IEEE Geoscience and Remote Sensing Magazine - March 2016 - 12
Fernandina
Range
SBAS
Meters
PO-SBAS Az
<-1.5
1
0
2005
0
2007
2003
0
2007
2003
Years
(b)
(a)
Range
2005
2007
(c)
Sierra Negra
PO-SBAS Rg
<-3
-20
2005
2007
PO-SBAS Az
<-1.5
0
m
m
0
Meters
Meters
cm/Year
Azimuth
SBAS
>2
>1.5
>3
2003
<-2
1
m
5
2003
cm
>2
Meters
PO-SBAS Rg
<-3
m
cm
>1.5
cm/Year
Azimuth
>3
-2
<-2
0
-6
2007
2003
Years
(e)
(d)
2003
2005
2007
(f)
FIgURE 3. Examples of a displacement time series obtained with SBAS and PO-SBAS for (a)-(c) Fernandina and (d)-(f) Sierra Negra. (a)
The LOS mean deformation velocity map computed through the SBAS approach and the displacement time series relevant to a point located
in the inner caldera, denoted by the black square. (b)-(c) Displacement during the period 2003-2007 computed through the PO-SBAS
approach along the range and the azimuth directions and the displacement time series of representative points located within the inner
caldera. Part (d) is the same as part (a) but is for Sierra Negra. Part (e) is the same as part (b) but is for Sierra Negra. Part (f) is the same
as part (c) but is for Sierra Negra. The displacement time series is relevant to the relative displacement between two points located across
the caldera, identified by the black boxes. The red lines refer to the Fernandina May 2005 eruption and to the Sierra Negra October 2005
eruption. (Figure used with permission from [117].)
uncertainty R U) given by the least squares inversion is
shown in
U = (P t R -R 1 P) -1 P t R -R 1 R
R U = (P t R -R 1 P) -1,
(3)
where U denotes the 3-D displacement vector with three
components, and P is the projection vector from the 3-D
displacement to displacements measured by correlation and
DInSAR. It is determined by the acquisition geometry: PLOS =
(-cos{sini, sin{sini, -cos i), Pazimuth = (sin{, cos{, 0) with
{ azimuth of the satellite trajectory and i the incident
12
angle. R corresponds to the vector of displacement measured by correlation and/or DInSAR, and R R and R U represent the error covariances of R and U, respectively.
In the possibilistic approach, no hypothesis is made
on the displacement errors, and they are represented and
propagated by possibility distributions. The output uncertainty takes into account the worst bound among all the
fused measurements (pessimistic approach). As a result,
even with more measurements, the output uncertainty is
not decreased. The solution (possibility distribution Ut
including the displacement value and the displacement
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