We study the state of deformation of Tenerife (Canary Islands) using Differential Synthetic Aperture Radar Interferometry (DInSAR). We apply the Small BAseline Subset (SBAS) DInSAR algorithm to radar images acquired from 1992 to 2005 by the ERS sensors to determine the deformation rate distribution and the time series for the coherent pixels identified in the island. Our analysis reveals that the summit area of the volcanic edifice is characterized by a rather continuous subsidence extending well beyond Las Cañadas caldera rim and corresponding to the dense core of the island. These results, coupled with GPS ones, structural and geological information and deformation modeling, suggest an interpretation based on the gravitational sinking of the dense core of the island into a weak lithosphere and that the volcanic edifice is in a state of compression. We also detect more localized deformation patterns correlated with water table changes and variations in the deformation time series associated with the seismic crisis in 2004.
 Tenerife (Canary Islands, Figure 1) is formed by a Shield Volcanic Complex (SVC) [Ancochea et al., 1990; Ablay and Kearey, 2000] and a Central Volcanic Complex (CVC) [Martí et al., 1994]. SVC is mostly submerged, forming about 90% of the island volume. From more than 10 Ma to present, the ascent of mantle-derived basaltic magmas has been focused along two main rift zones trending NE and NW and on a third subsidary S-trending rift [Carracedo et al., 2007]. CVC comprises the Las Cañadas composite volcano (from more than 3.5 Ma to 0.18 Ma) and the current active Teide-Pico Viejo stratovolcano (from 0.18 Ma to present). CVC is mostly composed of lavas that evolved from basaltic to phonolitic and is characterized by abundant explosive eruptions. CVC suffered several vertical collapses following explosive withdrawal of shallow (4–6 Km depth) magma chambers, occasionally accompanied by lateral collapses [Martí et al., 1997].
 The core of the island is formed by a prominent nucleus, responsible for high gravity, magnetic and seismic-velocities anomalies [Watts et al., 1997; Ablay and Kearey, 2000; Araña et al., 2000]. This nucleus is thought to be an ultramafic cumulitic complex, formed during the building of the SVC, see Figure 1. In response to the load of Tenerife and of the neighboring islands of La Gomera to the West and Gran Canaria to the Southeast, the lithosphere under Tenerife has been flexed downward by about 3500 m [Watts et al., 1997; Collier and Watts, 2001], bringing the total thickness of the volcanic pile above the oceanic crust to about 10500 m.
 Superficial spreading has been suggested for the Teide-Pico Viejo volcano on the basis of the existence, below its edifice, of clay-rich volcanoclastic layers sloping seaward, although characteristic basal compressional features are not observed in the morphology around its base [Márquez et al., 2008]. Buttressing and fractional spreading has also been suggested for the whole Tenerife Island by Walter  to interpret the formation of the rift zones of Tenerife Island. For this purpose, a set of analog experiments to simulate the volcano edifice spreading phenomena was carried out.
 In 2004, a seismic crisis occurred in Tenerife with a total number of 3000 recorded events (more than 350 located and 5 felt by the population) (IGN, Boletín de sísmos próximos, 2006, available at http://www.geo.ign.es). This seismic activity [Almendros et al., 2007] produced surface gravity changes, displacements and geochemical signatures [Gottsmann et al., 2006, 2008]. In this study we investigate ground deformation affecting Tenerife Island by analyzing Differential Synthetic Aperture Radar Interferometry (DInSAR) deformation time series and GPS measurements. The analysis of the displacements, coupled with structural and geological information and deformation modeling, allows us to provide an interpretation on the present state of stress evolution of Tenerife; we also detect displacements related with the 2004 seismic crisis.
2. DInSAR-SBAS Results
 We use the DInSAR technique that analyzes the phase difference (interferogram) of temporally separated SAR image pairs to measure ground deformation; the estimated displacements represent the projection of the surface deformation in the radar line-of-sight (LOS). We apply the Small BAseline Subset (SBAS) approach [Berardino et al., 2002] to determine the spatial distribution of the displacement rates and to generate the deformation time series of coherent pixels, with accuracies of about 1 mm/year and 5 mm, respectively [Casu et al., 2006]. The SBAS technique removes artifacts due to atmospheric inhomogeneities between acquisition pairs, observing that the atmospheric phase signal component is highly correlated in space but poorly in time. This filtering step also includes the compensation for the topography correlated atmospheric phase artifacts.
 We use 55 radar images acquired from descending orbits (Track 352, Frame 3037), see Table S1 of auxiliary material, by the ERS-1/2 satellites during 1992–2005. The differential interferograms are computed by performing a complex average (multilook) operation with 4 range looks and 20 azimuth looks, resulting in a pixel size of approximately 90 × 90 m. We analyze 182 multilook differential interferograms characterized by maximum perpendicular and temporal baseline values of about 400 m and 4 years, respectively, and by a maximum Doppler centroid separation of 1000 Hz.
Figure 2a shows the geocoded DInSAR map of the mean deformation rate and horizontal displacements measured by GPS between 2000 and 2006, superimposed on the DEM of the area. For both data types we use the reference station Rasca which shows no displacements during the study period relative to IGS station MAS1 at Gran Canaria [Fernández et al., 2005]. Once the GPS data are projected into the radar LOS we observe a good agreement (see Figure S1 of the auxiliary material) between the results of the two data sets, making our DInSAR analysis more robust. Figure 2a shows four funnel-shaped areas with high displacement rates. The first one, which has the largest magnitude, affects the area NW of Teide and close to the coast, surrounding the pixel marked by label “b” in Figure 2a (Figure 2b shows its displacement time series); in this case we measure a deformation rate of about 15 mm/year. The second area, labeled “c” in Figure 2a, is located in the upper section of the NW rift, outside Las Cañadas caldera. We detect a deformation rate of about 5–6 mm/year for the pixel whose deformation time series is shown in Figure 2c. Both of these deformation areas were previously investigated using classical DInSAR and GPS techniques [Fernández et al., 2003; 2005] and part of the deformation can be attributed to drops in water table interacting with existing faults. The third zone is located in the upper section of the NE rift (“d” label, with a deformation rate of about 5 mm/year, see Figure 2d). The last analyzed deformation is located within the south rift (“e” label in Figure 2a) and shows a deformation rate of about 3 mm/year; the time series relevant to pixel “e” is shown in Figure 2e.
 In addition to these localized patterns, the SBAS-DInSAR results reveal a large scale deformation pattern affecting a much larger portion of the volcanic island and that extends well beyond Las Cañadas caldera. In particular, the Teide-Pico Viejo volcano area has a rate of deformation of about 3–4 mm/year; for this zone Figure 2f shows the time series relevant to the pixel labeled as “f” in Figure 2a.
 We study the correlation between mean rate of deformation and topographic elevation, see Figure 2g. Note that, apart from the zones of maximum deformation, the measured rate of subsidence is clearly correlated to elevation. This correlation effect cannot be due to troposphere artifacts, because this would unrealistically imply a tropospheric induced phase component that consistently increased with time during the 14-years period of our study. Therefore, we conclude that the observed increasing rate of subsidence with elevation is related to geological processes occurring within the island. In addition, GPS measurements, Figure 2a, show a very limited amount of horizontal displacements that are correlated to local deformation processes, but they do not reveal a coherent large-scale deformation pattern. Accordingly, we infer that the deformation retrieved via the DInSAR analysis is mainly in the vertical direction.
3. Discussion and Conclusions
 Summarizing, we observe: (i) areas of localized higher subsidence (“b”, “c”, and “d” in Figure 2a) located outside the caldera at the NW and NE rifts; (ii) a lower subsidence area in the south rift (“e” in Figure 2a); (iii) a large-scale deformation pattern following the outline of the island; (iv) this pattern extends well beyond Las Cañadas caldera rim, see Figures 3a–3d, not introducing significant discontinuities in the deformation pattern; (v) the shape and position of the revealed pattern coincide with the extent of the dense core of the island [Gottsmann et al., 2008], see Figures 1b and 3e.
 Concerning the areas with localized deformation, identified by “b”, “c”, “d” and “e” in Figure 2a, they are characterized by less-dense or more-fracturated material relatively to the surroundings [Araña et al., 2000, Gottsmann et al., 2008]. Therefore, they can be more easily deformed due to water table variations, to the interaction with existing fractures or to seismo-volcanic unrest. In particular, we remark that the revealed localized subsidence effects show a significant correlation with the reported (CIATFE, Evolución de la superficie freática, 2008, available at http://www.aguastenerife.org/) water table variations (see Figure 3f).
 Moreover, if we look at Figures 2b–2f and S1 (see auxiliary material), we can observe, in addition to a rather constant displacement rate, variations in the deformation time series of the selected pixels associated to the beginning of the seismic crisis in 2004. This is the first time that this deformation signal has been detected with high spatially and temporally dense coverage.
 Regarding the origin of the revealed large-scale deformation pattern, extending beyond the caldera rim and characterized by a predominant vertical component, we do not favor the gravitational spreading effect because neither the GPS data indicate significant coherent radial displacements, which would be present in the case of spreading, nor the published data on the geology and geophysics of Tenerife show evidence of compressional structures around the base of the island. Also, the reported water table variations (Figure 3f) only show a clear correlation with the localized displacements, not with the large-scale deformation pattern. Accordingly, we propose that the measured deformation is directly related to gravitational sinking of the dense core of the island into a weak lithosphere, similarly to what described by Walker  for Oahu island in Hawaii. In addition, given that the crust has pronouncedly been inflected under the mass of Tenerife, following Borgia et al. [2005, and references therein], we propose that the volcanic edifice is in a state of compression.
 To support our interpretation we carry out a simplified modeling of vertical and radial (horizontal) displacements produced by mass loading, based on the model of Fernández and Rundle  (see auxiliary material for details). We consider a homogeneous half-space Earth model and a point source with a mass equal to the intrusive complex mass retrieved by Gottsmann et al.  (see Figure 3e and auxiliary material), located at different depths (8, 10, 12 and 14 km) to account for the depth loaded by the mass. To simulate viscoelastic displacements after initial loading, we decrease the shear modulus value of four orders of magnitude only for the part of the medium below the depth loaded by the intrusive mass. Figure 3g shows the results of the comparison between the DInSAR mean deformation velocity, projected along a 2D-axis symmetrically centered on the Teide volcano, and the modeled displacements at four different times: 50, 100, 200, 400 ka. We find that the vertical deformation obtained for a loaded depth between 12 and 14 km, with an acting time between 100 and 200 ka is consistent with the observed subsidence. Note also that the considered acting time is compatible with the observation that the gravity-driven deformation of the cumulitic complex cannot be older than the formation era of Las Cañadas volcano whose most recent products are dated between 1.9 and 0.2 Ma (see Figure 1). Moreover, if we consider 200 ka as Maxwell relaxation time, based on the parameters of the applied model, we achieve a value for the viscosity of the medium of about 1020 Pa*s, which is typical for the considered geodynamic scenario [Ranalli, 1995]. Finally, we also remark that the modelling results show quite negligible horizontal deformation components, which is in agreement with the GPS measurements.
 Obviously, the proposed loading model is only a first approximation of the geological, geophysical and geodetic observations, but it effectively supports the proposed gravitational-driven origin due to the sinking of the island's high density intrusive core into a weak underlying lithosphere.
 Our results clearly show the relevance of the DInSAR measurements for monitoring time and space evolution of large- and small-scale deformation. Moreover, we underline that, in Tenerife, GPS and leveling networks need to be improved and integrated with the SAR data to better characterize the detected patterns and to reveal eventual future signs of unrest, as shown by the 2004 crisis.
 This work has partially been sponsored by CRdC-AMRA and by the PREVIEW Project. We thank ESA for providing the SAR ERS data within the Cat-1 Project 3560; the Technical University of Delft, The Netherlands, for the precise ERS-1/2 orbits and the SRTM archive for the DEM. Research by JF, PJG and AGC has also been supported by Research Project CGL2005-05500-C02. We finally thank P. Lundgren and T. Walter for their helpful comments.