Corresponding author: G. Saccorotti, Istituto Nazionale di Geofisica e Vulcanologia, Via U. della Faggiola, 32 – 56126 Pisa, Italy. (email@example.com)
 We report observations of remotely triggered earthquakes at the Larderello-Travale Geothermal Field (Italy), following the Mw = 5.9 Po-Plain earthquake on 20 May 2012. Four distinct triggered events are recognized within a short (~25 s) time interval accompanying the sweeping of ~10s Rayleigh waves. Triggered sources are clustered at depths in between 4 km and 6 km. The magnitude and distance of the mainshock agree well with the triggering threshold previously proposed for The Geysers, California. For three out of four earthquakes, the Rayleigh wave dynamic stresses are mostly associated with extensional vertical (szz) and shear (sxz) components, which range up to 5 KPa. Once considering the structural setting of the area, the most likely triggering mechanism involves the rupture of normal faults which are kept close to failure by high-pressure crustal fluids.
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 Over the past two decades, a growing number of observations indicates that dynamic stresses from large earthquakes are capable of triggering earthquake activity at distances up to 10,000 km away [e.g., Hill and Prejean, 2007, and references therein]. In particular, most of dynamic triggering instances were reported for extensional regimes and geothermal/volcanic systems [West et al., 2005; Hill and Prejean, 2007]. To explain the triggering mechanisms, two main categories of physical processes have been proposed thus far. The first involves the direct failure of critically stressed faults. The second invokes the activation of crustal fluids by the passing dynamic stresses, with triggered seismicity developing as a secondary process. While the first model is more appropriate for explaining the prompt onset of seismicity during the dynamic stressing associated with passing seismic waves, only the second model can consistently explain the significant delay (hours to week) which is sometimes observed in the onset of triggering [Hill, 2008]. Although no single physical model is able to explain the whole range of dynamical triggering instances, their study is of primary importance as they likely hold clues to processes controlling fault slip and failure.
 In this letter, we examine triggered microearthquakes at the Larderello-Travale Geothermal Field (LTGF), Italy, following the Mw 5.9 earthquake that stroke the Po-plain on 20 May 2012. Similar to what reported in previous studies, triggered earthquakes occur during the sweeping of Rayleigh waves. In particular, triggering is associated with either peak or null ground displacement, corresponding to maxima in the normal and shear stresses, respectively. The lack of constraints on fault plane solution, and the inferred heterogeneity of the local stress field prevent from constraining the actual mechanism driving the triggering. The small entity of stresses at work, however, suggests that triggering occurred over faults already very close to failure.
 In the following sections, we first introduce the LTGF, followed by a description of the instrumental deployment used for the study. Then, we describe the triggered earthquakes and proceed with their location. Using seismograms from neighbor stations, we calculate the local phase velocity of Rayleigh wave and use it for deriving dynamic stresses at the triggered sources. These data are finally used to discuss some possible triggering mechanisms, in light of the structural and geological context of the area.
2 The LTGF
 Located in the western part of central Tuscany (Italy), LTGF hosts the oldest geothermal power plant of the world. LTGF is associated with a structural high within the inner Northern Apennines, which have been affected by extension since the Early-Middle Miocene. Heat flow is very high, ranging from a regional average of 120 mW/m2, to local peaks of up to 1000 mW/m2. The top of the reflective mid-lower crust is marked by a strong seismic reflector, named the K-horizon [Batini et al., 1978], located at depths between 3 km and 8 km below sea level. This reflector is thought to represent a level of fractured, silica-rich rocks close to a plastic state, hosting fluids in a supercritical state [Bertini et al., 2006]. The LTGF fault system is dominated by normal faults associated with the latest extensional episode which is lasting since the Pliocene. In particular, a re-examination of field data and seismic reflection lines indicates the presence of three major NW-trending, NE-dipping normal faults [Brogi et al., 2003]. The present-day stress field is very heterogeneous, as indicated by the large variability of fault plane solutions. These latter ones include normal faults with Apenninic (NW-SE) and anti-Apenninic (NE-SW) directions, and strike-slip mechanisms with the P-axis oriented in NW-SE directions [e.g., Kravanja et al., 2000, and reference therein].
3 Instruments and Data
 On 20 May 2012, a Mw 5.9 earthquake hit a densely populated area in the Po plain, west of the city of Ferrara, Italy (Figure 1). During the subsequent 13 days, six M > 5 events occurred; of these, the most energetic was a Mw = 5.8 quake occurred on May 29, 12 km WSW of the 20 May event. The tragic balance of this sequence is 17 casualties, hundreds of injured and severe damages to the historic and cultural heritage. The seismic sequence probably developed on a buried, EW-oriented thrust fault located at depths between 2 and 10–12 km, as also suggested by preliminary moment tensor estimates of the most energetic events. Figure 1 reports the location and focal solutions for the 20 May 2012 mainshock.
Table 1. Location of the Triggered Earthquakes
Err x (km)
Err y (km)
Err z (km)
2012 05 20
02 05 16.30
2012 05 20
02 05 21.80
2012 05 20
02 05 32.70
2012 05 20
02 05 41.18
 LTGF is seismically active and is routinely monitored by a seismic network from ENEL, the power company which operates the geothermal plants. Public permanent stations in the area are in operation only since mid-2010, when two instruments were installed as a part of the National Seismic Network of the Istituto Nazionale di Geofisica e Vulcanologia (INGV hereinafter; see Figure 1). By mid-May 2012, we complemented these two stations with eleven temporary instruments. The resulting array (LRD hereinafter) has an aperture of about 50 km and average station spacing around 10 km (Figure 1). Both permanent and temporary stations consist of 24-bit digital recorders, equipped with either broad-band (Nanometrics Trillium 120 s and Trillium 40s) or intermediate-period (Lennartz Le3D5s) three-component sensors. On average, the distance of the array from the epicentral area of the May 2012 Po Plain sequence is on the order of 190 km (Figure 1).
4 Remotely Triggered Earthquakes
 Figure 2 illustrates the seismicity at LTGF for the 14 May–20 June 2012 time interval, which encompasses the most significant earthquakes (Mw > 5) of the Po Plain sequence. We account for two catalogs: the first is that reported by INGV's national seismic network (http://iside.rm.ingv.it). The second is that retrieved from the LRD array by applying an automatic event detection procedure. Both catalogs are relative to a 30 km side square area (see Figure 1). For this region, the INGV catalog is inferred to be complete down to about ML = 1.6 +/- 0.2 (Supporting Information S01); for the analyzed time interval, it reports only three earthquakes (Figure 2). The LRD catalog is much richer (167 locations; see Figures 1 and 2), with a completeness threshold at ML = 0.6 +/− 0.2 (Supporting Information S1). The most striking feature of this latter catalog is a peak of earthquake activity on 2 June 2012, one day before the last energetic (Mw = 5.1) shock of the Po-plain (Figure 2). Due to the lack of detailed past catalogs, it is impossible to assess whether such increase in micro-seismicity represents a delayed response to the Po-plain earthquakes, rather than a typical feature of seismic energy release at LTGF. Apart from the time-localized peaks associated with the Po-plain shocks, the RMS amplitude of seismic background noise does not exhibit any significant variation throughout the analyzed time interval.
 The 20 May mainshock was recorded by 11 LRD stations, with peak ground velocities up to 2×10−3 m/s. After high-pass filtering of the velocity seismograms, a clear sequence of at least four earthquakes is observed in association with the transit of the surface waves, whose dominant period is on the order of 10 s (Figure 3). We test the hypothesis that these events are triggered by the Po-plain mainshock by applying the commonly used β-statistics value [Kilb et al., 2002] to the LRD catalog. We estimated the likelihood that four earthquakes within 1 min occur by random chance by calculating beta-values for a week-long time window before the mainshock and subsequent, 1 min long time windows following the S-wave arrival of the mainshock. Our results show a negligible probability of four randomly occurring events in any 1 min window (β ~ 19). This probability decreases further if one also requires coincident timing with surface waves from a distant quake. Although this additional constraint is hard to quantify formally, it provides additional support to the hypothesis that the local earthquakes are a consequence of the Po-plain main shock.
 The triggered earthquakes were recorded by enough LRD stations to be located reliably. For the locations, we used the probabilistic approach of [Lomax et al., 2009] acting on a gradient velocity model in which Vp ranges from 3000 m/s at the surface to 5500 m/s at 5 km depth, and then to 6000 m/s at 15 km depth. Vp/Vs ratio was kept constant and equal to 1.73. The four earthquakes span the central sector of LTGF, at depths between 4 and 6 km b.s.l (Table 1 and Figure 1).
 Approximate local magnitudes for these events (see Supporting Information S02) are in the range 0.5–1.1, thus above the completeness threshold of the LRD catalog.
 The polarization directions for a 40 s long time window encompassing the origin times of the triggered events are oriented radially to the source, thus suggesting a dominance of Rayleigh waves (Figure 1). By fitting a plane-wave to the inter-station differential times estimated via cross-correlation, we found that the Rayleigh wave-packets associated with the triggered events propagate from the source direction with an average phase velocity of 2400 m/s (see Supporting Information S3).
 As a first attempt toward evaluating the actual condition of triggering ground displacement, we assumed a plane-wave model and propagated the signal from reference station LA01 to the triggered hypocenters. Within the uncertainties associated with location errors, results indicate that events 1–3 are associated with peak vertical ground displacement, while event 4 occurs during null vertical ground displacement (Figure 4a).
 Separately, we used the equations of particle displacement for a 10 s Rayleigh wave and calculated strain and stress values along the radial-vertical plane [Gomberg and Davis, 1996; West et al., 2005; West, 2005; (Matlab code for Rayleigh wave strain/stress in a Poisson halfspace, available at http://kiska.giseis.alaska.edu/input/west/proj/wa_trigger/stress.html); Hill, 2008], using a half-space model with a Poisson ratio of 0.25, a shear modulus of 25 Gpa and the aforementioned Rayleigh-wave phase velocity (see Supporting Information S4). Figure 4b illustrates the depth dependence of the maximum absolute values of orthogonal (σxx and σzz) and shear (σxz = σzx) stresses on the plane of wave propagation, for a reference ground displacement of 1 mm. The curves for (σxx, σzz) and (σxz) are taken in correspondence of peak and null ground displacement, respectively, where the two types of stress attain their maximum values. While σxx is maximum at the surface and diminishes with depth, both σxz and σzz are zero at the surface and increase with depth till reaching a maximum at about 6 km below the surface. Finally, we fitted a sine wave to the extrapolated surface ground displacement at the triggered epicenters, and used the time-depth stress maps of Supporting Information S4 to obtain the ranges of dynamic stresses associated with individual triggered shocks (Figure 4c).
 As a consequence of location uncertainties, stresses at the triggered hypocenters span wide ranges, which could become even broader once accounting for the over-simplified velocity structure adopted in the calculation of the stress field. Within these limitations, however, it appears evident that for the depth interval where triggering occurred (4–6 km), the dynamic perturbation of the local stress field was mostly due to σzz and σxz. An exhaustive assessment of the triggering mechanism would require knowledge of the focal mechanisms, a determination which is hindered by the weakness of our events. We can suppose, however, that they originated on fractures consistent with the main structural features, i.e., NW-SE trending normal faults. Therefore, the Rayleigh wave stress orbits would be oriented almost perpendicularly to the fault's strike, a condition for which the triggering potential of the former wave-type is maximized [Hill, 2008]. Events 1, 3, and 4 are all dominated by positive (extensional) stresses. If we assume an extensional tectonic regime [e.g., Bertini et al., 2006] with principal stress oriented vertically, then the transient addition of dynamic terms [σzz, σxz] related to the transit of the Rayleigh wave would lead to the temporarily reduction of the stress normal to the fault plane, thus facilitating its failure. More difficult is to explain event 2, which occurred in concomitance of negative (compressional) peak vertical stresses. In this case, other triggering mechanism might have been at work. One possibility is that of a fluid-pumping process, in which the pressure increase associated with downward ground motion squeezes fluids from interconnected pore space into the nearby fault zones, thus greatly reducing its strength [e.g., Brodsky and Prejean, 2005].
5 Discussion and Conclusions
 Data presented in this study contribute to the growing body of evidences demonstrating that dynamic stresses propagating as seismic waves from large earthquakes are capable of triggering additional earthquakes up to distances of tens or even hundreds times the rupture length [e.g., Hill and Prejean, 2007, and references therein]. In our case, the main shock (Mw = 5.9) involved a fault length on the order of 10 km [Piccinini et al., 2012] and triggered earthquakes at a distance of about 190 km. This is in agreement with what reported by Gomberg and Davis  who, for that epicentral range, individuated a threshold at about M = 5.5 for the triggered seismicity at The Geysers, California. The second large shock of the Po-plain sequence (Mw = 5.8) occurred nine days after the mainshock here described, and it was recorded by the LRD array with a peak ground displacement about four times smaller than that associated with the 20 May mainshock. Although still above Gomberg and Davis  threshold, this second earthquake didn't induce any remote triggering. This fact can be explained by assuming that the small-sized fractures which ruptured during the 20 May mainshock released enough energy to move the responding site incrementally away from the near-critical state, thus lowering the triggering efficiency of the dynamic stresses induced by subsequent quakes. The time span between the two Po-plain mainshocks (9 days) could thus be considered as a lower bound on the “recharge time” of the small faults we described thus far.
 Similar to most reported triggering instances, our triggering observations are associated with long-period (~10s) Rayleigh waves impinging on a geothermal area characterized by an extensional regime. Our data suggest that at least two different triggering mechanisms might have been at work, involving either Coulomb failure of critically stressed fault, or fault weakening via increased fluid pore pressure. Disregarding the actual triggering mechanism, it is somehow surprising that failure occurred with dynamic stresses as low as 5 KPa. Though minute, however, such stress variations can lead to rupture if faults are already maintained close to failure by high pore fluid pressures. This consideration is buttressed by the fact that our triggered events occurred at depths compatible with the location of the K-horizon, at which near-lithostatic fluid pressure were encountered in exploration wells [Bertini et al., 2006].
 Thus far, the LRD array has allowed a consistent reduction of the completeness threshold of the seismic catalog at LTGF. Hopefully, future data from such improved deployment will contribute additional constraints for better defining the mechanisms which control fault failure in response to stress waves from remote sources.
 Claudio Chiarabba, Milena Moretti, Pasquale de Gori, Mario Anselmi, Marina Pastori, Lena Cauchie, Andrea Fiaschi, and the COREMO group are all sincerely acknowledged for their participation to the deployment and maintenance of the LRD array. We thank M. West for his careful revision of the manuscript.