This work is focused on advanced differential SAR interferometry (DInSAR) techniques for the generation of deformation time series from sequences of SAR images. We first present the basic rationale of these techniques providing some details of the most well known algorithms. Subsequently, through the analysis of selected case studies focused on the available C-band SAR data archives, we show the relevance of the retrieved spatially dense deformation time series for the comprehension of several geophysical phenomena. We finally introduce, again via a real case study, the advances brought in by the new generation X-band space-borne SAR sensors, highlighting new investigation possibilities for fast varying deformation phenomena.
 Differential SAR Interferometry (DInSAR) is a microwave remote sensing technique that enables the measurement of surface deformation with a centimeter to millimeter accuracy and with a large spatial coverage capability [Gabriel et al., 1989]. In particular, DInSAR exploits the phase difference (interferogram) between two SAR images of an investigated area relevant to temporally separated observations and provides a measurement of the ground deformation projected along the radar line of sight (LOS). Although DInSAR feasibility was demonstrated earlier, the technique reached wide popularity at the beginning of 90's with the successful experiments on ground deformation caused by the Landers earthquake in California [Massonnet et al., 1993] and on ice sheet motion in the Antarctica region [Goldstein et al., 1993].
 Since then, Differential SAR Interferometry has been applied to study a large variety of natural and anthropogenic phenomena [Massonnet and Feigl, 1998; Bürgmann et al., 2000] and represents nowadays a widely used tool for detection and mapping of surface displacements over large spatial scales. However, the interest of the scientific community has progressively moved from the investigation of single deformation episodes (earthquakes, volcano eruptions, etc.) toward the study of the temporal evolution of the detected displacements through the development of second generation (or advanced) DInSAR techniques [Ferretti et al., 2000; Berardino et al., 2002]. In this case, the information available from a sequence of DInSAR interferograms is simultaneously exploited to generate a deformation time series for each coherent point (i.e., where the phase information is preserved) included in the studied area. As a consequence of the SAR data redundancy exploited by these algorithms the deformation measurement precision significantly increases. Although this is a noteworthy result, the possibility to generate deformation time series itself represents an inherent added value of second generation DInSAR techniques.
 The aim of this paper is to illustrate, through a number of case studies, how such advanced techniques can be used to accomplish rather complex analyses of several geophysical phenomena. This is done first by exploiting some of the available large C-band (5.6 cm wavelength) SAR data archives, collected by the ERS-1, ERS-2 and ENVISAT sensors of the European Space Agency; in this case we can also benefit from the possibility to combine these multi-platform data to carry out very long term DInSAR investigations. Second, we focus on the new X-band (3.1 cm wavelength) space-borne systems characterized by high spatial resolution and short revisit times; in particular, we consider the COSMO-SkyMed (CSK) sensors operated by the Italian Space Agency and highlight their capability to investigate phenomena associated with rather fast dynamics.
2. Basic Rationale
 A first attempt to develop advanced DInSAR techniques is represented by the algorithms referred to as stacking approaches [Peltzer et al., 2001]; these techniques are focused on reducing the effects of the phase artifacts due to changes in the atmospheric conditions between the acquisition SAR pairs (atmospheric artifacts) and/or those due to the uncertainties in the sensor orbit information (orbital artifacts). The stacking techniques essentially calculate a weighted average of all the deformation velocities computed from single interferograms (the weights being the corresponding time spans) and allow to provide an improved estimate of the mean deformation rate of the investigated area.
 The Persistent Scatterers techniques operate on the pixels of the full resolution (single-look) images that are representative of resolution cells with a dominant scatterer, as originally shown within the Permanent Scatterers approach [Ferretti et al., 2000]. These targets are not significantly affected by the noise due to spatial and temporal decorrelation effects [Zebker and Villasenor, 1992; Ferretti et al., 2000], thus allowing to work also with a very large spatial and temporal separation (baseline) between the acquisition orbits. For these reasons, interferometric pairs can be chosen without any constraint on their spatial and temporal baselines, the simplest and most effective way being the selection of one single master image in common to the whole dataset. A sketch of such a spatial and temporal baseline configuration is shown in Figure 1a, with reference to a real ENVISAT dataset over the area of the Kilauea volcano in Hawaii. We show in Figure 1c the interferogram corresponding to the data pair highlighted in red in Figure 1a, which has a spatial baseline of about 900 meters and a temporal separation of about 9 months; although it appears to be completely decorrelated, isolated pixels can still preserve the coherence (hence the name “Persistent” Scatterers) although this will be apparent only after processing the whole dataset. This example makes it clear that a crucial step in this class of algorithms is the selection of the PS points to be processed.
 On the other hand, as said earlier, Small Baselines methods allow the exploitation of extended targets. The immediate advantage of this approach is the increased number of ground points that can be monitored [Lanari et al., 2004; Prati et al., 2010]; however, due to the spatial and temporal decorrelation effects affecting extended targets, the spatial and temporal baseline length of each data pair must be limited (hence the original name Small Baselines). It is clear that, with such constraints on the baselines, the choice of a single master for all the interferograms of the dataset is not doable and a multiple master strategy has to be adopted. An example of such a selection is shown in Figure 1b (same dataset of Figure 1a); moreover, we show in Figure 1d the interferogram corresponding to the data pair highlighted in red in Figure 1b, which has a spatial baseline of about 20 meters and a temporal separation of about 3 years; in this case the interferometric fringes are clearly visible and visually interpretable, to some extent, even before the dataset is combined into a time series. The drawback of the SB approach is the need of an appropriate interferometric data pair selection strategy that may cause the data to be arranged in few small baseline subsets separated by large baselines: in this case, subsets are independent of each other and therefore the time series inversion gives rise to an undetermined problem which can be solved, for instance, by searching for a minimum norm Least Squares solution via the Singular Value Decomposition method [Berardino et al., 2002]. Nonetheless, for a relatively large amount of data, the probability to obtain one single connected dataset is very high, as for the example shown in Figure 1b. Finally, it is noted that the SB techniques typically work at a reduced spatial resolution, through a complex averaging (multilook) operation on the interferograms, although these techniques can be also exploited for full spatial resolution DInSAR analyses [Lanari et al., 2004].
 Regardless of the selected approach or its particular implementation, the advanced algorithms offer many advantages with respect to classical DInSAR. First of all, atmospheric artifacts can be detected and filtered out because of their different space-time behavior with respect to the deformation signal [Ferretti et al., 2000, Berardino et al., 2002]. Second, topography artifacts and phase unwrapping errors can be mitigated by using the space-time data redundancy [Pepe and Lanari, 2006; Hooper and Zebker, 2007]. Moreover, possible orbital phase errors can be effectively compensated by using the measurements of a limited number of GPS stations [Gourmelen et al., 2010, and references therein]. All these characteristics contribute to improve the measurement final precision up to about 0.5–1 mm/year and 5–10 mm for deformation velocity maps and time series displacements, respectively [Casu et al., 2006; Lanari et al., 2007a].
 Once advanced DInSAR approaches have been established as a new, precise and reliable technique for measuring ground deformation, one could wonder whether the measurement precision improvement is the only advantage attainable to expense of an increased data processing complexity. In the following, through the analysis of a number of selected case studies, we show how the exploitation of the retrieved spatially dense deformation time series can effectively give a deeper insight into the geophysical analysis of the observed phenomena and to highlight the major impact that the new generation X-band SAR systems may have in this context.
3. Selected Case Studies
 Let us start our analysis by considering a large part of the San Francisco bay area and surroundings (California, USA), extending for about 90 × 90 km, that is a well known seismogenic area and represents a rather ideal test site because it is affected by several deformation phenomena. In this case study, as well as in the following ones, we apply the SBAS algorithm [Berardino et al., 2002]. This technique is used to process a dataset of 45 SAR images acquired by the ERS-1 and ERS-2 sensors on descending orbits, from middle 1992 to late 2000; following an interferogram multilook operation, the results are computed on an output grid with a 100 × 100 m spacing.
Figures 2a and 2b show two selected interferograms of the whole area relevant to the 1995–1999 and 1998–2000 periods, respectively, with a temporal overlap of about one year. The most evident deforming area is located to the South-East (Figure 2a) in correspondence to the Santa Clara basin, characterized by a complex network of permeable, water-bearing units that exchange groundwater [U.S. Geological Survey, 2000]; by comparing Figures 2a and 2b the different shape of the displacement patterns is clear. Moreover, another evident deforming area is in correspondence to the Hayward fault, see Figure 2a; note that the fault trace is more clearly visible in Figure 2a than Figure 2b, probably because of the larger time coverage, thus suggesting a rather linear temporal deformation behavior.
 Let us now move to the analysis of the DInSAR time series results that can be represented in a number of ways for emphasizing different deformation processes. The mean deformation velocity map, for instance, provides average information on the major surface displacement features, as shown in Figure 2c, where the Hayward fault is clearly distinguishable. In this case the displacement rates well characterize areas like the portion of the Hayward fault labeled as d in Figure 2c, where the temporal deformation behavior appears rather linear, as confirmed by the plot presented in Figure 2d. However, the real strength of the spatially dense DInSAR time series lies in their potential to analyze surface change signals that are spatially extended and not steady with time. This is the case of the Santa Clara basin where the non steady temporal deformation behavior is evident by considering the plot of Figure 2e, relevant to the area labeled as e in Figure 2c and characterized by seasonal variations. We may benefit of the retrieved DInSAR time series to deeply investigate the deformation of the Santa Clara basin via a correlation analysis [Lanari et al., 2007b]. To this end we remove the long term deformation trend and compute the correlation coefficient between each pixel's detrended time series and a sinusoid with one year period and variable amplitude and phase (i.e., time shift). For this site sinusoids have been already successfully used to approximate seasonal variations [Schmidt and Bürgmann, 2003], although in some cases the phase and amplitude may change from year to year. For each pixel, we search for the sinusoid amplitude and phase that provide the maximum correlation coefficient, the latter being mapped in Figure 3a; the corresponding amplitude (peak-to-peak) and time shift maps are shown in Figures 3b and 3c, respectively, for pixels with correlation greater than 0.6. Based on the results shown in Figures 3a–3c, several findings arise. First of all, Figure 3a clearly shows that the areas where deformation are highly correlated with the seasonal variations (see also two sample plots in Figures 3d and 3e) are sharply bounded by the northward extension of the Silver Creek fault indicated by continuous and dashed black line in Figures 3a–3c). This result is consistent with previous interpretation of DInSAR data across this fault as a hydrological barrier to groundwater flow [Schmidt and Bürgmann, 2003, and references therein; Bürgmann et al., 2006, and references therein]. Moreover, Figure 3b highlights that the zone with higher sinusoidal amplitude is close to the sharp discontinuity of the Silver Creek fault. Finally, Figure 3c suggests that the area in the western part of the aquifer has oscillations that peak earlier than those in the eastern part: sinusoids correlated to the point labeled as f (blue line) and f′ (red line) are plotted in Figure 3f and clearly show this effect, which is likely related to groundwater flow. These results demonstrate how the availability of spatially dense deformation time series, sufficiently sampled in time, provides a unique opportunity for detailed studies on the ongoing surface deformation phenomena.
 As a further example let us remain on the same DInSAR dataset but consider a completely different phenomenon; in this case we focus on the southern area of the Hayward fault highlighted in Figure 2a. Figure 3g shows a zoom of the mean deformation velocity map around the Camellia and Parkmeadow sites that were affected by an aseismic deformation (creep) event on February 1996 [Lanari et al., 2007a]; red dots illustrate the position of several alignment arrays covering the area [Lienkaemper et al., 2001], that we use as reference. In correspondence to these points we consider two box areas located on the opposite sides of the fault and average all the coherent pixels of the time series falling therein. The difference between these two averages is then computed in order to obtain the time series of relative displacements across the fault: the obtained results for the Camellia and the Parkmeadow sites are plotted (black triangles) in Figures 3h and 3i, respectively, where the creep event is successfully identified. Moreover, the LOS-projected alignment array data (red stars in Figures 3h and 3i), reported for comparison, show the high precision reached by the computed across-fault DInSAR measurements; indeed, the standard deviation of the differences between the DInSAR and the geodetic measurements does not exceed 3 mm. It is evident that this kind of analysis can be easily expanded, allowing the generation of across-fault deformation time series for the overall extension of the fault in correspondence to the coherent areas.
 Let us now focus on one of the most well known volcanic areas of the Earth, Mt. Etna (Italy), which is another very interesting test site affected by complex deformation phenomena. We produce temporally extended (1992–2008) deformation time series by combining the huge archive of ERS-1/2 images (available since 1992) with ENVISAT ones (available since 2002), via a slightly modified version of the SBAS approach [Pepe et al., 2005] applied to the overall dataset of 139 ascending and 120 descending SAR images. Maps of the mean deformation velocity components along ascending LOS, descending LOS, vertical and East-West directions as well as deformation time series of two selected sites are shown in Figures 4a–4f; a comparison with measurements of the GPS network of INGV [Puglisi et al., 2008] is also included and shows a generally good agreement.
 The volcano's flanks are composed of fault bounded blocks (Figure 4) that are characterized by homogeneous slip velocities, while adjacent blocks move at different rates [Solaro et al., 2010]. We wonder if we can identify blocks by just exploiting the deformation velocity maps. As an example, for the East flank's sector labeled as g in Figure 4f this is clearly the case. This result is further confirmed by plotting the time series corresponding to all the pixels belonging to this area (Figure 4g), which points out the time linearity of the deformation. However, for areas located on the West flank, block identification is more difficult; sector h (Figure 4f), for instance, does not even show a homogeneous velocity; in this case, time series plotting (Figure 4h, top) shows a “rigid” behavior of the sector only until 2000, when eruptive activities began to take place, thus masking out the much weaker motion. To filter out the signal related to major eruptions (occurred during 2001 and 2002–2003), time series for 1994–2000 and 2003–2008 periods are considered separately; moreover, for all the time series after 2003 the initial value is arbitrarily fixed to a same value (the mean deformation achieved in 2000). The obtained results, reported in Figure 4h (bottom), show that the residual motion of pixels belonging to sector h is homogeneous also during 2003–2008, thus permitting to recognize sector h as a rigid block [Solaro et al., 2010]. Once again, time series analysis is a key tool for obtaining such a result.
4. New Advances and Concluding Remarks
 We have already stressed the important role played by the C-band space-borne SAR sensors operating with nearly monthly revisit time. With respect to these radar systems and similarly to optical sensors, the aerospace scenario is moving towards SAR systems with improved spatial resolution and shorter revisit times. While the relevance of the former improvement is important in several applications [Prati et al., 2010], we focus here on the impact of the revisit time shortening with respect to the earlier C-band systems. In this context we remark that during the last years four new X-band satellites have been launched; three of these belong to the COSMO-SkyMed constellation and present an overall revisit time of 8 days, including also a 1 day tandem option. In order to show the benefit that may derive from such a shortening of the revisit time, we consider the L'Aquila area (Italy) that was affected by a Mw 6.3 earthquake on April 6, 2009. We focus here on the post-seismic deformation that is usually associated with a much subtler signal not easily detectable with traditional DInSAR techniques, especially for earthquakes with this order of magnitude.
 To investigate the deformation affecting L'Aquila zone and surroundings we have applied first the SBAS algorithm to a dataset of 42 ENVISAT images acquired between 2003 and 2009 from ascending orbits, with a look angle of about 23 degrees. The cumulative deformation map from 2003 to 2009 is reported in Figure 5a where the white square indicates the pixel labeled as c, whose deformation time series is plotted in Figure 5c (black triangles). The most evident features are the maximum deforming area located to the South-West of the point c, see Figure 5a, and the discontinuity characterizing the time series, see Figure 5c, occurring in correspondence to the earthquake event. Moreover, in the six month period after April 2009 a deformation trend can be also appreciated in the time series; in this case only six post-seismic ENVISAT acquisitions are available due to the (35 days) sensor revisit time, thus providing a too small SAR dataset for carrying out a reliable quantitative analysis on the retrieved post-seismic displacements.
 On the other hand, following the earthquake event, this site has been intensively imaged by the X-band SAR sensors of the CSK constellation. In particular, we consider the CSK data acquired also in this case from ascending orbits, during nearly the same six month post-seismic interval of the corresponding ENVISAT data. This COSMO-SkyMed dataset is characterized by a look angle of about 36 degrees and a fine spatial resolution of about 3 meters, in both azimuth and range directions, and is composed of 32 SAR images representing a significant number to effectively exploit the SBAS technique. The computed cumulative post-seismic deformation map is reported in Figure 5b. A comparison with the co-seismic map presented in Figure 5a highlights a northward migration of the maximum deforming area and an increase of the number of coherent pixels, due to the better spatial and temporal resolution of the CSK system.
 Let us now qualitatively compare the CSK deformation time series (red triangles) with the corresponding part of the ENVISAT one (black triangles), see Figure 5c and its blow-up in Figure 5d. Unsurprisingly, these two results are rather consistent. However, it is evident that the achieved temporal resolution improvement of the CSK measurements allows to identify the non linear post-seismic decay curve, while ENVISAT results would suggest a rather linear trend. These findings are in a rather good agreement with the independent observations presented by Amoruso and Crescentini . From this experiment it is immediately clear the major impact that such new sensor may have, through the use of advanced DInSAR techniques, for the analysis, interpretation and modeling of fast varying deformation phenomena, such as post-seismic displacements.
 As a final issue we want to remark that the advent of the new generation SAR sensors is not the only key element for advanced DInSAR developments. Indeed, the full exploitation of the already available archives of C-band SAR data, which are largely underused, is also of great importance for the comprehension of several geophysical phenomena. Accordingly, it is extremely relevant to develop and sustain initiatives for the extensive exploitation of the existing SAR data archives as the Geohazard Supersites (http://supersites.earthobservations.org/) whose aim is to provide direct access to large SAR data archives on selected sites prone to major natural hazards (earthquakes, volcanoes, ground motions, etc.). In this context, ESA recently decided to make their ENVISAT and ERS data archives freely available for academic use. This kind of action is essential for enlarging the community using DInSAR measurements, in order to fully establish the role of these new developments on the DInSAR technology not only in a scientific context but also into actual operational scenarios.
 This work has partially been supported by ASI and the Italian DPC. We thank ESA and ASI for providing SAR data, G. Puglisi for making us available the GPS measurements of Mt. Etna volcano, and L. Candela for supporting the CSK study on L'Aquila earthquake. We also thank E. Calais and F. Florindo for inviting us to contribute this frontier article.