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IMPROVED SOURCE IMAGING OF THE KLEIFARVATN EARTHQUAKE, ICELAND,
THROUGH A COMBINED USE OF ASCENDING AND DESCENDING INSAR DATA
Henriette Sudhaus & Sigurjón Jónsson
Institute of Geophysics, ETH Zurich, Schaffmattstr.30, 8093 Zurich, Schwitzerland
[email protected], [email protected]
ABSTRACT
We re-investigated the surface deformation of the
Kleifarvatn earthquake on Reykjanes Peninsula, an
event that was dynamically triggered by a moderate-
size magnitude 6.5 earthquake 80 km away on 17 June
2000. Two ERS-2 interferograms from descending and
ascending tracks were formed and used in combination
with campaign GPS measurements to invert for the
source parameters of rectangular faults for the
Kleifarvatn and the adjacent and smaller
Núpshlíðarháls earthquakes assuming uniform slip.
With our more complete data set that includes the
ascending ERS-2 data, we demonstrate an efficient
suppression of model parameter trade-offs between
fault dip and fault slip. We consider the correlated
noise of InSAR by propagating the full data covariance
to a weighting matrix, which balances the complete
data set consistently. Our best model agrees not only
with the regional faulting system, it is also supported
by locations of recently relocated aftershocks.
1. INTRODUCTION
On 17 June 2000 South Iceland was struck by a 6.5
magnitude earthquake that took place in the South
Icelandic Seismic Zone (SISZ). The emitted seismic
waves triggered several earthquakes west of the
epicentre on faults on the Reykjanes Peninsula, with
three of these reaching magnitudes about 5 [1]. As
these events were triggered dynamically, they
happened while secondary waves of the main shock
were still arriving at the local seismological network,
making computations of their earthquake source
parameters based on seismic waveforms difficult. Here
we focus on the larger Kleifarvatn earthquake. It is the
largest of the triggered events and was initially not
reported and actually later discovered by InSAR [2].
The assigned moment magnitude of only ~5, based on
the seismological observations, contradicts the
intensities inferred from surface cracks and rock fall in
the epicentral region [1]. Also, previous studies based
on InSAR and GPS data indicate that the moment of
the Kleifarvatn event corresponds to an earthquake of
magnitude 5.8 or more [2, 3].
On Reykjanes Peninsula and in the SISZ an oblique
transform zone connects spreading centres on the
Reykjanes Ridge with the Eastern Volcanic Zone in
Figure 1. Investigation area on the Reykjanes
Peninsula with the epicentres of the Kleifarvatn
earthquake (‘K’) and Núpshlíðarháls event (‘N’) and
locations of campaign GPS measurements.
central-south Iceland. The left-lateral shear is mostly
accommodated by north-south orientated and steeply
dipping right-lateral strike-slip faults (book-shelf
faulting) [4]. However, the earlier geodetic studies
mentioned above that focussed on the fault parameters
of the triggered events, found relatively shallow
dipping fault planes, which are in contradiction with
the established understanding of the regional faulting in
Southwest Iceland. The reason for this discrepancy is
likely related to trade-offs between fault dip and fault
slip direction (rake) when using radar data from only
one track in fault parameter inversions.
Here we complement the dataset used in these previous
studies with ERS-2 data from an ascending track and
we therefore have a good data coverage in the
epicentral region from two different viewing directions.
We then use all of these data to invert for fault
parameters of the two largest triggered events and
compare the results with previous models and other
information.
2. DATA
For our source inversion we use InSAR data from
ascending and descending tracks as well as GPS data
provided by Άrnadóttir et al. [3]. The descending
InSAR image was formed from ERS-2 scenes acquired
on 2 October 1999 and 16 September 2000 and the
perpendicular baseline B┴ between the two orbits is
only 5 m (Tab.1 & Fig. 2). As the B┴ -value has
influence on the coherence of the interferometric phase
and therefore on the overall quality of the
_____________________________________________________
Proc. ‘Envisat Symposium 2007’, Montreux, Switzerland 23–27 April 2007 (ESA SP-636, July 2007)
Table 1. The ERS-2 radar images used in this study.
interferogram, we were able to process the descending
image to a high resolution (pixel size ~ 20 m by 20 m).
In addition, we applied an adaptive filter to enhance the
quality of the interferogram [5] (filter window size 32,
filter exponent 0.8). The ERS-2 scenes forming the
ascending interferogram were recorded on 2 September
1999 and 17 August 2000 (Fig. 2). Although its B┴ is
also small (38 m) and the time span similar to the
descending case, the resulting correlation of the phase
signal is for some reason lower. In this case we multi-
looked the interferogram to suppress parts of the white
noise, by averaging complex values of three adjacent
pixels in range and azimuth directions to the cost of
resolution. The removal of the topographic phase and
the transformation from radar to geographic
coordinates (geocoding) were based on a digital
elevation model with a resolution of about 25 m. We
used the snaphu software for phase unwrapping, which
is a statistical-cost network-flow algorithm by Chen &
Zebker [6].
The dominant feature in the interferograms is the
deformation signature of the Kleifarvatn event around
the lake. To the southwest of lake Kleifarvatn, the
signal of the smaller Núpshlíðarháls event is visible.
The shape of the line-of-sight phase shifts points to
dominantly strike-slip mechanisms, consistent with the
regional faulting regime. Unfortunately, there are large
areas of decorrelation in the near field of both events,
so that possible superficial traces of the faults are not
observed in these data.
The campaign GPS data of Άrnadóttir et al. [3] cover a
large area of Reykjanes and come from measurements
that were carried out in 1998 and 2000. From the
measurement results of 1996, 1998 and 2000 they
inferred a model of interseismic ground motion. We
use their values of ground displacement between 1998
and 2000 corrected for the interseismic deformation
(Fig.1 & Fig.3). The eleven campaign GPS
measurements we considered agree very well with the
InSAR LOS displacement.
2.1 Subsampling
The InSAR data consist of several hundred thousand
data points, but as the data field is varying smoothly,
we can decimate the numerous phase values without
losing important information. We subsampled the
InSAR data sets with a quadtree algorithm [7] to obtain
a reasonable number of data points and a reasonable
spatial distribution. This algorithm subsequently
divides the InSAR images into boxes until the phase
values in each box do not exceed a certain variance
level. The average phase value of the contributing
pixels is then assigned to their focal point. The
algorithm therefore is sensitive to the variability of the
phase values across the area and to possible data gaps.
The threshold for the allowed variance of values within
a square is deduced from the level of the apparent
noise.
We used standard-deviation thresholds of 0.9 cm and
0.8 cm for the ascending and descending images,
respectively, which is higher than the root-mean-square
error of noise, but leads to a good representation of the
deformation field with only 634 data points (Fig. 3).
Data gaps result from decorrelation, phase unwrapping
errors and layovers, stretched out by geocoding.
Pass orbit Date BT [m]
Descending (master) 23267 10/02/1999 5
Descending 28277 09/16/2000
Ascending (master) 22844 09/02/1999 38
Ascending 27854 08/17/2000
Figure 2.a) ascending interferogram, b)
descending interferogram
3. OPTIMIZATION
We inverted for two rectangular faults with uniform
slip using a ’simulated annealing’ optimization
approach [8] followed by a nonlinear least square
fitting. In addition to the fault locations, dimensions,
orientations and mechanisms we estimate possible orbit
errors by including parameters of tilted planes (3 for
each InSAR image) in the optimization. The
deformation signal of the Núpshlíðarháls event is weak
in comparison to the Kleifarvatn event, so we cannot
reliably invert for its source parameters due to the
superposition of the two deformation signals.
Therefore, we put tight bounds on the location of the
smaller event and fixed its strike (after K. Vogfjörð,
personal communication) to stabilize the optimization.
In the fault parameter optimization we are seeking the
minimum of the following L2-norm:
( ( )) ( )T
obs pred obs prede = − −R Rd d d d (1)
where matrix R is a weighting matrix based on the data
covariance matrix Σ:
1−=
TΣ R R (2)
3.1 Data weighting
The three data sets (Fig. 3) are independent of each
other and have different uncertainties. The GPS data
are treated as uncorrelated and we apply the
uncertainties assigned by Άrnadóttir et al. [3]: 0.5 and 1
cm for the horizontal and vertical components,
respectively.
The InSAR data are known to exhibit spatially
correlated noise due to smoothly varying atmospheric
signal delays. We account for this by incorporating the
full data covariance matrix to balance the data in the
optimization consistently.
We assume the InSAR noise to be stationary across the
interferograms so that the noise statistics measured in
non-deforming parts of the image are a valid estimate
for the noise in the adjacent deforming areas we are
interested in. We furthermore assume noise isotropy
making the covariances depend only on distance h.
The variances are retrieved via sample semi-
variograms ˆ( )hγ (Eq. 3) and the covariances from
sample covariograms ˆ ( )C h (Eq. 4) [9]. These ‘quiet’
areas have about the same size as the deforming areas
and we begin the noise analysis by removing an overall
linear trend from them (Fig. 4 a & b). We then pick
randomly a sufficiently large number N of data-point
pairs d(ri) and d(rj) for each distance h to calculate the
Figure 4. Interferograms for noise measurements north of the deformed area. a) ascending; b) descending.
c) retrieved covariance functions for ascending (grey) and for descending (black) interferograms.
Figure 3. Subsampled InSAR data (left: ascending; right: descending) and GPS. The coseismic horizontal GPS
displacement vectors are shown as arrows. The colored circles give the radar line-of-sight projections of the GPS
displacement. The outlines of Lake Kleifarvatn and the coast are shown for reference.
sample variograms:
21ˆ( ) [ ( ) ( )]
2i j
i j
r r h
h d r d rN
γ−
= −∑≃
(3)
and sample covariograms:
1ˆ( ) ( ) ( )2
i j
i j
r r h
C h d r d rN −
= ⋅∑≃
. (4)
The data variance is given by the level of which the
sample variogram ˆ( )hγ forms a sill and it represents
the covariance value for zero distance. In presence of
white noise, the covariance functions therefore have a
step at a zero lag (Fig. 4 c). The variance is 1.5 ·10-5
m2
in the ascending image and is lower than the 2.5·10-5
m2 in the descending image. But as described above the
ascending image was processed to a lower resolution to
suppress uncorrelated noise. The covariance on the
other hand is lower in the descending image.
Therefore, it should be kept in mind that when
measuring the noise statistics individually in each
image we are including all effects of processing and
filtering.
For a continuous description of the covariances we fit
functions to the measured covariograms and thereby
define the covariance matrix. Since the covariance by
definition is a positive-definite function we use
function types ensuring positive-definiteness [9]: an
exponential decay of the type b·exp[-(h/a)] to represent
the descending covariance and an exponential decay
complemented by a cosine term, c·exp[-(h/a)]·cos(h/b),
to account for the anticorrelation present in the noise
structure of the ascending interferogram. For the latter
case a positive-definiteness is limited to parameter
values a<b.
We propagate the full data covariance matrix, defined
by the fitted functions, to a data covariance matrix of
the subsampled data, using the same linear operator as
for the subsampling. In this way the independent data
sets become comparable despite possible differences in
processing. The weighting function derived from the
covariance matrix then assigns individual weights to
the InSAR data points depending not only on the
variance, but also on the box size and (because we
consider the correlation) on the position with respect to
other data points. The data-point weights are shown in
Fig. 5.
4. RESULTS AND DISCUSSION
The best-fitting model (Fig. 6) for the Kleifarvatn event
has a fault plane that is 6.5 km long, 4.9 km wide, and
reaches the surface, which is similar to what was found
in the earlier studies by Pagli et al. [2] and Άrnadóttir
et al. [3]. Also, a fault strike of N9.5°E and the location
are in a fairly good agreement with the existing results.
However, unlike previous studies, we obtained an
almost vertical fault dipping 88 degrees to the east,
with 0.75 m of strike-slip and almost no dip-slip. In
addition, the geodetic moment is also slightly larger,
but is definitely in a general agreement with the earlier
magnitude estimates.
The model can explain the major part of the observed
deformation signal around Lake Kleifarvatn (Fig. 6-7).
However, the residuals show some systematic
undulations, primarily near the fault. We think this is
due to fault-slip complexities along the rupture that
cannot be reproduced by a simple rectangular fault
model and uniform slip. In particular, the deformation
signal between the two events is relatively poorly
explained by the model. And again we think the two
simple faults are not able to produce the complicated
signal in this area.
Figure 5. Weighting factors resulting from the fully propagated covariance matrix.
Furthermore, we find that we cannot constrain well the
fault parameters for the Núpshlíðarháls event, because
loosening the parameter bounds often leads to
unrealistic solutions. However, it is clear that we have
improved previous Kleifarvatn fault models with a
result that is in an agreement with hypocentre locations
of recently relocated aftershocks [10]. These events
form a plane that aligns very nicely with our fault
model. Future work on testing the robustness of the
Kleifarvatn fault model will provide reliable estimates
of the model parameter uncertainties.
Acknowledgements
We thank Steffen Knospe for his assistance in the
statistical analysis of the InSAR data. Furthermore, we
thank Kristin Vogfjörð and Sigurlaug Hjaltadóttir for
sharing results from seismological studies on both
events and Thóra Άrnadóttir for providing the GPS data.
The radar data in the study were provided by the
European Space Agency through Category-1 project
#3639.
Length
[km]
Width
[km]
Depth
[km]
Dip
[deg]
Strike
[deg]
Easting
[km]
Northing
[km]
strike-slip
[m]
dip-slip
[m]
Kleifarvatn 6.5 4.9 0 88 E 9 452.68 7086.41 0.75 0.07
Núpshlíðarháls 3.2 8.1 0.5 79 E 12 (fix) 444.38* 7087.15* 0.28 0.23
Table 2. Estimated model parameters of the Kleifarvatn and Núpshlíðarháls events. A star *) marks parameters with
tight bounds (see text)
Figure 7. Residuals between observed data (Fig. 3) and predicted data (Fig.6)
Figure 6. Model predictions of the best-fitting model. The fault model is plotted as a surface projection of the fault
plane. The thick line represents the upper edge of the fault.
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