Corresponding author.
A QUATERNARY PROTOTYPE FOR SPATIOTEMPORAL ANALYSIS OF
PERMANENT SCATTER INTERFEROMETRY
J. Wu 2, *, J. Cai\ C. Hu a , F. Xiao 3 , C. Liu a
aDept. of Surveying and Geo-Informatics, Tongji University, 1239 Siping Road, Shanghai, 200092, China-
(jcwu,cwhu)@mail.tongji.edu.cn, xfxf2001 @ 163.com, 290202.student@sina.com
blnstitute of Geodesy, Stuttgart University, Geschwister-Scholl-Str. 24D, 70174 Stuttgart, Germany - cai@gis.uni-
stuttgart.de
Commission VII, WG VII/2
KEY WORDS: Satellite Remote Sensing, Modeling, interferometric SAR (InSAR), SpatioTemporal Analysis, Ground
Deformation Hazards
ABSTRACT:
In this paper, a set of quaternary arc time series of the double phase differences formed by a PS (Permanent Scatter) with its
surrounding four PSs in each quadrant are processed together, where the spatial constrains on the parameters are included directly in
the adjustment model. Equations of this spatiotemporal analysis model are formulated. A simulation example using this new method
is presented. It shows that a priori information of the crustal deformation can be integrated into the integer least squares adjustment
model to improve the accuracy of parameters estimated.
1. INTRUDUCTION
Repeat-pass satellites SAR interferometry (InSAR) technology
has been used for providing EDMs with meter accuracy and
terrain deformations with millimetric accuracy (Hanssen, 2001).
It has significant advantages over traditional geodetic methods
for its larger spatial coverage with high spatial resolutions and
all weather running. InSAR technology has been used for
crustal deformation monitoring, such as ground subsidence,
slope slides, volcanoes and so on. However, the essential
limitations of InSAR are due to temporal and geometrical
decorrelation and atmospheric inhomogeneities effects on
interferometric phases. In 1999, a new interferometric method
based on permanent scatters, named PS-InSAR is proposed
(Ferretti, et al., 1999). This method uses the long time reliable
coherence properties of PSs to overcome the temporal and
geometrical decorrelation and also uses the time series of
interferometric phase differences of adjacent PSs to eliminate
the effects of the atmospheric inhomogeneities. Actually, in
Permanent Scatter Interferometry (PSI), a stack of N differential
interferograms of PSs are analyzed for phase unwrapping and
deformation parameters estimation. The conventional method
processes the time series of phase differences of the adjacent
PSs (usually called as double difference of arcs) using the
Integer Least Squares (ILS) method, such as the LAMBDA
(Least squares AMBiguity Decorrelation Adjustment method)
(Teunissen, 1995). Then the spatial closure conditions among
arcs are applied for validations and corrections of phase
ambiguities and parameters of models estimated (Kampes,
2006). And the temporal and spatial information in the
interferograms are used separately. This PSI method sometimes
fails to give correct estimations, so an integrated spatiotemporal
analysis method is expected to be able to solve this kind of
problem more efficiently.
Considering a set of quaternary arcs of time series radiated from
one chosen PS bearing both spatial and temporal information of
model parameters, we use these quaternary arcs of time series
as an elementary adjustment cell for double difference phase
ambiguity estimation. At first a prototype of the quaternary
spatiotemporal adjustment model is given. Then a simulated
example is demonstrated and the results are obtained. At last a
conclusion of this research is given.
2. QUATERNARY ADJUSTMENT MODEL
Supposing we have N+l SLC SAR images, based on the
optimal baseline (spatial and temporal) distribution (Adam, et
al., 2004), one image is chosen as master and the others as
slaves. Each slave image has been coregistered with the master
and N interferograms are obtained. With methods based on
temporal stability of amplitudes or phases of a pixel, the PS
candidates can be obtained (Kampes, 2006; Hooper, 2006). On
each PSs, the wrapped phase <j>* in differential interferogram k
can be decomposed to
=m*,+<c+<o<o <»
where W {■} is the wrapping operator, is the phase caused
by uncompensated topography, <fl k d is the phase caused by
displacement of the target in the time between master and
corresponding slave image acquisitions, a is the phase caused
by atmospheric delays, and ^ is the additive noise term, the
subscript x presents the position of the PS.