may be surprisingly difficult without the support of specific laboratory tests [99] [100].

Various difficulties hinder the identification of active faults (both seismic and aseismic) by geological and geomorphological survey. First, an unknown fraction of the active fault population is represented by buried shear fractures, which may have a weak morphological expression at the surface [101] [102] [103] [104]. For example, the buried reverse faults responsible for the May, 2012 Po Plain earthquakes did not produce surface faulting [105].

Some complications can also occur in the presence of marked fault scarps with measurable kinematic indicators:

1) An ancient tectonic feature can be mistakenly recognized as an active fault. For example, [106] refute the existence of a normal fault in the Val d’Agri (southern Apennines), which [107] consider as the source of the 1857 large earthquake (M_W = 7.12 [6] ). In this case, the detected triangular facets are not the traces of a normal active fault. Instead, they probably are flatirons, i.e. eroded remains of a limb of an ancient fold [106]. In fact, triangular facets may appear on any tectonic feature (normal fault, reverse fault and fold) and by selective erosion also [104] [108].

2) The morphological prominence of the fault scarp is not always a reliable indicator of its recent/present activity. A well-known example is the Gubbio fault (Gu in Figure 2), which bounds to the east the Gubbio intramontane basin. This 22 km long normal fault dips 60˚ - 70˚ to the west and forms a steep morphological escarpment, towering on the underlying flat basin. The cumulative throw, occurred in several stages since the Upper Miocene, reaches 2000 m [109]. However, evidence about the present activity of this fault is scarce. Only a strong earthquake has occurred near Gubbio (1984, M_W = 5.6 [6] and the role of the Gubbio fault is still debated. In fact, during that shock no coseismic fracture was observed near the fault [110] [111].

[104] also advises caution in assessing the recent activity of fault escarpments by morphotectonic analysis only. For example, [63] suggest the present activity of the Mt. Cetona normal fault (Ce in Figure 2), which bounds to the east the Radicofani basin. They also estimate a recent slip rate of about 0.6 mm/year. On the contrary, [53] state that this Pliocene fault is now inactive, since it is dissected by a Quaternary strike-slip fault system (St in Figure 2).

3) The so-called selective erosion, due to the different weathering of outcropping formations, can generate forms simulating normal active faults [108]. For example, the alleged active Cerbaie fault (Cb in Figure 2), located in the Valdarno inferiore basin, could actually be an erosional landscape [108].

4) A large landslide can generate a shallow deformation pattern simulating normal, strike-slip and reverse faults in the detachment area, sides and toe of the landslide respectively [112]. [113] discuss several features misinterpreted as active normal faults in the central Apennines.

Due to the above problems, mapped active faults may not correspond to actual seismic sources. For example, two large earthquakes hit the Mojave Desert (eastern California) in 1992 (Landers, M_W = 7.3) and 1999 (Hector Mine, M_W = 7.1). These shocks produced a pattern of coseismic faulting that significantly differs from the previously mapped active faults (Figure 4. 27 by [104] ).

In brief, the search for seismogenic structures by morphotectonic analysis should be supported by independent methodologies. In the next section I consider the use of the source mechanisms of small earthquakes that have recently occurred in the study area.

Global, national and local seismometric networks make possible recording many seismic events, most of which can be defined small earthquakes (M_W ≤ 5). The analysis of the micro-seismicity provides basic information in order to define the seismotectonic pattern of an actively deforming zone [114]. This kind of investigation is particularly important where tectonic deformation is slow and strong earthquakes are relatively rare. Furthermore, using micro-seismicity has the obvious advantage of dealing with actual (albeit small) seismic slip events.

The earthquake source mechanism (ESM), representing the geometry of the seismic fracture, is fully described by the seismic moment tensor [115]. As earthquakes are basically slip events on shear fracture, the seismic moment tensor is dominated by the double couple solution, represented by a couple of nodal planes and the related tensor eigenvectors (B, P, and T axes).

A set of ESMs allows us constraining the stress and strain tensors in the crustal volume affected by seismic activity [116] [117] [118]. Small earthquakes contribute little to the overall deformation of a given crustal volume [119]. However, the seismic strain style (i.e. the direction of the principal strain axes and the ratio between their amplitudes) is similar for large earthquakes and for small shocks. Therefore, micro-seismicity can be used to constrain the seismotectonic pattern [120]. Furthermore, small earthquakes re-distribute elastic stress on the involved faults, thus influencing the development of future seismicity [121].

Some previous works deal with the micro-seismicity of the study area, although the analysis is often limited to specific sectors. For example, a local seismometric network has provided several ESMs for the Larderello geothermal field (LGF in Figure 1 [122] [123] ). In particular, [124] considered 190 small seismic events (0.5 < M < 3.0), occurred in the western part of LGF from 1994 to 2000. The stress regime obtained inverting those ESMs is compatible with an active, NE-SW strike-slip fault, which could dissect at depth the NW-SE normal faults mapped in the Colline Metallifere zone (from n. 33 to n. 37 in Figure 2). Furthermore, the emplacement of the Larderello granitoid pluton would have been favored by a deep-seated, NE-SW strike-slip fault [52] [75].

[125] [126] consider the Apuan Alps and the adjacent depressions of Lunigiana and Garfagnana in north-western Tuscany. [127] describe the source mechanism of small earthquakes (M_W ≤ 4.7) occurred since 1992 until 2007 in a zone embracing the Romagna Apennines, Casentino and Valtiberina basins.

[128] consider the micro-seismicity (2.5 < M < 4.8) occurred in Italy in the period 1988-1995. The EMSs were obtained by the first-arrival polarity method. Then, [129] procedure was adopted to constrain the stress regime in various sectors of the Italian region. The two sectors named “Northern Tuscany” and “Pery-Tyrrhenian” include north-western Tuscany and the Tyrrhenian coast of Tuscany and Latium respectively. In both sectors, the estimated stress regime is extensional, with a ENE-WSW directed, sub-horizontal minimum compression axis (σ₃). In the stress regime map elaborated by [130] the study area is characterized by pure extension, with NE-SW σ₃.

However, the determination of the stress regime by ESM inversion is based on some assumptions that are not easily verifiable [117]. In fact, the inversion procedures require homogeneity of rock mechanical properties and uniformity of the stress state in the crustal volume considered. Furthermore, the source mechanisms should be independent each other, which is in contrast with the fault interaction expected by the rock elastic behavior [121].

[131] considered the seismicity of the central-northern Apennines recorded in the time interval 1981-2002 [132]. In particular, 424 ESMs were classified into 5 classes (normal, trans-tensional, strike-slip, trans-pressional and reverse) according to the fault direction, fault dip and slip vector. This analysis shows that normal and reverse faults represent only 40% of the total, while sinistral and dextral strike-slip faults reach 28%. Furthermore, the proportion of normal faults significantly decreases (from 33% to 4%) as hypocenter depth increases. [131] suggest that the typology and spatial distribution of ESMs does not support the conclusion drawn by [128] [130] who clearly distinguish an outer Apennine belt (where compression prevails) from an inner belt dominated by extension. Finally, [131] include inner Tuscany in their “West Central” sector, where available ESMs are not sufficient to clearly constrain a seismotectonic pattern.

So far, seismological evidence has not provided a widely shared interpretation of the active tectonics of Tuscany. In the next section I will discuss a new set of ESMs that could allow us to approach that objective.

Since 2005, the Italian Istituto Nazionale di Geofisica e Vulcanologia (INGV) has been processing seismic waveforms by the Time Domain Moment Tensor (TDMT) procedure. This concerns earthquakes having magnitude M_W ≥ 3.5, whose epicenter in located in Italy and neighboring countries [133].

The TDMT procedure is based on the algorithm developed at the University of Berkeley, California (http://seismo.berkeley.edu/~dreger/mtindex.html), which inverts the three-component waveforms recorded by broadband seismic stations. The synthetic seismograms used for seismic moment tensor inversion are calculated by means of a laterally homogeneous, 1D velocity model calibrated on a regional basis. The focal mechanism representation is obtained with the procedure developed by [134].

Using the ESMs derived by TDMT analysis has two important advantages: 1) they have been obtained from recent seismic recordings, which benefited from the modernization of the Italian seismometric network 2) the seismic moment tensor inversion methodology is common for all data considered. This eliminates the problems related to the use of ESMs having heterogeneous quality, as they were retrieved by different procedures [49] [131] [135].

Available ESMs can be downloaded from the dedicated website (http://terremoti.ingv.it/tdmt). Therefore, I have collected the source mechanism of seismic events occurred in Tuscany and surroundings from 2009 to 2019. The spatial distribution of the data collected from the TDMT catalog is shown in Figure4. The date, moment magnitude (3.17 < M_W < 5.09) and hypocenter depth (2 < H < 24 km) are reported close to the source mechanism symbol. Moreover, I have assigned to each datum an order number ranging from 1 to 41. Epicenter coordinates and basic nodal plane angles are reported in TableA1 of the Appendix. For each ESM, the stereographic projection of the focal sphere, with the poles of T and P axes, is shown in FigureA1 of the Appendix.

The strain style indicated by the ESMs suggests dividing data into 3 subsets, corresponding to 3 different sectors of the study area (I, II and III in Figure 4). Data numbering follows this grouping. Sector I (16 ESMs from n.1 to n.16) includes north-western Tuscany, with the Apuan Alps and the Lunigiana and Garfagnana basins (Figure 1 and Figure 2). Sector II (14 ESMs from n.17 to n.30) includes the Tuscan-Emilian-Romagna Apennines. Sector III (11 ESMs from No.31 to No.41) corresponds to inner Tuscany.

In this paragraph I describe the treatment of the geodetic measurements carried out in many GPS sites located in Italy and neighboring countries. Data come from 840 GPS permanent stations, whose location is shown in Figure 5. Since the treatment of GPS time series is detailed by [140] [141] [144]. I report here only basic information.

The GPS permanent stations belong to various geodetic networks, managed by research institution, professional organizations and commercial companies. However, all stations use good quality, dual frequency instruments. In addition, the adopted support always ensures tight coupling between the antenna and ground or building walls. [147] shown that the different ways of installing and managing GPS stations do not entail neither systematic noise increase in time series, nor important signal distortions. For this reason, the observations acquired by professional and commercial stations can be used for scientific studies also.

Data were analyzed with the GAMIT/GLOBK software [148] [149]. The International GNSS Service (IGS) provide information about the orbit of GPS satellites, data on Earth rotation and revolution, and parameters for modeling the electronic center of antennas. Due to the large number of stations, I adopted the distributed processing proposed by [150]. The initial part of the analysis is performed by dividing the initial network (all stations), into several subnets (clusters) containing a smaller number of sites. Therefore, the network was divided into 45 clusters. I inserted in each cluster the observations of at least 6 stations belonging to the European EUREF network, which guarantees measurement quality. Then, the daily solutions of all the subnets were combined by using the position of the common stations inserted in the different clusters as a constraint. This was done on the daily solutions of the subnets, thus obtaining a general daily solution.

As the different daily solutions may not be expressed in the same system, each solution must be referred to a single reference system. For this reason, the observations of 16 stations located around the Italian region were included in the subsequent analysis. Indeed, IGS provides position and velocity of these stations, referred to the International Terrestrial Reference Frame (ITRF). Consequently, the daily solutions of the geodetic network have been included in the updated ITRF2014 version, by using the position and velocity data provided by [151].

In order to insert each station in the ITRF2014, a 7-parameter Helmert transformation (3 translations, 3 rotations and a scale factor) was carried out, by means a weighted least squares approach which compares the calculated station coordinates with those provided by IGS. Finally, I obtained the time series of the daily position of each station: north component (measured from Equator), east component (measured from the Greenwich meridian) and elevation component (height on the WGS84 reference ellipsoid).

Then, the daily time series of the above components have been elaborated by [140] [141] procedure, in order to determine the velocity of the vertices of the geodetic network. The time series of each component was analyzed independently of the others, in order to eliminate any anomalous data (outliers) by using a specific software [152]. Once the anomalous data were eliminated, I obtained a first estimate of the station velocity, along with any discontinuities eventually caused by maintenance, or by nearby earthquakes. The above parameters, estimated by means of a weighted least square approach, were used to determine the theoretical time pattern of the three components of the position of each station. This theoretical trend is subtracted from the real trend, yielding a time series of residual. This residual series is then analyzed using a Lomb-Scargle approach [153] [154] in order to estimate the series frequency spectrum. Then, the spectrum is analyzed to determine the statistically significant periods of the 5 main seasonal signals. This search is carried out in the time interval ranging from 1 month to half of the entire observation period of the station, to avoid aliasing or indetermination problems.

The time series of the 3 components (without outliers) are analyzed again to determine a new estimate of the velocity, discontinuities, amplitude and phase of the 5 seasonal signals whose periods were estimated during the spectral analysis. Then a new theoretical daily trend is estimated and subtracted from the real one, to obtain a new time series of residuals. Finally, this last series is analyzed to determine the noise content. Using this information, it was possible to realistically estimate the errors associated with the station parameters.

In summary, the above procedure provided the velocity vector of each GPS station (described by the north, east and vertical components) and the related uncertainty.

The vector sum of the north and east velocity components gives the site absolute horizontal velocity. However, it is suitable for seismotectonic analysis subtracting the motion of the Eurasian plate from absolute velocity components. Therefore, I have used the plate rotation parameters provided by [151] to remove the Eurasia plate motion at each station. The residual velocity field (with respect to the Eurasian plate) is shown in Figure 5. This kinematic pattern updates previous results, based on a shorter observation time interval [140] [144] [155]. Indeed, this work use GPS measurements gathered in the last two decades (from 01/01/2001 to 30/04/2019).

The horizontal velocity field here presented confirms previous results [140] [155]. The GPS stations located on the Adriatic side of the Apennine belt show the highest horizontal velocity, with NNE-trending vectors reaching 6 mm/year (Figure 5). In the study area (included in the red box shown in Figure 5), the horizontal velocity clearly changes from the Adriatic to Tyrrhenian side. In the latter zone, including Tuscany, vectors are mostly NE-directed with modest amplitude (<3 mm/year). The divergence of horizontal velocity vectors between the Adriatic and Tyrrhenian sides implies active extension in the northern and central Apennines, as discussed in detail by [140] [155]. However, the study area needs an accurate reconstruction of the horizontal strain field, as described in the next paragraph.

The theory of small deformations allows us calculating the horizontal strain rate from the geodetic velocity field. For this work, I used the interpolation method developed by [140] [155].

First, I superimposed a regular grid to the GPS network. By using the GPS horizontal velocity vectors (Figure 5), a weighted least square method provided six kinematic parameters for each point of the grid: 2 velocity components and 4 velocity gradients [156]. Then, the 4 components of the horizontal strain rate tensor (and the related eigenvectors) were computed from the velocity gradients [157].

The weight factors entering in the interpolation method depend on both the uncertainty affecting the horizontal velocity components and proximity between grid points and the GPS sites. To attribute a larger weight to the stations closest to a given grid points, the weight factors are estimated by multiplying the variance of the velocity components by the exponential factor e − d i j / D where d_ij is the distance between the i-th grid point and the j-th GPS site, whereas D is the so-called attenuation distance [140] [157]. To improve the reliability of the results, I imposed two further geometric constraints [158] [159]: 1) the interpolated values are acceptable only if at least 3 GPS sites are located at a distance ≤D from the grid point 2) such GPS sites must be evenly distributed in the region surrounding the grid point (at least one for each 120˚ angular sector). If both these conditions are not met, the strain rate estimate is discarded.

Figure 6 shows the strain rate field obtained by using a 0.1˚ Latitude × 0.1˚ Longitude regular grid. The adopted attenuation distance is D = 50 km, about twice the average distance between the GPS stations shown in Figure 5 [140] [155].

The amplitude of the principal strain rate axes varies in the range 10⁻⁸ - 10⁻⁷ yr⁻¹ (Figure 6). Such values are lower than those observed at most active plate margins (>10⁻⁷ yr⁻¹). However, the study area deforms more rapidly than the adjacent foreland areas, such as the European continent north of the Alps, where the strain rate is much lower (10⁻¹⁰ - 10⁻⁹ yr⁻¹ [160] ). Values of the geodetic strain rate comparable to those shown in Figure 5 are reported by [146] for the central and southern Apennines.

In the study area, the horizontal lengthening axis always has a NE-SW direction. Consequently, the shortening axis is directed NW-SE (Figure 6). However, one can note important changes in the relative amplitude of the two eigenvectors. Along the Tuscan-Emilian-Romagna Apennine arc, lengthening is much larger than shortening, implying a pure (up to radial) extensional strain style (see box a in Figure 6). Instead, moving towards the Tyrrhenian coast the amplitude of the two axes becomes nearly equal. This highlights a strike-slip strain style (see box b in Figure 6). Furthermore, strain rate amplitude clearly decreases from the Apennine watershed to the Tyrrhenian coast (Figure 6).

The geodetic strain field is broadly consistent with the strain style highlighted by ESMs (Figure 4). Indeed, shallow earthquakes along the Apennine arc (sectors I and II of Figure 4) show an extensional mechanism. On the other hand, most events occurred within inner Tuscany (sector III of Figure 4) have strike-slip mechanisms. Moreover, the direction of the seismological T and P axes is compatible with the principal axis of the geodetic strain rate tensor (Figure 4 and Figure 6).

The zone represented in Figure 6 is larger than the study area. To the north, the figure shows the Po Valley zone affected by the May, 2012 seismic sequence. In this area the geodetic strain is dominated by N-S compression (see box c in Figure 6), in good agreement with the EMSs of the 2012 seismic events [3]. This agreement corroborates the close relationships between seismic and geodetic strain, even outside the study area.