Geology and seismicity distribution
The area struck by the 2016–2017 Central Italy seismic sequence was affected by a Late Miocene-Early Pliocene compressional phase, with about N-S trending east-verging anticlines and west-dipping thrust faults, followed by Late Pliocene–Quaternary extension with NW-SE trending normal faults (Fig. 1 and 14). The seismic sequence started with the Mw 6.0 Amatrice earthquake on 24 August 2016 and was followed by the Mw 5.9 Visso and Mw 6.5 Norcia earthquakes on 26 and 30 October, respectively (Fig. 1a). These three mainshocks nucleated on a set of aligned SW-dipping normal faults18-21. The entire sequence activated an 80 km long, NW-SE trending normal fault system (Fig. 1a). The rocks composing the seismogenic layer in this portion of the Apennines are well constrained by seismic reflection profiles and deep borehole data22,23, which have been integrated with surface geology observations, e.g., 24-27. Near the Norcia mainshock, seismic profiles (Fig. 1) image the geometry of the subsurface structures (see details in 14). Here the reflector corresponding to the top of the TE can be traced in the footwall of the M. Vettore fault, the structure that hosted the Mw 6.5 earthquake and produced surface breaks15. Below the TE, the top of the acoustic basement is located at 3.2 s Two Way Time, TWT (Fig. 1c), corresponding to 9 km of depth below sea level. The same reflector is imaged at 2.7 s TWT, corresponding to 7.5 km in the hangingwall of the Norcia Fault (Fig. 1b). Close to the Norcia hypocentre the subsurface geology can be schematically represented by carbonates and TE at depths < 4-5 km, TE at depths between 5 and 9 km and acoustic, phyllosilicate-rich basement below 9 km (Fig. 2a and details in 14). In this area, the presence of a dense seismic network and the application of improved earthquake detection and location techniques allowed the development of comprehensive earthquake catalogues10, 19-21. The integration of subsurface geology with earthquake location well depicts on-fault seismicity located on the SW-dipping Vettore fault (Fig. 2 and details in 18-21), but also highlights the presence of off-faults seismicity occurring within larger rock volumes of TE. A 6-8 km wide and up to 4 km thick zone of diffuse seismicity is located down-dip in the hangingwall of the mainshock rupture (Fig. 2a), and it mostly occurs after the Norcia mainshock (Fig. 2b vs. 2c). This seismicity extends both toward NNW and SSE along the strike of the activated Monte Vettore fault (Supplementary Fig. 1) and occurs mainly within the TE. Another example of off-fault seismicity is represented by kilometres long subvertical clusters of seismicity mostly located within the TE (C1-C3 in Fig. 2 and details in methods and Supplementary Fig. 2-4). Finally, off-fault seismicity within both TE and carbonates is also present at shallow crustal levels around major structures like the thrust fault located at about 2 km depth, in the footwall of the Vettore normal fault (Fig. 2a).
After reconstructing the geometry of the activated portions of the seismogenic layer and constraining the nature of the rocks involved in active deformation, we now analyse the frequency-magnitude distribution of on- and off-fault seismicity, respectively. We search for any systematic variation of the b-value, which is the seismic parameter that quantifies the proportion of small- to large-magnitude events, e.g., 28, 29. The b-value is sensitive to differential stress29, 30, fault roughness 31, and for some seismic sequences it has been used to discriminate foreshocks from aftershocks 32 but see also 33. On-fault seismicity is constrained by selecting events within 0.5 km from the fault plane whose geometry is clearly imaged by aftershock distribution and moment tensor solution (Fig. 1 and 2). Off-fault seismicity was determined by selecting earthquakes occurring within TE in: a) the diffuse zone of seismicity located down-dip in the hangingwall of the mainshock rupture, hereinafter referred to as down-dip hangingwall seismicity, DHwS; and b) the sub vertical clusters (C1-C3 schematically reported in Fig. 2, see also Methods and Supplementary Fig. 2-4). The b value is calculated using the revised maximum likelihood estimate34, 35. Our results show that b values for on-fault events are different and systematically lower than those obtained for off-fault seismicity. In particular, b-values of on-fault and off-fault DHwS events are respectively 1.28 and 1.69 before Visso-Norcia (Fig. 3a), and respectively 1.34 and 1.51 for the entire seismic sequence (Fig. 3b, and Supplementary Table 1). Widening the on-fault at 1 km or extending the DHwS of ± 1 km along strike yields essentially the same results. The b value for clusters hosted in TE is in the range 1.55-1.81 (Fig. 3c, and Supplementary Table 1). We note that for the entire seismic sequence (Fig. 3b), the b value of DHwS is lower than that evaluated before the Visso-Norcia mainshocks. Such a reduction of b-value can be explained by the stress increase, e.g., 29, 30, affecting the DHwS area after the Visso-Norcia mainshocks19. Before the Visso-Norcia mainshocks, the DSHw is characterized by a larger b-value, which is comparable to those obtained for the TE clusters.
Style of deformation of Triassic Evaporites, TE
Evaporitic rocks are generally considered to act as ductile detachment horizons, even at low temperature and pressure, for many fold-and-thrust belts around the world36, including the Apennines22. In some active areas, evaporitic rocks are considered relevant also for seismogenic processes37, 38. In the study area, the TE formation consists of a thick, mechanically complex sedimentary succession composed of centimetric- to decameter-scale interbeds of Ca-sulphate rocks, gypsum predominantly at depth < 1 km and anhydrite at greater depths39, and dolostones. Seismic profiles and boreholes show that the average thickness of the TE succession is ~2 km, but it can increase up to 4 km due to folding and thrusting (Fig. 2a and 14). In the seismically active area of the Apennines TE do not crop out and have been drilled only in few deep boreholes39, whereas to the west of the active area, in western Umbria and in Tuscany, exhumed outcrops of TE are exposed40. TE outcrops show a complex style of deformation, across a range of scales. To describe deformation observed in the TE in both outcrops and experiments we use the following terminology. Brittle deformation refers to discrete and localized failure accommodated along fractures and faults, which display elasto-frictional behaviour and stress-drop, e.g.,41. Ductile deformation refers to distributed deformation accommodated without stress drop via folding or distributed failure by pervasive cataclastic shear bands42.
At the hundreds of meters scale, TE show ductile deformation represented by folding of the gypsum/anhydrite and boudinage of the dolostones layers (Fig. 4a and b). Folding is highlighted by gneissic transposed fabric (Fig. 4b and 4c), which derives by the superposition of tectonic fabrics on the earlier compositional layering. Folding in the anhydrite layers produces fractures and domino-like structures in the dolostone layers (Fig. 4c and c). These rotated faults in dolostones detach into gypsum/anhydrite rocks (Fig. 4d), emphasizing the interplay between brittle and ductile deformation in the rheological heterogeneous TE. Small displacement normal faults are also present at the boundary between gypsum/anhydrite rocks and dolostones (Fig. 4e). Intense fluid-assisted brittle fracturing (Fig. 4e) and small displacement normal faults are documented within the larger dolostone blocks. Large displacement (>100 m) normal faults (Fig. 5) are characterized by a fault core where most of the slip is localized along fault parallel principal slipping surfaces made of a fine-grained, dolomite-rich cataclasite40. The damage zone of major faults consists of foliated (fault-parallel foliation) gypsum/anhydrite rocks and heavily fractured dolostones (Fig. 5).
Rock vs. fault rheology
The rheological behaviour of dolostones and anhydrite rocks is investigated in rock deformation tests at pressure and temperature conditions equivalent to those present at seismogenic depths in the Apennines. Dolomite brittle behaviour is documented in a series of triaxial tests up to high pressure and temperature43. The failure mode of anhydrite samples, collected from deep boreholes in the TE of the Apennines, is shown in triaxial loading tests conducted at constant confining pressure, Pc = 100 MPa, and different levels of fluid pressure, Pf = 60, 80, 90 MPa (Fig. 6a and 44). At low effective pressure, Pe = Pc -Pf, or for very high fluid pressure levels (black curves in Fig. 6a), after yielding and a phase of deformation at constant differential stress the sample undergoes brittle failure with a sudden stress-drop and the development of a localized fault and a thick, 1-2 mm, gouge layer. At higher effective pressure (blue and red curves in Fig. 6a), after yielding, the sample undergoes ductile failure at constant differential stress with no sudden stress drop and the development of a pervasive network of distributed shear bands (Fig. 6c top panel).
The integration of field observations and rock deformation tests shows that the bulk rheology of rock assemblages of TE is controlled by ductile deformation (i.e., folding and ductile failure of the anhydrites in Fig. 4, 6a). However, high pore fluid pressure conditions in the TE can also cause localized brittle failure (Fig. 6a) and the development of large displacement brittle normal faults (Fig. 5). Such faults show fault rock assemblages of cataclasites and fault gouge, which are typical of the elasto-frictional regime, e.g., 41. Friction tests on anhydrite-dolomite fault gouges show a linear relationship between normal and shear stress, in agreement with a brittle failure envelope45. Anhydrite-dolomite fault gouges also show significant fault healing and velocity weakening behaviour (Fig. 6b). This type of frictional properties indicates that TE fault cores, like those observed in the field (Fig. 5), can gain elastic strain energy when locked during the interseismic cycle, and promote frictional instabilities when, during tectonic loading, frictional strength is overcome. Frictional instabilities are frequently observed on these fault gouges (Fig. 6b and 46). The instabilities are facilitated by grain-size reduction and localization along dolomite-rich principal slipping surfaces (Fig. 6c bottom panel), similar to those observed in the field (Fig. 5).