1. Details on the InSAR methods
Differential Synthetic Aperture Radar interferometry (DInSAR) provides a means to estimate ground
displacements at city-scale when sufficient data has been acquired by a satellite. It is commonly used
for monitoring centimeter per year ground deformation of large size. The principles of the method are
to analyze the phase differences between two or more radar scenes acquired at different dates. Once
corrected from the topographic components, phase differences are proportional to variations of the
distance between a given ground target and the satellite (modulo half wavelength), thus providing an
estimate of ground displacement along the satellite’s line of sight (LOS). Conventional DInSAR
deformation maps are often hampered by atmospheric phase delay and interferometric signal
decorrelation that reduce the performances of the measurement (e.g., Massonnet and Feigl, 1998).
To address this limitation, advanced DInSAR techniques use a large data set and focus on ground
targets with specific radiometric characteristics, namely the Persistent Scaterrers (PS; e.g. Ferretti et
al., 2001; Wegmuller et al., 2004). This PS Interferometry (PSI) processing technique iteratively
isolates the atmospheric component of the interferometric phase difference, copes with temporal and
geometric decorrelation of the signal and improves the information on the target altitude. Previous
studies have demonstrated that PSI is adapted to monitoring slow and rather linear deformations,
sometimes reaching sub-millimeter per year precision (Raucoules et al., 2009).
Our study uses those two approaches to investigate potential vertical land motions in Alexandria. On
the one hand, PSI is used to estimate slow and rather linear deformation rates. On the other hand, a
DInSAR approach (but including, and post-processing large interferogram sets to improve the
reliability of the results) is used to identify possible more rapid or non-linear deformation potentially
not detected by the PSI approach. This combined analysis is justified by the fact that a low temporal
sampling of the SAR scenes (35 days at minimum) and/or a low spatial density of PS may result in
phase unwrapping errors in the PSI approach in case of relatively abrupt ground motions (See
recommendation 6 from the latest PSI intercomparison and validation exercise in Raucoules et al.,
2009).
In the PS approach, we aim at producing highly precise ground velocities in the neighborhood of the
GPS and tide gauge locations (see main text). This implies adopting a SAR processing scheme that
favors the precision of the result over the number of selected PS. We therefore selected a high
amplitude mean/dispersion ratio threshold. We focused on the period where both permanent GPS and
SAR data were available, i.e. 2003 to 2010. Because the permanent GPS does not show any significant
deformation, it was chosen as a reference stable point in the SAR processing. We used 49 radar scenes
acquired over Alexandria by the C-band SAR Envisat satellite over 2003-2010. We used the
Interferometric Point Target Analysis (IPTA) to produce a mean velocity map over the period 20032010. IPTA is a Persistent Scatterers Interferometric analysis (PSI).
DInSAR is used to identify potential subsiding or uplifting areas where a PS would have possibly been
rejected in the previous procedure. We used a procedure similar to that described by Usai et al. (2003);
Le Mouelic et al. (2005) or Pepe et al. (2005), namely the Multi-Baseline (MB) algorithm
implemented in the Gamma software (Wegmüller et al., 2009). In this procedure, a subset of
interferograms were selected visually based on phase noise, apparent residual topographic component,
and phase patterns that could be associated to atmospheric effects. These interferograms were then
used to produce a phase screens time series that can be interpreted as deformation. A mean velocity
map can then be derived from this time series.
2. Details on the interpretation of the PSI data and the evaluation of the uncertainties
1. Phase unwrapping
A common issue of conventional DInSAR and PSI techniques is the phase unwrapping, due to the fact
that the ground displacements between two images are measured modulo half the wavelength (i.e.
28mm in the case of the Envisat C band SAR). For instance, could one PS located near the tide gauge
be affected by unwrapping problems in our application to the Alexandria region? In such a case, the
real deformation rate of the PS would be larger than 3.5mm/yr in the Line of Sight of the SAR
instrument (the displacement in the LOS should be at least 28mm over the 8 years of measurement).
This would mean that : (1) either the point is an outlier: in this case, it is not a good approximate of
the ground motion affecting the instruments area; (2) or the zone is affected by a subsidence greater
than 3.5mm/yr. However, in this case, this deformation should be observed by DInSAR and by the PS
nearby. In Alexandria, we did not detect any hint of such large deformation in the areas surrounding
the geodetic instruments. This illustrates the interest of considering the results of PSI together with
those of conventional DInSAR.
2. PSI results interpretation
How to interpret the PSI results? First, the persistent scatterers refer to a particular target within a cell
with particular radiometric and geometric properties. However, in a complex urban environment, it is
in general not possible to relate the persistent scatterer with an actual object on the field. This has the
following implications for the application of the method: (1) the analysis should not be based on one
PS but on a group of PS near the area of interest, (2) even if stability is observed, it cannot be excluded
that a particular (e.g. local) ground motion is affecting the instrument. A consequence for future
applications is that without an independent validation, the analysis of PS or conventional DInSAR data
alone is not sufficient to definitively ensure that no ground motions are affecting the instruments. In
the case study of Alexandria, the Kuo et al. (2004) method provides an independent validation which
is in agreement with our combined PSI/GPS results. In other studies, leveling surveys surrounding the
geodetic instruments could be used.
3. PS velocity uncertainties
How to interpret the spatial variability of the linear trends measured from the PS? This variability
includes two components: (1) the noise level; (2) the natural variability of the PS deformations
themselves (i.e. due to the various physical deformation processes affecting the natural targets). In this
paper, we evaluated the precision of the PS velocity estimates at 0.7 mm/year by calculating the
standard deviation of the PS velocities in areas a priori affected by homogeneous ground motions.
These values are provided in the table below for some areas mentioned in the paper. The Figures S3
and S4 show the persistent scatterers nearby the GPS station and tide gauge, respectively.
Location
Around the GPS
Between the GPS and
the former tombolo
Within the former
Standard deviation of
PS velocities (mm/yr)
0.79
0.67
0.78
Nb. of PS considered
336
119
272
tombolo
Table 1. Examples of the variability of PS velocity trends in a few areas in Alexandria from our PSI
analysis.
In order to investigate the effect of time-correlated observations, including apparent cyclic effects, on
the estimated velocities we performed the regression for single persistent scatterers using a full
covariance matrix. The time correlation was accounted for with a power-law process. The power-law
noise amplitude and the time-dependence (spectral index) were estimated using the maximum
likelihood estimator (MLE). The MLE results showed an almost null time-correlation, that is, the
individual PS time series are mostly dominated by uncorrelated (white) noise. Eventually, these formal
uncertainties from the robust regression have been found in agreement with the repeatability (standard
deviation) of the nearby spatial velocity estimates. The latter approach of evaluating the uncertainties
provide, however, a somewhat more independent approach since it includes different PS with different
noise and local physical variability. Anyway, the two approaches have yielded similar results.
4. Long wavelength deformation and possible tilt in the results
The results from the InSAR stacking analysis showed that there is no large scale subsidence in the
historical city center of Alexandria. There were locally unwrapping issues at the boarder of the large scale
scene and in isolated spots. In order to monitor the subsidence along the Mariut Lake and possibly elsewhere, the
13 most coherent interferograms were selected covering a period from 2004 to 2010. The Figure S5 revealed
subsidence along the Mariut Lake, but low phase unwrapping issues can be noted in the city. The color scale is 1.4 cm/year (red, subsidence) to +1.4 cm/year (blue, uplift). These results agree with those of Mora (2010)
showing a subsidence along the Mariut Lake.
An important limitation of InSAR is its inability to detect long wavelength deformation due to
insufficiently accurate satellite orbit information or to long wavelength atmospheric effects. To
overcome this limitation, Bock et al. (2012) corrected the bias (tilt) in the LoS ground motion velocity
field (tilt) using GPS data from four permanent stations well distributed around the area of interest. In
our case study, only one permanent GPS station is available. Based on the geological assumption that
the Pleistocene sandstone ridges at Alexandria should follow a similar vertical ground motion in the
southwest/northeast direction, we extracted the PS from two transects of 200 m width in that direction
which is parallel to the coastline (Figure S6). We then estimated the tilt by computing the trend of
each PS time series transects (Figure S7). Both transects yielded a similar linear trend of 0.04 to 0.05
mm/km/year affecting our ground motion velocity maps in the southwest/northeast direction. This tilt
corresponds to 0.1 mm/year differential motion between the tide gauge and the GPS station. The tilt in
that direction can be neglected in our area of interest.
In the perpendicular direction, the tilt cannot be estimated accurately with this method because the
length of the area with PS is too short for a reliable trend estimation. However, in that direction the
differential velocity of the PS between the GPS station and the tide gauge is in agreement with the
differential velocity inferred from the GPS velocity on the one hand and from the combined satellite
altimetry and tide gauge data on the other hand, that is, the PS indicate a differential motion of 0.6
mm/year and the GPS – Satellite altimetry and tide gauge indicate 0.45 mm/year; see manuscript);
hence suggesting that whatever the direction the long wavelength tilt has negligible impact on the
relatively narrow area of interest here.
Finally, it is worth mentioning here that InSAR and PSI techniques have in general lower performance
in vegetated areas. This accounts here for the lack of PS outside the city of Alexandria. However,
other techniques such as SqueezeSAR or the use of L-band SAR data can reveal ground motions in
such vegetated areas.
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