IS MAGMA GENERATED DUE TO RETREATING ICE CAPS, LIKELY TO ERUPT?
CONSTRAINTS ON LOWER-CRUSTAL STRESS FROM INSAR
Andrew Hooper1 , Benedikt Ófeigsson2 , Freysteinn Sigmundsson2 , Halldór Geirsson 3 , Páll Einarsson4 , and Erik
Sturkell5
1
Delft Institute of Earth Observation and Space Systems, Delft University of Technology, Delft, Netherlands, Email:
[email protected]
2
Nordic Volcanological Centre, University of Iceland, Reykjavik, Iceland, Email: [email protected]
3
Icelandic Meteorological Office, Reykjavik, Iceland, Email: [email protected]
4
Institute of Earth Sciences, University of Iceland, Reykjavik, Iceland, Email: [email protected]
5
Department of Earth Sciences, University of Gothenburg, Gothenburg, Sweden, Email: [email protected]
ABSTRACT
The shrinking of ice caps on volcanoes can lead to the
generation of additional magma, due to decompressionmelting of the mantle beneath. In Iceland, it is estimated
that the ongoing reduction in mass of the largest ice cap,
Vatnajökull, results in the formation of approximately
14 million m3 yr−1 new melt. How much of this extra
magma will eventually erupt depends on what proportion
will be trapped within the crust. Simple elastic models
of the decrease in surface load as ice melts predict additional tensile stresses in the lower crust that could accommodate extra magma. The true stress evolution in
the lower crust is, however, difficult to estimate due to
the poorly-constrained ductile nature there. During 20072008 a lower-crustal dike intrusion was detected 20 km
north of the ice cap at 12 to 20 km depth. We use this intrusion to estimate the stress tensor in the lower crust, using InSAR, GPS and seismicity data as constraints. Our
results indicate that there is significant shear stress acting on the dike, which leads to shearing of the dike walls.
The orientation of the minimum horizontal normal stress
is approximately coincident with the plate spreading direction and the magnitude implies a relaxation time on
the order of 1000 years. This implies that tensile stresses
induced by the melting of the ice cap can build over time
resulting in at least some of the extra magma generated
being trapped within the crust.
magmatic processes [1]. These processes lead to the generation of new crust both by eruption of lava at the surface and by intrusion of magma within the crust. Many of
the active volcanoes are overlain by ice caps, which have
been shrinking over the past century. Reduction in the ice
load can lead to magma generation in the mantle due to
decompression melting and it is estimated that the current
rate of ice loss for the largest ice cap, Vatnajökull, results
in the formation of approximately 14 million m3 of additional magma every year [2]. All things being equal, any
extra magma input into the crust, could be expected to
erupt. However, removal of the ice load also affects the
stress state in the crust, which has the potential to alter
the quantity of magma that can be accommodated within
it. In this paper, we investigate the current state of stress
and the predicted changes in the stress state due to the
melting of Vatnajökull ice cap.
66N
Kverkfjöll
volcanic
system
65N
Key words: Iceland; Ice; Stress; Eruption; InSAR.
64N
1.
INTRODUCTION
24W
The divergent plate boundary between the NorthAmerican and Eurasian plates in Iceland is expressed as a
series of rift zones connected by transform zones (Fig. 1).
Spreading across rift zones, of 19.7 mm yr−1 , continuously builds up stress that is released by tectonic and
_____________________________________________________
Proc. ‘Fringe 2009 Workshop’, Frascati, Italy,
30 November – 4 December 2009 (ESA SP-677, March 2010)
22W
20W
18W
16W
14W
Figure 1. Regional Setting. Iceland in shaded relief after [3]. White shading indicates the permanent ice caps,
yellow shading indicates the volcanic systems, the red
dashed lines indicate zones of divergence and the black
solid lines indicate transform zones.
2
N
Dyke
migrated with time north-eastwards. The dominant focal
depths lie between 14 and 20 km, well below the purely
brittle zone estimated to be 6-7 km thick in this region
[6].
60
55
45
40.
35
Ice Loss (cm/yr)
50
30
25
20
S
S
0
N Pa/yr
10
Dike
20
-60
-40
-20
0
20
40
2000
1500
1000
500
60
Figure 2. Vatnajökull ice loss model. Above, the model
for the annual reduction in ice thickness. Below, the instantaneous deviatoric stress rate estimated from the ice
loss rate, for a N-S section through the ice cap. Colour
indicates the magnitude of the deviatoric stress rate (positive indicates tensile), and the black lines indicate the
intersection of the N-S section with the plane perpendicular to the minimum normal stress.
We used radar data acquired by the European Space
Agency’s Envisat satellite, to form two interferograms
spanning the period of activity, which provide estimates
of the ground displacement in two different groundsatellite directions (Fig. 4). Analysis of other radar data
acquired between 2003 and 2006 indicate that the spatial
pattern of the background and seasonal signal approximates a tilted plane. The dominant noise term due to orbit
errors and propagation through the atmosphere also approximates a plane so we estimated the best-fitting plane
from areas outside of the deforming region in each interferogram, and subtracted it.
GPS data were acquired continuously at three sites and
campaign-style at a further six sites. The continuous stations show a change in velocity towards the end of April
2007. From the horizontal GPS data, we simultaneously
estimated the background motion, due predominantly to
plate spreading, the seasonal motion due to snow-loading,
0
Earthquakes
Fault Planes
ICE LOSS MODELLING
We modelled the instantaneous elastic stress change due
to the annual reduction in ice load of Vatnajökull (Fig. 2).
This was achieved by integration over the ice cap of the
Green’s functions for a point load, weighted by the annual
ice thickness reduction. The ice thinning is estimated to
be 25 cm yr−1 in the centre of the ice cap and ∼60 cm
yr− 1 at the edge [4], and we interpolated linearly in between. The results indicate a zone of tensile deviatoric
stress in the lower crust, where extra magma could be accommodated. Because of the high geothermal gradient
beneath Iceland, the crust below approximately 6-7 km
is able to relax by ductile flow. Thus the true state of
stress cannot be predicted from elastic theory alone. The
viscosity structure of the lower crust is, however, poorlyconstrained, with variation expected both vertically and
laterally due to temperature, pressure and compositional
variation. Instead, we use a recent dike intrusion to the
north of Vatnajökull to probe the stress state of the lower
crust directly.
3.
DIKE INTRUSION
Between February 2007 and April 2008, swarms of small
deep-seated earthquakes were detected within the Kverkfjöll volcanic system in north-eastern Iceland [5]. The activity originated in the region of Mt. Upptyppingar, and
10
15
20
25
−5
0
5
10
Azimuth 171˚(km)
1
65.1
0.8
65.08
65.06
0.6
65.04
0.4
Opening (m)
2.
Depth (km)
5
65.02
0.2
65
64.98
16.3
16.2
16.1
16
0
Figure 3. Dike model results. Above, the posterior probability distribution of dike locations in profile, looking
from 261◦ . Below, surface projections of the mean of the
marginal posterior probability distribution for the opening of each element. Relocated M>0 Earthquake epicentres between February 2007 and the April 2008 [5] are
plotted as black circles.
3
65.2˚
65.2˚
65.1˚
65.1˚
65˚
65˚
64.9˚
64.9˚
64.8˚
64.8˚
km
km
64.7˚
−16.6˚
−16.4˚
5 10
0
−16.2˚ −16˚
−15.8˚
−15.6˚
−16.6˚
−16.4˚
5 10
0
−16.2˚ −16˚
−15.8˚
−15.6˚
64.7˚
Figure 4. Interferograms spanning the entire intrusion period. Left, the phase of ascending interferogram formed from
acquisitions on 27 June 2007 and 16 July 2008, and right, the phase of descending interferogram from acquisitions on 14
July 2007 and 28 June 2008. The phase data are wrapped with a bilinear phase trend estimated from the non-deforming
areas of the interferogram (not shown) subtracted. Each colour fringe represents 2.8 cm of displacement in groundsatellite direction. The black arrows represent the satellite direction of travel with the ticks indicating the look direction.
Epicentres of Mw >0 earthquakes that occurred during the corresponding period are plotted as black circles (data from
the SIL database of the Icelandic Meteorological Office).
and the additional velocity between July 2007 and March
2008, shown in Fig. 5. We did not use the vertical GPS
data, which are dominated by the seasonal signal.
4.
INTRUSION MODELLING
The vertical deformation (Fig. 5) forms an upwards
bulge, with maximum displacement to the south and
east of the zone of seismicity. The horizontal motion is
strongly asymmetric with displacements predominantly
in a south-easterly direction. Initially, we modelled the
geodetic data using elastic half space models for various
simple geometries. The asymmetry of the motion precludes most source geometries but we found that a tilted
rectangular tensile dislocation [7] provides a reasonable
fit to both data sets.
In order to estimate the stress tensor within the crust, we
developed a boundary-element model. We assumed lithostatic pressure and an unknown deviatoric stress within
the host rock, hydrostatic overpressure within the source,
and a traction-free interface. We divided the potential
source area into smaller elements, each of which could be
active or not, and let the amount of relative opening and
slip for each element be controlled by the stress boundary conditions. This model is an extension to the model
of Yun et al. [8]. Our model differs in two ways. Firstly, a
hydrostatic rather than a uniform pressure boundary condition is assumed. This means that, given a magma den-
sity less than that of the host rock, the overpressure decreases with depth. Secondly, we allow for a regional
deviatoric stress, which we estimate in our inversion. We
assumed the density difference between the magma and
surrounding rock to be 250 kg m−3 , and a Poisson’s ration of 0.27 [9]. We included vertical variation in elastic
stiffness to our model by treating the Earth as a series of
horizontal elastic layers overlaying an elastic half space
[10] with stiffness values for each layer calculated from
seismic profiles [9].
We used the corrected InSAR and GPS data to constrain
the model. We estimated 1-D covariance functions for the
error terms in the interferograms from the non-deforming
regions. The errors in the GPS velocities were estimated
using the percentile bootstrapping algorithm [11]. We assumed the errors were sampled from a multivariate Gaussian distribution and used a Markov chain Monte Carlo
algorithm to build the posterior probability distribution
of the model parameters [12, 13].
The results for dike location and opening are shown in
Fig. 3. There is a high degree of overlap between the dike
location and the earthquake hypocentres, which were not
used to constrain the dike location. The fit to the data
is shown in Fig. 5. Although the difference between the
interferometric phase and model phase is significant in
places, the spatial structure of the residual phase is consistent with the estimated spatial structure of the signal
due to lateral variation in atmospheric propagation. The
volume of the intrusion is 0.040 to 0.047 km3 at 95%
confidence.
4
Data
Model
Residuals
65.1
65
64.9
64.8
-7
cm
7
30 mm/yr
64.7
65.1
65
64.9
64.8 -2
cm
5
64.7
16.6 16.4 16.2 16 15.8 15.6
16.6 16.4 16.2 16 15.8 15.6
16.6 16.4 16.2 16 15.8 15.6
Figure 5. Model fit. Above, eastwards displacements derived from ascending and descending lines-of-sight, assuming
negligible contribution from northwards displacements. Below, vertical displacements derived under the same assumption. Left figures show the displacements derived from the interferograms, middle figures show displacements derived
from the optimal model, and the left figures show the residuals between the two. Also shown on the top middle figure are
the horizontal GPS velocities in black, with 2σ error ellipses, and the velocities predicted by the optimal model in red. The
outline of the opening patches for the optimal model are shown in white, and epicentres of relocated Mw >0 earthquakes
[5] are indicated by black dots.
The direction of minimum normal stress cannot be solved
uniquely but can be constrained to a sub-vertical plane.
If it is assumed to be horizontal then it strikes 129 ± 9◦ ,
with a magnitude of ∼10 MPa. This is consistent with
the direction of plate spreading. Assuming that platespreading is accommodated over a length scale of ∼100
km gives an instantaneous tensile stressing rate of ∼0.01
MPa yr−1 . This is likely an upper bound as lower crustal
strain can be expected to localise in the hotter zone beneath the spreading axis to the east. This then implies a
minimum relaxation time of 1000 years.
5.
DISCUSSION AND CONCLUSIONS
The dike was not emplaced perpendicular to the maximum tensile stress, as is commonly the case, which lead
to significant shearing of the dike walls. The question as
to what controlled the orientation of this deep crustal intrusion remains, but if not the deviatoric stress, then presumably it was due to contrasting mechanical properties
within the host rock. Perhaps the dike was guided by a
former intrusion emplaced under different stress conditions, such as would have existed at the end of the last ice
age.
The orientation of the minimum normal stress in the
lower crust is consistent with the plate-spreading direction. The magnitude of the deviatoric stress implies a
relaxation time of at least 1000 years, which is at the
higher end of previous estimates of the viscosity below
the brittle crust. This further implies that tensile stresses,
induced in the lower crust by the melting of the ice cap,
can build over time. This will result in at least some of
the extra magma generated being trapped within the crust
so that not all of the extra magma will be erupted.
ACKNOWLEDGEMENTS
Envisat ASAR data were provided by ESA under project
AOE212.
5
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