IEEE Geoscience and Remote Sensing Magazine - March 2016 - 10

Standard Deviation
of Stack (mm/Year)

Stacked Range Change
Rate (mm/Year)
-4 -2

0
2
(a)

6 0

2
(b)

FIgURE 1. (a) The linear range change rate and (b) standard devia-

tion of the linear range change rate obtained from the stacking of
13 independent interferograms in the San Francisco Bay Area from
1992 to 2000. (Figure used with permission from [77].)

are combined to retrieve a surface displacement with reduced uncertainty. In the case of complementarity, they
are combined to retrieve a surface displacement with a
larger spatial extension or of a higher level (e.g., the 3-D
displacement field). The second group corresponds to
the processing from measurements to model parameters.
Surface displacement measurements are combined to estimate the geometrical parameters of a physical deformation
model in cases of redundancy and complementarity.
From raw measurements
to Fused measurements
In the case of redundancy, the common and intuitive approach consists of averaging all available measurements to
obtain an estimation that is as precise as possible [75]-[78].
However, this approach is subject to difficulty in determining the contribution of each measurement and the limitation of computational capacity while dealing with large volume data sets. Figure 1 gives an example of interferograms
stacking for displacement measurement on the Hayward
fault in the San Francisco Bay Area from 1992 to 2000 [77].
For this, 37 interferograms with spatial baselines fewer
than 200 m and temporal baselines longer than one year
are selected. The set of 37 interferograms is stacked by dividing the cumulative range change by the cumulative time
span, which preferentially weighs the range change rate of
those interferograms with longer temporal baselines. Afterward, interferograms where more than 5% of the coherent
phase exceeds three standard deviations from the stacked
results are removed. Finally, a subset of 13 independent interferograms is selected for the stacking, and the standard
deviation is used as an uncertainty measure associated
10

with the stacked range change rate. Thanks to this stack,
the atmospheric artefacts in individual interferograms are
reduced significantly.
In the case of spatial complementarity, a mosaic is
usually performed to obtain a displacement measurement over large areas, which is very useful to generate
displacement maps at global scale [18], [19], [67]. Figure 2
shows the annual velocity field obtained from the featuretracking of Landsat images to measure glacier flow over
the Karakoram. Figure 2(a) shows the result for a single
pair (i.e., the pair with the highest spatial coverage among
all available pairs). Many gaps appear in saturated areas
or areas covered by clouds (corresponding to measurements with a signal-to-noise ratio below four), which
limits the percentage of estimates over glaciers to 70%.
Velocities in stable areas, which are expected to be null,
are in the range of 10 m/year due to orthorectification
errors. On the other hand, Figure 2(b) shows the velocity obtained from the fusion of 29 annual pairs available
for the period 1999-2001 and taking the median value
at each location. The spatial coverage is increased to 94%
thanks to the complementarity from one pair to another.
Velocities in stable areas are reduced to 2 m/year thanks
to the redundancy and because the orthorectification
errors are not coherent [19].
In the case of temporal complementarity, measurements time series can be used to follow the temporal evolution of the event with an appropriate method, such as
PS and SBAS approaches [41]-[43], [45], [49], [79]. These
approaches have been modified and improved since their
first applications. Variants of the SBAS approach such as
pixel-offset (PO) SBAS [26] and parallel SBAS [80] have
been developed to make use of PO measurements and
to deal with large data sets. Variants of the PS approach,
such as SqueeSAR [81], have been developed to improve
the performance of the PS technique proposed previously. Along with PS interferometry, SAR tomography-based
approaches allow for an improvement in the detection
of PSs in urban areas [82]-[86]. Figure 3 gives an example of a surface displacement time series obtained with
SBAS [49] and PO-SBAS [26] for Fernandina and Sierra
Negra. The temporal evolution of the surface displacement for these two calderas is characterized thanks to
the temporal complementarity. The eruptions for both
calderas have been well identified by the abrupt change
of the displacement magnitude from the time series. Regarding the quantification of the uncertainty associated
with the displacement time series, it constitutes a truly
complex task. For PS approaches, because of the iterative
process (including the temporal phase unwrapping and
the spatial integration) adopted by most PS approaches,
the propagation of the input uncertainty and the quantification of the final uncertainty seem extremely difficult. The phase standard deviation is usually used as
an indicator of the quality of the displacement velocity
obtained. However, this parameter is strongly related
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