IEEE Geoscience and Remote Sensing Magazine - March 2016 - 11

60
45
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15
0
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km
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Velocity (m/Year)

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y Comp.

105

x Comp.

120

Velocity (m/Year)

y Comp.

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(b)

FIgURE 2. The ice flow velocity magnitude obtained from feature-tracking of Landsat images over the Karakoram for (a) a single annual pair and
(b) the fusion of 29 annual pairs over the period 1999-2001. The white gaps correspond to areas where no measurements are available. In (a), the
spatial coverage is 70%, while it is increased to 94% in (b). The insets show histograms of the velocity in stable areas for each component.

to the nonlinear motion according to [50] and, thus, is
not an appropriate indicator of the displacement uncertainty. For SBAS approaches, the main difficulty also lies
in the quantification of the phase unwrapping error. In
[7], the root-mean-square misclosure is calculated to assess the phase unwrapping quality, but no clear uncertainty associated with the final displacement time series
is provided.
In the case of geometrical complementarity [from diverse
acquisition geometries such as different incident angles,
different orbital directions (descending and ascending),
and different displacement directions (range and azimuth)],
the 3-D displacement at the Earth's surface is usually retrieved by a linear inversion in least square sense to interpret
the surface displacement field in a homogeneous and intuitive way [12], [39], [87]-[89]. For example, in the displacement measurement of the Kashmir, Pakistan, earthquake
in 2005, surface displacement measurements from the correlation of SAR amplitude images and DInSAR, including
ascending and descending passes and different incident
angles, are available. Both redundancy and spatial and geometrical complementarity exist. In particular, correlation
and DInSAR measurements issued from the same pair of
SAR images are available, and these two types of measurements essentially provide complementary displacement
information. On one hand, the correlation measurements
are reliable in areas where the displacement is large (usually
close to the deformation source), while DInSAR measurements are mainly available in areas where the displacement
is small (usually far from the deformation source). On the
other hand, besides the displacement measurement in the
LOS direction, the correlation measurements provide displacement measurements in the azimuth direction, which
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is complementary to the DInSAR measurements. Regarding the redundancy of displacement measurement in the
LOS direction provided by both measurements in areas of
moderate displacement, the correlation measurements can
be used to check the existence of phase unwrapping error
and to retrieve the absolute displacement value in DInSAR
measurements because the relative displacement value is
obtained from the phase. In addition, since the precision of
DInSAR measurement is much higher than that of correlation measurements, the contribution of DInSAR measurement is naturally more significant than that of correlation
measurements.
For the Kashmir earthquake example, 23 surface displacement data sets were available in total. Two fusion
strategies, namely joint inversion and prefusion, were
investigated together with two uncertainty propagation approaches: one based on the probability theory
and the other based on the possibility theory [90], [91].
In joint inversion, all available measurements are used
simultaneously in the inversion. The prefusion consists
of a fusion step before inversion. This fusion step can
be performed using the mean value, the median value
of a set of measurements, or by selecting the best one
according to certain criteria, e.g., the reliability of measurements or the signal-to-noise ratio. Afterward, the
refined data sets are input in the inversion. In the probabilistic approach, displacement errors are assumed
random and independent, which is an optimist hypothesis that cannot be justified in most cases. They are
represented and propagated by Gaussian distributions.
With this hypothesis, the more measurements that are
fused, the smaller the output uncertainty becomes.
The solution (displacement value U and displacement
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - March 2016