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

sudhaus@erdw.ethz.ch, sj@erdw.ethz.ch

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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