Flank instability is common at volcanoes, even though the subsurface structures, including the depth to a detachment fault, remain poorly constrained. Here, we use a multidisciplinary approach, applicable to most volcanoes, to evaluate the detachment depth of the unstable NE flank of Mt. Etna. InSAR observations of Mount Etna during 1995–2008 show a trapdoor subsidence of the upper NE flank, with a maximum deformation against the NE Rift. The trapdoor tilt was highest in magnitude in 2002–2004, contemporaneous with the maximum rates of eastward slip along the east flank. We explain this deformation as due to a general eastward displacement of the flank, activating a rotational detachment and forming a rollover anticline, the head of which is against the NE Rift. Established 2D rollover construction models, constrained by morphological and structural data, suggest that the east-dipping detachment below the upper NE flank lies at around 4 km below the surface. This depth is consistent with seismicity that clusters above 2–3 km below sea level. Therefore, the episodically unstable NE flank lies above an east-dipping rotational detachment confined by the NE Rift and Pernicana Fault. Our approach, which combines short-term (InSAR) and long-term (geological) observations, constrains the 3D geometry and kinematics of part of the unstable flank of Etna and may be applicable and effective to understand the deeper structure of volcanoes undergoing flank instability or unrest.
 Flank instability affects many volcanoes worldwide. While the surface extent of an unstable area may be reasonably well-constrained, the 3D structure, in particular the depth to the detachment, the relations to the structures confining the unstable area at the surface, and the possible relations to magmatic activity, are more ambiguous [e.g., van Wyk de Vries and Francis, 1997; Voight and Elsworth, 1997]. Mt. Etna provides an excellent example of this process, as the geometry of its unstable flank is well-constrained at the surface but highly debated at depth [e.g., Solaro et al., 2010, and references therein].
 The NE flank of Mt. Etna consists of the NE Rift, delimited to the E by the normal Piano Provenzana Fault (PPF, Figure 1c). To the NE, the PPF becomes the left-lateral transtensive PFS, kinematically connected to the NE Rift [Garduño et al., 1997; Groppelli and Tibaldi, 1998]. About 10 km to the SE of the NE Rift are the Ripe della Naca Faults (RNF); in between, lies the ENE rift [Azzaro et al., 1997; Tibaldi and Groppelli, 2002]. Here we attempt to reconcile geological and geodetic data, presenting a geometric and kinematic model for instability of the NE flank of Etna.
2. InSAR and Geological Observations on the NE Flank
 We use InSAR time series from 1995 to 2008 to analyze the surface deformation on the unstable portion of the NE flank, which constitutes the northwestern-most part of the unstable eastern flank (Figure 1b) [Solaro et al., 2010]. The dataset (same as that of Solaro et al. ) was acquired by the ERS-1/2 and ENVISAT sensors on both ascending (Track 129, Frame 747) and descending (Track 222, Frame 2853) orbits. By applying the SBAS technique [Berardino et al., 2002], the vertical and East-West components of the mean deformation velocity and deformation time series were produced, with time-series average to annual samples.
 To analyze in detail the deformation of the NE flank, we subdivided the InSAR time-series in 3 sub-intervals, from 1995 to 2000, that corresponds to a period of relative quiescence at the PPA, from 2002 to 2004 that covers the 2002–2003 unresting period, and the period after it (2005–2008). Vertical ground displacement in the Piano Provenzana Area (PPA), between the NE Rift and RNF, shows subsidence during 1995 to 2008, with a maximum rate of 9 cm/yr close to the ENE rift during 2002–2004 (Figures 1b–1d) and decaying to 0 near the RNF. Specifically, as shown by the ∼NW-SE trending profile from the NE Rift to RNF (AA′ (Figure 1c)), from 1995 to 2000 the vertical displacement is negligible; from 2002 to 2004, the displacement shows a marked increase, with maximum subsidence towards the NW; during 2005–2008, the subsidence occurs at much less rate (Figure 1d). To the SE, the RNF area acts as a NE-SW-trending horizontal rotational axis for the observed subsidence. To the NW, the offset between the NE Rift and the deforming PPA probably occurs near the PPF. The 2002–2004 culmination of the subsidence is associated with eastward slip of ∼1.5 m along the nearby PFS, which occurred during the 2002–2003 eruption [Acocella and Neri, 2005; Palano et al., 2006].
 To better constrain the evolution of the deformation through time, we compile displacement time series for the vertical and EW components of deformation on the PPA from 1995 to 2008 (Figures 1f and 1g). From 1995 to 2000, the vertical and EW motions are linear, with negligible subsidence and westward motion of 2–3cm/yr; after 2002, both components indicate rapid subsidence and eastward motion, which is at a maximum along the NW edge of the PPA (point c2 (Figures 1b–1d)). Although at the RNF there is a small discontinuity in the EW motion, the vertical motion does not vary significantly (point c1 (Figures 1b–1d)). The PPA is therefore undergoing a trapdoor subsidence, tilting down to the NW, with the deformation rate at a maximum in 2002–2004.
 Based on this result, we test the possibility that trapdoor-style deformation of the PPA has been an ongoing process. We consider a ∼NW-SE trending profile on a 10-m-resolution DEM, from which the mean slope of the volcano has been removed using a linear function (Figure 1e). The resulting topography dips down to the NW between the PPF and the RNF, suggesting a long-term process that causes the development of a tilted surface on the upper NE slope of the volcano.
 The limit of this tilted area to the NW is the PPF and it is expected that the long-term tilting of the PPA caused vertical displacement along the PPF. We estimate the fault throw along the PPF, considering the height of the fault scarp from its SW end to the PFS (Figure 2a). The scarp height reaches a maximum of ∼120 m in the west, and decreases towards the NE (Figures 2b–2d). Although we use topography to assess scarp elevation, our results are consistent with geological data and long-term vertical displacement, observed for instance at two half cones dissected along the PFS close to Mareneve village (star location in Figure 2a [Tibaldi and Groppelli, 2002]). The overall displacement of PPF, as deduced from its topography, constrains the amount of the longer-term tilt of the unstable part of the NE flank.
 We conclude from the joint analysis of InSAR and structural data that InSAR-observed tilt associated with eastward displacement of the upper NE flank is a long-term process related to the NE Rift activation (∼15000 years ago [Tibaldi and Groppelli, 2002, and references therein]). This suggests that the tilt revealed by InSAR data may be the surface expression of the activation of a longer-term rotational detachment, forming a rollover anticline next to the NE Rift, mainly developed during episodes of eastward flank slip acceleration (as in 2002–2004).
3. Rollover Geometric Model
 Both the short- and long-term deformation pattern may be explained by the activity of a rotational detachment on the east side of the NE Rift, forming a rollover extensional structure [Xiao and Suppe, 1992, and references therein; Mauduit and Brun, 1998]. Following established procedures [White et al., 1986; Dula, 1991], we construct a 2D inclined-shear rollover geometric model to estimate the deep geometry of the detachment below the PPA (see auxiliary material). Although such geometric constructions are simplified and do not consider heterogeneities associated with natural rock properties that may affect α, the general good agreement between rollover models and natural subsurface structures imaged by high quality seismic data, validate such construction approach [Dula, 1991].
 The rollover geometric model construction we present requires 4 main parameters (Figures 2e and S1 of the auxiliary material), that are a) the Coulomb shear angle of the rollover fold (α), b) the fault dip angle (β), c) the fault throw (T), and d) the distance separating the stable portions at the sides of the rollover (AB).
 In our model, the Coulomb shear angle (α) is constrained between 30° and 45° from the vertical, typical for a range of volcanic products [e.g., Watters et al., 2000]. 2) The fault dip angle (β) is between 80°–90°, as observed on the field at the PPF [Neri et al., 2004]. 3) The fault throw (T) is estimated at the maximum PPF scarp (120 m), representative of the long-term vertical movement of the unstable NE flank. 4) The AB distance separating the stable areas in the footwall and hangingwall (from the RNF to the PPF (Figures 2a and 2e)) is = 7 km. Using the above values, we construct a series of models that provide a full range of possible detachement depths from 2650 and 5250 m (Figure 2f). The most likely fault profile considering the geologic, morphological and material characteristic data at the PPA (α = 30°, as for basaltic material; β = 80°) provides a depth to detachment of 4.1 km below the surface (Figure 2f). Additional models considering scarp offsets of 50m and 200m provide similar detachment depths, suggesting a poor influence of the value of the scarp offset on the detachment depth.
4. Discussion and Conclusion
 We have used an integrated approach to assess the geometry and kinematics of the unstable NE flank of Etna. InSAR data show a tilt in the PPA area, confined by the NE Rift and the RNF. This tilt is associated with the eastward slip of the unstable flank, suggesting the development of a rollover anticline during extension along the PPF. Rollover construction models constrained by longer-term geological data suggest that the deeper boundary of the sliding block coincides with an eastward-dipping detachment, lying at 4.1 km below the surface (around 2 km bsl). Our modeled depth to the detachment is consistent with the clustering of seismicity above 2–3 km bsl along the western part of the PFS, which suggests a S-dipping fault plane along the westernmost PFS [Neri et al., 2005; O. Cocina, personal communication]. Moreover, our estimated depth and associated uncertainties are broadly consistent with the depth of the detachment inferred by the inversion of GPS data [e.g., Bonforte et al., 2009]. These consistencies suggest that the western-most part of the PFS dips southward, to merge with the basal detachment inferred to lie at ∼4 km below the surface.
 The proposed model also implies that the development of the rollover structure is largely episodic and related to major events of flank slip, connected with dike emplacement along the NE Rift and slip along PFS. The occurrence of an episodic instability on the flank of a volcano, consistent with previously published studies at Etna [Neri et al., 2009; Solaro et al., 2010], is probably a common feature of many volcanoes, even though in one of the best-known cases (Kilauea, Hawaii), flank instability is largely continuous over several years [Montgomery-Brown et al., 2009]. The occurrence of a largely episodic instability at Etna supports the possibility that the volcanic and tectonic evolution of the edifice occurs in a discrete and possibly cyclic way [e.g., Behncke and Neri, 2003].
 The 2D model proposed above is expected to be applicable to the entire PPA, as this appears characterized by a consistent deformation and structure. However, while we do not have reliable data to define the continuation of this structure to the S, to the N the deformation is limited by the PFS. Therefore, we attempt to reconstruct the probable 3D structure of the northwestern-most part of the unstable flank (Figure 3). The 3D model takes into account for the homogeneous conditions met in PPA and their confinements against PFS to the north, which is not expected to provide any significant variation in the depth of the detachment. In the 3D model, a geometric continuity and kinematic consistency among the PPF, the PFS and the basal detachment is postulated. While the PPF forms the head scarp of the unstable upper flank, the S-dipping PFS constitutes its lateral ramp; both are connected with the detachment at depth (Figure 3).
 The NE flank of the volcano is the best location to constrain the existence and location of a detachment at depth. Despite inverse models of GPS data [Bonforte et al., 2009, and references therein] and other indirect evidence [e.g., Borgia et al., 1992; Neri et al., 2004], no other constraints can currently support the extent or existence of a detachment outside the NE flank. It is possible that the eastward and southward continuation of motion of the detachment grades a broader area of slip and is more difficult to characterize.
 Our study may also explain the tectonic and magmatic features observed in the PPA area. Rollover systems from high resolution seismic reflection profiles and analog models show grabens induced by apical extension along the rollover anticline, above the flattening portion of the listric normal fault [McClay and Scott, 1991]. The aligned cinder cones forming the ENE rift (see Figure 1c) indicate a buried laterally-propagated dike system [Tibaldi and Groppelli, 2002] trending parallel to the strike of the tilted area, coincident with a buried graben identified through geophysical data [Azzaro et al., 1997]. Based on these similarities, the ENE rift may represent the surface expression of a magma-filled graben induced by lateral dike injections from the central conduit, focusing above the flattening of the detachment at depth where the maximum tensile stress is expected (Figure 3). The magmatic and tectonic activity of the ENE rift is consistent with flattening of the detachment and therefore it may be related to the development of the rollover structure during flank instability. However, a similar relationship is not observed at other volcanoes subject to flank instability (i.e., Kilauea) and cannot be considered diagnostic.
 Our study shows how an integrated approach that combines high-density spatial deformation data, obtained over a relatively short-period (10–15 years; InSAR data), with geological data, from years to thousands of years, may lead to a model that explains both the longer- and shorter-term behaviour on the unstable NE flank of Mt. Etna, also defining its 3D structure. In particular, defining the 3D geometry and kinematics of the most unstable part of the NE flank of Etna allows for better characterization of the possible hazards related to episodic flank instability, including earthquakes, volcanic activity, and volcano-tectonic interactions.
 Finally, our approach provides an effective and unique means to understand the deeper structure of volcanoes, otherwise not detectable using a single (short-term InSAR analysis or geology) approach alone. Our approach may be generally applicable to other actively deforming volcanoes characterized by flank instability and whose deeper structure is poorly known, for example Piton de la Fournaise, Fogo and Tenerife.
 This work was partially funded by INGV and the DPC-INGV project “Flank”, and partially by the ASI (SRV project). The authors acknowledge the two anonymous reviewers for their constructive comments.