We investigate the 2004–2006 uplift phase of Campi Flegrei caldera (Italy) by exploiting the archive of ascending and descending ENVISAT SAR data acquired from November 2002 to November 2006. The SBAS-DInSAR technique is applied to generate displacement mean velocity maps and time series. An appropriate post-processing step is subsequently applied to map the areas whose temporal deformation behavior is correlated with that of the maximum uplift zone. Our results show that the deformation also extends outside the volcanological limits of the Neapolitan Yellow Tuff caldera, without significant discontinuities. The DInSAR data are inverted by considering a finite spheroid and an isotropic point-source. The inversion results suggest that the new uplift is characterized by a source location similar to the previous small uplift event of 2000 and to the long term subsidence of the 1990's. In particular, the source is located at a depth of about 3.2 km and very close to the city of Pozzuoli (about 800 m offshore, to the SW); the associated volume variation is about 1.1 106 m3/year.
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 Campi Flegrei (CF) is a densely populated volcanic caldera located at the western edge of Napoli bay (Southern Italy). The caldera was formed by two main collapse events related to the eruption of the Campanian Ignimbrite (CI, 37 ka B.P.) and of the Neapolitan Yellow Tuff (NYT, 12 ka B.P.) [Orsi et al., 1999]. Post-caldera volcanic activity has been mainly explosive, with the latest eruption in 1538 [Di Vito et al., 1987]. Much evidence of long-term inflation and deflation episodes over the past 2000 years can be found inside the CF volcanic district [Marriner et al., 2006]. From 1969 to 1984 the area experienced episodes of rapid uplift, generating a cumulative displacement that exceeded 3.5 m with a maximum rate of 1 m/year in the period 1982–1984 [Orsi et al., 1999; Battaglia et al., 2006]. Since 1985, the caldera has undergone a long subsidence trend [Lundgren et al., 2001], interrupted by inflation episodes, in particular, early in 1989 and during the summer 2000, when a maximum deformation of about 5 cm, associated with a deformation rate of about 10 cm/year, was detected [Lanari et al., 2004]. A new uplift episode started in the second half of 2004 and has been analyzed by using data from tiltmeters, precision leveling and the 5 continuous GPS stations located in the area [Troise et al., 2007].
 In this work we investigate the renewed uplift event by using the DInSAR technique referred to as the Small BAseline Subset (SBAS) algorithm [Berardino et al., 2002] that allows us to produce displacement time series and mean velocity maps. In particular, we exploit the overall archive of ascending and descending ENVISAT SAR data acquired from November 2002 to November 2006. From the DInSAR deformation time series we retrieve the uplift pattern, computed from the two SAR viewing geometries, relevant to the summer 2004–November 2006 time span and we analyze its spatial and temporal characteristics with an unprecedented level of detail. Finally, the inversion of the DInSAR measurements is performed by a direct search of the parameter space of spherical and spheroidal sources, followed by a Bayesian statistical analysis.
2. SBAS-DInSAR Analysis
 The SBAS-DInSAR algorithm allows us to detect earth surface displacements and to analyze their temporal evolution by generating mean deformation velocity maps and time series, projected along the radar line of sight (LOS), with an accuracy of about 1 mm/year and 5 mm, respectively [Casu et al., 2006]. In this study, the SBAS technique is applied to a set of 30 ENVISAT SAR data acquired from ascending (Track: 129, Frame: 809) and 26 from descending (Track: 36, Frame: 2781) orbits, with 23° radar look-angle at mid-scene, from November 2002 to November 2006 (see auxiliary material). We compute 108 and 80 differential interferograms from the ascending and descending data, respectively, with a pixel dimension of about 100 m × 100 m, obtained through a complex averaging (multilook) operation [Franceschetti and Lanari, 1999]. Finally, the multilook interferograms are inverted through the SBAS procedure and the corresponding displacement time series are retrieved for each investigated coherent pixel.
 In order to focus on the renewed uplift phase, we select the DInSAR data in the time interval between the summer of 2004 and the end of 2006. Subsequently, we compute the ascending (Figure 1a) and descending (Figure 1b) mean deformation velocity maps. Both maps detect the uplift phase, with maximum deformation up to 2 cm/year localized in the area of the Pozzuoli city harbor. To investigate in detail the retrieved displacement signals, we analyze the deformation time series computed on the spatial grid common to both SAR geometries, involving more than 5000 coherent pixels. In particular, we properly combine the ascending and descending deformation time series in order to retrieve the east-west (EW) and vertical deformation components. This result is achieved by first interpolating, via a simple linear regression, the available LOS-projected time series pairs on the temporal grid relevant to both ascending and descending SAR acquisition times; subsequently, the interpolated data are merged following the lines of the approach proposed by Manzo et al. . This leads to the computation of time series pairs relevant to the EW and vertical deformation components.
 In the following we focus on the retrieved vertical deformation because their accuracy is significantly higher than that achieved for the EW one (more than twice [see Casu et al., 2006]), due to the 23° radar look-angle. The mean vertical deformation velocity map is shown in Figure 1c, clearly identifying the extent and amplitude of the detected uplift and a residual subsidence affecting the Vomero area. The inset in Figure 1c shows a comparison between the estimated DInSAR vertical deformation velocity and the corresponding leveling measurements, made available to us in the maximum uplift area. The good agreement between the two data sets is evident. This result is further confirmed by evaluating the standard deviation of the differences between the estimated DInSAR and leveling vertical velocities and between the corresponding time series; the former is of about 1.3 mm/year while the latter amounts to 3 mm. We benefit from the 3D characteristics (2D-space and 1D-time) of the SBAS-DInSAR data to carry out a correlation analysis following the approach outlined by Tizzani et al. . However, instead of using LOS measurements, we exploit the retrieved highly accurate vertical deformation time series. We map the caldera areas whose displacement time series correlate with that of the pixel in the maximum uplift zone. Note that this point corresponds to the leveling benchmark identified by the white star labeled as d1 in Figure 1c; for this pixel the vertical DInSAR (triangles) and leveling (stars) deformation time series are shown in Figure 1e. Figure 1d shows the resulting mean vertical deformation rate map, including the pixels characterized by a correlation value greater than 0.75. We also superimpose the volcanological boundaries of the NYT and CI calderas. The vertical deformation time series of the three selected pixels, labeled as d2, d3 and d4 in Figure 1d, are also shown in the plots of Figure 1f–1h, respectively.
3. Inversion of the Deformation Source
 We invert the detected displacements by adopting analytical models, consisting of pressure sources expanding in an elastic, homogeneous and isotropic half-space. We consider two source models: the isotropic point-source [Mogi, 1958], hereafter called MOGI and the finite volume spheroid [Yang et al., 1988], hereafter called YANG. We jointly invert the ascending and descending mean deformation velocity data on the pixels of the DInSAR grid shown in Figure 1d, with associated error of ±1 mm/year. The inversion is performed in two steps. We find good fitting regions of the parameter space that minimize a misfit function (reduced χ2); this is accomplished by the Neighborhood Algorithm [Sambridge, 1999a], which is widely used to solve nonlinear inverse problems both for seismology and geodesy [e.g., Trasatti et al., 2008]. The second step is the appraisal of the entire model space to extract information about the distribution, resolution and trade-offs of the parameters [Sambridge, 1999b]. The results of this stage, based on Bayesian theory, consist of Posterior Probability Density (PPD) functions shown in Figures 2a–2h for both MOGI and YANG, while the mean values of the measured parameters are shown in Table 1. Inversions are carried out using DOiT, a web-based geodetic data analysis interface [Tagliaventi et al., 2007].
Table 1. Mean Values for the MOGI and YANG Model Parametersa
ΔV, 106 m3/year
The values of the reduced χ2 resulting from the Neighborhood Algorithm are also included.
Figures 2a–2d show that source locations and volume variations are well constrained by the inversion for both models (Sx and Sy are within 300 m and Sz within 80 m). Also the volume variations are very similar, being 1.14 and 1.17 106 m3/year for MOGI and YANG, respectively. The width of PPD curves can be considered an indicator of the parameter estimation accuracy: the estimates for the MOGI model are very well defined. PPDs for the additional YANG parameters are shown in Figures 2e–2h. The spheroid is oriented along the EW direction, with a dip angle of 21°. The ratio between semi-major and semi-minor axes is 1.5: the resulting spheroid is a quasi-spherical source. The spheroid axes cannot be retrieved with appreciable accuracy since the PPD associated with the a parameter is not peaked around a single value. Even though we compute its mean value (see Table 1), it would be more appropriate to consider the range 1 ≤ a ≤ 2 km. Indeed, values for a in this range do not make any significant difference in the model predictions. Results of the computation of the 2D marginal PPDs of both MOGI and YANG models are also shown in the auxiliary material. It is worth mentioning that similar results are obtained if we consider, in the inversion, all the available DInSAR pixels instead of the subset of points shown in Figure 1d. However, the PPD curves we obtained are significantly wider, clearly indicating a loss of inversion accuracy; this implies that appropriate selection of the pixels used for the inversion process represents a relevant issue. Figures 2i and 2j show the residuals between the ascending and descending deformation velocity components and the corresponding MOGI predictions; the same applies to Figures 2k and 2l for YANG. As expected from the computed χ2 values (shown in Table 1), the residuals are comparable. The ascending deformation is slightly better reproduced than the descending component, particularly for the Baia-Miseno area that is affected by negative residuals (i.e. predictions lower than observed data) in the westernmost side. The difference between the results for the two radar acquisition geometries warrants a deeper investigation that is beyond the scope of this paper: however, our first interpretation is related to the lower accuracy of the descending DInSAR products, due to the more limited SAR image data set. Figure 2m shows a comparison between mean vertical deformation rate of SAR data (triangles) and inversion results (MOGI, red and YANG, blue) in correspondence of the sites (red stars) drawn in Figure 1c; both models follow the data trend with very similar performances.
4. Discussion and Conclusions
 We present the SBAS-DInSAR results for the deformation affecting the CF caldera in the time interval summer 2004 - November 2006. We map the caldera areas whose deforming behavior is highly correlated with that of the maximum uplift zone located in the Pozzuoli zone. This analysis, which can be carried out only by exploiting the spatially dense temporal information provided by DInSAR technology, demonstrates that the deformation induced by the 2004–2006 uplift event is not significantly constrained by the NNW and WSW sectors of NYT caldera boundary. Moreover, the uplift extends beyond the CI boundary in correspondence to the western limits of the Miseno zone (Figures 1d and 1g). This is a new finding with respect to what has been reported for this uplift phase [Troise et al., 2007] as well as for the 1982–1984 unrest episode [Orsi et al., 1999]. In addition to this point we also highlight that the retrieved deformation does not show any significant spatial discontinuity; this may be due to the negligible impact of the buried discontinuities, also reported as ring-faults, in the presence of an event of limited amplitude such as the 2004–2006 uplift. Based on this evidence, we invert the detected displacements by adopting simplified analytical models, consisting in pressure sources expanding in an elastic, homogeneous and isotropic half-space. This choice is justified by the previous analysis since no significant discontinuities are observed for the surface deformation across the volcanological limits of the NYT caldera, at least for the observed uplift event. Source inference from DInSAR data suggests that the new uplift episode affecting the CF caldera has strong similarities with previous uplift and subsidence events [Lundgren et al., 2001; Lanari et al., 2004; Battaglia et al., 2006; Gottsmann et al., 2006]. In particular, the retrieved locations of the spheric and spheroidal models are very close to the city of Pozzuoli (about 800 m offshore, to the SW) at a depth of about 3.2 km. Both models show comparable performances since the spheroid is quasi-spherical (mean axes ratio 1.5); their common parameters (position and volume variation) are within statistical uncertainties and their misfits are similar.
 We are aware that the reliability of the inversion can be biased by the simplified modeling of the source and of the medium. As an example, Amoruso et al.  modeled the 2004–2006 GPS and leveling data by means of a penny-shaped crack embedded in a stratified medium, retrieving a source depth comparable to our results. However, there is a trade off between data and source model assumptions, making direct comparisons difficult. Reliable source inferences should be performed by using accurate data and limiting model assumptions. Recently, Trasatti et al.  developed a technique to perform inversions based on numerical forward models, assuming general pressure sources in complex media. These DInSAR data will be further studied by adopting this procedure. The plastic rheology can impact the source inference even more than the elastic heterogeneities, as demonstrated by Trasatti et al.  for the 1982–84 uplift at CF.
 The magmatic/hydrothermal nature of the frequent inflation and deflation episodes at CF is nowadays still a matter of debate. In this context, the analysis of the spatially dense DInSAR time series can be a key element to asses the characteristics of the deformation source. In particular, the proposed correlation analysis, based on a joint exploitation of the spatial and temporal density of the DInSAR measurements, allows us to make a robust inference of the deformation source. This may definitely contribute to the hazard mitigation at CF caldera. Moreover, it may have a broader impact for the analysis of volcanic processes in general.
 This work has partially been sponsored by CRdC-AMRA, ASI and GNV. We thank ESA, which has provided the ENVISAT SAR data through the Cat-1 1065. We also thank INGV-Osservatorio Vesuviano, particularly C. Del Gaudio, for the leveling measurements, P. Lundgren for revising and proofreading the text, and J. Famiglietti for his helpful remarks and suggestions.