Atmospheric Effects in SAR Interferometry

ATMOSPHERIC EFFECTS IN SAR INTERFEROMETRY, IMPLICATIONS ON
INTERPRETATION AND MODELING SURFACE DEFORMATION: A CASE STUDY OF
THE 1999 (MW=7.4) IZMIT EARTHQUAKE, TURKEY
Ziyadin Çakir(1), Jean-Bernard De Chabalier(2), Alexis Rigo(3), Rolando Armijo(2)
(1)
Institute de Physique du Globe, Strasbourg, France, Email: [email protected]
Institute de Physique du Globe, Paris, France, Email : [email protected]
(3)
Observatoire Midi-Pyrénées - CNRS, Toulouse, France, Email: [email protected]
(2)
SUMMARY
We show in this study that the coseismic interferograms of the 17 August 1999 Izmit, Turkey earthquake include
atmospheric signal correlated with topography. The phase-elevation ratio decreases with increasing elevation, reaching up
to 10 cm of relative phase delay. Although the phase-elevation ratio also varies laterally, a simple, horizontally uniform
model for atmospheric effects is calculated using a digital elevation model. Correction of the observed interferograms with
this model reveals that some of the anomalies in the fringe pattern, which were previously interpreted to be the sign of
triggered slip, are most probably due to the changes in atmospheric conditions. The model also reveals some large scale
artefacts previously undetected.
1
INTRODUCTION
Synthetic Aperture Radar interferometry (InSAR) has proved to be a powerful tool in mapping surface deformation with
sub-centimetre accuracy and fine resolution over a wide area [1,2,3]. There is however some limiting sources of error in
interferometric SAR measurements. Atmospheric effects are assumed to be one of the most limiting factors of differential
interferometry as atmospheric artifacts are often difficult to recognize and correct [4,5,6,7,8,9].
In order to highlight the possible confusion made between atmospheric effects correlated with topography and surface
deformation, we use, in this study, the ERS1 co-seismic interferogram of the August 17, Izmit (Turkey) event, Mw=7.4
that occurred on the North Anatolian Fault in the sea of Marmara region, Turkey (Fig. 1a). The atmospheric artifacts are
revealed by subtracting a synthetic co-seismic interferogram from the observed data. We will also demonstrate that such
artifacts can be subtle to detect and thus might be misleading when interpreting small to large scale deformations seen in
interferograms of displacement fields.
2
DATA ANALYSIS
Leaving aside the main features of the co-seismic data discussed elsewhere [10,11], some anomalies are present in the
interferograms. The anomalies appear as systematic and persistent short wavelength deflections and bending in the fringe
pattern, particularly at north of the Geyve basin and Mudurnu valley (thick arrows in Figs. 1a and 1b). We interpret them
as anomalies because they could not have been produced by the surface deformation due to the main earthquake, and thus
they require an additional source. Because the anomalies are located along the known active faults, they were previously
interpreted as sympathetic or triggered slip induced by the main rupture [12;13,14,10]. However, although less
pronounced, the same kind of patterns can also be seen elsewhere in the interferogram. For example, a similar bending is
present east-southeast of the Lake Iznik. When analyzed together with topography, bending and deflection of fringes
appear to coincide also with the mountain ridges and valleys and the fringes hug the topography like contour lines. These
observations suggest that the anomalies may also be due to the correlation between the phase signal and the topography.
The correlation cannot be derived from errors in the digital elevation model used to remove the topographic contribution
to the interferogram since the sensitivity of the interferogram to the topography is very low due to high altitude of
ambiguity (over 3300 m in the image center).
Because the fringes arising from atmospheric effects correlated with topography are interfered with the ones due to coseismic surface deformation, the effects are not completely revealed and thus can not be calibrated very well. Therefore,
the phase gradient due to the co-seismic surface displacement needs to be removed. We do this by subtracting our model
(Fig. 1c) from the ERS1 interferogram (Fig. 1a) and obtain a residual interferogram shown together with topographic
contours in Fig. 1d. As seen in Fig 1.d, the residual signal is very well correlated with topography, which is more evident
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Proc. of FRINGE 2003 Workshop, Frascati, Italy,
1 – 5 December 2003 (ESA SP-550, June 2004) 1_cakir
in regions with strong topographic variation. For example, the correlation between the residual signal and topographic
elevation is robust in the southernmost part of the interferogram where the residual phase amounts to about 2 cm up to
1300 m of elevation (Figs. 2a and 2b). There the residual signal mimics the topography very well, which is better seen in
the profile shown in Fig. 2a. Residual signal in either side of the Mudurnu valley is nearly symmetric forming a trough
whose axis coincides with the axis of the valley which is controlled by an active fault zone (Fig. 1d). In a similar way, the
residuals in the Geyve area reveal the elliptical shape of the Geyve basin very well. The phase-elevation correlation in the
northern side of the surface rupture is relatively less pronounced since the topography is rather flat there. But, the
topographic correlation is evident at Hendek to the north of the eastern termination of the fault rupture.
Fig 1. Observed (a, b) and synthetic (c) coseismic interferograms of the August 17, 1999 Izmit earthquake. White and
blue lines show the mapped and modelled surface rupture, respectively. Dashed lines are known active faults. Arrows
indicate the location of anomalies in the fringe pattern west of Iznik lake and along the Mudurnu valley. (d) Residual
interferogram obtained by subtracting the model (Fig. 1c) from the data (Fig. 1a). Black lines are topographic elevation
contours with an interval of 500 m. White dashed boxes show the locations where residual phases corresponding the same
elevation are calculated to construct profiles shown in Fig. 2b.
3
MODELING ATMOSPHERIC EFFECTS
In areas where the correlation between topography and residuals appears to be strong, residual signals were measured in
boxes (shown with dashed rectangles in Fig. 1d) and the mean values of the all the residuals at the same elevations were
calculated at 20 m interval (Fig. 2b). As expected, the signal delay is not the same everywhere and varies with elevation
indicating that the change in the atmosphere was not quite uniform, neither horizontally or vertically in the scale of the
image frame. Although the phase-elevation ratio varies from one place to other, it appears to decrease with increasing
elevation everywhere in a curvilinear manner.
To model the atmospheric effects we use a curve of reverse exponential function (Fig. 2b). To obtain an overall optimum
model for the entire interferogram a curve is fitted to a profile of elevation versus averaged residual signal (black line in
Fig. 2b). The chosen curve thus gives a smooth model with a minimal misfit due to local variations in the phase-elevation
ratio. Because the relationship between the residual phase and topography is generally curvilinear, the misfit occurs where
the gradient of residual phase varies significantly from that of the model, in particular, at lower elevations (mostly below
500 m). The resulting phase-elevation model produced using a digital elevation model (SRTM-90m) is shown in Fig. 3a.
The DEM was filtered in order to avoid high frequency undulations in topography.
4
CORRECTION OF THE OBSERVED AND SYNTHETIC INTERFEROGRAMS
The interferogram obtained after subtracting the phase-elevation model from the data (Fig. 3b) is shown in Fig 3c. As seen
in this figure, deflection of fringes in the Mudurnu and Geyve regions, as well as elsewhere in the southern parts of the
data, is almost removed. Corrections can be locally improved. For example, deflected fringes across the Mudurnu valley
can be further straighten if the model curve is fitted to the phase-elevation profile measured there (Fig. 4).
Fig. 2. Relationship between elevation and residual phase. (a) Profile of residual phase and topographic elevation (see Fig.
1c for the location). (b) Plot showing the mean residuals versus topographic elevation calculated at five different sites
within the interferogram (white dashed boxes in Fig. 1d). The thick black line is the optimum curve to model atmospheric
artefacts.
Fig. 3. Modelling the atmospheric effects and correcting the observed and synthetic interferograms. (a) Phase-elevation
model (e.g. atmospheric model). (b) Observed interferogram. (c) Corrected interferogram after subtracting the phaseelevation model (b-a). (d) Corrected synthetic coseismic interferogram (Fig. 1c) after adding the phase-elevation model.
Circle shows where a large scale atmospheric artefact is present in the data.
In addition, the two parameters of the reverse exponential function (α and β) can be interpolated. Our tests show that such
models do not improve the correction significantly as stated above the misfit becomes apparent where the gradient of the
model curve differs considerably from that of phase-topography profiles. We therefore prefer to keep a simple
horizontally uniform model also because of the bias and complexities in the interpolation methods. In order to clearly
illustrate the effects and extend of the artifacts, we added the artifact model to the synthetic coseismic interferogram (Fig.
3d). Resembles of fringe pattern between the data (Fig. 3b) and corrected models is striking; noise, bending and
deflections seen in the entire data being almost reproduced. Apart from these secondary features, a large scale correction
is revealed in north easternmost side of the interferogram. There fringes trend E-W in the data (dashed circle in Fig. 3b)
but, after the correction (Fig. 3c) their trend becomes SE-NW closing around the eastern end of the surface rupture as
predicted by synthetic model (Fig. 1c). When the possibility of atmospheric effects is not considered such an E-W trend of
fringes implies that either the easternmost fault segment (i.e. Karadere segment) dips to the north or the fault rupture
continues further east than it is observed in the field. Therefore, this phenomenon may also be misleading when modeling
a large scale deformation.
Fig. 4. Correction of ERS1 data in the Mudurnu region using a model curve fitted to the phase-elevation profiles measured
there (see Fig. 2b).
5
DISCUSSION AND CONCLUSIONS
As illustrated in Figs. 3 and 4, the anomalies seen along some of the active faults can be removed perfectly well with a
phase-elevation model. This strongly suggests that the deflection of the fringes that was previously interpreted as a sign of
triggered slip at some places were most likely reproduced by the signal delay between the two images due to the fairly
homogenous changes. It is observed that the phase-elevation ratio is not linear, but decreases exponentially with
increasing elevation from sea level to the top of the mountains.
A simple phase-elevation model (even a linear one) may account for most of the artifacts in an interferogram and answer
whether or not a signal or an anomaly in the fringe pattern could be possibly related to atmospheric effects correlated with
topography even though it exists in other interferograms. It is, therefore, worthwhile to make a simple phase-elevation
model prior to analyses of surface deformation and remove them from interferograms when possible. This is especially
crucial when studying subtle deformation such as interseismic loading, post-seismic deformation and subsidence where
strong topography is present.
6
ACKNOWLEDGEMENTS
SAR data are provide by ESA project AO-354.
7
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