a minimum curvature combination method for the generation...
TRANSCRIPT
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A Minimum Curvature Combination Method for the Generation of Multi-Platform DInSAR Deformation
Time-Series Antonio Pepe(1), Giuseppe Solaro(1), Claudio Dema (2)
(1) IREA-CNR, via Diocleziano 328, 80124 Napoli (Italy)
(2) Università degli Studi della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza (Italy)
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Summary • A DInSAR-based technique for the retrieval of 3-D (Up-Down, East-West, North-
South) deformation time-series through a multi-angle/multi-platform combination strategy is presented.
• A post-processing strategy, relying on a Minimum-Curvature assumption, is applied to sequences of LOS-projected time-series to recover inherent displacement time-series components.
• It does not require the simultaneous processing of large SAR data archives …
• The algorithm can be seen as a further development of the M-SBAS* processing algorithm, however …
• … and can be applied with no restrictions at all concerning the DInSAR tool (SB or PS-oriented) used for the retrieval of LOS displacement time-series.
• Information on the reconstruction quality of used LOS time-series as well as external data (GPS/leveling) can also be used to better constrain the solution to data.
• S. Samsonov, N. d’Oreye , “Multidimensional time-series analysis of ground deformation from multiple InSAR data sets applied to Virunga Volcanic Province”, Geophysical Journal International 191, pp. 1095-1108, 2012.
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Algorithm Overview First SAR Data Set
DInSAR Tool1
LOS1 Filtered Deformation
time-series
Residual Topography
Γ1 Reconstruction Quality
Factor
M-th SAR Data Set
DInSAR ToolM
LOSM Filtered Deformation
time-series
Residual Topography
ΓM Reconstruction Quality
Factor
Minimum Curvature SVD-
based LOS Displacement Time-Series
Combination
East-West Time-Series
Up-Down Time-Series
North-South Time-Series
External Data
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Algorithm Overview
Time
The algorithm allows the generation of “long-term” times-series of the 3-D components of deformation by combining M (independently retrieved) radar LOS-projected deformation time-series.
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Algorithm Overview
Time
The algorithm allows the production of “long-term” times-series of the 3-D components of deformation
We extend the M-SBAS strategy to a wider scenario where:
-LOS measurements, potentially retrieved using different DInSAR tools, are combined in a post-processing phase;
-Additional data (GPS/levelling) can also be jointly exploited;
-LOS time-series (instead of unwrapped interferograms) are combined;
-At variance with M-SBAS, a minimum-curvature combination is used.
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Acquisition Geometries
EAST
UP
NORTH
Desc
Near Polar-Orbit Trajectories
small LOS sensibility to N-S components is small
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Mathematical Framework
(*)
Similarly to SBAS, the system of equations (*) is reformulated (for each pixel) with respect to the unknowns, representing the displacement velocity vectors between consecutive time epochs
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Mathematical Framework
This linear system is underdetermined with more unknowns than independent equations.
1. Berardino P. et alii: “A new Algorithm for Surface Deformation Monitoring based on Small Baseline Differential SAR Interferograms”, IEEE Trans. Geosci. Remote Sensing, Vol. 40, No. 11, pp. 2375-2383, November 2002.
Equations
Unknowns
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Mathematical framework On a pixel-by-pixel basis, a quality index for the obtained LOS-projected time-series is now available (e.g., the temporal coherence Γ).
Depending on the number of SAR acquisitions N, DInSAR time-series accuracy empirically decrease as:
1. Berardino P. et alii: “A new Algorithm for Surface Deformation Monitoring based on Small Baseline Differential SAR Interferograms”, IEEE Trans. Geosci. Remote Sensing, Vol. 40, No. 11, pp. 2375-2383, November 2002.
with .To solve this linear system, the SVD-method is applied1.
Accordingly, the system can be reformulated as:
(**)
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The system (**) is regularized introducing additional equations.
Minimum Curvature Method
In our case, we impose that acceleration between consecutive time acquisition is minimal; this is done adding following equations:
We remark that in the M-SBAS case, the regularization conditions imposed the solution had Minimum-velocity Norm (MN).
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Minimum Curvature Method
with λ being a regularization factor.
The regularized system is solved in a LS sense with respect to the v unknowns, which temporally integrated lead to the 3-D time-series of displacement. While additional measurements (coming from GPS/levelling campaigns, or Pixel-Offset-based N-S measurements) are available, they can be treated as further sets to be used in the optimization.
Then:
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However, since the LOS sensitivity to North-South components of deformation is rather small:
with:
Minimum Curvature Method
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Let us consider two sets of SAR data collected (for instance) over ascending/descending orbits
Joint exploitation of Ascending / Descending data
ENVISAT Simulated Case
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Linear Deformation
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated
Simulated
MN
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Linear Deformation
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated
Simulated
MC
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Linear Deformation + Jumps
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated
Simulated
MN
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Linear Deformation+Jumps
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated
Simulated
MC
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Quadratic Deformation
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated
Simulated
MN
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Quadratic Deformation
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated
Simulated
MC
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Effect of Noise: Large Signals
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Simulated
MN
Estimated Gaussian σ=0,75 cm
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Effect of Noise: Large Signals
Time [day]
Time [day]
Disp
lace
men
t [cm
] Di
spla
cem
ent [
cm]
UP
EAST
Estimated Gaussian σ=0,75 cm
Simulated
MC
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Piton de La Fournaise Area
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Piton de La Fournaise
ASCENDING 48 ASAR/ENVISAT IMAGES DESCENDING
35 ASAR/ENVISAT IMAGES >20
<-20
cm/y
ear
>10
<-10
cm/y
ear
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>20
<-20
cm/y
ear
Piton de La Fournaise
ASCENDING 11 ALOS-1 IMAGES
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>10
<-10
cm/y
ear
UP-DOWN WEST-EAST
Piton de La Fournaise
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UP-DOWN WEST-EAST
Piton de La Fournaise
ALOS ENV. ASC ENV. DES
Time [year]
Disp
lace
men
t [cm
] UP EAST
Time [year]
Disp
lace
men
t [cm
]
April 2, 2007
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Conclusion • A DInSAR-based approach for the retrieval of the 3-D (Up-Down, East-West, North-
South) deformation time-series through a multi-angle/multi-platform LOS displacement combination strategy has been presented.
• Experiments conducted on simulated and real SAR data sets demonstrate the validity of the approach.
• A Minimum-Curvature (MC) combination approach has been implemented.
• The method can be used to combine LOS displacement time-series independently achieved also by different DInSAR tools (SB- and/or PS-like).
• External data (GPS/levelling measurements) and/or Pixel-Offset/MAI-based N-S time-series can be simply integrated in the proposed scheme.