static stress changes induced by the magmatic intrusions during the 2002–2003 etna eruption

Static stress changes induced by the magmatic intrusions

during the 2002–2003 Etna eruption

Gilda Currenti,1 Ciro Del Negro,1 Gaetana Ganci,1,2 and Charles A. Williams3,4

Received 27 July 2007; revised 8 August 2008; accepted 10 September 2008; published 31 October 2008.

[1] The shallow intrusive processes that occurred during 2002–2003 Etna eruption, aswell as the complex interaction between the magma intrusive events and the tectonicresponse of the volcano’s eastern flank, are investigated with numerical deformationmodeling and the estimation of changes in the static Coulomb stress. Grounddeformation and volcanologic evidence clearly indicate a composite mechanism ofintrusion on both the southern and northeastern flanks of the volcano. Geodetic datainversions have been based on a homogeneous elastic half-space model, althoughgeological data and seismic tomography indicate that Mt. Etna is elasticallyinhomogeneous and that rigidity layering and heterogeneities are likely to affect themagnitude and pattern of the deformation field. To account for topographic effects, as wellas a complicated distribution of material properties, we use the finite element method(FEM) to provide a more realistic model. The presence of medium heterogeneitystrongly affects the amplitudes of the static stress changes. Seismicity matches wellthe areas of positive increase in the static stress caused by the intrusive events along thesouthern and northeastern flanks. The changes in the state of stress generated by thesouthern dike produce an extensional stress field that favors magma propagation alongthe north-east Rift. The highest seismic releases were associated with the activation oftwo fault systems, the Timpe Fault System and the Pernicana Fault. The static stresschanges resolved onto these faults indicate that the magma intrusions on the southernand northeastern flanks encouraged these seismogenic structures to slip.

Citation: Currenti, G., C. Del Negro, G. Ganci, and C. A. Williams (2008), Static stress changes induced by the magmatic intrusions

during the 2002–2003 Etna eruption, J. Geophys. Res., 113, B10206, doi:10.1029/2007JB005301.

1. Introduction

[2] The 2002–2003 Etna eruption was a highly complexeruptive event, as it simultaneously consisted of lateralactivity on the north-east flank and eccentric activity onthe south flank [Neri et al., 2005; Allard et al., 2006]. Themorphological changes caused by this eruption were sub-stantial. The most spectacular product was the large pyro-clastic cone that grew at about 2800-m elevation on thesouth flank. Smaller (but nonetheless impressive) cones andspatter ramparts were built by eruptive activity on the north-east flank. The eruption lasted 9 days on the north-eastflank and 94 days on the south flank, delivering about 30 �106 m3 of lava (more than two-thirds of which was emplacedon the South flank) and a further 20–25 � 106 m3 of tephra[Clocchiatti et al., 2004; Andronico et al., 2005].

[3] In terms of volcano monitoring, this was the bestdocumented eruption of Etna thus far. Dense networks ofseismic and geodetic monitoring devices produced a steadyflow of data throughout the eruption. During the night of26–27 October 2002, an intense seismic sequence heraldedand accompanied the opening of two eruptive fracturesystems on both the north-east and south flanks of Etnavolcano (Figure 1). A total of 874 Md � 1 earthquakes wererecorded from the beginning of the seismic swarm until theend of the eruption. The swarm decayed over about 2 weeksand most of the seismic energy was released during the first4 days (470 events of a total of 874, Mmax = 4.4). Thespace-time pattern of the epicenters showed an almoststationary distribution in the central part of the volcano on26 October during the first hours of the swarm and a veryclear migration toward the north-east rift early in themorning on 27 October [Barberi et al., 2004]. At the sametime, a set of extensional fractures trending north-south(horizontal displacements between 10 and 50 cm) formed atthe base of the north-east crater [Branca et al., 2003]. In thefollowing hours powerful lava fountains and ash columnsoccurred on the south flank, along a north-south fracturefield, and an eruptive fracture system opened on thenortheastern flank, nearly to the north-east rift [Andronicoet al., 2005]. The eruption was followed by eastern flankmovement, surface ruptures, and seismic swarms. After a

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B10206, doi:10.1029/2007JB005301, 2008

1Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania,Catania, Italy.

2Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi,Universita di Catania, Catania, Italy.

3Department of Earth and Environmental Sciences, Rensselaer Poly-technic Institute, Troy, New York, USA.

4Now at GNS Science, Lower Hutt, New Zealand.

Copyright 2008 by the American Geophysical Union.0148-0227/08/2007JB005301$09.00

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decrease in the daily earthquake rate, a sharp resumptiondue to the activation of new seismically active volumes inthe south–east flank was observed on 29 October. Fractur-ing affected some structural alignments on the southeastflank, causing severe damage in Santa Venerina village. Theseismicity was mainly related to the magma intrusion alongthe north-east rift, although the highest seismic releaseswere associated with the activation of two fault systems:(1) the Pernicana Fault, which is a local volcanic edificefeature, and (2) the Timpe Fault System, which representsthe inland extension of the Malta Escarpment regional fault.The majority of earthquakes (about 80%) occurred at depthsranging between �2 and 2 km with respect to sea level[Barberi et al., 2004]. Seismic analysis revealed a complexkinematic response of the eastern flank dominated by faststress propagation and reorientation [Barberi et al., 2004].[4] In concomitance with the seismic crisis, during a

48-h period encompassing the beginning of the eruption,marked ground deformation was recorded through GPS andpermanent tilt stations. GPS displacement vectors indicatedthe occurrence of a wide ground deformation field at thescale of the entire volcanic edifice displaying a clear patternalmost symmetrical to a NE-SW direction [Aloisi et al.,2003]. All tilt stations on the northern and western flanksdetected changes of tens of microradians (50–60 mrad),while minor variations (a few microradians 10–15 mrad)characterized the responses of the southern stations [Aloisi etal., 2003]. Although the deformation recorded by the tilt-meters largely culminated by local midnight on 26 October,a number of stations recorded tilt changes starting at diversetimes and showing different durations. Aloisi et al. [2003]determined that the geodetic observations were consistentwith a response of the edifice to a composite mechanism ofintrusion on both the southern and northeastern flanks of thevolcano. The inversion of tilt components and horizontaland vertical GPS changes, recorded over the time interval26–27 October spanning the eruption onset, required avertically rising magma intrusion in the southern flank

and a lateral intrusion propagating along the northeasternsector. Aloisi et al. [2003] thus performed an inversion withtwo tensile sources, using an analytical elastic half-spacedislocation model [Okada, 1992]. Patane et al. [2005]reviewed the GPS data and integrated them with seismicdata to better constrain the size, shape and evolution of thetwo intrusive dike-like bodies.[5] All inversions were based on a homogeneous elastic

half-space model [Aloisi et al., 2003; Patane et al., 2005],although geological data and seismic tomography indicatethat Mt. Etna is elastically inhomogeneous [Chiarabba etal., 2000; Patane et al., 2006], and that layering and lateralinhomogeneities in the elastic rigidity and heterogeneitiesare likely to affect the magnitude and pattern of thedeformation field [Zhao et al., 2004]. Indeed, despite theclear sequence of volcano-tectonic events and the quantityof data collected, the interaction between magmatic eventsand tectonic processes responsible for the kinematics of theseismogenic structures occurring during the 2002–2003eruption is still under debate. The large recorded deforma-tion pattern of the east flank occurred in response to theintrusive event, which was also responsible for the reacti-vation of the Pernicana Fault. Stress changes associatedwith dike-like intrusions are one of the basic mechanismsresponsible for the kinematics of the east flank [Neri et al.,2003].[6] Walter et al. [2005] investigated the interaction

between magmatic events (eruptions and intrusions) andsudden flank displacements. They used the three-dimensionalboundary element program Poly3D [Thomas, 1993] forsimulating the volcano-tectonic events and calculatingchanges in the static stress field within a homogeneous andisotropic media. The 2002–2003 events were interpreted asthe result of interrelated processes consisting of the pre-eruptive intrusion of magma and the inflation of the volcano,which induced movements of the volcano’s east flank,facilitated the eruption, and promoted the slip of a muchlarger part of the eastern and southeastern flanks. However,some factors were not considered in their analysis: (1) thedike source parameters were not constrained using evidencefrom geophysical observations; (2) the stress field wascomputed without considering the ground deformationassociated with the assumed volcanic sources; and (3) thenumerical model included only the Mt. Etna topographydisregarding the mechanical heterogeneities due to thermalstructure, a hydrothermally altered volcanic core or amechanically stiff basement.[7] We use the finite element method (FEM) to overcome

these simplifications and to provide a more realistic overallmodel, which considers topographic effects as well ascomplicated distributions of material properties. Computa-tions of the ground deformation and stress changes deter-mined by the geodetic data inversion [Aloisi et al., 2003,2006] were performed to investigate the interaction betweenthe dike intrusions and the fault systems that were reactivatedlater. From this point of view, the 2002–2003 Etna eruptionoffers a good case study to gain insight into the complexinteractions between magma intrusive events and tectonicresponses because of (1) the high-quality ground deformationdata, which have been widely used to constrain the size,shape and evolution of the intrusive sources [Aloisi et al.,2003; Patane et al., 2005] and (2) the good characterization

Figure 1. Schematic map showing the area affected by the2002–2003 Etna eruption. Black solid lines trace the mainfaults on the volcano edifice. PFS, Pernicana Fault System;TFS, Timpe Fault System [after Walter et al., 2005].

B10206 CURRENTI ET AL.: STATIC STRESS CHANGES ON MT. ETNA

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of the variety of seismic signals, which have providedaccurate three-dimensional hypocentral distributions of therecorded seismicity in the period spanning the intrusion[Barberi et al., 2004].

2. Numerical Modeling

[8] A fully three-dimensional finite element simulation isperformed to study in a more realistic way the grounddeformation observed on Mt. Etna during the onset of the2002–2003 eruption. We investigate how the topographyand the complex medium heterogeneity can affect theresults. The modeling is conducted using the Lithomop

finite element code [Williams and Wadge, 2000]. Thecomputational domain is a volume extending 100 � 100 �50 km to avoid artifacts in the numerical solution due to theproximity of the external boundaries. For boundary con-ditions, the displacements on the outermost lateral bound-aries and on the bottom are fixed to zero, while theboundary at the ground surface, generated using a digitalelevation model of Mt. Etna from the 90 m Shuttle RadarTopography Mission (SRTM) data and a bathymetry modelfrom the GEBCO database http://www.gebco.net/), is free.Using LaGriT, a three-dimensional grid generation codefrom Los Alamos National Laboratory http://lagrit.lanl.gov), the computational domain was meshed into 448474

Figure 2. (top) Young’s modulus distribution derived from seismic tomography investigation [afterChiarabba et al., 2000]. (bottom) Empirical relations between seismic p-wave propagation velocities VP

and density values (solid lines [after Christensen and Mooney, 1995; Gardener et al., 1974]). Apolynomial relationship was derived by fitting the empirical relations (dashed line).


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isoparametric, and arbitrarily distorted tetrahedral elementsconnected by 78163 nodes. The mesh resolution is about100 m around the source dikes, about 500 m in the 20 �20 km area around the summit craters and decreases to 2 kmin the far field. The source geometry and the dislocationparameters of the intrusive dikes are based on the results ofgeodetic data inversion [Aloisi et al., 2003]. To simulate thetwo dike intrusions we assigned dislocation boundary con-ditions implemented using ‘‘split nodes’’ [Melosh andRaefsky, 1981] to the nodes lying on the dike surfaces.[9] The elastic parameters were estimated using VP values

inferred from seismic tomography [Chiarabba et al., 2000].The subsurface elastic heterogeneities of the medium wereincluded in the numerical model by assigning to eachelement in the meshed domain the value of the Young’selastic modulus interpolated at the element location. In thisway, smooth elastic medium heterogeneities, instead ofsharp boundary layers, may be included that are likely abetter approximation for many geological settings. A Pois-son’s ratio of 0.25 is assumed which is a reasonable

approximation for Mt. Etna. Under this assumption, theYoung’s modulus, E, is related to the medium’s density rand seismic wave velocity VP through the followingrelation:

E ¼ 5

6rV 2

P ð1Þ

When estimating density values, there exist severalempirical laws in literature that relate seismic wavevelocities and density values on the basis of subsurfacegeometry of geologic units and of chemical composition ofthe Earth’s crust [Brocher, 2005]. We have derived a densitymodel of the crust by using four density-velocity empiricalrelationships [Gardener et al., 1974; Christensen andMooney, 1995; Brocher, 2005]. These laws are interpolatedby means of a third-order polynomial function that yieldsthe following relationship:

r ¼ 1:2861þ 0:5498Vp � 0:0930V 2p þ 0:007V 3

p ð2Þ

where r is the medium density. Using these relationships,the range of density values was estimated to range from2000 to 3200 kg/m3 as the depth increases. These densityvalues are in agreement with the crustal structure of Mt.Etna inferred from compositional studies [Corsaro andPompilio, 2003]. The elastic Young’s modulus varies from11.5 GPa at shallower depth to 150 GPa at greater depth(Figure 2).The high variability of the elastic materialproperties is expected to affect the ground deformationand therefore the stress field. A good approach to estimatehow medium heterogeneity and topography may affect thesolutions is to evaluate each one separately and compare theresults. Therefore we conducted four numerical simulationsin which we considered (1) a homogeneous elastic mediumwith a flat upper surface (HomFlat), (2) a homogeneouselastic medium with the real topography of Mt. Etna(HomTopo), (3) an elastically heterogeneous medium with aflat upper surface (HetFlat), and (4) an elastic heterogeneousmedium with the real topography (HetTopo).

3. Ground Deformation

[10] Discrepancies with respect to the analytical resultsare expected on ground deformation values predicted by thenumerical models because of the medium heterogeneity andthe irregular topography of Mt. Etna [Currenti et al., 2007].Indeed, the volcano edifice is rather asymmetric having aprominent mass deficit in the eastern sector with respect tothe western sector in the region of Valle del Bove. Firstly,we evaluate the accuracy of the numerical solution bycomparing the HomFlat model with the analytical solutionof a homogeneous half-space model [Okada, 1992] inwhich a Young’s modulus of 62.5 GPa is assumed. Thedomain was proven to be big enough to avoid numericalartifacts in the solution due to the boundary conditionsapplied over a finite domain. A good match between theanalytical and the numerical solution is obtained in theregion of interest (Figure 3). To quantify the accuracy ofthe numerical solutions, a normalized mean misfit function

Figure 3. Comparison between analytical (gray scale) andnumerical (dashed line) solution for a homogeneous half-space model.


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with respect to the analytical solution is defined as[Williams and Wadge, 2000; Currenti et al., 2008]:

dm Uð Þ ¼XN

i¼1

UFEi � UAN

i

�� =XN

i¼1

UANi

�� ð3Þ

where UiFE is the computed deformation at the ith node for

the numerical model and UiAN is the corresponding resultfor the analytical model. The misfit function values dmcomputed for each deformation component m = x, y, z are0.12, 0.14, and 0.05, respectively.[11] The deformations for the HomTopo, HetFlat and

HetTopo models are computed and the total displacementsexpected at the ground surface are evaluated to estimate thediscrepancies among the four considered models (Figure 4).All three of the more complicated models (HomTopo,HetFlat and HetTopo) display surface displacement patternsdifferent from those of the simple model based on theassumption of a homogeneous half-space medium. Thediscrepancies among the models are mainly restricted tothe volcano summit area because of the accentuated topo-graphy. The homogeneous models (HomFlat and Hom-Topo) do not show significant differences compared withheterogeneous ones (HetFlat and HetTopo). Therefore whenconsidering a dislocation with a constant slip vector on itssurface, the effect of material heterogeneity for a Poissonian

medium is negligible on the resulting ground deformation.Above the magmatic intrusion centerline, the model gen-erates a deflation in the vertical component, which isdistinctive of the tensile component due to the magmaticintrusion (Figure 5). Since the magmatic source is quiteshallow, the extent of this deflation is a few hundred meters.Thanks to the high resolution of our mesh (100 m aroundthe magmatic intrusion), we are also able to capture thisfeature.[12] To better evaluate the perturbations with respect to

the analytical results, we calculated the displacement field atthe locations of continuously running GPS stations. In ourmeshed domain we introduced nodes at the positions of theGPS stations to avoid inaccuracies that might be introducedby interpolating our numerically computed displacements tothese points. Figure 6 shows the horizontal component ofGPS data together with results achieved by the HomFlat,HomTopo, HetFlat, and HetTopo numerical models. Signif-icant differences with respect to the HomFlat model areobtained at the summit stations (EPDN, ETDF, and EPLU).Nevertheless, the HetTopo numerical model is not able togive an explanation for the higher displacement observed onthe summit area. No comparison can be made at EPLU,since no data are available at this station. The GPS datafrom EPDN and ETDF stations were disregarded in theanalytical inversion because their proximity to the surface

Figure 4. Total displacement field at the ground surface due to the south and north-east intrusions(black dashed lines) for the HomFlat (a), HomTopo (b), HetFlat (c), and HetTopo (d) models.


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fracture system makes the near field effect predominant[Aloisi et al., 2003]. Since our numerical models assume thesource parameters determined by the geodetic data inver-sion, a match with these data is not expected. Indeed, theanalytical model itself [Aloisi et al., 2003] does not work atthese stations. Discrepancies of at most a few centimetersamong the numerical models are observed at the otherstations (Figure 6). In fact, almost all the GPS stations arelocated far enough from the summit so that they are notsignificantly affected by the topography.

4. Stress Changes

[13] The temporal and spatial pattern of the seismicactivity associated with the 2002–2003 Etna eruption[Barberi et al., 2004; Acocella et al., 2003] can be regardedin terms of stress transfer caused by the magmatic intrusiononto active north-east rift zones and faults [Feuillet et al.,2006]. From early morning on 27 October, the PernicanaFault began moving and surface fractures propagated sea-ward [Neri et al., 2003]. To better understand the interac-tions between tectonic and intrusive processes, we analyzedthe stress changes computed by the numerical models alongthe north-east rift zones, the Pernicana Fault and the TimpeFault System. We computed the horizontal normal stresschanges to study the stress transferred onto the north-eastrift dike, while we computed the Coulomb stress changes toinvestigate the role magmatic processes play in the volca-no’s eastern flank movement. To comprehend how the dikeintrusions could have promoted the Pernicana Fault and

Timpe Fault System to slip we computed the induced stressby means of Coulomb failure function defined by:

DCFF ¼ Dt þ m Dsn þDPð Þ ð4Þ

Figure 5. Vertical component (a) and the meshed domain (b) for the HetTopo model. The mesh isrefined around the magmatic sources and becomes coarser at greater distance.

Figure 6. Horizontal component of ground deformationconsidering HomFlat (a), HomTopo (b), HetFlat (c), andHetTopo (d) numerical models. The recorded deformation atcontinuously running GPS stations (solid squares) is alsoshown [after Aloisi et al., 2003]. The dashed lines representthe modeled dike projection on the south and north-eastrifts.


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where Dt is the shear stress in the direction of slip on thereceiver fault, Dsn is the normal stress change, m is thefriction coefficient and DP is the pore pressure change.Stress redistribution has to account for pore pressurechanges, because magmatic intrusions can perturb the stateof stress of a crustal volume and can cause a variety ofhydrologic phenomena, which can be explained by theporoelastic response to the induced strain field. Porepressure acts against the normal stress change, effectivelyreducing the resistance to shear fracture and the resistance tosliding [Ranalli, 1995]. Because the stress changes occur ona timescale that is too short to cause the loss or gain of porefluid, the pore pressure changes on that timescale areusually associated with the undrained response of themedium [Rice and Cleary, 1976; Cocco and Rice, 2002].Under undrained conditions, the pore pressure resultingfrom a change in stress is given by:

DP ¼ �BDskk

3ð5Þ

which is called the isotropic poroelastic model, where Dskkis the volumetric stress and B is the Skempton coefficient,

which laboratory tests indicate can vary in the rangebetween 0.5 and 0.9.[14] Another model, known as constant apparent friction

model, is usually adopted in whichDP is proportional to thenormal stress changes as:

DP ¼ �BDsn: ð6Þ

Substituting equation (6) in equation (4) leads to thefollowing relation:

DCFF ¼ Dt þ m0Dsn; ð7Þ

and to the definition of the apparent friction coefficient m0 =m(1 � B). The two expressions for the pore pressurechanges can yield different results. Beeler et al. [2000]found that the constant apparent friction model may providemisleading estimates of stress changes. In the following, weuse both equations to compute Coulomb stress changes andcompare the results.[15] Based on the Coulomb failure criterion, failure on a

fault is favored if the Coulomb stress change is positive andinhibited if the Coulomb stress change is negative [Cocco

Figure 7. Horizontal normal stress changes induced by the southern dike intrusion (black dashed line)and projected onto a constant orientation aligned with the north-east rift (red dashed line) for HomFlat(a), HomTopo (b), HetFlat (c), and HetTopo (d) numerical models. The seismic events (white circles)accompanying the dike propagation are also plotted [from Barberi et al., 2004].


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and Rice, 2002]. The value at which the Coulomb failurecriterion is met is not known, but recent studies point outthat Coulomb stress changes higher than 1 bar are consid-ered to be significant [Toda et al., 1998; Toda and Stein,2002]. A variety of values for the friction coefficient andSkempton coefficient are usually used [Cocco and Rice,2002]. Assumptions for the values of the Skempton coeffi-cient B and the friction coefficient m can affect the DCFFestimates [Beeler et al., 2000]. We carried out computationsof the Coulomb stress changes assuming B = 0.8 and m =0.5, so that m0 = 0.4, generally used in stress transfercomputations on Mt. Etna [Feuillet et al., 2006; Walter etal., 2005].[16] The stress tensor can be resolved directly onto the

adopted fault planes when the geometry as well as thefaulting mechanism of the secondary (receiver) fault areknown; however, if the geometry and mechanism of thesecondary fault are unknown the best practice is to resolvethe stress tensor onto optimally oriented planes (OOPs). Insuch a case, the regional stress and stress perturbationscaused by volcanic sources are used to compute the orien-

tation of planes most likely to fail and the stress change isresolved onto these orientations [King et al., 1994]. TheOOPs are identified by finding the optimal orientations thatmaximize at each node of the computation domain theCoulomb stress changes given by the total stress tensor,defined as:

Dstij ¼ sr

ij þDsvij ð8Þ

where srij is the regional stress tensor and Dsvij is the stressperturbation induced by the volcanic source. At each nodetwo equivalent OOPs associated with a particular focalmechanism are found [Nostro et al., 1997]. The orientationsof the OOPs strongly depend on the orientation andmagnitude of the regional stress field [King and Cocco,2000; McCloskey et al., 2003]. Once the orientations of theOOPs are determined, the normal and shear stress changesonto these planes are computed only by the stressperturbation Dsvij using equation (4).

Figure 8. Coulomb stress changes and optimally oriented slip planes (OOPs) generated by the intrusivedikes (black dashed lines) for the HomFlat (a), HomTopo (b), HetFlat (c), HetTopo (d) models. The linesrepresent the orientations of the left-lateral (red) and the right-lateral (blue) planes. The white arrowsshow the orientation of the regional stress field. The focal mechanisms of the most energetic seismicevents along the Pernicana Fault (red) and the Timpe Fault System (blue) are reported [from Barberi etal., 2004].


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4.1. North-East Rift

[17] The magma intruded in the southern flank startedsuddenly on October 26 at about 21:00 GMT, producingintense explosive activity and lava effusion. About 5 hourslater, a long field of eruptive fractures propagated radiallyalong the northeastern flank of the volcano [Aloisi et al.,2006; Del Negro et al., 2004]. The changes in the state ofstress generated by the southern dike could have affectedthe likelihood for the intrusion propagating along the north-east rift. To investigate a possible interaction between thesesubsequent intrusive events, we examined the stress transferassociated with the southern dike intrusion onto the north-east rift. Following the standard sign convention for stress(i.e., extension is positive), we computed the horizontalnormal stress changes projected onto a constant orientationaligned with the north-east rift for all the models HomFlat,HomTopo, HetFlat and HetTopo (Figures 7a–7d) on a mapview at 1000 m b.s.l.. Besides the amplitude and the shapeof stress patterns, all the numerical models show a positivestress change area around the north-east rift. The HomTopoand HetTopo numerical models demonstrate how the stresspattern is affected by Mt. Etna topography. The mediumheterogeneity strongly influences the amplitude of the stress

field because of the lower value assigned to the Young’smodulus at shallower depths with respect to the homoge-neous models (Figure 7). The southern dike intrusionproduced a horizontal normal stress gradient (more than0.1 MPa) along the N24�E striking dike. The positive stresschange in the northeastern area shows that the verticallyrising dike-like magma body in the southern flank of thevolcano generated an extensional stress field, which pro-moted the lateral intrusion propagating along the preexistingcrustal fracture system of the north-east rift.

4.2. Pernicana Fault and Timpe Fault System

[18] We resolved the stress tensor generated by both thesouthern and northern dike intrusions onto the optimallyoriented strike-slip faults and mapped structural trends of thePernicana Fault and the Timpe Fault System. We computedthe optimally oriented plane (OOP) following King et al.[1994]. The choice of the regional stress field orientation isproblematic at Mt. Etna because it is extremely heteroge-neous due to the complex tectonovolcanic setting. Stressfield orientations inferred from focal solutions indicated ahorizontal s1 oriented from N285� to N15� [Barberi et al.,2004; Gresta et al., 2005]. Using a horizontal s1, oriented

Figure 9. Map view of Coulomb stress changes generated by the southern and northern dike intrusions(black dashed lines) resolved onto Pernicana Fault (red line). The fault is mapped by a vertical planeoriented 100�N. For all the models HomFlat (a), HomTopo (b), HetFlat (c), HetTopo (d), a positivestress change area surrounds the Pernicana Fault and well matches the seismicity recorded from 27 to29 October (white circles) [from Barberi et al., 2004].


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N337�, we obtain an optimally oriented plane withorientations ranging from N340� to N20� for a left-lateralstrike-slip fault and N110� to N157� for a right-lateralstrike-slip fault. The DCFF was computed for all themodels HomFlat, HomTopo, HetFlat and HetTopo on asurface at 1000 m b.s.l. (Figure 8). The heterogeneityand the topography strongly perturb the Coulomb stresschanges. Effects due to topography are most evident inthe summit area (Figures 8a–8d, 9a–9d, and 10a–10d)and do not affect the foot of the volcanic edifice. Instead,the medium heterogeneity influences the magnitude of thestress change which is very sensitive to variations in thecrustal rigidity [Zhao et al., 2004]. At shallow depths,where the shear modulus reaches a low value (4.6 GPa),the stress change values of the heterogeneous models candecrease by about 20% compared with homogeneousmodels.[19] The Pernicana Fault and Timpe Fault System showed

two different styles of kinematics that are not compatiblewith the same orientation of the stress fields, even if theywere contemporaneously active after the north-east rift dikeintrusion. The rupture along the Timpe Fault System is

optimally oriented while the Pernicana Fault is not optimallyoriented (Figure 8). Particularly, the focal mechanisms ofthe most energetic seismic events that occurred on TimpeFault System are in good agreement with the predicted slipdirection. In such structurally complex areas, it is advisableto resolve directly the stress field onto the mapped structuraltrends [Steacy et al., 2005]. Therefore we resolved the stresschanges, generated by the southern and northern dikeintrusions, onto a vertical plane oriented N100� with leftlateral motion for the Pernicana Fault and onto a verticalplane oriented N145� with right lateral motion for the TimpeFault System [Walter et al., 2005]. Using the isotropicporoelastic model, the Coulomb stress changes were com-puted on a surface at 1000 m b.s.l. depth for the PernicanaFault and at 3750 m b.s.l. for the Timpe Fault System,corresponding to the mid-depths of the seismic faulting,respectively. Figure 9 emphasizes the clear differencebetween the DCFF resulting from resolving stress changesonto the Pernicana fault plane inferred from geologicalstructural constraints and that resulting from OOPs. TheCoulomb stress change decreases from 0.8 MPa for thehomogeneous models (HomFlat and HomTopo) to 0.6 MPa

Figure 10. Coulomb stress changes induced by the southern and northern dike intrusions (black dashedlines) for the HomFlat (a), HomTopo (b), HetFlat (c), HetTopo (d) models. The stress tensor is projectedonto Timpe Fault System (red lines) represented with a vertical plane oriented 145�N. The epicenterlocations of the earthquakes that occurred soon after the magmatic intrusions are also reported (whitecircles) [from Barberi et al., 2004].


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for the heterogeneous models (HetFlat and HetTopo), whichgives a difference of 0.2 MPa in the most western part of thePernicana Fault. The DCFF resolved onto the Timpe FaultSystem is quite similar to that resulting from OOPs, sincethe Timpe faulting system is seen to be optimally oriented(Figure 10). In the heterogeneous models (HetFlat andHetTopo) the Coulomb stress changes display a significantpositive increase as a result of the high rigidity bodycentered below the SE sector [Chiarabba et al., 2000].Positive Coulomb stress changes well match the seismicpattern and values less than 1 bar are obtained along boththe Timpe Fault System and the Pernicana Fault. Thereforethe structures have reached a critical state and small stressperturbations were enough to encourage the faults to slip.Similar computations were also performed using the apparentfriction model (Figure 11), which provides results compa-rable to the isotropic poroelastic model.[20] In all the numerical models, the Timpe Fault System

is encouraged to slip and it is optimally oriented. Walter etal. [2005] found that dike intrusions along the north-eastand south rifts induce a Coulomb failure stress decreasealong the Timpe Fault System. The HomTopo numericalmodel, which could be considered equivalent to the modelused by Walter et al. [2005], produces a positive stresschange. Therefore the discrepancy could be ascribed to thedifferent source geometry assumed for the intrusive dikes.The main difference is related to the dike widths. Walter etal. [2005] used dikes having a 7-km width, whereas we used

dike geometries coming from geodetic inversions thatprovided a width of 1.8 km for the southern intrusion and4.6 km for the northeastern intrusion [Aloisi et al., 2003]. Ifthe dike widths are increased, higher ground deformationthan that recorded is obtained.

5. Conclusions

[21] A finite element modeling approach was applied toevaluate ground deformation and the resulting stress redis-tributions in response to magmatic processes occurringduring the 2002–2003 Etna eruption. The finite elementmethod allows us to include the effects of topography andelastic heterogeneities and appraise their effects on theexpected displacement and stress fields. Our results showthat heterogeneity and topography engender deviations fromanalytical results in the deformation and stress fields pro-duced by the intrusive dikes on the southern and northeast-ern flanks of Mt. Etna under elastic conditions; however,such perturbations are more significant in the volcanosummit area and disappear several kilometers from thesummit.[22] The intrusion within the southern flank was able to

produce an extensional stress field that favored magma-filled fracture propagation along the north-east rift. Lavaserupted from the southern fissure differ chemically fromthose erupted along the north-east rift [Andronico et al.,2005]. Such features suggest that two different magmas

Figure 11. Map view of Coulomb stress changes generated by the southern and northern dike intrusions(black dashed lines) and resolved onto the Pernicana Fault (a) and the Timpe Fault System (b) for theHetTopo model assuming the apparent friction model. Three-dimensional view of the Coulombstress changes along the Pernicana Fault (c) and Timpe Fault System (d). The seismicity recorded from27 to 29 October (white circles) [from Barberi et al., 2004] is also reported.


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reached the surface through independent pathwaysconnected to distinct fracture systems and local storageregions at depth [Monaco et al., 2005]. Magma eruptedfrom the northeastern fissure was a partially degassedmagma normally residing within the central conduits andthe shallow plumbing system. Therefore this magma wasalready filling the north-east crater conduit, as indicated bysummit eruptive activity observed several months prior tothe eruption [Andronico et al., 2005]. The vertically risingdike-like magma body under the summit craters could haveproduced cracks encouraging the magma from the north-east crater conduit to intrude along the north-east rift zone[Dieterich et al., 2000; Gargani et al., 2006; Hill et al.,2002]. Computations of Coulomb stress changes show thatseismicity matches well areas of increased static stresschange caused by the intrusive event along the southernand northeastern flanks. Extension along the north-east riftzone was followed by left-lateral movement of the Perni-cana Fault and right-lateral movement along the TimpeFault System. The presence of medium heterogeneitystrongly affects the amplitudes of the static stress changes.Since recent studies of stress triggering effects indicate thata few bars differences in stress could increase or decreaseseismicity in fault areas [Harris and Simpson, 1998; King etal., 1994], the role of medium properties may becomecrucial. All the numerical models explored produce stressmaps that indicate that the Timpe Fault System and thePernicana Fault are encouraged to slip. Particularly, theHetTopo numerical model, which includes the topographyand medium heterogeneity, predicts static stress changes ofa few bars. This is an indication that the structures werealready in a critical state and the intrusion and eruption haspromoted the occurrence of fault rupture.

[23] Acknowledgments. This study was undertaken with financialsupport from the ETNA project (DPC-INGV 2004–2006 contract) and theVOLUME project (European Commission FP6-2004-Global-3). This workwas developed in the frame of the TecnoLab, the Laboratory for theTechnological Advance in Volcano Geophysics organized by DIEES-UNICT and INGV-CT. This research was also supported in part by theSouthern California Earthquake Center. SCEC is funded by NSF Cooper-ative Agreement EAR-0106924 and USGS Cooperative Agreement02HQAG0008. The SCEC contribution number for this paper is 1215.This research was also supported in part by NSF grant EAR/ITR-0313238.We are grateful to Carl Gable for giving us useful hints in building the meshwith LaGriT. We would like also to thank the Associate Editor MichaelRyan and the reviewers Paul Lundgren and Roger Delinger for theirconstructive comments, which improved the manuscript.

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static stress changes induced by the magmatic intrusions during the 2002–2003 etna eruption

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