Volcano deformation at active plate boundaries: Deep magma ......Volcano deformation at active plate boundaries: Deep magma accumulation at Hekla volcano and plate boundary deformation

Volcano deformation at active plate boundaries: Deep magmaaccumulation at Hekla volcano and plate boundarydeformation in south Iceland

Halldór Geirsson,1 Peter LaFemina,1 Thóra Árnadóttir,2 Erik Sturkell,3

Freysteinn Sigmundsson,2 Matthew Travis,1 Peter Schmidt,4 Bjorn Lund,4

Sigrún Hreinsdóttir,5 and Rick Bennett6

Received 24 April 2012; revised 1 October 2012; accepted 3 October 2012; published 20 November 2012.

[1] Most magmatic systems on Earth are located at actively deforming plate boundaries.In these systems, the magmatic and plate boundary deformation signals are intertwined andmust be deconvolved to properly estimate magma flux and source characteristics of themagma plumbing system. We investigate the inter-rifting and inter-seismic deformationsignals at the Eastern Volcanic Zone (EVZ) – South Iceland Seismic Zone (SISZ)ridge - transform intersection and estimate the location, depth, and volume rate formagmatic sources at Hekla and Torfajökull volcanoes, which are located at the intersection.We solve simultaneously for the source parameters of the tectonic and volcanicdeformation signals using a new ten-year velocity field derived from a dense networkof episodic and continuous GPS stations in south Iceland. We find the intersectionof the axes of the EVZ and the SISZ is located within the Torfajökull caldera, which itselfis subsiding. Deformation at Hekla is statistically best described in terms of a horizontalellipsoidal magma chamber at 24�2

+4 km depth aligned with the volcanic system andincreasing in volume by 0.017�0.002

+0.007 km3 per year. A spherical magma chamber centeredat 24�2

+5 km depth with a volume rate of 0.019�0.002+0.011 km3 per year, or a vertical pipe-shaped

magma chamber between 10�1+3 km and 21�4

+7 km with a volume rate of 0.008�0.001+0.003 km3

per year are also plausible models explaining the deformation at Hekla. All threemodels indicate magma accumulation in the lower crust or near the Moho under Hekla.

Citation: Geirsson, H., P. LaFemina, T. Árnadóttir, E. Sturkell, F. Sigmundsson, M. Travis, P. Schmidt, B. Lund, S.Hreinsdóttir, and R. Bennett (2012), Volcano deformation at active plate boundaries: Deep magma accumulation at Hekla volcanoand plate boundary deformation in south Iceland, J. Geophys. Res., 117, B11409, doi:10.1029/2012JB009400.

1. Introduction

[2] At divergent plate boundaries magmatism is intimatelylinked with the accommodation of relative plate motion andformation of oceanic crust. Along these plate boundaries,central volcanic systems accumulate magma in crustal magmachambers that is later erupted on the seafloor and/or injectedalong rift systems forming sheeted dike complexes. To

understand the inter-eruptive deformation of these volcanicsystems, one must also take into account the secular plateboundary deformation signal across these systems. In the caseof ridge-transform (or ridge – non-transform) intersections,the kinematics of the transform adds increased complexityto the deformation field. In this study we investigate thesources of deformation of two active volcanic systems,located at the intersection of a ridge and transform fault sys-tem in south Iceland.[3] Iceland is a sub-aerial manifestation of the North

American – Eurasian divergent plate boundary, the Mid-Atlantic Ridge. The location of the Icelandic hot spot relativeto the plate boundary results in diverse magma-tectonicinteractions and excessive volcanism when compared to therest of the northern Mid-Atlantic Ridge. The ridge-hot spotinteraction here has resulted in repeated eastward ridge jumps,manifest as propagating and overlapping ridge segments thatare connected by transform fault systems [e.g., Hey, 1977].The ridge segments in Iceland are characterized by volcaniczones comprised of central volcanoes and associated fissureswarms elongated along the plate boundary. In south Iceland,the overlapping Western (WVZ) and Eastern Volcanic Zones

1Department of Geosciences, Pennsylvania State University, UniversityPark, Pennsylvania, USA.

2Nordic Volcanological Center, Institute of Earth Sciences, Universityof Iceland, Reykjavik, Iceland.

3Department of Earth Sciences, University of Gothenburg, Göteborg,Sweden.

4Department of Earth Sciences, Uppsala University, Uppsala, Sweden.5Institute of Earth Sciences, University of Iceland, Reykjavik, Iceland.6Department of Geosciences, University of Arizona, Tucson, Arizona,

USA.

Corresponding author: H. Geirsson, Department of Geosciences,Pennsylvania State University, Deike Building, University Park, PA 16802,USA. ([email protected])

©2012. American Geophysical Union. All Rights Reserved.0148-0227/12/2012JB009400

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B11409, doi:10.1029/2012JB009400, 2012

B11409 1 of 18

(EVZ) accommodate the total North America – Eurasia platemotion of �19 mm/yr [Sigmundsson et al., 1995; LaFeminaet al., 2005; Árnadóttir et al., 2009] and are connected bythe South Iceland Seismic Zone (SISZ), a transform fault

system. The Reykjanes Peninsula (RP) connects these seg-ments with the offshore Reykjanes Ridge (Figure 1).[4] Hekla volcano and Torfajökull caldera are central

volcanoes located near the intersection of the EVZ and the

Figure 1. Observed horizontal GPS velocities in south Iceland for the period 2000.5 to 2010.0 relativeto the North American plate superimposed on a shaded relief map. The velocities are calculated fromepisodic and continuous GPS time series, with co-seismic offsets for the two magnitude 6.1 earthquakesin May 2008 removed (black stars; see text). Vector uncertainties are 1-sigma. The summit location ofHekla (He) is shown with a white star. Black diamonds are the locations of the two magnitude 6.5 earth-quakes in June 2000. The 2000 and 2008 earthquakes occurred on north-trending, right-lateral strike-slip“bookshelf” faults (thin black lines). Fissure swarms (dark gray shading) from Einarsson andSæmundsson [1987]; glaciers (white overlying topography) and lakes and rivers (white) are shown.Abbreviations: To: Torfajökull; K: Katla; E: Eyjafjallajökull; B: Bárðabunga; Vat: Vatnajökull glacier.The inset figure shows the expression of the Mid-Atlantic Ridge in Iceland. The study area is outlinedby a dashed box. The North American – Eurasian plate boundary is drawn with a thin line and the relativehalf-spreading rates are indicated with white arrows [DeMets et al., 2010]. Abbreviations: NA: NorthAmerican plate; EU: Eurasian plate; RR: Reykjanes Ridge; RP: Reykjanes Peninsula; WVZ: WesternVolcanic Zone; SISZ: South Iceland Seismic Zone; EVZ: Eastern Volcanic Zone; NVZ: Northern VolcanicZone; HFF: Húsavík-Flatey Fault; GOR: Grímsey Oblique Rift; KR: Kolbeinsey Ridge.

GEIRSSON ET AL.: VOLCANO-TECTONIC DEFORMATION IN ICELAND B11409B11409

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SISZ (Figure 1). Hekla has been studied extensively since1968 using various geodetic methods including dry- andcontinuous tilt, electronic distance measurements (EDM),borehole strain meters, episodic and continuous GPS, andInSAR [Sturkell et al., 2006b; Ofeigsson et al., 2011]. Theestimated depths for the magma chamber at Hekla usingthese various geodetic methods range from 5 to 17 km[Kjartansson and Gronvold, 1983; Sigmundsson et al.,1992; Linde et al., 1993; Tryggvason, 1994; Sturkell et al.,2005; Ofeigsson et al., 2011]. These measurements havealso revealed a cyclic deformation pattern of steady pre-eruptive inflation followed by co-eruptive dike formationand rapid deflation [Tryggvason, 1994;Ofeigsson et al., 2011].Since its last eruption in February – March 2000, Hekla hasbeen inflating continuously [Ofeigsson et al., 2011; Scheiber-Enslin et al., 2011] (also this study).[5] Torfajökull caldera, 20 km east of Hekla, is the largest

rhyolitic center in Iceland. Historical rifting episodes in 872and 1477, which extended along the EVZ from Bárðabunga

central volcano into Torfajökull (Figure 1), as well asgeologic studies, demonstrate that volcanism at Torfajökullis intimately connected to rifting episodes of the EVZ[MacDonald et al., 1990; McGarvie et al., 1990]. Recentgeodetic studies indicate the western part of Torfajökull cal-dera has been subsiding for almost two decades and that platespreading takes place within the caldera [Scheiber-Enslinet al., 2011].[6] The surface deformation at Hekla and Torfajökull

central volcanoes is complicated because of the proximity ofthe volcanoes to the intersection of the SISZ and EVZ[LaFemina et al., 2005; Árnadóttir et al., 2006, 2009;Scheiber-Enslin et al., 2011]. Geodetic studies across theseplate boundary segments demonstrate inter-rifting elasticstrain accumulation in the EVZ [Sigmundsson et al., 1995;Jónsson et al., 1997; LaFemina et al., 2005; Árnadóttiret al., 2006, 2009; Scheiber-Enslin et al., 2011], and inter-,co-, and post-seismic deformation in the SISZ [Sigmundssonet al., 1995; Árnadóttir et al., 2006; Decriem andÁrnadóttir, 2012]. The last major rifting episode in theEVZ was the 1783–1784 Laki fissure eruption, which placesthe present deformation field well into the inter-riftingperiod [LaFemina et al., 2005]. Furthermore, strain in the�60 km wide EVZ has been shown to accumulate mostrapidly in the western part of the EVZ from Torfajökull toBárðabunga (Figure 1) [LaFemina et al., 2005; Scheiber-Enslin et al., 2011]. The SISZ, however, had significantearthquakes in 2000 [e.g., Árnadóttir et al., 2005] and 2008[Hreinsdóttir et al., 2009]. Major earthquakes in theeast-trending SISZ occur predominantly on north-trendingright lateral strike-slip faults (Figure 1); this style of defor-mation has been termed bookshelf faulting [Einarssonet al., 1981] and is typical of migrating transform zones[Morgan and Kleinrock, 1991]. Nevertheless, interseismicdeformation in the SISZ has been shown to be consistentwith a single east-trending shear zone below the brittle crust(�15 km) [Sigmundsson et al., 1995; Árnadóttir et al.,2006; Decriem and Árnadóttir, 2012].[7] In addition to the tectonic and magmatic deformation

signals described above, the recent melting of Icelandic gla-ciers causes a widespread uplift signal with maximum upliftrates exceeding 20 mm/yr (Figure 2) [Árnadóttir et al., 2009].The vertical deformation field at Hekla is further complicatedby relative subsidence centered on Hekla [Ofeigsson et al.,2011], which has been interpreted as loading of the crust byrecent lava flows [Grapenthin et al., 2010; Ofeigsson et al.,2011]. Considering all of the above mentioned processes,we use a new ten-year GPS-derived velocity field to simul-taneously estimate (1) the horizontal location, depth and rateof volume change of the magma chamber at Hekla volcano,testing different models for magma chamber geometry;(2) the depth and rate of volume change of a subsidencesource at Torfajökull caldera; and (3) the location and lockingdepths of the SISZ and EVZ plate boundary segments.

2. GPS Data, Processing, and Site Velocities

[8] Our analysis is based on a combination of episodic(eGPS) and continuous GPS (cGPS) data (Table 1). EpisodicGPS measurements in Iceland started in 1986 [Foulgeret al., 1993]. Since then numerous GPS measurement cam-paigns, normally separated by one or several years, have

Figure 2. (a) Observed and (b) GIA-corrected vertical GPSvelocities in south Iceland. 1-sigma uncertainties are shownas thin lines extending from tip of vector. Symbols are asin Figure 1.


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been conducted in south Iceland. The eGPS measurementsconsist typically of 1 to 5 day observation periods. In 2006, adense, six site cGPS array was installed at Hekla as part of anationwide cGPS network [Geirsson et al., 2010], fromwhich we also include data in our analysis. The array isdesigned to investigate pre-eruptive magma accumulationand co-eruptive dike emplacement at Hekla. The GPS datawere processed using the GIPSY/OASIS II (version 5)software, in a standard Precise Point Positioning (PPP) mode[Zumberge et al., 1997] and using orbits from the Jet Pro-pulsion Laboratory in the ITRF2005 reference frame[Altamimi et al., 2007]. We removed data points from thetime series that had uncertainties more than five times largerthan the median uncertainties for the entire data set (1.2 mm,1.5 mm and 4.2 mm in north, east and vertical, respectively)in any component.[9] We limit our data period from 2000.5 to 2010.0 (with a

few exceptions, see below and Table 1) to minimize theeffects of transient deformation that may affect our positiontime series and therefore velocity estimates. Specifically, wewant to avoid the February–March 2000 Hekla eruption[Ofeigsson et al., 2011], co-seismic deformation from thetwo June 2000 Mw 6.5 earthquakes in the SISZ [Pedersenet al., 2003; Árnadóttir et al., 2005], and magmatic defor-mation associated with the 2010 Eyjafjallajökull eruption(Figure 1) [Sigmundsson et al., 2010]. Although our timeseries start after the June 2000 SISZ earthquakes, sites inthe SISZ were affected by post-seismic deformation [Jónssonet al., 2003; Árnadóttir et al., 2005; Decriem and Árnadóttir,2012], with the largest signal occurring before 2002[Decriem and Árnadóttir, 2012]. We therefore exclude databefore 2002.5 from all sites within 30 km of the two June2000 earthquake epicenters in order to avoid post-seismicdeformation (Figure 1 and Table 1).[10] We must also consider deformation caused by the

two �Mw 6.1 earthquakes that occurred in the western SISZon May 28, 2008 (Figure 1) [Hreinsdóttir et al., 2009]. Wecorrect the position time series at our GPS sites for theco-seismic displacements associated with these earthquakesusing the uniform slip model of Decriem et al. [2010], whichis based on cGPS data (auxiliary material Data Set S1).1 ThecGPS sites closest to the May 2008 earthquakes show rapidpost-seismic deformation, and additional transient deforma-tion from geothermal utilization in the same region since2006 [Geirsson et al., 2010]. We therefore exclude thesesites from our analysis.[11] Site velocities were calculated using weighted least

squares linear fits to the time series in ITRF2005 (Table 1)after correcting for co-seismic displacements from the May2008 earthquakes. We only use sites with observations thatspan more than 1.5 years within the study period. Seasonalcomponents were not used for the cGPS sites in order to treatthe episodic and continuous sites in exactly the same manner.Velocity uncertainties were calculated as in Geirsson et al.[2006]. Using the analysis of Blewitt and Lavallée [2002],we estimated the difference in velocities between accountingand not accounting for the seasonal signals for our cGPS sitesto be typically one order of magnitude smaller than the

uncertainties (auxiliary material Text S1 and Data Sets S2and S3). The horizontal velocities were transformed fromITRF2005 to a North America-fixed reference frame usingthe Euler vector from the MORVEL plate motion model(Figure 1) [DeMets et al., 2010].[12] The vertical velocity field in Iceland shows wide-

spread uplift (Figure 2a). The shape of the uplift signal weobserve (Figure 2a) is similar to what was observed byÁrnadóttir et al. [2009], with the highest rates observedtoward the center of Iceland and decreasing with distancefrom Vatnajökull. Our uplift rates, however are higher thanthose reported by Árnadóttir et al. [2009], which werederived from eGPS data from nation-wide campaigns in 1993and 2004, and cGPS data ending in 2004. Our analysis ofGPS data for the longest running cGPS sites in Icelandreveals increased uplift rates since �2003 or 2004 (auxiliarymaterial Figure S1). We note that due to this velocityincrease, the vertical velocity estimates of sites using pre-2003 data may be somewhat biased toward lower rates.However, the bulk of our data set is from post-2003 (Table 1)and thus the rates are minimally biased. Geodetic and gravitymeasurements have revealed increased uplift rates in Green-land and Iceland since �2004, which has been interpreted asan elastic response to increased melting rates of the glaciers[Jiang et al., 2010; Khan et al., 2010].[13] We assume the increased uplift rates (Figure 2a and

auxiliary material Figure S1) are caused by enhanced glacio-isostatic adjustment (GIA) (elastic and viscoelastic rebound)due to increased melting of Icelandic glaciers and hence, as afirst approximation, we scale the model results of Árnadóttiret al. [2009] to minimize the observed vertical signal(Figure 2b). Specifically, we apply horizontal and verticalvelocity corrections to our site velocities based on a geody-namic model of Earth’s response to estimated recent icemelting histories of the largest glaciers in Iceland [Árnadóttiret al., 2009]. The model has a 10 km thick elastic layer,underlain by a 30 km thick viscoelastic layer (1 � 1020 Pa s)over a viscoelastic halfspace (1 � 1019 Pa s). We scale thecorrections (horizontal and vertical velocities) from the modelby a factor of 1.5, found by minimizing the vertical signal inIceland (Figure 2b). We acknowledge that a more detailedstudy of the increased uplift rates is needed; this is the subjectof ongoing research. The horizontal velocity corrections basedon the scaling of the above model range from �1 to 5 mm/yr(Figure 3 inset and auxiliary material Data Set S4). We presentthe fully corrected (i.e., the May 2008 co-seismic- andGIA-corrected) horizontal velocity field relative to stableNorth America (Table 2) in Figure 3.

3. Modeling

3.1. Model Description

[14] North America – Eurasia plate motion is the dominantsignal in our new GIA-corrected horizontal velocity field(Figure 3). The volcanic deformation signals from Hekla andTorfajökull are not obvious at first glance in the correctedhorizontal and vertical velocity fields (Figures 3 and 2b).To model the tectonic and magmatic processes in southIceland, we apply a combination of kinematic elastic blockmodels and volcanic source models in an elastic half-space,with a shear modulus of 30 GPa and a Poisson ratio of0.25. Figures 4a–4f show the contributions to the deformation

1Auxiliary material data sets are available at ftp://ftp.agu.org/apend/jb/2012jb009400. Other auxiliary materials are available in the HTML.doi:10.1029/2012JB009400.


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Table 1. Site Information and Calculated Site Velocities in the ITRF2005 Reference Framea

Site Latitude Longitude

Time Spanb (year)

Nc

Velocitiesd (mm/yr)

Start End East North Up

ALMA 64.256 �21.129 2003.7 2009.5 4 �9.2 � 1.2 18.9 � 0.9 4.7 � 3.5BISK 64.249 �21.094 2003.7 2009.5 3 �8.4 � 0.7 18.8 � 1.1 6.6 � 1.8BJAL 64.099 �19.104 2000.8 2009.5 6 �0.1 � 0.5 17.3 � 0.6 17.3 � 1.8BLAU 63.952 �19.364 2002.6 2009.6 5 8.0 � 0.9 15.6 � 0.8 19.6 � 1.8BOTA 63.656 �18.246 2004.6 2009.5 4 9.2 � 0.9 13.4 � 0.9 15.6 � 5.5BREI 64.183 �18.391 2001.6 2009.6 3 �0.2 � 0.6 15.0 � 0.6 23.9 � 1.0BRS2 63.948 �19.558 2007.6 2009.6 2 6.9 � 1.5 17.5 � 1.0 19.4 � 3.8BRSK 63.941 �19.540 2001.6 2009.6 7 4.5 � 0.6 14.0 � 0.4 22.6 � 1.7BUDH 64.240 �19.325 2006.6 2010.0 c �4.3 � 0.8 18.2 � 0.8 16.6 � 2.2BULA 63.802 �18.560 2000.5 2009.6 5 7.1 � 0.7 13.8 � 0.4 19.3 � 1.6DIMO 64.223 �20.951 2003.7 2009.5 3 �9.1 � 0.5 19.0 � 1.0 3.7 � 0.9DOMA 64.035 �19.130 2001.6 2009.5 5 2.0 � 0.6 16.1 � 0.4 16.5 � 2.0DROP 63.914 �19.574 2001.6 2009.6 5 3.9 � 0.8 13.9 � 0.5 14.4 � 3.9ELDH 63.685 �18.357 2000.5 2009.6 5 8.0 � 0.4 13.5 � 0.5 15.7 � 1.5FAGR 63.882 �18.230 2001.6 2009.6 5 6.2 � 0.6 12.5 � 0.7 21.1 � 1.5FAXI 63.830 �19.467 2002.6 2009.6 4 6.0 � 1.0 15.4 � 0.6 19.1 � 1.9FEDG 64.025 �19.689 2004.4 2009.4 c �1.7 � 1.8 16.7 � 1.3 14.0 � 3.3FITC 64.337 �19.592 2007.6 2010.0 c �3.3 � 4.5 19.7 � 1.3 15.2 � 3.6FJOC 64.875 �18.006 2007.7 2010.0 c �7.9 � 1.5 26.3 � 1.4 23.3 � 5.7FLAG 63.995 �20.265 2002.8 2009.3 7 �3.2 � 0.6 16.7 � 0.6 12.6 � 2.0FOSS 64.354 �21.462 2003.8 2008.4 3 �9.4 � 1.3 19.4 � 0.9 7.2 � 3.1FROS 64.010 �19.044 2000.8 2004.7 5 2.3 � 1.1 17.7 � 1.1 16.0 � 4.7GALT 63.998 �18.273 2001.6 2009.6 5 3.2 � 1.0 13.7 � 0.8 23.8 � 1.6GELD 64.052 �20.292 2003.7 2009.3 8 �7.5 � 0.7 17.6 � 0.5 14.5 � 1.6GJBA 64.239 �21.036 2003.7 2009.5 3 �9.2 � 0.6 18.7 � 0.7 �2.9 � 1.3GLER 64.023 �19.802 2006.4 2010.0 c �3.9 � 1.1 18.6 � 0.9 15.5 � 2.3GOLA 63.660 �19.322 2005.3 2010.0 c 7.4 � 1.2 13.9 � 0.9 13.3 � 2.9GRFL 63.941 �19.918 2002.5 2009.5 5 �2.3 � 0.7 13.7 � 0.6 15.5 � 2.7GULL 64.327 �20.122 2001.5 2003.7 3 �12.1 � 2.8 18.5 � 1.6 9.6 � 4.0HAFU 64.012 �19.842 2005.3 2009.5 4 �5.6 � 0.8 19.0 � 0.5 25.0 � 2.8HALD 64.183 �19.419 2001.6 2009.6 4 �3.6 � 0.6 19.1 � 0.7 20.5 � 2.5HAMR 63.622 �19.986 2000.5 2007.0 15 5.6 � 0.5 15.1 � 0.5 12.2 � 1.5HAUC 64.711 �18.345 2007.7 2010.0 c �7.0 � 1.3 24.5 � 1.1 25.6 � 4.0HAUD 63.969 �19.964 2006.9 2010.0 c �3.8 � 1.1 15.3 � 1.0 11.7 � 2.5HEHA 63.959 �18.668 2001.6 2009.6 6 4.1 � 0.8 15.7 � 0.5 20.4 � 1.8HEKR 64.012 �19.658 2006.4 2010.0 c �0.2 � 1.3 16.1 � 1.2 9.7 � 3.1HEND 63.830 �20.473 2002.8 2007.6 6 4.6 � 1.0 17.8 � 0.9 13.2 � 3.5HESA 64.047 �19.561 2006.7 2009.8 c �0.4 � 1.4 17.7 � 1.3 13.3 � 4.7HGJA 64.254 �21.109 2003.7 2009.5 3 �9.1 � 0.8 18.4 � 0.7 5.1 � 0.9HIAK 64.333 �22.034 2003.7 2005.3 3 �11.3 � 1.8 20.1 � 1.8 2.4 � 3.6HLFJ 64.277 �20.136 2006.6 2010.0 c �7.4 � 0.8 18.2 � 0.8 9.7 � 2.1HNAU 64.076 �19.049 2001.6 2009.5 3 0.5 � 0.7 16.3 � 0.6 15.6 � 1.7HRAF 63.959 �19.218 2000.8 2009.6 8 4.3 � 0.6 14.6 � 0.9 9.9 � 2.0HRAS 63.936 �19.205 2001.6 2007.6 7 4.2 � 1.1 17.4 � 0.8 18.8 � 1.9HVEL 64.873 �19.561 2006.6 2010.0 c �10.1 � 0.9 21.9 � 0.8 13.4 � 2.3HVOL 63.526 �18.848 2000.5 2010.0 c 8.3 � 0.4 11.7 � 0.3 10.3 � 1.0INSK 64.683 �19.534 2008.6 2010.0 c �7.3 � 2.5 21.9 � 2.0 17.4 � 5.5ISAK 64.119 �19.747 2002.5 2010.0 c �5.2 � 0.5 20.5 � 0.4 16.4 � 1.0JOKU 64.310 �18.240 2001.4 2008.3 20 �3.5 � 0.8 15.2 � 0.5 32.5 � 2.6KALD 64.359 �18.857 2001.6 2003.6 2 �2.5 � 1.8 17.6 � 2.4 11.4 � 4.9KALF 63.947 �17.689 2004.6 2009.5 5 6.0 � 0.8 11.3 � 0.7 29.8 � 5.1KALT 63.897 �20.656 2007.0 2010.0 c 4.0 � 1.1 16.3 � 0.9 5.9 � 2.4KARA 64.257 �21.187 2003.7 2009.5 2 �8.3 � 0.4 19.0 � 0.3 1.2 � 0.8KELD 63.824 �20.085 2001.5 2009.4 9 3.0 � 0.8 15.2 � 0.6 12.0 � 2.4KGIL 63.859 �18.974 2001.6 2009.7 7 6.3 � 0.7 17.0 � 0.5 14.8 � 2.0KIDJ 63.997 �20.775 2002.5 2010.0 c �2.6 � 0.4 19.2 � 0.3 5.6 � 0.8KKLO 63.864 �19.054 2001.6 2009.7 5 6.0 � 0.7 17.4 � 0.6 17.9 � 3.0KOPS 64.172 �20.279 2002.8 2009.3 9 �8.0 � 0.9 18.0 � 0.7 16.1 � 3.0KRHR 63.948 �20.100 2002.8 2009.4 8 �1.7 � 0.9 16.2 � 0.4 14.2 � 2.1KROK 64.066 �19.396 2000.8 2009.5 9 2.2 � 0.6 18.6 � 0.6 17.7 � 1.5KVFE 64.207 �18.725 2001.6 2009.5 3 �0.9 � 0.8 16.3 � 0.6 21.0 � 1.4KYLI 63.991 �18.918 2001.6 2009.5 3 2.2 � 0.4 16.8 � 0.6 14.1 � 1.1L257 64.081 �18.885 2007.6 2009.5 2 2.6 � 1.9 16.9 � 2.3 4.3 � 4.0LAHR 63.988 �19.060 2001.6 2009.5 9 2.1 � 0.6 16.0 � 0.7 14.1 � 3.0LAMH 64.443 �20.385 2003.7 2009.5 2 �9.8 � 0.5 19.5 � 0.6 13.4 � 1.9LANG 64.311 �19.333 2001.6 2003.7 2 �8.5 � 1.7 18.4 � 1.6 0.8 � 5.2LAUF 63.904 �19.368 2001.6 2009.6 7 7.3 � 1.4 16.9 � 1.0 15.9 � 2.2LAUN 64.094 �19.210 2001.6 2009.6 4 �0.8 � 0.9 16.8 � 0.7 18.4 � 1.6LAVA 64.209 �20.866 2003.7 2005.3 2 �12.1 � 1.9 18.1 � 3.1 6.1 � 5.1LFEL 64.526 �19.759 2006.6 2010.0 c �7.9 � 1.0 18.8 � 0.8 13.9 � 2.5


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Table 1. (continued)

Site Latitude Longitude

Time Spanb (year)

Nc

Velocitiesd (mm/yr)

Start End East North Up

LIHO 63.990 �19.263 2001.6 2009.6 7 4.0 � 0.8 16.2 � 0.6 16.7 � 1.6LJOF 64.248 �18.485 2001.6 2009.5 3 �2.6 � 1.0 16.0 � 0.4 29.5 � 1.6LYTI 63.907 �20.433 2004.4 2009.3 7 3.2 � 0.8 15.8 � 0.8 14.2 � 3.6MAEL 63.802 �18.966 2000.5 2009.6 5 6.8 � 0.4 16.2 � 0.4 17.0 � 1.4MJSK 63.933 �19.672 2006.4 2009.0 c 1.9 � 1.8 13.3 � 1.2 10.1 � 3.3MOHN 64.025 �19.691 2000.8 2006.4 7 �1.4 � 1.2 17.3 � 1.1 17.4 � 3.6MORK 63.657 �19.895 2001.4 2004.4 4 4.4 � 2.3 14.3 � 1.9 11.4 � 4.7MUFE 63.980 �19.541 2001.6 2009.6 7 3.0 � 0.8 15.0 � 0.6 19.1 � 1.9NAEF 63.997 �19.907 2004.4 2007.6 3 �6.8 � 0.7 17.8 � 1.1 28.6 � 2.3NBJA 64.049 �19.669 2003.6 2009.7 5 �1.8 � 0.6 16.7 � 0.6 8.4 � 2.7NLAN 64.224 �18.206 2001.6 2009.6 4 �1.7 � 0.6 14.1 � 0.4 29.8 � 2.2NOFA 63.929 �18.635 2001.6 2007.6 3 3.7 � 1.0 16.0 � 0.5 19.5 � 1.7NOHR 64.009 �19.042 2004.7 2009.5 5 1.1 � 0.7 16.3 � 1.5 10.3 � 2.3NONH 63.903 �20.317 2002.8 2009.3 9 2.6 � 0.7 16.4 � 0.7 13.3 � 1.8NORS 64.035 �19.717 2006.4 2009.7 c �1.6 � 1.5 17.1 � 1.4 14.4 � 2.9NOXL 64.009 �19.597 2000.8 2009.6 7 �1.6 � 0.5 16.1 � 0.5 16.1 � 1.1PALA 63.884 �19.726 2001.6 2009.6 7 2.5 � 0.8 13.0 � 0.5 16.8 � 1.3PSI1 63.851 �19.600 2007.6 2009.6 3 8.5 � 1.5 17.8 � 1.2 10.1 � 3.2PSU2 63.801 �19.351 2007.6 2009.6 3 10.7 � 1.9 16.1 � 1.9 14.5 � 3.7PSU3 63.942 �18.219 2007.6 2009.6 3 2.3 � 3.4 15.1 � 1.9 10.7 � 5.6PSU4 63.986 �18.061 2007.6 2009.6 3 7.5 � 3.4 12.2 � 2.9 10.9 � 6.3PSU5 63.934 �17.916 2007.6 2009.6 3 6.5 � 2.0 18.0 � 3.7 22.8 � 4.4PSU6 64.026 �18.564 2007.6 2009.5 2 5.8 � 3.3 17.6 � 1.2 12.8 � 4.7PSU7 63.972 �18.834 2007.6 2009.5 3 3.1 � 1.7 16.8 � 1.9 6.6 � 3.7PSU8 64.184 �18.839 2007.6 2009.6 3 �2.4 � 1.8 17.4 � 1.1 10.1 � 3.0RAUK 64.027 �19.591 2000.8 2009.6 8 �0.5 � 0.6 17.3 � 0.5 19.5 � 2.1RETT 63.973 �20.044 2002.8 2009.4 7 �3.1 � 0.9 15.8 � 0.6 17.2 � 3.1REYK 64.139 �21.955 2000.5 2010.0 c �10.7 � 0.4 19.5 � 0.3 �1.3 � 1.0REYZ 64.139 �21.955 2000.5 2006.0 c �11.0 � 1.4 19.6 � 0.6 �0.8 � 1.9SARP 64.467 �21.266 2008.7 2009.9 c �7.4 � 4.4 23.4 � 4.4 1.6 � 7.6SATU 63.881 �19.250 2001.6 2009.6 7 7.4 � 0.8 18.6 � 0.8 16.0 � 1.6SAUR 63.984 �20.425 2007.1 2010.0 c �1.6 � 0.9 16.9 � 0.8 9.3 � 2.2SBJA 64.017 �19.763 2003.7 2009.7 4 �1.2 � 0.5 16.1 � 0.7 20.6 � 1.6SKAL 64.218 �21.445 2003.8 2005.3 2 �10.2 � 3.3 15.2 � 2.9 0.2 � 7.4SKDA 64.377 �20.666 2008.6 2010.0 c �9.3 � 2.6 18.6 � 1.9 4.0 � 5.2SKHR 63.837 �19.882 2003.6 2009.6 5 2.8 � 1.5 13.4 � 0.6 17.6 � 1.8SKJA 64.081 �19.599 2001.6 2009.5 5 �1.8 � 0.5 19.6 � 0.6 20.5 � 1.3SKOT 64.226 �21.012 2003.7 2005.3 2 �8.5 � 1.6 19.4 � 3.7 2.7 � 3.6SKRO 64.557 �18.378 2000.7 2010.0 c �7.3 � 0.5 21.3 � 0.3 25.7 � 1.2SLAN 64.106 �18.456 2001.6 2009.6 4 1.6 � 0.3 14.7 � 0.3 23.0 � 1.7SNAE 63.736 �18.632 2000.5 2009.5 8 7.6 � 0.3 14.1 � 0.3 17.1 � 1.2SOHO 63.552 �19.247 2000.5 2010.0 c 6.2 � 0.4 11.4 � 0.4 12.7 � 1.1STKA 64.439 �18.822 2006.6 2010.0 c �5.8 � 0.8 18.6 � 0.7 22.3 � 2.2STOB 64.446 �20.729 2003.7 2009.5 3 �9.8 � 0.9 18.6 � 1.3 7.1 � 1.6STOR 63.753 �20.212 2002.8 2010.0 c 5.0 � 0.4 15.0 � 0.4 8.0 � 1.2TAGL 64.130 �19.352 2001.6 2009.6 3 �0.8 � 0.5 18.5 � 0.6 19.9 � 1.7TBRU 63.924 �20.659 2005.3 2009.3 5 1.0 � 0.7 17.7 � 0.7 11.6 � 1.7TEIG 63.881 �17.759 2003.6 2009.6 4 7.9 � 0.7 10.7 � 1.2 22.9 � 2.2THJO 64.054 �19.866 2002.8 2009.4 8 �6.2 � 0.7 20.4 � 0.4 18.3 � 1.8THRA 63.821 �19.198 2000.5 2009.6 6 6.9 � 0.4 18.0 � 0.5 13.2 � 2.0THVE 63.861 �18.742 2001.6 2009.7 6 6.8 � 0.5 15.3 � 0.4 19.6 � 1.3TINF 63.975 �18.765 2001.6 2009.5 4 4.0 � 0.7 16.1 � 0.5 19.4 � 2.1TJAG 64.450 �20.649 2003.7 2009.5 3 �10.4 � 1.0 19.0 � 0.4 9.7 � 2.6UXAV 64.435 �20.988 2003.7 2005.3 2 �6.6 � 4.7 21.5 � 2.9 �7.3 � 2.3VAKO 64.248 �21.092 2003.7 2009.5 3 �8.8 � 0.7 18.3 � 0.6 2.5 � 1.5VALA 64.077 �19.523 2003.6 2009.5 6 �1.2 � 1.0 18.0 � 1.4 21.2 � 1.9VAVI 64.246 �21.066 2003.7 2009.5 3 �8.1 � 0.9 18.7 � 1.0 3.2 � 0.8VEDR 64.128 �21.904 2000.8 2003.2 2 �9.7 � 1.4 19.0 � 2.0 0.4 � 3.4VMEY 63.427 �20.294 2000.6 2010.0 c 6.5 � 0.3 15.5 � 0.3 4.0 � 0.8

aThe time series were corrected for co-seismic offsets from the May 2008 earthquakes (auxiliary material Data Set S1). Velocity uncertainties are 1sigma.

bStart and end of measurements used in this study.cNumber of campaigns, “c” for continuous data.dVelocity uncertainties are 1 sigma.


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field from the different components of an exemplary modelset-up. We treat the North American and Eurasian plates asrigid blocks with elastic deformation taking place on the plateboundary. We assume the relative North America – Eurasiablock motion (Figure 4f) is described by the Euler vectorfrom theMORVEL plate motion model [DeMets et al., 2010].The plate boundary segments are defined as finite, verticalrectangular dislocations in an elastic half-space [Okada,1985], with the interseismic strain accumulation modeled asthe sum of block motion and back slip on the plate boundarysegments (Figures 4c–4e), similar to Murray and Segall[2001]. Each segment is modeled with uniform componentsof opening and shear, such that the total displacement on thesegments is in agreement with the far-field block motion(i.e., �19 mm/yr at an azimuth of 102�E). In this study, we

allow the coordinates of the intersections of plate boundarysegments to be free parameters throughout the modeling,enabling us to directly solve for the best fitting plate boundarymodel and parameters. Because we do not observe significantdeformation across the WVZ (Figure 3), we only modelthe SISZ and EVZ, including a plate boundary segmentrepresenting the RP (Figure 1). The locking depth of theRP is fixed to 7 km based on the modeling of episodic GPSmeasurements [Árnadóttir et al., 2006; Keiding et al., 2008].[15] Magmatic deformation sources are modeled as sub-

surface bodies that change in volume. For Hekla volcano,we tested different source geometries, including a sphericalsource [Mogi, 1958; McTigue, 1987], a rectangular dike anda rectangular sill [Okada, 1985], a finite ellipsoid [Yang et al.,1988], and a closed vertical pipe [Bonaccorso and Davis,

Figure 3. GIA and co-seismic corrected horizontal velocities. These velocities are used as input for themodeling. The inset shows the scaled horizontal GIA signal, which we removed from the observed velocities.Note that the inset has a different velocity scale, and covers the same geographical area, as the main figure.Symbols as in Figure 1.


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1999]. We assume constant volumetric rates [Delaney andMcTigue, 1994; Tiampo et al., 2000] for the sources becausethe GPS time series do not provide evidence for any significanttemporal changes in site velocities in addition to the GIA signal.For Torfajökull we only apply the spherical source geometry.

Table 2. GPS Velocities Relative to Stable North America[DeMets et al., 2010], Corrected for 2008 Earthquake Offsets andGIAa

SiteEast

(mm/yr)North(mm/yr)

Up(mm/yr)

ALMA 1.9 � 1.2 1.0 � 0.9 �2.6 � 3.5BISK 2.8 � 0.7 0.9 � 1.1 �1.0 � 1.8BJAL 10.7 � 0.5 �0.5 � 0.6 1.3 � 1.8BLAU 18.8 � 0.9 �2.3 � 0.8 5.4 � 1.8BOTA 18.1 � 0.9 �2.9 � 0.9 1.4 � 5.5BREI 11.2 � 0.6 �2.2 � 0.6 2.2 � 1.0BRS2 17.9 � 1.5 �0.4 � 1.0 6.1 � 3.8BRSK 15.4 � 0.6 �3.9 � 0.4 9.5 � 1.7BUDH 6.6 � 0.8 0.5 � 0.8 0.7 � 2.2BULA 16.5 � 0.7 �3.1 � 0.4 3.4 � 1.6DIMO 2.1 � 0.5 1.2 � 1.0 �4.4 � 0.9DOMA 12.8 � 0.6 �1.8 � 0.4 1.0 � 2.0DROP 14.8 � 0.8 �4.1 � 0.5 1.6 � 3.9ELDH 17.0 � 0.4 �3.0 � 0.5 1.5 � 1.5FAGR 16.0 � 0.6 �3.7 � 0.7 3.4 � 1.5FAXI 16.9 � 1.0 �2.7 � 0.6 5.7 � 1.9FEDG 9.2 � 1.8 �1.1 � 1.3 1.3 � 3.3FITC 7.6 � 4.5 2.0 � 1.3 �0.5 � 3.6FJOC 1.5 � 1.5 3.7 � 1.4 1.6 � 5.7FLAG 7.7 � 0.6 �1.1 � 0.6 2.9 � 2.0FOSS 1.8 � 1.3 1.2 � 0.9 0.8 � 3.1FROS 12.9 � 1.1 �0.1 � 1.1 0.3 � 4.7GALT 13.7 � 1.0 �2.7 � 0.8 4.2 � 1.6GELD 3.5 � 0.7 �0.2 � 0.5 4.0 � 1.6GJBA 1.9 � 0.6 0.9 � 0.7 �10.7 � 1.3GLER 7.1 � 1.1 0.8 � 0.9 3.3 � 2.3GOLA 18.2 � 1.2 �3.6 � 0.9 �2.8 � 2.9GRFL 8.6 � 0.7 �4.2 � 0.6 4.4 � 2.7GULL �1.2 � 2.8 1.0 � 1.6 �3.4 � 4.0HAFU 5.4 � 0.8 1.1 � 0.5 13.2 � 2.8HALD 7.3 � 0.6 1.3 � 0.7 5.6 � 2.5HAMR 16.4 � 0.5 �2.6 � 0.5 3.1 � 1.5HAUC 3.1 � 1.3 3.7 � 1.1 1.7 � 4.0HAUD 7.2 � 1.1 �2.5 � 1.0 0.6 � 2.5HEHA 14.4 � 0.8 �1.6 � 0.5 3.2 � 1.8HEKR 10.7 � 1.3 �1.8 � 1.2 �3.1 � 3.1HEND 15.5 � 1.0 0.0 � 0.9 5.7 � 3.5HESA 10.5 � 1.4 �0.2 � 1.3 �0.2 � 4.7HGJA 2.1 � 0.8 0.5 � 0.7 �2.4 � 0.9HIAK �0.5 � 1.8 1.9 � 1.8 �2.1 � 3.6HLFJ 3.6 � 0.8 0.7 � 0.8 �2.9 � 2.1HNAU 11.3 � 0.7 �1.5 � 0.6 �0.6 � 1.7HRAF 15.0 � 0.6 �3.3 � 0.9 �4.9 � 2.0HRAS 14.9 � 1.1 �0.6 � 0.8 3.8 � 1.9HVEL 0.4 � 0.9 1.1 � 0.8 �3.8 � 2.3HVOL 17.2 � 0.4 �4.6 � 0.3 �2.6 � 1.0INSK 3.3 � 2.5 2.7 � 2.0 �1.2 � 5.5ISAK 5.7 � 0.5 2.7 � 0.4 3.5 � 1.0JOKU 8.5 � 0.8 �2.8 � 0.5 7.2 � 2.6KALD 8.6 � 1.8 �0.4 � 2.4 �7.7 � 4.9KALF 15.8 � 0.8 �3.8 � 0.7 7.7 � 5.1KALT 14.8 � 1.1 �1.6 � 0.9 �1.6 � 2.4KARA 2.8 � 0.4 1.0 � 0.3 �5.9 � 0.8KELD 13.9 � 0.8 �2.6 � 0.6 2.4 � 2.4KGIL 16.3 � 0.7 �0.7 � 0.5 �1.4 � 2.0KIDJ 8.3 � 0.4 1.3 � 0.3 �1.8 � 0.8KKLO 16.3 � 0.7 �0.4 � 0.6 1.8 � 3.0KOPS 3.0 � 0.9 0.2 � 0.7 5.6 � 3.0KRHR 9.3 � 0.9 �1.6 � 0.4 4 � 2.1KROK 13.1 � 0.6 0.8 � 0.6 3.4 � 1.5KVFE 10.3 � 0.8 �1.3 � 0.6 1.9 � 1.4KYLI 12.7 � 0.4 �0.9 � 0.6 �2.3 � 1.1L257 13.5 � 1.9 �0.6 � 2.3 �13.0 � 4.0LAHR 12.7 � 0.6 �1.8 � 0.7 �1.7 � 3.0LAMH 1.5 � 0.5 2.1 � 0.6 �0.3 � 1.9LANG 2.4 � 1.7 0.6 � 1.6 �15.2 � 5.2LAUF 18.1 � 1.4 �1.1 � 1.0 1.9 � 2.2LAUN 10.0 � 0.9 �1.0 � 0.7 3.0 � 1.6

Table 2. (continued)

SiteEast

(mm/yr)North(mm/yr)

Up(mm/yr)

LAVA �1.0 � 1.9 0.3 � 3.1 �2.2 � 5.1LFEL 2.7 � 1.0 0.8 � 0.8 �2.9 � 2.5LIHO 14.8 � 0.8 �1.7 � 0.6 2.0 � 1.6LJOF 8.9 � 1.0 �1.6 � 0.4 8.0 � 1.6LYTI 14.2 � 0.8 �1.9 � 0.8 5.2 � 3.6MAEL 16.5 � 0.4 �1.8 � 0.4 0.4 � 1.4MJSK 12.8 � 1.8 �4.6 � 1.2 �2.3 � 3.3MOHN 9.5 � 1.2 �0.6 � 1.1 5.0 � 3.6MORK 15.3 � 2.3 �3.4 � 1.9 1.7 � 4.7MUFE 13.8 � 0.8 �2.9 � 0.6 5.8 � 1.9NAEF 4.1 � 0.7 0.0 � 1.1 17.1 � 2.3NBJA 9.1 � 0.6 �1.1 � 0.6 �4.5 � 2.7NLAN 10.2 � 0.6 �3.0 � 0.4 5.0 � 2.2NOFA 13.8 � 1.0 �1.2 � 0.5 2.5 � 1.7NOHR 11.8 � 0.7 �1.5 � 1.5 �5.7 � 2.3NONH 13.6 � 0.7 �1.3 � 0.7 4.3 � 1.8NORS 9.3 � 1.5 �0.7 � 1.4 1.8 � 2.9NOXL 9.3 � 0.5 �1.8 � 0.5 3.0 � 1.1PALA 13.4 � 0.8 �5.0 � 0.5 4.9 � 1.3PSI1 19.4 � 1.5 �0.3 � 1.2 �2.5 � 3.2PSU2 21.5 � 1.9 �2.0 � 1.9 0.2 � 3.7PSU3 12.6 � 3.4 �1.1 � 1.9 �8.6 � 5.6PSU4 17.9 � 3.4 �3.6 � 2.9 �10.0 � 6.3PSU5 16.4 � 2.0 2.5 � 3.7 2.1 � 4.4PSU6 16.5 � 3.3 0.6 � 1.2 �6.0 � 4.7PSU7 13.6 � 1.7 �0.7 � 1.9 �10.0 � 3.7PSU8 8.7 � 1.8 �0.2 � 1.1 �8.5 � 3RAUK 10.4 � 0.6 �0.6 � 0.5 6.4 � 2.1RETT 7.9 � 0.9 �2.0 � 0.6 6.6 � 3.1REYK �0.1 � 0.4 1.3 � 0.3 �5.4 � 1REYZ �0.3 � 1.4 1.4 � 0.6 �5.0 � 1.9SARP 4.1 � 4.4 5.1 � 4.4 �6.2 � 7.6SATU 18.1 � 0.8 0.5 � 0.8 1.2 � 1.6SAUR 9.3 � 0.9 �0.9 � 0.8 0.4 � 2.2SBJA 9.7 � 0.5 �1.8 � 0.7 8.4 � 1.6SKAL 0.8 � 3.3 �2.9 � 2.9 �5.8 � 7.4SKDA 2.3 � 2.6 1.0 � 1.9 �7.1 � 5.2SKHR 13.8 � 1.5 �4.5 � 0.6 6.8 � 1.8SKJA 9.2 � 0.5 1.8 � 0.6 7.1 � 1.3SKOT 2.7 � 1.6 1.6 � 3.7 �5.1 � 3.6SKRO 3.7 � 0.5 1.7 � 0.3 2.0 � 1.2SLAN 12.7 � 0.3 �2.3 � 0.3 3.0 � 1.7SNAE 16.7 � 0.3 �2.8 � 0.3 1.9 � 1.2SOHO 16.3 � 0.4 �5.0 � 0.4 �1.0 � 1.1STKA 5.4 � 0.8 0.3 � 0.7 1.8 � 2.2STOB 1.9 � 0.9 0.8 � 1.3 �4.1 � 1.6STOR 15.8 � 0.4 �2.8 � 0.4 �0.6 � 1.2TAGL 10.0 � 0.5 0.6 � 0.6 5.0 � 1.7TBRU 11.8 � 0.7 �0.2 � 0.7 4.1 � 1.7TEIG 17.5 � 0.7 �4.7 � 1.2 3.4 � 2.2THJO 4.7 � 0.7 2.6 � 0.4 6.4 � 1.8THRA 17.5 � 0.4 �0.1 � 0.5 �2.2 � 2.0THVE 16.6 � 0.5 �2.1 � 0.4 3.4 � 1.3TINF 14.4 � 0.7 �1.3 � 0.5 2.4 � 2.1TJAG 1.3 � 1.0 1.3 � 0.4 �2.2 � 2.6UXAV 5.0 � 4.7 3.4 � 2.9 �17.0 � 2.3VAKO 2.4 � 0.7 0.4 � 0.6 �5.1 � 1.5VALA 9.7 � 1.0 0.1 � 1.4 7.4 � 1.9VAVI 3.1 � 0.9 0.8 � 1.0 �4.5 � 0.8VEDR 1.0 � 1.4 0.8 � 2.0 �3.9 � 3.4VMEY 16.8 � 0.3 �2.2 � 0.3 �2.3 � 0.8

aSee auxiliary material Data Set S1 for details on 2008 earthquakeoffsets, and see auxiliary material Data Set S4 for details on GIA.


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3.2. Parameter Optimization and Uncertainties

[16] For the best fit parameter estimation, we use aMonte Carlo-type simulated annealing algorithm followingCervelli et al. [2001] and Árnadóttir et al. [2009], minimiz-ing the weighted sum of squares of the residuals, WRSS =S(Vi � Mi)

2/si2, where M denotes the model predictions

and Vi are the observed earthquake- and GIA-correctedvelocity components (Table 2 and Figures 2b and 3) with

uncertainties si. We do not account for correlations betweenvelocity components in our analysis. We compare the levelof fit of different models, for example a spherical sourceversus a dike for Hekla, by the WRSS and the reduced chi-square measure, cv

2 = WRSS/(N � p), where N is the numberof data (three times the number of stations when using allthree velocity components) and p is the number of freeparameters in the optimization. If there is an improvementin WRSS when more parameters are added to the model,

Figure 4. Calculated horizontal velocity contribution of (a–f) each of our preferred best fit model (modelPBHmTm) components to (g) the combined model prediction. Figures 4a and 4b show the predictedvelocities from spherical (Mogi) sources at Hekla and Torfajökull. Figures 4c, 4d, and 4e show the backslip contributions of Reykjanes Peninsula (RP), South Iceland Seismic Zone (SISZ), and Eastern VolcanicZone (EVZ), respectively. Figure 4f shows the motion of the Eurasian block relative to a fixed NorthAmerica block. The sum of the back slip and block motion equals the interseismic deformation. Note thatthe velocity scale varies between plots. See Table 4 for best fit parameter values. The best fitting plateboundary location is shown with a dashed line, and the best fitting sources for Hekla and Torfajökullshown as a white triangle and a white inverted triangle, respectively. Symbols as in Figure 1.


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a standard F test is used to verify if the improvement isstatistically significant, following Stein and Gordon [1984].[17] Parameter uncertainties are estimated in a separate

step by adding Gaussian noise to the velocities correspondingto the velocity uncertainties and re-running the optimizationprocess 400 times, each time with different input velocities[e.g., Metzger et al., 2011; Liu et al., 2011]. The distributionof the resulting best fit parameters (Figure 5) is used to definethe upper and lower confidence limits for each parameter.All uncertainties are consistently reported at the 1-sigmalevel. We acknowledge that the actual uncertainties may be

larger than we report, because in the uncertainty estimatewe do not account for model set-up (e.g., values of elasticparameters, the choice of a specific North America – EurasiaEuler vector, or whether the WVZ is included) or uncertain-ties resulting from corrections made to the data (i.e., theco-seismic offsets and GIA corrections).

3.3. Spherical Volcanic Sources and the PlateBoundary

[18] In order to find the model that best describes theobservations using the fewest number of parameters, we test

Figure 5. Correlation plots for model parameters for the spherical source model for Hekla (PBHmTm),obtained using perturbed velocities (400 model runs). Each dot is a best fit value for a perturbed velocityfield. The boundaries of the graphs represent the search range for each parameter. The source depth andstrength for the Hekla source show the strongest correlation. Hekla e (east) and Hekla n (north) representthe location of the Hekla source (in km from the summit of Hekla). Hekla d and Hekla v represent thedepth (in km) and volume rate (in 106 m3/yr), respectively. SISZ LD and EVZ LD represent the lockingdepths of the SISZ and EVZ. For the intersection of the plate boundary axis (in degrees of latitude andlongitude), R-S n represents the north coordinate of the RP – SISZ intersection; S-E n and S-E e representthe north and east coordinates of the SISZ – EVZ intersection, respectively; E-N e represents the eastcoordinate of the EVZ – NVZ intersection.


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eight models with increasing complexity (Table 3). All of themodels use the same input velocities (Table 2 and Figure 3),and the same parameter search boundaries for an even com-parison, unless explicitly noted. We first run a plate boundarymodel with no magmatic deformation sources (model PB).This model has six free parameters: two for the lockingdepths of the EVZ and SISZ, and four for the plate boundaryintersections: one for the north coordinate of the RP-SISZintersection (we found that the east coordinate was alwaysvery poorly constrained and hence fixed it to the same valueas Árnadóttir et al. [2009]), two for the coordinates of theSISZ-EVZ intersection, and one for the east coordinate of theEVZ-NVZ intersection (we fixed the north coordinate ofthe EVZ-NVZ intersection to the same value as Árnadóttiret al. [2009]). This model (PB) results in cv

2 = 8.17 (Table 3).[19] Next we add a spherical (Mogi) source for Hekla,

which adds four parameters (source location and volume rate)for a total of ten parameters (model PBHm). The optimalparameter values for this model result in cv

2 = 5.36. An F testverifies that this model is statistically better (>99% confi-dence) than model PB. Next we add a point source forthe subsidence at Torfajökull (model PBHmTm). We foundthat the data cannot constrain the location of the Torfajökullsubsidence source and therefore fixed its location to that deter-mined by Scheiber-Enslin et al. [2011], who used a combi-nation of eGPS, leveling and InSAR data. The Torfajökullsource thus adds two more parameters (depth and volumerate) for a total of twelve parameters (Table 3). The optimalparameters for this model result in cv

2 = 5.33. The improve-ment in fit when adding a deformation source for Torfajökull(Table 3) is small compared to solving only for Hekla andthe plate boundary, and is not statistically significant at the99% confidence level; however, this model agrees with othergeodetic observations [Scheiber-Enslin et al., 2011]. There-fore, we include the Torfajökull source in all subsequentmodels.[20] To visualize the magnitude of the deformation signals

from Hekla and Torfajökull we subtract the plate boundarydeformation component from the results of model PBHmTmfrom the observed velocities, leaving only a signal fromHeklaand Torfajökull in the data (Figure 6a). The horizontal com-ponent of the inflation signal from Hekla extends over southIceland, with a maximum predicted rate of <3.5 mm/yr at adistance of 16 km from Hekla and, according to our best fitparameters to model PBHmTm (Table 4), falls below 1 mm/yrat 60 km distance. The model prediction for the best fitting

point sources at Hekla and Torfajökull, shown as white arrowsin Figure 6a, is in fair agreement with the observations.However, subtle systematic differences between the modeland observations, in particular, rapidly changing velocities atsites west and north of the summit of Hekla, might suggest anadditional shallow magmatic source or different magmaticsource geometry. We tested whether an additional inflatingspherical source could explain the velocity misfits, solvingagain simultaneously for the plate boundary, a shallow and adeep spherical source at Hekla, and a subsidence source atTorfajökull (model PBHmmTm). The best fitting shallowspherical source was located 6–11 km W of the summit andat 3–8 km depth, and inflating at 0.0004–0.0014 km3/yr.The deeper source in this model is located 2–8 km E of thesummit and at 23–33 km depth. This model has cv

2 = 5.17and is statistically better (>99% confidence) than the singlesource model for Hekla. This model is appealing to explainthe rapidly varying velocities west of Hekla (Figure 6a),however, we find the result geologically perplexing becausethere are no active volcanic systems west of Hekla and themodel (PBHmmTm) predicts magma chambers laterallyoffset by �17 km, the approximate distance between theHekla and Torfajökull magma chambers. We thus prefer thesingle source model (PBHmTm).

3.4. Other Models of the Geometry of the HeklaMagma System

[21] The morphology and eruptive history of Heklavolcano demonstrate that the volcano is elongated in anortheast-southwest direction (N60�E) and that eruptionsoccur along the >8 km long Heklugjá eruptive fissure andsub-parallel fissure swarms [Thorarinsson, 1967]. It has beenproposed that the magma chamber under Hekla is elongatedin a northeast-southwest direction along the volcanic system[Gudmundsson et al., 1992]. We test four additional sourcegeometries for the inflation signal at Hekla to examine ifthere are tendencies for an elongated source along the Heklavolcanic system or deformation associated with a verticalmagma chamber. For each model we re-estimate the optimalparameters for the plate boundary and a spherical sourcefor Torfajökull as before.[22] In model PBHdTm we incorporate a dike for the

Hekla inflation source and solve for the central location,depth to the top, strike, length, width, and opening rate of thedike (total of 15 parameters). This model has a significantlyworse fit (cv

2 = 8.08) than the spherical source model(Table 3). The parameters of the dike are poorly constrainedand the model appears not to be applicable for inter-eruptivemagma accumulation at Hekla.[23] In model PBHsTm we test a rectangular sill model

for Hekla, where we solve for the location, depth, length,width, and opening rate of the sill. The strike was fixed to60� (the approximate strike of Hekla). This model hascv2 = 6.60 and fits the data worse than PBHmTm (Table 3).

The dimensions and opening rate of the sill are poorlyconstrained, with no clear correlation between the lengthand width of the sill. The estimated depths range from 24 to37 km.[24] In model PBHeTm we test an ellipsoidal source. We

solved for horizontal location, depth, pressure increase, andsemimajor axis of the ellipsoid, a total of 5 parameters inaddition to the eight representing the plate boundary and

Table 3. Comparison of Different Model Results

Modela Number of Parameters WRSS cv2

PB 6 3012 8.17PBHm 10 2019 5.36PBHmTm 12 1998 5.33PBHpTm 13 1996 5.34PBHeTm 13 1911 5.11PBHmmTm 16 1917 5.17PBHdTm 15 3007 8.08PBHsTm 14 2460 6.60

aModel naming scheme as follows: PB: solve for plate boundaryintersections and locking depths; H: include a source for Hekla; T: includea source for Torfajökull. Lower case letters indicate the type of volcanicsource model: m: Mogi (spherical) source; p: pipe source; mm two Mogisources; d: dike; s: sill; e: ellipsoid.


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Torfajökull. We found that we had to fix or tightly constrainsome of the ellipsoid parameters to obtain stable solutions.Specifically, we fixed the plunge to 0� (horizontal ellipsoid),the semiminor axis to 1 km, and the strike to 60�. We alsotested a strike of 40�, which gave a slightly worse fit, and 50�,which gave a similarly good fit as 60�. We apply equation 18of Tiampo et al. [2000] to obtain the volume rate for thissource. The ellipsoidal model fits the GPS velocities signifi-cantly better (>99% confidence) than the spherical sourcemodels PBHmTm and PBHmmTm (Table 3) with cv

2 = 5.11.The best fit model predicts the rapid motion west of Hekla(Figure 6b), better than the spherical model (Figure 6a).However, the model does not improve the fit to sites imme-diately north of Hekla. The best fit ellipsoid has a total lengthof 22–38 km and is at a depth of 22–28 km (Table 4).We verified that the deformation is identical from an ellipsoidwith a shorter semiminor axis (e.g., 0.1 km) and highervolume rate; therefore we are not sensitive to the totalvolume of the ellipsoid.[25] In the last model (PbHpTm), we tested a closed

vertical pipe model [Bonaccorso and Davis, 1999] for Hekla.The closed pipe model approximates deformation from avertically dipping, prolate spheroid [Yang et al., 1988] withthe semiminor axis much smaller than the semimajor axis.This model predicts a characteristic local subsidence centeredon the volcano (Figure 7) and is thus an interesting alternativemodel to the Hekla lava-loading model [Grapenthin et al.,2010]. We again solved simultaneously for the plate bound-ary and Torfajökull source parameters. For the pipe we solvedfor its horizontal location, the depths to the top and bottom ofthe pipe, and the volumetric rate. The results indicate topdepths of 9–13 km and bottom depths of 17–28 km for thepipe (Table 4). The best fitting parameters give cv

2 = 5.34,quite similar to our spherical source model, PBHmTm.The best fit model predicts higher velocities near Hekla thanmodels PBHmTm and PBHeTm (Figure 6c).

4. Discussion

[26] Magmatic systems in Iceland are intimately relatedwith the divergent plate boundary, accommodating relativeplate motion through repeated rifting events. Surface defor-mation in south Iceland is driven by North America - Eurasiarelative plate motion along the RP, SISZ and EVZ, mag-matism at central volcanoes, and the effects of rapid glacialmelting [Árnadóttir et al., 2009]. The SISZ-EVZ intersec-tion in south Iceland is atypical compared to most mid-oceanridge-transform intersections, because of the interactionbetween the Icelandic hot spot and the Mid-Atlantic Ridge atthis latitude. Nevertheless, secular plate motion across theplate boundary segments and at their intersection dominatesthe horizontal surface velocities (Figure 3) masking volcanicdeformation at Hekla volcano and Torfajökull caldera(Figure 6). Our models account for inter-seismic and inter-rifting elastic strain accumulation on the SISZ and EVZ,respectively, in order to investigate the inflation source atHekla, and subsidence source at Torfajökull. The combinedplate boundary and volcanic sourcemodels explain most of thehorizontal GPS site velocities and the residuals are small(Figure 8). The horizontal ellipsoid model (PBHeTm) fits theobserved velocities best (Table 3). Comparing the fit of the

Figure 6. The horizontal velocity field at the SISZ-EVZintersection (black vectors) after subtracting from the observa-tions, the plate boundary deformation using the best fit plateboundary parameters of models (a) PBHmTm, (b) PBHeTm,and (c) PBHpTm. Best fit location of the plate boundary(Table 4) is shown with a dashed black line for each model.The residual signal is dominated by inflation at Hekla, andto a lesser degree, deflation at Torfajökull. The white vectorsshow model predictions for Hekla and Torfajökull deforma-tion sources. The location of the best fitting source forHekla and the fixed source at Torfajökull are shown as a whitetriangle and a white inverted triangle, respectively. Symbolsas in Figure 1.


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models to the signal from Hekla and Torfajökull (Figures 6a–6c), we conclude that although model PBHeTm is statisticallysuperior, models PBHmTm and PBHpTm (spherical and pipe-shaped models of Hekla, respectively) remain plausibleoptions. Below we discuss the results and implications of theseparate models and model components.

4.1. The SISZ and EVZ Plate Boundary Segments

[27] Despite the simple representation of the SISZ andEVZ plate boundary segments, our model explains most ofthe horizontal velocity field (Figure 8). The plate boundaryparameters are quite similar for each of the three best fitmodels (Table 4). We discuss below the plate boundaryresults in terms of model PBHmTm. The assumption thatpresent-day North America – Eurasia motion is described

by the MORVEL plate motion model [DeMets et al., 2010],is reasonable at this level of detail (Figure 8). A few sitessouth of the central SISZ have eastward residual velocities(Figure 8) and sites in the southern part of the WVZ are notvery well fit. This may be related to our modeling of the SISZand RP (Figures 4c and 4d), each as single-segment trans-form fault systems with constant locking depths, instead ofusing a variable depth to the brittle-ductile transition zonealong the SISZ as determined by seismic data [Stefánssonet al., 1993]. Sites in the northern part of the EVZ haveresidual northward azimuths (Figure 8), similar to residualtrends observed by Árnadóttir et al. [2009].[28] The intersection of the SISZ and EVZ was found to

be within the Torfajökull caldera (Table 4), although thereexist solutions from the perturbed input velocities that arewell north and east of Torfajökull (Figure 5; S-Ee versusS-En). The best fit location for the intersection of the SISZand the EVZ (63.96�0.03

+0.10 �N, �19.32�0.06+1.10 �E) is similar to

what has been inferred before from seismicity in the SISZ,previous geodetic studies, geology, and observations of the

Table 4. Best Fit Parameters and 1-Sigma Uncertainties forModels PBHmTm, PBHpTm, and PBHeTm

ParameterPBHmTm(Sphere)

PBHpTm(Pipe)

PBHeTm(Ellipsoid)

SearchRange

HeklaEasta (km) �2.5�1.4

+5.2 �0.6�1.0+1.3 �0.9�1.5

+2.6 �6 to 6

Northa (km) �0.2�3.4+0.9 �0.9�1.6

+1.0 �1.1�1.7+0.9 �6 to 6

Depth (km) 24�2+5 - 24�2

+4 1 to 40

Vol. rate (106 m3/yr) 19�2+11 8�1

+3 17�2+7 1 to 40

Top depth (km) - 10-1+3 - 0.1 to 40b

Bottom depth (km) - 21�4+7 - 3 to 40b

Long axis (km) - - 12�1+7 0.5 to 30

Short axis (km) - - 1c

Torfajökull Spherical SourceNorth (�N) 63.93c

East (�E) �19.22c

Depth (km) 15�5+8 11�3

+4 11�3+7 1 to 40

Vol. rate (106 m3/yr) �1.5�4.0+0.6 �1.3�1.2

+0.4 �1.1�2.9+0.3 �40 to 0

Coordinates of Plate Boundary Segment IntersectionsRP-SISZ (�N) 64.03�0.03

+0.02 64.02�0.02+0.03 64.02�0.02

+0.02 63.9 to 64.1

RP-SISZ (�E) �21.24c

SISZ-EVZ (�N) 63.96�0.03+0.10 63.97�0.03

+0.08 63.98�0.02+0.09 63.8 to 64.1

SISZ-EVZ (�E) �19.32�0.06+1.10 �19.08�0.15

+0.90 �19.25�0.06+0.90 �20 to �17

EVZ-NVZ (�N) 64.9c

EVZ-NVZ (�E) �16.5�0.6+0.5 �16.2�0.9

+0.3 �16.4�0.7+0.4 �18 to �14

RR-RP (�N) 63.7c

RR-RP (�E) �23.8c

Locking Depths of Plate Boundary SegmentsSISZ (km) 15�2

+3 18�2+2 21�3

+3 1 to 30

EVZ (km) 11�2+5 13�3

+5 10�2+2 1 to 30

RP (km) 7c

Strike of Plate Boundary Segmentsd

SISZ (�) 94�8+3 92�5

+4 92�6+3

EVZ (�) 51�17+4 52�20

+6 52�11+3

aDistance from the summit of Hekla, 63.992�N, �19.667�E.bFor the pipe model, the depth to the top must be less than the depth to

the bottom.cFixed parameter.dDerived from the intersections of RP (Reykjanes Peninsula), SISZ

(South Iceland Seismic Zone), EVZ (Eastern Volcanic Zone), and NVZ(Northern Volcanic Zone).

Figure 7. (top) Vertical and (bottom) radial velocities as afunction of distance from the best fitting spherical source forHekla (Table 4). Deformation from the plate boundary andTorfajökull (model PBHmTm) have been removed fromthe observations. Solid line shows the predicted velocityprofile for the best fit spherical source (Table 4) and dashedline the predicted deformation for the best fit vertical pipemodel (Table 4) at the same horizontal location as the spher-ical source.


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topography of the volcanic ridges characteristic of the EVZ[e.g., Soosalu and Einarsson, 2005; LaFemina et al., 2005;Árnadóttir et al., 2009; Scheiber-Enslin et al., 2011]. Wedo not find correlations between the location of the SISZ-EVZ intersection and the depth or volume rate of the Heklainflation or Torfajökull deflation sources (Figure 5). This islikely the case for Hekla because it lies closer to the axis ofthe SISZ than the EVZ (Figure 6). Seismicity at Hekla duringnon-eruptive periods resembles patterns of seismicity in theSISZ, which also suggests that Hekla is in the SISZ [Soosaluand Einarsson, 2005]. Our model result for the location ofthe SISZ axis coincides with the center of historical seis-micity and zone of bookshelf faulting in the SISZ (Figure 8)[e.g., Einarsson, 1991]. The axis of the EVZ (i.e., the centerof plate spreading) falls in the western part of the EVZ(Figure 8) as found previously [LaFemina et al., 2005;Scheiber-Enslin et al., 2011].[29] For the SISZ we estimate a locking depth of 15þ3

�2 km,comparable to the 15þ8

�5 km estimated by Árnadóttir et al.[2006], but somewhat higher than previous estimates of7þ3�2 km and 9.5 km by Árnadóttir et al. [2009] and Decriem

and Árnadóttir [2012], respectively. We interpret the lockingdepth of the SISZ as a proxy for the depth to the brittle-ductiletransition. Árnadóttir et al. [2006] modeled both a singleeast-trending fault and multiple north-trending “bookshelf”faults for the SISZ and concluded that the single east-trendingfault model had fewer parameters and fit the data better.The best fit locking depths in the SISZ seem to dependmore on the choice of source model for Hekla (Table 4), butdo not show a clear correlation with any of the othermodel parameters (Figure 5). Our locking depth estimate ismostly constrained by data from the eastern part of theSISZ and is somewhat deeper than the maximum depth forearthquakes of 12 km for this area [Stefánsson et al., 1993;Árnadóttir et al., 2006].

[30] The locking depth we estimate for the EVZ is 11þ5�2 km,

similar to the depth of 13þ7�3 km for the northern part of

the EVZ found by LaFemina et al. [2005] using 2-D elastichalf-space models. However, it is greater than the 3:0þ1:2

�0:7 kmfor a profile crossing the EVZ north of Torfajökull[LaFemina et al., 2005]. Scheiber-Enslin et al. [2011]obtained a locking depth of 5 � 2.5 km for a similar profilenorth of Torfajökull using longer time series than LaFeminaet al. [2005]. Estimated locking depths within and south ofTorfajökull indicate depths <7 km [LaFemina et al., 2005;Scheiber-Enslin et al., 2011]. Using a sparser but moreregional data set spanning 1993 to 2004, Árnadóttir et al.[2009] found a locking depth of 6–10 km when modelingthe EVZ.[31] We interpret the locking depth in the EVZ as the brittle

- ductile transition [LaFemina et al. 2005]. It is difficultto obtain independent estimates of the brittle thickness ofthe crust within the EVZ, because this zone has been essen-tially aseismic outside the central volcanoes in recent decades[Einarsson, 1991; Jakobsdóttir, 2008]. Our locking depthestimate of the EVZ is governed by the width of thedeforming zone in the EVZ as is apparent in the velocity field(Figure 1). Our estimates of locking depth may be biasedbecause we do not attempt to solve for varying opening ratesalong the EVZ as in LaFemina et al. [2005] nor apply morecomplicated models for the geometry of the EVZ [Traviset al., 2011]. However, our representation of the EVZ fitsthe observed velocities adequately (Figure 8). Thus we do notpursue here further different models of the EVZ.

4.2. Subsidence of Torfajökull Caldera

[32] The horizontal velocity field indicates motion towardthe western end of Torfajökull caldera, indicating subsidenceof the caldera (Figure 6a). This is consistent with the findingsof Scheiber-Enslin et al. [2011]. Our results for the subsi-dence source at Torfajökull are not well constrained. TheTorfajökull deflation source that best fits our observations islocated at 15þ8

�5 km depth and deflates at a volumetric rate of�1:5þ0:6

�4:0 � 10�3 km3/yr (Table 4, model PBHmTm). Oursensitivity analysis (Figure 5) shows tradeoffs between theTorfajökull volume and Hekla source parameters. The hori-zontal source location was constrained to that reported byScheiber-Enslin et al. [2011] as determined from eGPS, tilt,and InSAR measurements, however, our depth estimate isdeeper than their estimate of 5 km depth. The maximumhorizontal velocity from our Torfajökull source is less than1.0 mm/yr (Figure 4b), which is on the same order as ourmeasurement uncertainties (Table 2). Deformation sourcemodels do not distinguish between different mechanisms forcontraction such as cooling of a magma chamber, pressurechanges in geothermal systems, magma drainage, or loadingby recent, thick lava flows. Soosalu and Einarsson [2004]find an aseismic volume at �8 km depth that they inferredas a coolingmagma chamber. However, Soosalu and Einarsson[2004] also note that shear waves travel through this volumewithout detectable attenuation and thus this body cannotcontain a large fraction of melt. Furthermore, Lippitsch et al.[2005] do not find any direct evidence for a magma chamber,but note that a sharp cut-off in seismicity below 3 km depthand high geothermal activity may indicate the existence ofa cooling magma chamber below this depth.

Figure 8. Residual velocity vectors after subtracting the bestfitting model (PBHmTm) from the observations. The bestfitting plate boundary geometry is shown with a dashed lineand the source locations for Hekla and Torfajökull are shownas a white triangle and a white inverted triangle, respectively.Symbols as in Figure 1.


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4.3. Decadal Inflation of Hekla Volcano

4.3.1. Depth and Location of the Magma Chamber[33] All our models predict that the deformation source of

Hekla is deep – at lower crust or Moho depths. The best fitsingle spherical source (PBHmTm) for Hekla is at 24þ5

�2 kmdepth, and the best fit ellipsoidal source (PBHeTm) is at24þ4

�2km depth (Table 4). These depths are somewhat deeper

than the 17 � 3 km depth that Ofeigsson et al. [2011] foundfrom modeling of InSAR data for the inter-eruptive periods1993–2000 and 2003–2008. Profiles of the observed andpredicted horizontal and vertical velocities as a function ofdistance from Hekla (Figure 7), demonstrate that the depthof the source is constrained more by the horizontal velocitiesthan the vertical velocities. The vertical velocities are scatteredand have large uncertainties, however, they do indicate thatthere is uplift associated with Hekla, overprinted with relativesubsidence centered on Hekla, in accordance with InSARdata [Ofeigsson et al., 2011].[34] In order to verify that the magma chamber at Hekla is

indeed required to be deep to fit the GPS velocities, weperformed a number of tests to see if the results were robust.To test the impact of the scaled GIA corrections (auxiliarymaterial Data Set S4) on the results, we reran modelPBHmTmwithout these corrections using only the horizontalvelocities. This resulted in a depth of 22þ6

�3km for the Hekla

source (auxiliary material Data Set S5), insignificantlydifferent from the results from the glacially corrected data set.To test whether sites far away from Hekla that were not fit bythe models (e.g., sites in theWVZ, or the northern EVZ) wereaffecting the depth estimate at Hekla, we applied the best fitparameters for the plate boundary and Torfajökull frommodel PBHmTm (Table 4) and solved for a single sphericalsource at Hekla using only sites within 50 km of Hekla. Thisresulted in depths of 19.5–21.5 km for the magma chamberat Hekla. Furthermore, we tested if neglecting possiblelava loading affects the depth estimate of model PBHmTm.We applied predicted corrections for the lava loading(R. Grapenthin, personal communication, 2011) to the vertical(maximum of 8.5 mm/yr) and horizontal (maximum of0.9 mm/yr) GPS velocities, and re-ran model PBHmTm,solving for the plate boundary and point sources for Heklaand Torfajökull. This resulted in a best fit depth for the Heklasource of 25þ1

�2km, comparable to the 24þ5

�2km depth obtained

by modeling the original velocity field (Table 4). We thusconclude that the GPS data necessarily imply a deep sourcefor the magma chamber at Hekla, deeper than 20 km.[35] Earlier geodetic studies of Hekla volcano found shal-

lower depths for the modeled magma reservoir. Kjartanssonand Gronvold [1983] used EDM data collected in a 10 monthperiod following the 1980 – 1981 eruption and found a sourcedepth of 7–8.5 km. Tryggvason [1994] compiled tilt and EDMmeasurements spanning the 1970, 1980–81 and 1991 eruptionsand inter-eruptive periods demonstrating a sawtooth patternfor Hekla inflation and rapid co-eruptive deflation [see alsoSturkell et al., 2006b]. From these data, Tryggvason [1994]estimated the source to be at 5–6 km depth and centered 4–6 km N or NW of the summit. Other studies that tried toestimate the source location place it �2 km south of thesummit [Kjartansson and Gronvold, 1983]; under the summit[Sigmundsson et al., 1992]; or around 1 km east of the

summit [Ofeigsson et al., 2011]. The source location we findis either slightly west of the summit, or located roughly at theaxis of the volcano (Table 4). Sigmundsson et al. [1992]estimated a depth of 9þ6

�7 km for the source of the 1991eruption using campaign GPS data, noting that the smallaperture and low GPS network density close to Hekla for the1991 eruption made it difficult to constrain the source depthand strength for the eruption. The same is likely true for theEDM and tilt measurements. Using borehole strain data,Linde et al. [1993] obtained a depth of 6.5 km for the 1991co-eruptive signal. This depth was later revised to �11 km[Jónsson et al., 2004]. Sturkell et al. [2005] found a depth of11 km for the 2000 eruption magma source using boreholestrain and tilt data.[36] In addition to geodetic methods, geochemical and

geophysical methods have been used to constrain the magmaplumbing system at Hekla. Petrologic analyses of Heklaeruptive products indicate that the magma is stored at depthsgreater than 11–12 km [Moune et al., 2007; D. Geist, personalcommunication, 2012] and depths of 17.7 to 34.0 km [Kelleyand Barton, 2008], prior to eruptions. Soosalu and Einarsson[2004] demonstrated by studying S-wave attenuation thatthere cannot be an extensive magma chamber under Heklabetween 4 and 14 km. Our observations of rapidly changingvelocities west of Hekla (Figures 6a–6c) could indicate anadditional inflation source at shallow or intermediate depthswest of Hekla, however, there is no geologic evidence for anactive magmatic system in this region (see testing of twospherical sources in the Modeling section). The lack of ahydrothermal system at Hekla also supports the idea that thereis no long-lived shallow magmatic system. A joint inversionof the GPS and InSAR time series may improve our under-standing of whether or not a shallowmagma plumbing systemexists at Hekla.[37] Modeling of seismic and gravity data sets suggests

Moho depths of 25–30 km for the Hekla region [Darbyshireet al., 2000; Allen et al., 2002; Kaban et al., 2002]. Ourmodel results can thus be interpreted to represent magmaaccumulation at the base of the crust or at deep levels in thelower crust under Hekla. Although evidence for magmaaccumulation at or near the Moho for many Icelandicvolcanic centers has been found with geochemical methods[Kelley and Barton, 2008], geodetic studies in Iceland haveso far only detected deformation of one such region. Geodeticdata collected at the Krafla volcanic system, north Iceland,was interpreted in terms of magma accumulation at deeplevels in the crust (�21 km) or at the crust-mantle boundary[de Zeeuw-van Dalfsen et al., 2004]. Additionally, there isgeodetic evidence for lower crustal intrusions in northernIceland. For example, an intrusion east of the Askja volcanicsystem has been modeled to be in the lower crust (depths of12–20 km) [Hooper et al., 2011], and continuous subsidenceat Askja has been interpreted using two subsidence sources,with the deeper one at �16 km depth [Sturkell et al., 2006a].Due to the great depths, which result in small surface defor-mation signals, geodetic methods only detect deformationfrom magma chambers at or near the Moho that have highmagma supply rates.4.3.2. Geometry of the Hekla Magma Chamber[38] Although the source of deformation under Hekla is

deep, and the surface deformation is small, we investigate the


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geometric properties of the magma chamber under Heklawith our dense geodetic network. We tested three geometri-cally different models that fit our data set well, each withdifferent implications. The spherical model (PBHmTm) isthe simplest geometrically, yet the horizontal ellipsoid modelhas the overall best fit to the GPS data (Table 3), and matchesconceptually axial magma accumulation under central vol-canic systems in Iceland [e.g., Gudmundsson et al., 1992]and along mid-ocean ridge segments [Sinton and Detrick,1992]. An alternative model is the pipe or finger shapedmagma chamber reaching from�21 km up to�10 km belowthe surface (Table 4). Although this model (PBHpTm) has aworse fit than the horizontal ellipsoid, it offers an explanationof the observed central subsidence at Hekla, as an alternativemodel to the lava loading model [Grapenthin et al., 2010;Ofeigsson et al., 2011]. A deformation profile for our best fitpipe-shaped magma chamber (Table 4) is shown in Figure 7in comparison to the observed velocities and the best fitsingle spherical magma chamber. The vertical signal is lowerin amplitude, with localized subsidence in the center. Thewidth of the subsidence area, according to the pipe model, iscorrelated with the depth to the top of the pipe, and theamplitude increases with a lower Poisson ratio [Bonaccorsoand Davis, 1999]. The closed pipe model is also in betteragreement with geochemical data and co-eruptive strain andtilt deformation signals that indicate depths of �11 km[Sturkell et al., 2005], compared to the spherical model.The actual shape of the magma plumbing system may be acombination of all these models or have more complexgeometries.4.3.3. Magma Budget of Hekla[39] Although the surface deformation rates caused by the

deep magma chamber at Hekla are small, we do not observeany significant temporal changes in the GPS site time serieswithin the observation period. This indicates that Hekla vol-cano has been steadily inflating within our observation period(2000.5 to 2010.0). Hekla has had 18 documented summiteruptions and five eruptions outside the summit area since1104. The last eruption was in 2000 [Höskuldsson et al.,2007] and before that in 1991 [Gudmundsson et al., 1992],1980–81 [Grönvold et al., 1983], and 1970 [Thorarinssonand Sigvaldason, 1972]. Before the 1 km3 1947 eruption[Thorarinsson, 1967], which preceded the 1970 eruption, therepose period was typically 50–100 years. Tephrachronolo-gical studies reveal a maximum average repose time of160 years for the past 8000 years [Larsen and Eiriksson,2008]. The average effusion rate for historical eruptionsduring the past 1000 years is around 0.01 km3 per year[Thorarinsson, 1967; Grönvold et al., 1983]. The 2000eruption produced �0.19 km3 DRE of lava and tephra[Höskuldsson et al., 2007], corresponding to an averageeffusive rate of �0.02 km3/yr since the 1991 eruption. Theseeffusion rates do not take into account the volume of co-eruptive dikes that form during the eruptions, nor otherintrusions, which might be significant for the total magmabudget of Hekla.[40] The best fitting magma supply rate we find for Hekla

is 0:019þ0:011�0:002

km3/yr for the spherical model (PBHmTm).The volumetric rate we find is directly correlated with theestimated depth of the source (Figure 5). Thus, although the

uncertainties are large, the range of acceptable models whenconsidering a combination of depth and volume is wellconstrained. While the ellipsoidal source suggests a similarvolumetric rate (Table 4), the best fit pipe-shaped modelindicates only about half the volume rate (0:008þ0:003

�0:001km3/yr).

Our estimates of volume rate, for the spherical and ellipsoidalmodels, are similar to that found by Ofeigsson et al. [2011].[41] Our models do not account for compressibility of

magma in the magma chamber; therefore, the actual magmasupply rate may be larger than the volumetric increase of themagma chamber [Johnson et al., 2000]. However, Mouneet al. [2007] observe that Hekla’s basaltic magmas areundersaturated in volatiles at depths below 9 km, thus thecompressibility of the magma is likely not as important asfor other volcanoes, for example Soufriere Hills volcano[Voight et al., 2010]. It is more likely that the simplifiedrheology we apply has a greater effect. At the depths weobtain for the magma chamber under Hekla, viscoelasticrheologies are probably more appropriate and can eitheramplify or decrease the signal from the actual magma supplyrate [e.g., Bonafede et al., 1986; Dragoni and Magnanensi,1989]. Because the elastic and viscoelastic parameters arenot well known, we consider our simplified models animportant contribution to research at Hekla, and implydirections for continuing investigations. Because Hekla isalready overdue for an eruption according to the ‘decadal’eruption pattern (i.e., the last four eruptions have occurredevery �10 years since 1970), and our time series indicate aconstant magma supply rate at Hekla since 2000, the nexteruption could likely be larger in volume than the 2000eruption.

5. Conclusions

[42] Using GPS data from 2000.5 to 2010.0 we estimatethe location and strength of the magma source at Heklavolcano while simultaneously solving for the inter-seismic(SISZ) and inter-rifting (EVZ) plate motion signals. Usingsimplified models of the plate boundary segments, we verifythat the plate boundary follows the most seismically andvolcanically active areas in Iceland. We constrain the centerof the intersection of the SISZ and the EVZ to be within theTorfajökull caldera. Estimated locking depths of the easternpart of the SISZ and the EVZ are 15þ3

�2km and 11þ5

�2km,

respectively. We find the magma chamber under Hekla to beat approximately 24 km depth, when we interpret thedeformation signal to be caused by a horizontal ellipsoid or aspherical source. This depth corresponds with the lowercrust or crust-mantle boundary in this region. A pipe-shapedmagma chamber at depths between 10þ3

�1 and 21þ6�3 km fits

the data equally well as the spherical magma chamber,contributes to central subsidence observed at Hekla, andmight be in better harmony with other geophysical andgeochemical observations. The estimated magma supply rateat Hekla, on the order of 0.01 to 0.03 km3/yr, is comparableto average historical effusive rates.

[43] Acknowledgments. We are grateful to all those taking part incollecting the GPS data, in particular Halldór Ólafsson. We thank AssociateEditor Mark Behn and two anonymous reviewers for their thorough andthoughtful comments. This project was funded by grant NSF EAR


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0711456 (PL), NSF EAR 0711446 (RB); Penn State; RANNIS projects‘Volcano Anatomy’ and ‘High Rate GPS Measurements in Iceland’; theUniversity of Iceland Research Fund; EU project VOLUME. This materialis based on services provided by the UNAVCO Facility with support fromthe National Science Foundation (NSF) and National Aeronautics andSpace Administration (NASA) under NSF Cooperative Agreement EAR-0735156. Figures were produced with the GMT software [Wessel andSmith, 1998].

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