Coupled magma chamber inflation and sector collapse slip observed with synthetic aperture radar interferometry on Mt. Etna volcano P. Lundgren, 1 P. Berardino, 2 M. Coltelli, 3 G. Fornaro, 2 R. Lanari, 2 G. Puglisi, 3 E. Sansosti, 2 and M. Tesauro 2 Received 1 June 2001; revised 6 May 2002; accepted 30 October 2002; published 14 May 2003. [1] 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. INDEX TERMS: 8434 Volcanology: Magma migration; 8419 Volcanology: Eruption monitoring (7280); 8414 Volcanology: Eruption mechanisms; 1244 Geodesy and Gravity: Standards and absolute measurements; KEYWORDS: Etna, volcano, deformation, radar, interferometry Citation: Lundgren, P., P. Berardino, M. Coltelli, G. Fornaro, R. Lanari, G. Puglisi, E. Sansosti, and M. Tesauro, Coupled magma chamber inflation and sector collapse slip observed with synthetic aperture radar interferometry on Mt. Etna volcano, J. Geophys. Res., 108(B5), 2247, doi:10.1029/2001JB000657, 2003. 1. Introduction [2] 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 Rasa ` , 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 [Rasa ` 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 Rasa ` , 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. [3] Differential synthetic aperture radar (SAR) interfer- ometry 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 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B5, 2247, doi:10.1029/2001JB000657, 2003 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. 2 Istituto per il Rilevamento Elettromagnetico dell’Ambiente (IREA- CNR), Naples, Italy. 3 Istituto Nazionale di Geofisica e Vulcanologia, Catania, Italy. Copyright 2003 by the American Geophysical Union. 0148-0227/03/2001JB000657$09.00 ECV 4 - 1
Transcript
Coupled magma chamber inflation and sector collapse slip observed
with synthetic aperture radar interferometry on Mt. Etna volcano
P. Lundgren,1 P. Berardino,2 M. Coltelli,3 G. Fornaro,2 R. Lanari,2 G. Puglisi,3
E. Sansosti,2 and M. Tesauro2
Received 1 June 2001; revised 6 May 2002; accepted 30 October 2002; published 14 May 2003.
[1] Volcanoes deform dynamically due to changes in both their magmatic system andinstability of their edifice. Mt. Etna features vigorous and almost continuous eruptiveactivity from its summit craters and periodic flank eruptions. Even though its shape is thatof a large stratovolcano, its structure features two rift systems and a flank collapsestructure 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 renewederuptive activity in late 1995. We use synthetic aperture radar (SAR) data from bothascending and descending ERS satellite tracks. Comparison of independent interferogramscovering the first 2 years of the inflationary period shows a pattern consistent withinflation of the volcano. Calculation of the tropospheric path delay based onmeteorological data does not change this interpretation. Interferograms from late summer1995–1996 show no significant deformation. Joint inversion of interferograms fromascending and descending satellite tracks require both inflation from a spheroidalmagmatic source located beneath the summit at 5 km below sea level, and displacement ofthe east flank of Etna along a basal decollement. Both sources of deformation werecontemporaneous within the resolution of our data and suggest that inflation of the centralmagma chamber acted to trigger slip of Etna’s eastern flank. These results demonstratethat flank instability and recharge of a volcano’s magma system must both be consideredtoward understanding how volcanoes work and in their hazard evaluation. INDEX TERMS:
Eruption mechanisms; 1244 Geodesy and Gravity: Standards and absolute measurements; KEYWORDS: Etna,
volcano, deformation, radar, interferometry
Citation: Lundgren, P., P. Berardino, M. Coltelli, G. Fornaro, R. Lanari, G. Puglisi, E. Sansosti, and M. Tesauro, Coupled magma
chamber inflation and sector collapse slip observed with synthetic aperture radar interferometry on Mt. Etna volcano, J. Geophys. Res.,
108(B5), 2247, doi:10.1029/2001JB000657, 2003.
1. Introduction
[2] Mt. Etna is a large (3350 m elevation) stratovolcanolocated along the east coast of the island of Sicily insouthern Italy (Figure 1). It is characterized by frequenteruptions with quasi-persistent strombolian activity at thesummit craters, often evolving into lava fountaining, andfrequent lava flow eruptions from both the summit cratersand flank fissures. Mt. Etna is located at the convergencebetween the Eurasian and African plates that producedifferent stress domains around it; to the east and northeast(in the Calabrian-Ionian area), the stress field is mainlytensional while a compressive domain is present to the west
(in Sicily) [Cocina et al., 1997]. One of the major structuralfeatures of Etna is two large fault systems, the Pernicana tothe NE [Azzaro et al., 1998; Groppelli and Tibaldi, 1999]and the Trecastagni/Mascalucia-Tremestieri faults to the SE[Lo Giudice and Rasa, 1992]. These faults connect througha series of rifts crossing the summit craters to define a largeunstable sector that encompasses the eastern third of thevolcano [Rasa et al., 1996]. This sector of the volcano issliding toward the sea to the east, and toward the south,along a poorly constrained basal decollement [Lo Giudiceand Rasa, 1992; Borgia et al., 1992, 2000]. Thus inaddition to inflation and deflation of the volcano relatedto changes in volcanic activity, we might expect to measuredeformation related to the structural instability of thevolcano.[3] Differential synthetic aperture radar (SAR) interfer-
ometry is a valuable technique for measuring differentialsurface displacements of volcanoes over intermediate tolong 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
1Jet Propulsion Laboratory, California Institute of Technology,Pasadena, California, USA.
2Istituto per il Rilevamento Elettromagnetico dell’Ambiente (IREA-CNR), Naples, Italy.
3Istituto Nazionale di Geofisica e Vulcanologia, Catania, Italy.
Copyright 2003 by the American Geophysical Union.0148-0227/03/2001JB000657$09.00
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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 volcanoand its surrounding region. The earliest application ofInSAR to volcano deformation [Massonnet et al., 1995]was applied to Mt. Etna, demonstrating this technique’sgreat potential. Lanari et al. [1998] extended the data setexamined by Massonnet et al. [1995] into the subsequentquiescent period from 1993 to 1995, showing that followingthe flank eruption that ended in 1993, Etna began to inflate.They modeled the SAR interferograms assuming a pointsource and found solutions generally in the 7–15 km depthrange, roughly located beneath the summit.[4] This study expands upon the study of Lanari et al.
[1998] by looking at a larger set of European remote sensingsynthetic aperture radar (ERS SAR) images forming agreater number of interferograms from both ascending anddescending satellite data, and through improvement in thesource analysis. We calculate differential interferogramscovering a greater area around the volcano by using anextended digital elevation model (DEM). We expand thedeformation uplift interpretation by considering the effectsof the troposphere following the methodology of Delacourtet al. [1998]. The emphasis of this study is on improvedanalysis of the deformation source properties by invertingthe InSAR data for more complex deformation sources andby considering more than one source process. Finally, thisstudy provides a more complete assessment of the defor-mation source mechanisms and their interactions.
2. Sar Interferometry
[5] InSAR is a recent technique that uses repeat passsatellite 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 concernedwith the calculation of interferograms using SAR data fromthe ERS satellites (ERS-1 and ERS-2). These satellites fly intandem along the same orbit 1 day apart, and use a C-band(5.6 cm) radar.[6] We use the ‘‘two-pass’’ method to generate differ-
ential interferograms. This technique involves subtractingtwo images to calculate an interferogram containing theeffects of topography [Zebker and Goldstein, 1986] andEarth curvature. We use the Jet Propulsion Laboratory-California Institute of Technology (JPL-Caltech) devel-oped ROI_PAC software package to process these SARdata. We compute the differential interferogram byremoving a synthetic interferogram that simulates theeffects of topography and the geometric effects of Earthcurvature, based upon precise knowledge of the twosatellite orbits and the topography. We use the preciseorbits archived by the European Space Agency (ESA) andwe then reestimate the satellite baselines through crosscorrelation of the two amplitude images to subpixelresolution. To compute the topographic contribution, weuse a DEM that is a mosaic of the U.S. NationalInformation and Mapping Agency (NIMA) DTED 90 mDEM and the IIV-CNR DEM with an accuracy of 5–10m. For example, at perpendicular orbital separations of100 m, a 10-m error in the DEM corresponds to adisplacement error of much less than 1 mm, and thereforeis not significant.[7] A list of the interferometric pairs considered in this
study is given in Table 1. Figures 2–4 show interferogramsspanning roughly 2 years from the summer of 1993 to thespring-fall of 1995. Each of the interferograms shown isunwrapped (although we display all interferograms with a2.8 cm color cycle for display purposes), meaning that theactual differential line-of-sight (LOS) displacements havebeen computed. Figures 2 and 4b are from ascending ERSpasses, while Figures 3 and 4a are from descending passes.Several important observations can be made regarding thesedata.1. 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 towardthe SAR).2. Interferograms from both ascending and descending
passes spanning from 1993 to spring/early summer 1995have a lower LOS displacement amplitude than thoseextending later into the summer and fall of 1995.3. Interferograms covering comparable periods, both
within and between ascending and descending passes, havesimilar displacement amplitudes and fringe patterns.4. Interferograms from ascending and descending passes
have patterns that are skewed toward the observingdirection of the radar and do not match the topography.[8] The remaining interferograms span shorter time peri-
ods during 1995 and 1996 and are shown in Figures 5 and 6.A detailed interpretation of these InSAR data will beassessed later in terms of possible deformation or atmos-pheric noise. There are two questions we wish to resolvefrom this data set: (1) Are the observed fringe patterns dueto surface deformation or due to atmospheric noise? (2)How can we explain the significant differences in fringe
Figure 1. Shaded relief topography of Mt. Etna. Contoursare at intervals of 500 m starting at 500 m. Map covers thesame area covered by each of the interferograms in Figures2–6. Solid line segments outline the main faults boundingthe eastern sector collapse structure.
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Table 1. Interferometric SAR Data Parametersa
Track Satellite 1 Satellite 2 Orbit 1 Orbit 2 Date 1, YMD Date 2, YMD jB?j Quality Figures
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 indicatesources 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).
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patterns observed between ascending and descending trackinterferograms over similar times?
3. Tropospheric Effects
[9] One of the potential error sources for InSAR is theatmospheric heterogeneities, due to convective instabilities[Goldstein, 1995], topographically correlated wind-drivenmoisture accumulation [Fujiwara et al., 1998], or due to
layered structure that causes topographically correlatedphase delays [Tarayre and Massonnet, 1996]. For Etna, inparticular, all or portions of concentric fringe patterns havebeen attributed to the latter effect [Delacourt et al., 1998;Beauducel et al., 2000]. For a volcano, the size of Etnalocated adjacent to a relatively warm marine environmentthe problem could be particularly acute. Simple tropo-spheric models that calculate the change in path delay basedupon the difference in temperature, pressure, and humidity
Figure 2. Unwrapped, geocoded SAR interferograms for approximately 2-year time separations fromascending satellite tracks. Color wheel is set to 2.8 cm per cycle of range displacement. Backgroundimage is the radar backscatter amplitude image from the reference image. (a) 1993/08/08–1995/04/18interferogram. (b) 1993/07/04–1995/05/24. (c) 1993/07/04–1995/08/01. (d) 1993/07/04–1995/08/02.
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can predict several centimeters for the lower 2 km ofatmosphere [Delacourt et al., 1998; Bonforte et al., 1999].The correlation of such models with atmospheric thickness,or topography, complicates the interpretation of volcanodeformation (or apparent deformation), which also gener-ally correlates with topography. The goal of this section is toestablish whether or not the large signals we find for theperiod 1993–1995 are surface deformation, atmosphericeffects, or some combination thereof.
[10] Two methods have been applied to Etna for estimat-ing the effects of a layered atmosphere. The first, byDelacourt et al. [1998] or Bonforte et al. [1999], calculatesthe expected fringe pattern based on independent meteoro-logical data at the time of the ERS observations. The second,by Beauducel et al. [2000], estimates a topographicallycorrelated signal directly from the observed interferograms.[11] To gain insight into the amount of tropospheric
correction expected, we apply the method of Delacourt et
Figure 3. Unwrapped, geocoded SAR interferograms for approximately 2-year time separations fromdescending satellite tracks. Color wheel and background image is the same as in Figure 2. (a) 1993/06/06–1995/07/05. (b) 1993/07/30–1995/10/01. (b) 1993/07/11–1995/09/12. (d) 1993/05/21–1995/08/27.
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al. [1998] to the ascending interferograms in this study (themeteorological data required for the approach of Bonforte etal. [1999] are not available for the time period of this study).As with the study of Delacourt et al. [1998], we usemeteorological data from Trapani, located on the westerntip of Sicily, some 200 km west of Mt. Etna. Despite theinherent limitations of these data, they are the only data wehave found available with temperature, pressure, andhumidity for the time of the ascending track ERS fly over.We find that the displacement amplitudes of the observedversus expected uplift or subsidence pattern are generallywithin one fringe (2.8 cm) of range displacement for mostof the interferograms considered in the 1993–1995 period(Figure 7).
[12] The second approach to consider is the direct assess-ment of the layered tropospheric differential path delay fromindividual interferograms. A recent study by Beauducel et al.[2000] calls into question whether Etna interferograms showdeformation or are mostly atmospheric effects. The methodof Beauducel et al. [2000] simultaneously solves for thetropospheric delay at four different elevations (0, 1, 2, and3 km) plus the pressure amplitude of a point volcanic sourceof Mogi [1958] at a fixed location and depth. The inversionis performed on a predefined set of points in the interfero-grams that lie in areas of highest correlation in all interfero-grams and which are selected evenly distributed withelevation (though not evenly distributed in map view).One of the potential liabilities of this approach is that the
Figure 4. Unwrapped, geocoded SAR interferograms for approximately 2-year time separations and thejoint inversion solution for a single spheroidal source. Box in each observed image outlines the area usedin the joint source inversions. (a) Observed descending interferogram, 1993/06/06–1995/09/12. (b)Observed ascending interferogram 1993/08/08–1995/10/10. (c) Modeled surface displacements in theradar LOS direction for a single spheroidal pressure source at 5-km depth. Top panel corresponds to thedescending track and bottom panel corresponds to the ascending track. (d) Residual (observed minusmodeled LOS displacements). (e) Side view of the spheroidal pressure source (viewed from 190�clockwise from north). (f) Map view of modeled source.
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selected points do not evenly sample the volcano’s surface. Ifa topographically correlated signal is sought, then its spatial(map-view) distribution does not matter. In contrast, alimited spatial sampling could severely limit the identifica-tion of a volcanic source if the distribution of points is notsensitive to the expected asymmetry of a volcanic source.[13] Beauducel et al. [2000] argue that sequences of
independent interferograms spanning similar time periodscould show similar fringe patterns due to layered tropo-
spheric conditions that persist for several months at a time.One-dimensional tropospheric models such as that used byDelacourt et al. [1998] calculate path delays based on thetemperature and humidity of the troposphere with height.Such a model would predict much stronger effects fromsummer to winter, but variable effects when consideringsummer to summer tropospheric delays (for example) wheretemperature and humidity values would be expected tofluctuate with passing weather systems. Therefore it would
Figure 5. Unwrapped, geocoded SAR interferograms for tandem (1-day separation) data. Color wheeland background image are the same as in Figure 2. (a) 1995/06/27–1995/06/28. (b) 1995/08/01–1995/08/02. (c) 1995/09/05–1995/09/06. (d) 1996/04/02–1996/04/03.
LUNDGREN ET AL.: VOLCANO SAR INTERFEROMETRY ON MT. ETNAVOLCANO ECV 4 - 7
seem highly unlikely that the independent interferogramsshown in Figures 2–4 could be so similar and yet be largelydue to atmospheric effects.[14] Assuming that no resolvable deformation takes place
over 24 hours, we can gain some insight into the level ofatmospheric effects we might expect by looking at ERS-1-ERS-2 tandem interferograms (Figure 5). The first twotandem InSAR data show approximately one cycle of phasethat roughly conforms to the topography of Etna (Figures 5aand 5b), while the latter two show no significant topo-graphically correlated signal (Figures 5c and 5d). In addi-tion, the two pairs in Figures 5a and 5b have opposite signsto the fringe patterns, as might be expected for a randomlyoccurring atmospheric effect.[15] One final point is that all the interferograms over the
period 1993–1995 exhibit an inflationary signal. If a signalwere dominantly atmospheric, we would expect imagestaken during the same season to have a fringe pattern thatdiffered in sign among different pairs depending on thedaily weather (i.e., ‘‘uplift’’ or ‘‘subsidence’’). For this timeperiod on Etna we do not find that, instead we find a patternconsistent in shape and displacement amplitude, and con-sistent with GPS observations over this same period [Puglisiet al., 2001]. Additionally, not only do the ascending and
Figure 6. Unwrapped, geocoded SAR interferograms for late 1995 and 1996. Color wheel andbackground image are the same as in Figure 2. All interferograms except Figure 6f are from ascendingdata. (a) 1995/09/06–1995/11/14. (b) 1995/09/06–1995/11/15. (c) 1995/10/10–1996/10/30. (d) 1995/08/01–1996/04/03. (e) 1995/08/02–1996/04/03. (f ) 1995/08/09–1996/04/09.
Figure 7. Observed (solid lined bar) versus modeled(observed minus troposphere correction) interferogram peakdeformation amplitude.
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descending fringe patterns not conform to the topography,but also they maintain the same patterns between independ-ent interferograms from the same satellite track (andbetween adjacent tracks in the case of descending ERSdata). Yet the fringe patterns are fundamentally differentbetween the ascending and descending tracks, an unex-pected observation if the patterns were due solely to alayered atmospheric effect. In contrast, interferograms dur-ing late 1995 or from late 1995 to 1996 are either flat orwith a small apparent deflationary signal (Figure 6).
4. Modeling the Source
[16] The simplest volcano deformation source is a pointpressure source in an elastic half-space [Mogi, 1958]. Thissimple source approximation has been adequate to fit manyexamples of volcano surface deformation [Dvorak andDzurisin, 1997], and is not significantly different from thesurface deformation expected from a finite spherical sourcewhen the source depth is greater than twice the cavitydiameter [McTigue, 1987].[17] The deformation that is observed in these interfero-
grams is consistent with the expected deformation patternfor a cavity pressure or subhorizontal tensile source. Thesteep incidence angle (�21�–26� from zenith for this dataset) of the ERS radar means that InSAR is most sensitive tovertical displacements. Since Dieterich and Deker [1975]showed that vertical displacements alone do not discrim-inate well between different axisymmetric pressure sources,it becomes harder to distinguish between source types,particularly for deep sources. Thus point and finite sphericalsources appear alike, and anisotropic deformation patternscannot distinguish well between elongated (spheroidal orellipsoidal) pressure cavities and horizontal sills.[18] Lanari et al. [1998] solved for the best fitting point
pressure source in an elastic half-space using a grid-searchtechnique. In this study, we analyze a larger data set thatincludes SAR images from both ascending and descendingsatellite tracks. Differences in the modeling (inversiontechnique) and the type of source geometries (extended,asymmetric) allow us to refine our interpretation of thesource and find a source location that is more consistentwith other studies. Finally, by jointly inverting both ascend-ing and descending interferograms we overcome some ofthe limitations of one-component LOS displacementsobserved by InSAR and more completely characterize thevolcano source processes. This last consideration is the mostcrucial. With only ascending data, the interferograms forthis time period are consistent with a simple pressure sourceelongated in a NNE-SSW direction (Figure 4). Examinationof the interferograms from descending data reveals a patternof deformation with a significant lobe of deformationextending over the NE flank of Etna. This deformationpattern is evident from a number of independent interfero-metric pairs and from different satellite tracks (Figures 3and 4). This deformation shape does not conform to thetopography of Etna, precluding a simple atmosphericexplanation tied to topography and seasonally correlatedin such a way as to replicate among independent interfero-grams [Beauducel et al., 2000].[19] We solve for the location, pressure, and geometric
properties of different deformation sources using a Leven-
berg-Marquardt nonlinear optimization algorithm [Press etal., 1986]. The Levenberg-Marquardt algorithm is a steepestdecent derivative-based method that seeks to avoid localminima through manipulation of the step in model param-eter values when the model fit does not improve oversuccessive iterations. Multiple sources can be consideredby simply increasing the solution space linearly with thenumber of sources. Inversions for an elastic half-spaceconsidering a point source [Mogi, 1958] yield a reasonablesolution, but examples from the 1993–1995 inflation showthat the elliptical pattern of the deformation requires anasymmetric source (Figures 2 and 4). Therefore we willconcentrate our inversions on spheroidal [Yang et al., 1988]and tensile dislocations [Okada, 1985]. Either a spheroidalor a subhorizontal tensile source can reasonably fit anelliptical deformation pattern. We found the spheroidalsource produced a better fit to the shape of the observeddeformation. A horizontal tensile source has a steeper-sided,broader-range displacement pattern compared to the moretapered pattern found for the spheroidal source. When weconsider 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 c2 for the Okada,Mogi, and Yang solutions at 2.9, 2.5, and 2.4, respectively.Therefore we will consider modeling the observed infla-tionary deformation with a spheroidal source.[20] For each unwrapped interferogram, the standard
deviation in the multilook phase (where the number oflooks refers to the product of the number of pixels averagedin the parallel and cross-track directions) is calculated basedon the single-pixel correlation coefficient using the Cramer-Rao formula
sf ¼ sqrt 1� g2� �
= g sqrt Nð Þ½
where sf is the standard deviation of the phase (in radians),g is the single-look correlation, and N is the total number oflooks [Sorenson, 1980; Rosen et al., 2000]. Because it isbased on the correlation in the single-look image, thisapproach is independent of the effects that filtering andsmoothing have on reducing the phase variations.[21] The spheroidal pressure source [Yang et al., 1988] is
a prolate spheroid (spherical to cigar shaped, two smalleraxes of equal length) with arbitrary plunge and azimuth.Inverting for this source requires solving for eight param-eters: x, y, z define the spheroid center coordinates, �P isthe excess pressure at the spheroid surface, a is the semi-major axis, and c is the length from the spheroid center tothe focus, f and q are the azimuth and plunge of the a axis,respectively, plus an arbitrary constant shift of the differ-ential LOS displacements for each interferogram.[22] To model fault slip or fault tensile dislocations, we
use the analytical expressions of Okada [1985]. Inversionfor a dislocation involves estimating up to 10 parameters: x,y, z, define the location of the fault, L and W are the lengthand width, respectively, d and f are the dip and strike, andUi represents the three fault slip components (strike slip, dipslip, and tensile).[23] Recent studies have shown that a volcano’s top-
ography should have a significant effect both on thedisplacement amplitude and the shape of the surface defor-mation [Williams and Wadge, 1998, 2000; Cayol and
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Cornet, 1998; Folch et al., 2000]. In the analysis ofWilliams and Wadge [1998], they showed that a finiteelement model for volcano deformation that incorporatedthe topography of Mt. Etna had a significant effect on theexpected surface deformation. For a given source depth(below sea level) and pressure change, the deformationdecreases with increasing elevation compared to a half-space. They attributed this to a simple geometric argumentthat a point at higher elevation has a greater radial distanceto the source, thus reducing the amplitude of the displace-ments at the elevated point relative to what it would havebeen at sea level. The application of the approach ofWilliams and Wadge [1998] is straightforward; at each datapoint, the effective source depth to that point is the half-space depth plus the elevation of that point. Thus for a 3-kmdepth source a point at sea level ‘‘sees’’ a source at 3-kmdepth, whereas a point at 3-km elevation is deformed as ifthe source were at 6-km depth. The study of Williams andWadge [2000] applies a perturbation approach to moreaccurately correct for topographic effects compared to theapproach of Williams and Wadge [1998]. Its main limitationis the extensive development that is required to apply it tothe spheroidal and dislocation sources considered in thisanalysis, which is beyond the scope of this study. Thereforewe apply the topographic correction method of Williamsand Wadge [1998].
4.1. Ascending Interferograms
[24] Five interferograms have very similar shapes to theirdeformation patterns (Figures 2 and 4b). Each of theseinterferograms has either the 1993/07/04 or 1993/08/08ERS-1 SAR image as a reference image. This reflects thelimited number of interferograms that are possible given the35-day repeat of the ERS orbit, the requirement of smallperpendicular baselines, and for Etna the usefulness of SARdata acquired from late April to November, when the higherelevations are free of snow cover. Each of these 1993images can form two interferograms with images acquiredin the spring and then later in the summer or fall of 1995.The similarity of these interferograms formed with inde-pendent images, and the increase in LOS displacementamplitude of the interferograms from the spring to sum-mer/fall 1995, are consistent with the fringes being mostlydue to deformation and is the basis for the conclusionsobtained by Lanari et al. [1998].
4.2. Descending Interferograms
[25] Interferograms from descending satellite images(Figures 3 and 4a) show a significant number of fringesthat define a relatively simple pattern that does not corre-spond with the topography of Etna. The same pattern isfound in interferograms from independent images and fromtwo adjacent satellite tracks (ERS tracks 222 and 494). Theinterferogram 1993/06/06–1995/09/12 spans a similar timeperiod as the longest of the four ascending interferogramsmodeled above. However, the uplift pattern is not as simpleand has an additional lobe centered beneath the NE flank ofEtna. The other descending interferograms for the 1993–1995 time period also share features with the fringe patternand displacement amplitude found in the 1993/06/06–1995/09/12 interferogram, though with lesser displacementamplitude and/or higher atmospheric noise.
[26] The interferograms from track 494 are noisier andhave greater areas of decorrelation over the eastern slopes ofEtna due to layover of the near-range SAR data where theincidence angle is smaller (and lower angle slopes are laidover). In addition, these interferograms have more small-scale atmospheric perturbations. Despite the lower overallquality of these interferograms, they exhibit a similar lobeof positive range displacement over the NE flank of Etna asobserved in the interferograms from track 222.
4.3. Joint Inversions
[27] There are two questions we wish to address: (1) Whyare ascending and descending interferograms similar inpattern and displacement amplitude to each other withintheir respective groups? (2) Why do 2-year ascending anddescending interferograms have such different patternsbetween them?[28] Our answer to the first question is that the ascending
and descending interferograms are dominated by surfacedeformation, the argument we made in section 3. Theanswer to the second question can be explained by consid-ering a more complex explanation for the deformationsources. For modeling purposes, we will consider theascending and descending pair of interferograms (1993/08/08–1995/10/10, and 1993/06/06–1995/09/12), shownin Figure 4.[29] An interferogram represents the projection of the
surface displacements onto different satellite look vectors,therefore simple inflationary sources are expected to looksomewhat different for ascending and descending interfero-grams with maxima of the same magnitude, but shiftedtoward their respective radar look directions. In the case ofthe aforementioned ascending and descending InSAR data,the large displacement amplitude that is observed in thedescending interferogram beneath the NE flank does nothave a corresponding signature of similar magnitude on theascending interferogram (Figure 4).[30] One possible solution to this problem, which mainly
affects the east flank, is presented by considering other thansimple volcano inflationary sources. Indeed, there is evi-dence that the deformation of Mt. Etna from 1993 to 1995was the sum of several sources, not all due to magmamovement within the volcano. In addition to the effect of amedium depth source located at 3–6 km below sea level,there is evidence for brittle deformation of importantstructures on Etna’s eastern flank, such as the Pernicanafault [Puglisi et al., 2001]. The displacements of GPS pointson Etna from 1993 to 1996 [Puglisi et al., 2001; A.Bonforte and G. Puglisi, Ground deformation studies onMt. Etna from 1994 to 1995 using static GPS measure-ments, submitted to Journal of Geophysical Research,2002] confirm the eastward movement of this flank, ashypothesized in models that interpret it as a sector collapsestructure [Lo Giudice and Rasa, 1992; Borgia et al., 1992].A general agreement exists in the definitions of the northern(Pernicana fault), northwestern and western (northeast andsouthern 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; Rasa et al.,1996; Borgia et al., 2000; Froger et al., 2001]. The most
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controversial point is the location and orientation of thedecollement allowing eastward movement of the east flank[Lo Giudice and Rasa, 1992; Borgia et al., 1992, 2000;Rasa et al., 1996; Firth et al., 1996]. InSAR measurementsprovided conclusive evidence of fault slip on the TM faultsystem along the southern boundary of the sliding eastflank, as well as anticline growth beneath the adjacentportion of the southern flank immediately to the southwestof the fault system [Borgia et al., 2000; Froger et al., 2001].[31] Unlike an inflationary volcanic source, a subhorizon-
tal eastward thrusting fault (flat or dipping shallowly backtoward the center of the volcano) would have greaterdisplacement amplitude on the descending interferogramsthan the ascending interferograms. This is due, in part, to acancellation of the horizontal and vertical displacements forthe ascending InSAR data and summation for the descend-ing data.[32] To test this, we have jointly inverted the 1993/08/
08–1995/10/10 and 1993/06/06–1995/09/12 interfero-grams to solve for one spheroidal pressure source and acombination of two fault dislocation sources in an elastichalf-space corrected for the distance-related effects of top-ography [Williams and Wadge, 1998]. We solve for the dip-slip and strike-slip components on a shallowly dippingdecollement and a near-vertical fault. Table 2 gives thevalues for these solutions. For the horizontal decollement,the orientation and slip component (slip to the east) wereconstrained. Otherwise, all parameters were estimated. Theshape of the deformation pattern over the eastern flank ofEtna constrained the fault dimensions reasonably well.Figure 8 shows the results for this inversion, with the sourcegeometry 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 asignificant reduction in error. For example, given the morethan 60,000 points in the interferogram a simple F test[Stein and Gordon, 1984] yields F > 4000 relative to thespheroidal source. For the increase in model parameters to
be significant, the value of F must only be >1 for such alarge number of degrees of freedom (at 99% significance Fapproaches 1 as the number of degrees of freedom in bothmodels becomes �1). While the value of F we find is verylarge, the highly correlated nature of InSAR data is notaccounted for in our analysis. InSAR data correlation hasbeen recently addressed by Jonsson et al. [2001]. If wefollowed the approach of Jonsson et al. [2001] and reducedthe number of data by 2 orders of magnitude, we would stillexpect a significant value for F. This is due to the largenumber of points retained and the data reduction algorithmused, which keeps more points in the areas of higher fringerates: the same areas that most affect the differences inmodel fit.
5. Discussion
[33] This study demonstrates both the strengths andpossible limitations of InSAR for measuring and monitoringvolcano deformation. InSAR provides a detailed image ofsurface deformation over large areas. Active volcanoes,such as Etna, have large areas that are free of vegetationand provide high correlation over large time separationsbetween the SAR images. However, as shown in otherInSAR studies of Etna and in this study, there can besignificant problems due to atmospheric phase perturba-tions, and the procedures to overcome this have not beenwell assessed for Etna. Our attempts to model troposphericeffects for individual interferometric pairs based on themeteorological data from Trapani suggested that for thedates considered, the tropospheric correction did not sig-nificantly change the interferogram displacement ampli-tudes (Figure 7).[34] Instead, several observations support our contention
that the observed fringe patterns during this study periodwere largely due to surface deformation.1. Interferograms spanning the quiescent period from
1993 to 1995 consistently show that Mt. Etna volcanoinflated (Figures 2–4).2. All the observed 2-year interferograms show similarly
shaped fringe patterns with similar LOS displacementamplitudes among ascending and descending tracks. Theobserved deformation pattern is maintained across inter-ferograms formed from summer 1993 with April and May1995 images compared with those formed into the latesummer and fall of 1995 when the apparent seasonal effectsattributed by Beauducel et al. [2000] should be significant.3. The observed interferogram fringe patterns are con-
sistent with the projection of the three-dimensional surfacedisplacements for a volcanic source onto the radar LOS, afeature not expected for a topographically correlatedtropospheric effect, which should more strictly conform totopography.
[35] Joint inversion of ascending and descending inter-ferograms provides an integrated interpretation of thedeformation. By adding a simple pair of dislocations repre-senting subvertical and subhorizontal components of theeastern sector collapse, we are able to fit most of theobserved deformation (Figures 8 and 9).[36] This model must be evaluated in terms of its limi-
tations and assumptions. We leave aside an in-depth dis-cussion on the limitation of treating the upper crust as a
Table 2. Source Parameters for the Solution Shown in Figure 9a
ParameterSpheroidalCavity
HorizontalDislocation
VerticalDislocation
X 1.8 ± 0.0 7.6 ± 0.1 2.6 ± 0.0y �1.7 ± 0.0 1.3 ± 0.1 �0.4 ± 0.1d 4.8 ± 0.0 2.9 ± 0.1 0.5 ± 0.1a or L 4.1 ± 0.1 4.9 ± 0.3 3.5 ± 0.1b or W 2.0 ± 0.1 5.2 ± 0.3 4.4 ± 0.2d �19 ± 0.5 0b 88 ± 0.0f 12 ± 0.0 180b 9.9 ± 0.0U1 . . . 0b 0.50 ± 0.03U2 . . . 0.21 ± 0.02 0.38 ± 0.02P or U3 4.3 ± 0.4 0b �0.22 ± 0.02aSource (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 thecenter 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, anddepth d refer to the ‘‘upper right’’ corner in the convention of Okada[1985]. The spheroid semimajor (a) and semiminor (b) axes, dislocationlength (L), width (W ), and location parameters (x, y, d ) are in kilometers.The plunge/dip (d) and azimuth/strike (f) are in degrees. The strike, dip,and tensile slip (U1 – 3) are in meters. The spheroid pressure change (P) is inmegapascals. The constant offsets that were estimated for the ascending anddescending InSAR data were �0.022 and �0.003 m, respectively.
bParameter value not estimated by inversion.
LUNDGREN ET AL.: VOLCANO SAR INTERFEROMETRY ON MT. ETNAVOLCANO ECV 4 - 11
Figure 8. Joint inversion results for the topographically corrected elastic half-space model. (a) Data.Top, descending interferogram range displacements for 1993/06/06–1995/09/12. Bottom, ascendinginterferogram range displacements for 1993/08/08–1995/10/10. (b) Residual. (c) Model. (d) Profilesthrough the data (solid) and model (dashed). Blue north–south. Red east–west. Top profiles correspondto the descending interferogram. Bottom profiles correspond to the ascending interferogram.
ECV 4 - 12 LUNDGREN ET AL.: VOLCANO SAR INTERFEROMETRY ON MT. ETNAVOLCANO
homogeneous, elastic half-space. A volcano poses a partic-ularly difficult problem given the lack of constraint on boththe geometry and dynamics of its source. A more immediatelimitation with our solution is the effect of topography. Thelargest misfit in the modeling occurs over the higherelevations of Etna, where fairly detailed deformation pat-terns (apparent near-surface rift motion beneath the southrift zone and the detail in the lobes of positive rangedisplacement over the NW summit region, Figure 8) arenot well modeled with the source lying some 3 km beneaththe summit. How this limitation in our modeling affects theinversion solution is not clear and would require a moresophisticated approach incorporating three-dimensionalnumerical models. It would be expected that the dislocation
source directly beneath the summit would be the mostaffected. This might explain, for example, the contraction(negative U3 component) rather than the expansion wemight have expected given the motion of the horizontaldislocation beneath the eastern flank. However, the strongleft-lateral strike-slip component found for this feature isrequired by the model to contribute to the strong positiverange displacements to the SW and NE of the summit. Themodel’s misfit to the data reflects the limitations of consid-ering a small number of very simple sources and the likelyneed of placing some of the subvertical dislocation withinthe volcano edifice as suggested from microgravity data[Budetta et al., 1999].[37] Integration of petrological, geological, and geophys-
ical data has recently been applied to model the buoyancy ofMt. Etna magma (R. A. Corsaro and M. Pompilio, Buoy-ancy of magmas at Mt. Etna, submitted to Terra Nova,2002). This study shows that this magma has neutralbuoyancy above 15 km depth up to sea level. Consequently,rising magma tends to stop in small reservoirs in the uppercrust, where cooling/crystallization processes producemagma differentiation until positive buoyancy is attained,allowing the ascent to resume. Seismic tomography resultsconstrain the plumbing system, showing that no largemagma chamber exists below Mt. Etna, while several smallliquid-filled volumes are identified [Laigle et al., 2000].Among the latter, the westernmost has a position, dimen-sions, and orientation compatible with the spheroidal sourceresulting from the InSAR inversion.[38] 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 individualstructures. Clearly, highly active volcanoes require highertemporal sampling to detect transient deformation and caremust be taken when modeling or interpreting interferograms(or other deformation measurements) that span time inter-vals containing significant volcanic activity.[39] Notwithstanding these limitations, the joint inversion
solution quantifies a previously poorly understood defor-mation process on Etna. Our findings are similar to thesouth flank sliding of Kilauea volcano [Owen et al., 1995,2000]. The amplitude of deformation over the NE flank ofEtna observed on the descending interferograms from 1993to 1995 and during the summer of 1995 is not observed ondescending interferograms during late 1995–1996 follow-ing the resumption of eruptive activity (Figure 6). Thissuggests that the inflation of the magma chamber and themotion of the eastern flank were related, with the increase inpressure within the chamber acting as a force on the easternflank of the volcano. This effect was first suggested byBorgia et al. [2000] from InSAR observations and supportsthe mechanism proposed by Puglisi et al. [2001] to explainthe GPS data in relation to the July 1994 seismicity.[40] We can place an upper bound on the expected radial
displacement of the spheroidal magma chamber’s surface byconsidering a spherical cavity with radius and pressurechange equal to those of the spheroidal cavity’s minor axisand pressure change, respectively [Delaney and McTigue,1994]. Using an elastic shear modulus value for basalt of 30GPa, we would expect displacement of the cavity walls onthe order of 10 cm. This is a similar order of magnitude as
Figure 9. Three-dimensional views of the source modelcorresponding to the inversion shown in Figure 8. Top, mapview of the shaded, transparent topography with the sourcesvisible. In this view, the subvertical dislocation appears as athick line above the spheroidal source. To the east lies thesubhorizontal decollement dislocation. Bottom, horizontalview from the south (S10�W). Topography of Etna is shownto scale. Below the subvertical dislocation and thespheroidal source are visible.
LUNDGREN ET AL.: VOLCANO SAR INTERFEROMETRY ON MT. ETNAVOLCANO ECV 4 - 13
the calculated slip on the basal decollement. The similarityin magnitude of the magma chamber radial expansion andthe slip on the decollement suggest that the chamberexpansion triggered slip of the flank system. The triggeredmotion of a portion of the volcano due to magma chamberinflation has been recognized using both InSAR [Borgia etal., 2000] and land-based geodesy [Puglisi et al., 2001].This study models, for the first time, the coupling betweenthe magma chamber inflation and motion of a large portionof a volcano.
6. Conclusions
[41] SAR interferograms show that during the 1993–1995 quiescent period, Mt. Etna inflated. Interferogramsspanning 1993–1995 show a similar pattern. The simpleelliptical shape of the deformation pattern and similarityamong interferograms with independent images indicatethat this is true surface deformation related to deep-seatedprocesses and not an atmospheric artifact. The ellipticalpattern of the ascending interferograms spanning 1993–1995 and the cross-sectional shape of the deformation arebest fit by a spheroidal cavity centered at a depth of �5 kmwith a pressure change of �4 MPa (Table 2).[42] The dissimilar deformation patterns computed from
ascending and descending ERS tracks can be explainedthrough a simple combination of the inflating spheroidalpressure source, motion of the NE flank of Etna along thebasal decollement, and a near-vertical dislocation beneaththe summit. By jointly inverting the data from two differentlook directions, we overcome the limitation of one-compo-nent range displacements while maintaining InSAR’s densespatial coverage. This shows the importance of combiningascending and descending interferograms.[43] The deformation magnitude increased for both the
descending and ascending interferograms from spring tolate summer/fall of 1995 prior to the renewed eruptiveactivity in 1995. This shows the potential of InSAR as animportant tool for volcano hazard forecasting and mitiga-tion, if more frequent measurements were available to betterquantify this process. The simultaneous inflation of themagma chamber and slip of the east flank show theimportance of understanding the entire system for volcanohazard assessment.
[44] Acknowledgments. We thank the European Space Agency forthe raw ERS SAR data, part of which was supplied under ERS AO3.359. F.Crampe, G. Peltzer, and P. Rosen provided important insight regardingROI_PAC processing issues. C. Delacourt kindly provided meteorologicaldata from Trapani. We thank G. Mattioli, F. Sigmundsson, and T. Dixon fortheir insightful reviews. Part of this work was conducted at the JetPropulsion Laboratory, California Institute of Technology, under contractwith the National Aeronautics and Space Administration.
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�����������������������P. Berardino, G. Fornaro, R. Lanari, E. Sansosti, and M. Tesauro, Istituto
per il Rilevamento Elettromagnetico dell’Ambiente (IREA-CNR), ViaDiocleziano, 328, I-80124 Naples, Italy.M. Coltelli and G. Puglisi, Istituto Nazionale di Geofisica e Vulcanologia,
Piazza Roma, 2, I-95123 Catania, Italy.P. Lundgren, Jet Propulsion Laboratory, California Institute of Technol-
ogy, 4800 Oak Grove Drive, MS 300-233, Pasadena, CA 91109-8099,USA. ([email protected])
LUNDGREN ET AL.: VOLCANO SAR INTERFEROMETRY ON MT. ETNAVOLCANO ECV 4 - 15
