Volcanoes deform dynamically due to changes in both their magmatic system and instability of their edifice. Mt. Etna features vigorous and almost continuous eruptive activity from its summit craters and periodic flank eruptions. Even though its shape is that of a large stratovolcano, its structure features two rift systems and a flank collapse structure similar to Hawaiian shield volcanoes. We analyze European remote sensing (ERS) satellite differential interferometric synthetic aperture radar (InSAR) data (1993–1996) for Mt. Etna spanning its quiescence from 1993 through the initiation of renewed eruptive activity in late 1995. We use synthetic aperture radar (SAR) data from both ascending and descending ERS satellite tracks. Comparison of independent interferograms covering the first 2 years of the inflationary period shows a pattern consistent with inflation of the volcano. Calculation of the tropospheric path delay based on meteorological data does not change this interpretation. Interferograms from late summer 1995–1996 show no significant deformation. Joint inversion of interferograms from ascending and descending satellite tracks require both inflation from a spheroidal magmatic source located beneath the summit at 5 km below sea level, and displacement of the east flank of Etna along a basal decollement. Both sources of deformation were contemporaneous within the resolution of our data and suggest that inflation of the central magma chamber acted to trigger slip of Etna's eastern flank. These results demonstrate that flank instability and recharge of a volcano's magma system must both be considered toward understanding how volcanoes work and in their hazard evaluation.
 Mt. Etna is a large (3350 m elevation) stratovolcano located along the east coast of the island of Sicily in southern Italy (Figure 1). It is characterized by frequent eruptions with quasi-persistent strombolian activity at the summit craters, often evolving into lava fountaining, and frequent lava flow eruptions from both the summit craters and flank fissures. Mt. Etna is located at the convergence between the Eurasian and African plates that produce different stress domains around it; to the east and northeast (in the Calabrian-Ionian area), the stress field is mainly tensional while a compressive domain is present to the west (in Sicily) [Cocina et al., 1997]. One of the major structural features of Etna is two large fault systems, the Pernicana to the NE [Azzaro et al., 1998; Groppelli and Tibaldi, 1999] and the Trecastagni/Mascalucia-Tremestieri faults to the SE [Lo Giudice and Rasà, 1992]. These faults connect through a series of rifts crossing the summit craters to define a large unstable sector that encompasses the eastern third of the volcano [Rasà et al., 1996]. This sector of the volcano is sliding toward the sea to the east, and toward the south, along a poorly constrained basal decollement [Lo Giudice and Rasà, 1992; Borgia et al., 1992, 2000]. Thus in addition to inflation and deflation of the volcano related to changes in volcanic activity, we might expect to measure deformation related to the structural instability of the volcano.
 Differential synthetic aperture radar (SAR) interferometry is a valuable technique for measuring differential surface displacements of volcanoes over intermediate to long time intervals (months to years) [Massonnet et al., 1995; Lanari et al., 1998; Lu et al., 1998, 2000; Wicks et al., 1998; Jonsson et al., 1999; Amelung et al., 2000; Lundgren et al., 2001]. Interferometric SAR (InSAR) provides a dense (less than 100 m pixel size) sampling over a large area (100 × 100 km2) that is ideal for covering an entire volcano and its surrounding region. The earliest application of InSAR to volcano deformation [Massonnet et al., 1995] was applied to Mt. Etna, demonstrating this technique's great potential. Lanari et al.  extended the data set examined by Massonnet et al.  into the subsequent quiescent period from 1993 to 1995, showing that following the flank eruption that ended in 1993, Etna began to inflate. They modeled the SAR interferograms assuming a point source and found solutions generally in the 7–15 km depth range, roughly located beneath the summit.
 This study expands upon the study of Lanari et al.  by looking at a larger set of European remote sensing synthetic aperture radar (ERS SAR) images forming a greater number of interferograms from both ascending and descending satellite data, and through improvement in the source analysis. We calculate differential interferograms covering a greater area around the volcano by using an extended digital elevation model (DEM). We expand the deformation uplift interpretation by considering the effects of the troposphere following the methodology of Delacourt et al. . The emphasis of this study is on improved analysis of the deformation source properties by inverting the InSAR data for more complex deformation sources and by considering more than one source process. Finally, this study provides a more complete assessment of the deformation source mechanisms and their interactions.
2. Sar Interferometry
 InSAR is a recent technique that uses repeat pass satellite radar images to calculate topography or surface change [e.g., Gabriel et al., 1989; Massonnet and Feigl, 1998; Rosen et al., 2000]. For this study, we are concerned with the calculation of interferograms using SAR data from the ERS satellites (ERS-1 and ERS-2). These satellites fly in tandem along the same orbit 1 day apart, and use a C-band (5.6 cm) radar.
 We use the “two-pass” method to generate differential interferograms. This technique involves subtracting two images to calculate an interferogram containing the effects of topography [Zebker and Goldstein, 1986] and Earth curvature. We use the Jet Propulsion Laboratory-California Institute of Technology (JPL-Caltech) developed ROI_PAC software package to process these SAR data. We compute the differential interferogram by removing a synthetic interferogram that simulates the effects of topography and the geometric effects of Earth curvature, based upon precise knowledge of the two satellite orbits and the topography. We use the precise orbits archived by the European Space Agency (ESA) and we then reestimate the satellite baselines through cross correlation of the two amplitude images to subpixel resolution. To compute the topographic contribution, we use a DEM that is a mosaic of the U.S. National Information and Mapping Agency (NIMA) DTED 90 m DEM and the IIV-CNR DEM with an accuracy of 5–10m. For example, at perpendicular orbital separations of 100 m, a 10-m error in the DEM corresponds to a displacement error of much less than 1 mm, and therefore is not significant.
 A list of the interferometric pairs considered in this study is given in Table 1. Figures 2–4 show interferograms spanning roughly 2 years from the summer of 1993 to the spring-fall of 1995. Each of the interferograms shown is unwrapped (although we display all interferograms with a 2.8 cm color cycle for display purposes), meaning that the actual differential line-of-sight (LOS) displacements have been computed. Figures 2 and 4b are from ascending ERS passes, while Figures 3 and 4a are from descending passes. Several important observations can be made regarding these data.
All the interferograms during this time period give a sense of surface change that is positive in the satellite LOS (i.e., uplift and/or horizontal surface displacements toward the SAR).
Interferograms from both ascending and descending passes spanning from 1993 to spring/early summer 1995 have a lower LOS displacement amplitude than those extending later into the summer and fall of 1995.
Interferograms covering comparable periods, both within and between ascending and descending passes, have similar displacement amplitudes and fringe patterns.
Interferograms from ascending and descending passes have patterns that are skewed toward the observing direction of the radar and do not match the topography.
Definitions are as follows: YMD is year, month, day; and is read 920927 as September 27, 1992; ∣B⟂∣ is the magnitude of the perpendicular baseline orbit separation of the InSAR pair. Quality is graded “A,” “B,” “C,” with A being the best quality. The lowercase letters following the letter grade indicate sources of degradation. An “a” means atmospheric noise, either layered or extreme spatial heterogeneity. A “c” means significant correlation problems, usually associated with snow cover for late autumn to spring, or due to layover on the eastern slopes of Etna for descending tracks (222 and 494).
 The remaining interferograms span shorter time periods during 1995 and 1996 and are shown in Figures 5 and 6. A detailed interpretation of these InSAR data will be assessed later in terms of possible deformation or atmospheric noise. There are two questions we wish to resolve from this data set: (1) Are the observed fringe patterns due to surface deformation or due to atmospheric noise? (2) How can we explain the significant differences in fringe patterns observed between ascending and descending track interferograms over similar times?
3. Tropospheric Effects
 One of the potential error sources for InSAR is the atmospheric heterogeneities, due to convective instabilities [Goldstein, 1995], topographically correlated wind-driven moisture accumulation [Fujiwara et al., 1998], or due to layered structure that causes topographically correlated phase delays [Tarayre and Massonnet, 1996]. For Etna, in particular, all or portions of concentric fringe patterns have been attributed to the latter effect [Delacourt et al., 1998; Beauducel et al., 2000]. For a volcano, the size of Etna located adjacent to a relatively warm marine environment the problem could be particularly acute. Simple tropospheric models that calculate the change in path delay based upon the difference in temperature, pressure, and humidity can predict several centimeters for the lower 2 km of atmosphere [Delacourt et al., 1998; Bonforte et al., 1999]. The correlation of such models with atmospheric thickness, or topography, complicates the interpretation of volcano deformation (or apparent deformation), which also generally correlates with topography. The goal of this section is to establish whether or not the large signals we find for the period 1993–1995 are surface deformation, atmospheric effects, or some combination thereof.
 Two methods have been applied to Etna for estimating the effects of a layered atmosphere. The first, by Delacourt et al.  or Bonforte et al. , calculates the expected fringe pattern based on independent meteorological data at the time of the ERS observations. The second, by Beauducel et al. , estimates a topographically correlated signal directly from the observed interferograms.
 To gain insight into the amount of tropospheric correction expected, we apply the method of Delacourt et al.  to the ascending interferograms in this study (the meteorological data required for the approach of Bonforte et al.  are not available for the time period of this study). As with the study of Delacourt et al. , we use meteorological data from Trapani, located on the western tip of Sicily, some 200 km west of Mt. Etna. Despite the inherent limitations of these data, they are the only data we have found available with temperature, pressure, and humidity for the time of the ascending track ERS fly over. We find that the displacement amplitudes of the observed versus expected uplift or subsidence pattern are generally within one fringe (2.8 cm) of range displacement for most of the interferograms considered in the 1993–1995 period (Figure 7).
 The second approach to consider is the direct assessment of the layered tropospheric differential path delay from individual interferograms. A recent study by Beauducel et al.  calls into question whether Etna interferograms show deformation or are mostly atmospheric effects. The method of Beauducel et al.  simultaneously solves for the tropospheric delay at four different elevations (0, 1, 2, and 3 km) plus the pressure amplitude of a point volcanic source of Mogi  at a fixed location and depth. The inversion is performed on a predefined set of points in the interferograms that lie in areas of highest correlation in all interferograms and which are selected evenly distributed with elevation (though not evenly distributed in map view). One of the potential liabilities of this approach is that the selected points do not evenly sample the volcano's surface. If a topographically correlated signal is sought, then its spatial (map-view) distribution does not matter. In contrast, a limited spatial sampling could severely limit the identification of a volcanic source if the distribution of points is not sensitive to the expected asymmetry of a volcanic source.
Beauducel et al.  argue that sequences of independent interferograms spanning similar time periods could show similar fringe patterns due to layered tropospheric conditions that persist for several months at a time. One-dimensional tropospheric models such as that used by Delacourt et al.  calculate path delays based on the temperature and humidity of the troposphere with height. Such a model would predict much stronger effects from summer to winter, but variable effects when considering summer to summer tropospheric delays (for example) where temperature and humidity values would be expected to fluctuate with passing weather systems. Therefore it would seem highly unlikely that the independent interferograms shown in Figures 2–4 could be so similar and yet be largely due to atmospheric effects.
 Assuming that no resolvable deformation takes place over 24 hours, we can gain some insight into the level of atmospheric effects we might expect by looking at ERS-1-ERS-2 tandem interferograms (Figure 5). The first two tandem InSAR data show approximately one cycle of phase that roughly conforms to the topography of Etna (Figures 5a and 5b), while the latter two show no significant topographically correlated signal (Figures 5c and 5d). In addition, the two pairs in Figures 5a and 5b have opposite signs to the fringe patterns, as might be expected for a randomly occurring atmospheric effect.
 One final point is that all the interferograms over the period 1993–1995 exhibit an inflationary signal. If a signal were dominantly atmospheric, we would expect images taken during the same season to have a fringe pattern that differed in sign among different pairs depending on the daily weather (i.e., “uplift” or “subsidence”). For this time period on Etna we do not find that, instead we find a pattern consistent in shape and displacement amplitude, and consistent with GPS observations over this same period [Puglisi et al., 2001]. Additionally, not only do the ascending and descending fringe patterns not conform to the topography, but also they maintain the same patterns between independent interferograms from the same satellite track (and between adjacent tracks in the case of descending ERS data). Yet the fringe patterns are fundamentally different between the ascending and descending tracks, an unexpected observation if the patterns were due solely to a layered atmospheric effect. In contrast, interferograms during late 1995 or from late 1995 to 1996 are either flat or with a small apparent deflationary signal (Figure 6).
4. Modeling the Source
 The simplest volcano deformation source is a point pressure source in an elastic half-space [Mogi, 1958]. This simple source approximation has been adequate to fit many examples of volcano surface deformation [Dvorak and Dzurisin, 1997], and is not significantly different from the surface deformation expected from a finite spherical source when the source depth is greater than twice the cavity diameter [McTigue, 1987].
 The deformation that is observed in these interferograms is consistent with the expected deformation pattern for a cavity pressure or subhorizontal tensile source. The steep incidence angle (∼21°–26° from zenith for this data set) of the ERS radar means that InSAR is most sensitive to vertical displacements. Since Dieterich and Deker  showed that vertical displacements alone do not discriminate well between different axisymmetric pressure sources, it becomes harder to distinguish between source types, particularly for deep sources. Thus point and finite spherical sources appear alike, and anisotropic deformation patterns cannot distinguish well between elongated (spheroidal or ellipsoidal) pressure cavities and horizontal sills.
Lanari et al.  solved for the best fitting point pressure source in an elastic half-space using a grid-search technique. In this study, we analyze a larger data set that includes SAR images from both ascending and descending satellite tracks. Differences in the modeling (inversion technique) and the type of source geometries (extended, asymmetric) allow us to refine our interpretation of the source and find a source location that is more consistent with other studies. Finally, by jointly inverting both ascending and descending interferograms we overcome some of the limitations of one-component LOS displacements observed by InSAR and more completely characterize the volcano source processes. This last consideration is the most crucial. With only ascending data, the interferograms for this time period are consistent with a simple pressure source elongated in a NNE-SSW direction (Figure 4). Examination of the interferograms from descending data reveals a pattern of deformation with a significant lobe of deformation extending over the NE flank of Etna. This deformation pattern is evident from a number of independent interferometric pairs and from different satellite tracks (Figures 3 and 4). This deformation shape does not conform to the topography of Etna, precluding a simple atmospheric explanation tied to topography and seasonally correlated in such a way as to replicate among independent interferograms [Beauducel et al., 2000].
 We solve for the location, pressure, and geometric properties of different deformation sources using a Levenberg-Marquardt nonlinear optimization algorithm [Press et al., 1986]. The Levenberg-Marquardt algorithm is a steepest decent derivative-based method that seeks to avoid local minima through manipulation of the step in model parameter values when the model fit does not improve over successive iterations. Multiple sources can be considered by simply increasing the solution space linearly with the number of sources. Inversions for an elastic half-space considering a point source [Mogi, 1958] yield a reasonable solution, but examples from the 1993–1995 inflation show that the elliptical pattern of the deformation requires an asymmetric source (Figures 2 and 4). Therefore we will concentrate our inversions on spheroidal [Yang et al., 1988] and tensile dislocations [Okada, 1985]. Either a spheroidal or a subhorizontal tensile source can reasonably fit an elliptical deformation pattern. We found the spheroidal source produced a better fit to the shape of the observed deformation. A horizontal tensile source has a steeper-sided, broader-range displacement pattern compared to the more tapered pattern found for the spheroidal source. When we consider the effects of topography on these elastic half-space solutions we find that the relative fits of the single-source solutions change, with the reduced χ2 for the Okada, Mogi, and Yang solutions at 2.9, 2.5, and 2.4, respectively. Therefore we will consider modeling the observed inflationary deformation with a spheroidal source.
 For each unwrapped interferogram, the standard deviation in the multilook phase (where the number of looks refers to the product of the number of pixels averaged in the parallel and cross-track directions) is calculated based on the single-pixel correlation coefficient using the Cramer-Rao formula
where σϕ is the standard deviation of the phase (in radians), γ is the single-look correlation, and N is the total number of looks [Sorenson, 1980; Rosen et al., 2000]. Because it is based on the correlation in the single-look image, this approach is independent of the effects that filtering and smoothing have on reducing the phase variations.
 The spheroidal pressure source [Yang et al., 1988] is a prolate spheroid (spherical to cigar shaped, two smaller axes of equal length) with arbitrary plunge and azimuth. Inverting for this source requires solving for eight parameters: x, y, z define the spheroid center coordinates, ΔP is the excess pressure at the spheroid surface, a is the semimajor axis, and c is the length from the spheroid center to the focus, ϕ and θ are the azimuth and plunge of the a axis, respectively, plus an arbitrary constant shift of the differential LOS displacements for each interferogram.
 To model fault slip or fault tensile dislocations, we use the analytical expressions of Okada . Inversion for a dislocation involves estimating up to 10 parameters: x, y, z, define the location of the fault, L and W are the length and width, respectively, δ and ϕ are the dip and strike, and Ui represents the three fault slip components (strike slip, dip slip, and tensile).
 Recent studies have shown that a volcano's topography should have a significant effect both on the displacement amplitude and the shape of the surface deformation [Williams and Wadge, 1998, 2000; Cayol and Cornet, 1998; Folch et al., 2000]. In the analysis of Williams and Wadge , they showed that a finite element model for volcano deformation that incorporated the topography of Mt. Etna had a significant effect on the expected surface deformation. For a given source depth (below sea level) and pressure change, the deformation decreases with increasing elevation compared to a half-space. They attributed this to a simple geometric argument that a point at higher elevation has a greater radial distance to the source, thus reducing the amplitude of the displacements at the elevated point relative to what it would have been at sea level. The application of the approach of Williams and Wadge  is straightforward; at each data point, the effective source depth to that point is the half-space depth plus the elevation of that point. Thus for a 3-km depth source a point at sea level “sees” a source at 3-km depth, whereas a point at 3-km elevation is deformed as if the source were at 6-km depth. The study of Williams and Wadge  applies a perturbation approach to more accurately correct for topographic effects compared to the approach of Williams and Wadge . Its main limitation is the extensive development that is required to apply it to the spheroidal and dislocation sources considered in this analysis, which is beyond the scope of this study. Therefore we apply the topographic correction method of Williams and Wadge .
4.1. Ascending Interferograms
 Five interferograms have very similar shapes to their deformation patterns (Figures 2 and 4b). Each of these interferograms has either the 1993/07/04 or 1993/08/08 ERS-1 SAR image as a reference image. This reflects the limited number of interferograms that are possible given the 35-day repeat of the ERS orbit, the requirement of small perpendicular baselines, and for Etna the usefulness of SAR data acquired from late April to November, when the higher elevations are free of snow cover. Each of these 1993 images can form two interferograms with images acquired in the spring and then later in the summer or fall of 1995. The similarity of these interferograms formed with independent images, and the increase in LOS displacement amplitude of the interferograms from the spring to summer/fall 1995, are consistent with the fringes being mostly due to deformation and is the basis for the conclusions obtained by Lanari et al. .
4.2. Descending Interferograms
 Interferograms from descending satellite images (Figures 3 and 4a) show a significant number of fringes that define a relatively simple pattern that does not correspond with the topography of Etna. The same pattern is found in interferograms from independent images and from two adjacent satellite tracks (ERS tracks 222 and 494). The interferogram 1993/06/06–1995/09/12 spans a similar time period as the longest of the four ascending interferograms modeled above. However, the uplift pattern is not as simple and has an additional lobe centered beneath the NE flank of Etna. The other descending interferograms for the 1993–1995 time period also share features with the fringe pattern and displacement amplitude found in the 1993/06/06–1995/09/12 interferogram, though with lesser displacement amplitude and/or higher atmospheric noise.
 The interferograms from track 494 are noisier and have greater areas of decorrelation over the eastern slopes of Etna due to layover of the near-range SAR data where the incidence angle is smaller (and lower angle slopes are laid over). In addition, these interferograms have more small-scale atmospheric perturbations. Despite the lower overall quality of these interferograms, they exhibit a similar lobe of positive range displacement over the NE flank of Etna as observed in the interferograms from track 222.
4.3. Joint Inversions
 There are two questions we wish to address: (1) Why are ascending and descending interferograms similar in pattern and displacement amplitude to each other within their respective groups? (2) Why do 2-year ascending and descending interferograms have such different patterns between them?
 Our answer to the first question is that the ascending and descending interferograms are dominated by surface deformation, the argument we made in section 3. The answer to the second question can be explained by considering a more complex explanation for the deformation sources. For modeling purposes, we will consider the ascending and descending pair of interferograms (1993/08/08–1995/10/10, and 1993/06/06–1995/09/12), shown in Figure 4.
 An interferogram represents the projection of the surface displacements onto different satellite look vectors, therefore simple inflationary sources are expected to look somewhat different for ascending and descending interferograms with maxima of the same magnitude, but shifted toward their respective radar look directions. In the case of the aforementioned ascending and descending InSAR data, the large displacement amplitude that is observed in the descending interferogram beneath the NE flank does not have a corresponding signature of similar magnitude on the ascending interferogram (Figure 4).
 One possible solution to this problem, which mainly affects the east flank, is presented by considering other than simple volcano inflationary sources. Indeed, there is evidence that the deformation of Mt. Etna from 1993 to 1995 was the sum of several sources, not all due to magma movement within the volcano. In addition to the effect of a medium depth source located at 3–6 km below sea level, there is evidence for brittle deformation of important structures on Etna's eastern flank, such as the Pernicana fault [Puglisi et al., 2001]. The displacements of GPS points on Etna from 1993 to 1996 [Puglisi et al., 2001; A. Bonforte and G. Puglisi, Ground deformation studies on Mt. Etna from 1994 to 1995 using static GPS measurements, submitted to Journal of Geophysical Research, 2002] confirm the eastward movement of this flank, as hypothesized in models that interpret it as a sector collapse structure [Lo Giudice and Rasà, 1992; Borgia et al., 1992]. A general agreement exists in the definitions of the northern (Pernicana fault), northwestern and western (northeast and southern rift systems) boundaries of the sector collapse, while the southern boundaries of the sector are more diffuse, spread across the Ragalna and the Trecastagni/Mascalucia-Tremestieri (and associated faults that we will label as “TM”) fault systems [Rust and Neri, 1996; Rasà et al., 1996; Borgia et al., 2000; Froger et al., 2001]. The most controversial point is the location and orientation of the decollement allowing eastward movement of the east flank [Lo Giudice and Rasà, 1992; Borgia et al., 1992, 2000; Rasà et al., 1996; Firth et al., 1996]. InSAR measurements provided conclusive evidence of fault slip on the TM fault system along the southern boundary of the sliding east flank, as well as anticline growth beneath the adjacent portion of the southern flank immediately to the southwest of the fault system [Borgia et al., 2000; Froger et al., 2001].
 Unlike an inflationary volcanic source, a subhorizontal eastward thrusting fault (flat or dipping shallowly back toward the center of the volcano) would have greater displacement amplitude on the descending interferograms than the ascending interferograms. This is due, in part, to a cancellation of the horizontal and vertical displacements for the ascending InSAR data and summation for the descending data.
 To test this, we have jointly inverted the 1993/08/08–1995/10/10 and 1993/06/06–1995/09/12 interferograms to solve for one spheroidal pressure source and a combination of two fault dislocation sources in an elastic half-space corrected for the distance-related effects of topography [Williams and Wadge, 1998]. We solve for the dip-slip and strike-slip components on a shallowly dipping decollement and a near-vertical fault. Table 2 gives the values for these solutions. For the horizontal decollement, the orientation and slip component (slip to the east) were constrained. Otherwise, all parameters were estimated. The shape of the deformation pattern over the eastern flank of Etna constrained the fault dimensions reasonably well. Figure 8 shows the results for this inversion, with the source geometry shown in Figure 9. Adding the two dislocations (and their 15 additional parameters) cuts the reduced chi-square for the model in half from 2.4 to 1.1. This is a significant reduction in error. For example, given the more than 60,000 points in the interferogram a simple F test [Stein and Gordon, 1984] yields F > 4000 relative to the spheroidal source. For the increase in model parameters to be significant, the value of F must only be >1 for such a large number of degrees of freedom (at 99% significance F approaches 1 as the number of degrees of freedom in both models becomes ≫1). While the value of F we find is very large, the highly correlated nature of InSAR data is not accounted for in our analysis. InSAR data correlation has been recently addressed by Jonsson et al. . If we followed the approach of Jonsson et al.  and reduced the number of data by 2 orders of magnitude, we would still expect a significant value for F. This is due to the large number of points retained and the data reduction algorithm used, which keeps more points in the areas of higher fringe rates: the same areas that most affect the differences in model fit.
Table 2. Source Parameters for the Solution Shown in Figure 9a
Source (S) 1 is a spheroidal source [Yang et al., 1988]. Sources 2 and 3 are for a dislocation [Okada, 1985]. The x and y locations are relative to the center of the area shown in Figure 1 (longitude = 14.9783, latitude = 37.7616), depth, d, is relative to sea level. For the dislocations, the x, y, and depth d refer to the “upper right” corner in the convention of Okada . The spheroid semimajor (a) and semiminor (b) axes, dislocation length (L), width (W), and location parameters (x, y, d) are in kilometers. The plunge/dip (δ) and azimuth/strike (ϕ) are in degrees. The strike, dip, and tensile slip (U1–3) are in meters. The spheroid pressure change (P) is in megapascals. The constant offsets that were estimated for the ascending and descending InSAR data were −0.022 and −0.003 m, respectively.
 This study demonstrates both the strengths and possible limitations of InSAR for measuring and monitoring volcano deformation. InSAR provides a detailed image of surface deformation over large areas. Active volcanoes, such as Etna, have large areas that are free of vegetation and provide high correlation over large time separations between the SAR images. However, as shown in other InSAR studies of Etna and in this study, there can be significant problems due to atmospheric phase perturbations, and the procedures to overcome this have not been well assessed for Etna. Our attempts to model tropospheric effects for individual interferometric pairs based on the meteorological data from Trapani suggested that for the dates considered, the tropospheric correction did not significantly change the interferogram displacement amplitudes (Figure 7).
 Instead, several observations support our contention that the observed fringe patterns during this study period were largely due to surface deformation.
Interferograms spanning the quiescent period from 1993 to 1995 consistently show that Mt. Etna volcano inflated (Figures 2–4).
All the observed 2-year interferograms show similarly shaped fringe patterns with similar LOS displacement amplitudes among ascending and descending tracks. The observed deformation pattern is maintained across interferograms formed from summer 1993 with April and May 1995 images compared with those formed into the late summer and fall of 1995 when the apparent seasonal effects attributed by Beauducel et al.  should be significant.
The observed interferogram fringe patterns are consistent with the projection of the three-dimensional surface displacements for a volcanic source onto the radar LOS, a feature not expected for a topographically correlated tropospheric effect, which should more strictly conform to topography.
 Joint inversion of ascending and descending interferograms provides an integrated interpretation of the deformation. By adding a simple pair of dislocations representing subvertical and subhorizontal components of the eastern sector collapse, we are able to fit most of the observed deformation (Figures 8 and 9).
 This model must be evaluated in terms of its limitations and assumptions. We leave aside an in-depth discussion on the limitation of treating the upper crust as a homogeneous, elastic half-space. A volcano poses a particularly difficult problem given the lack of constraint on both the geometry and dynamics of its source. A more immediate limitation with our solution is the effect of topography. The largest misfit in the modeling occurs over the higher elevations of Etna, where fairly detailed deformation patterns (apparent near-surface rift motion beneath the south rift zone and the detail in the lobes of positive range displacement over the NW summit region, Figure 8) are not well modeled with the source lying some 3 km beneath the summit. How this limitation in our modeling affects the inversion solution is not clear and would require a more sophisticated approach incorporating three-dimensional numerical models. It would be expected that the dislocation source directly beneath the summit would be the most affected. This might explain, for example, the contraction (negative U3 component) rather than the expansion we might have expected given the motion of the horizontal dislocation beneath the eastern flank. However, the strong left-lateral strike-slip component found for this feature is required by the model to contribute to the strong positive range displacements to the SW and NE of the summit. The model's misfit to the data reflects the limitations of considering a small number of very simple sources and the likely need of placing some of the subvertical dislocation within the volcano edifice as suggested from microgravity data [Budetta et al., 1999].
 Integration of petrological, geological, and geophysical data has recently been applied to model the buoyancy of Mt. Etna magma (R. A. Corsaro and M. Pompilio, Buoyancy of magmas at Mt. Etna, submitted to Terra Nova, 2002). This study shows that this magma has neutral buoyancy above 15 km depth up to sea level. Consequently, rising magma tends to stop in small reservoirs in the upper crust, where cooling/crystallization processes produce magma differentiation until positive buoyancy is attained, allowing the ascent to resume. Seismic tomography results constrain the plumbing system, showing that no large magma chamber exists below Mt. Etna, while several small liquid-filled volumes are identified [Laigle et al., 2000]. Among the latter, the westernmost has a position, dimensions, and orientation compatible with the spheroidal source resulting from the InSAR inversion.
 The sources derived for the modeled interferograms (Figure 9) cannot address the dynamics of the deformation (as seen in the growth in uplift during summer 1995, Figures 2–4) or the relative activity of the individual structures. Clearly, highly active volcanoes require higher temporal sampling to detect transient deformation and care must be taken when modeling or interpreting interferograms (or other deformation measurements) that span time intervals containing significant volcanic activity.
 Notwithstanding these limitations, the joint inversion solution quantifies a previously poorly understood deformation process on Etna. Our findings are similar to the south flank sliding of Kilauea volcano [Owen et al., 1995, 2000]. The amplitude of deformation over the NE flank of Etna observed on the descending interferograms from 1993 to 1995 and during the summer of 1995 is not observed on descending interferograms during late 1995–1996 following the resumption of eruptive activity (Figure 6). This suggests that the inflation of the magma chamber and the motion of the eastern flank were related, with the increase in pressure within the chamber acting as a force on the eastern flank of the volcano. This effect was first suggested by Borgia et al.  from InSAR observations and supports the mechanism proposed by Puglisi et al.  to explain the GPS data in relation to the July 1994 seismicity.
 We can place an upper bound on the expected radial displacement of the spheroidal magma chamber's surface by considering a spherical cavity with radius and pressure change equal to those of the spheroidal cavity's minor axis and pressure change, respectively [Delaney and McTigue, 1994]. Using an elastic shear modulus value for basalt of 30 GPa, we would expect displacement of the cavity walls on the order of 10 cm. This is a similar order of magnitude as the calculated slip on the basal decollement. The similarity in magnitude of the magma chamber radial expansion and the slip on the decollement suggest that the chamber expansion triggered slip of the flank system. The triggered motion of a portion of the volcano due to magma chamber inflation has been recognized using both InSAR [Borgia et al., 2000] and land-based geodesy [Puglisi et al., 2001]. This study models, for the first time, the coupling between the magma chamber inflation and motion of a large portion of a volcano.
 SAR interferograms show that during the 1993–1995 quiescent period, Mt. Etna inflated. Interferograms spanning 1993–1995 show a similar pattern. The simple elliptical shape of the deformation pattern and similarity among interferograms with independent images indicate that this is true surface deformation related to deep-seated processes and not an atmospheric artifact. The elliptical pattern of the ascending interferograms spanning 1993–1995 and the cross-sectional shape of the deformation are best fit by a spheroidal cavity centered at a depth of ∼5 km with a pressure change of ∼4 MPa (Table 2).
 The dissimilar deformation patterns computed from ascending and descending ERS tracks can be explained through a simple combination of the inflating spheroidal pressure source, motion of the NE flank of Etna along the basal decollement, and a near-vertical dislocation beneath the summit. By jointly inverting the data from two different look directions, we overcome the limitation of one-component range displacements while maintaining InSAR's dense spatial coverage. This shows the importance of combining ascending and descending interferograms.
 The deformation magnitude increased for both the descending and ascending interferograms from spring to late summer/fall of 1995 prior to the renewed eruptive activity in 1995. This shows the potential of InSAR as an important tool for volcano hazard forecasting and mitigation, if more frequent measurements were available to better quantify this process. The simultaneous inflation of the magma chamber and slip of the east flank show the importance of understanding the entire system for volcano hazard assessment.
 We thank the European Space Agency for the raw ERS SAR data, part of which was supplied under ERS AO3.359. F. Crampé, G. Peltzer, and P. Rosen provided important insight regarding ROI_PAC processing issues. C. Delacourt kindly provided meteorological data from Trapani. We thank G. Mattioli, F. Sigmundsson, and T. Dixon for their insightful reviews. Part of this work was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.