EE/Ae 157 b
Week 4b
Interferometric Synthetic Aperture Radar:
Differential Interferometry
EE/Ge 157 b, Week 4
4-1
DIFFERENTIAL INTERFEROMETRY
HOW DOES IT WORK?
•
•
•
•
Three-pass “repeat track” interferometry uses
two baselines (B1 , 1 ); (B2 , 2 ) to acquire
interferograms at different times.
Despite exaggeration in picture on the right,
the incidence angles and absolute ranges are
nearly the same.
Now suppose that the surface deformed
slightly between the second and third
acquisitions in such a way that the range
changed by an amount 
In the repeat-track implementation of
interferometry, the signal travels each path
twice, since the transmitter and receiver are in
the same place. Therefore, the
interferometric phase is
 
EE/Ge 157 b, Week 4
2

2  range 
4


B1
B2

  1

   2  
range
4-2
DIFFERENTIAL INTERFEROMETRY
HOW DOES IT WORK? (continued)
•
As shown before, the interferometric phase
between the first and second acquisition can
be written as
4
4
1  
B1 sin  0  1  
B1 cos  0  1 

•

Similarly, we can write the interferometric
phase between the first and third acquisition
as
 2  
•

4

B2 sin  0   2  
4

B2 cos  0   2  
B1
B2

  1
4



   2  
Subtracting the “flat earth” components,
leaves us with the two flattened
interferograms:
4
1 flat  
B1 cos  0  1 
 2 flat

4
4

B2 cos  0   2  



EE/Ge 157 b, Week 4
4-3
DIFFERENTIAL INTERFEROMETRY
HOW DOES IT WORK? (continued)
•
Let us look at the flattened phase of the
second interferogram in more detail
4
4
 2 flat  
B2 cos  0   2  


•

The first term is the phase due to the presence
of topography
4
 2topo  
B2 cos  0   2 

•
The second term is related to the change in
the range for the third acquisition
 2change  
•
4


B1
B2

  1

   2  

The topography has to change by an amount
equal to the ambiguity height for the first
term to change by a cycle, whereas only a
range change equal to half the wavelength is
required to produce the same amount of
phase change in the second term
EE/Ge 157 b, Week 4
4-4
DIFFERENTIAL INTERFEROMETRY
HOW DOES IT WORK? (continued)
•
Now, let us rescale the phase of the first
interferogram as if it was acquired with the
same baseline as the second one:
 B cos( 2   ) 

1 flat  1 flat  2
B
cos(



)
1
 1

•
Next, we subtract this rescaled interferogram
from the second interferogram
4
   2 flat  1 flat   

•
•

B1
B2

  1

   2  
This is the so-called differential
interferogram.
Any residual phase in the differential
interferogram therefore is related to a change
in the range (or path length) to the surface
EE/Ge 157 b, Week 4
4-5
DIFFERENTIAL INTERFEROMETRY
What can cause the range to change?
•
•
There could be several causes for a change in
range.
Suppose the surface actually changed in the
vertical direction due to subsidence or
inflation. The change in range is then
  h cos
•
Or, say the surface moved in the horizontal
direction, such as in the case of a glacier.
The change in range is then


h
Vertical Movement
  y sin 
•
Surfaces can move in both directions at the
same time, also. In that case, we need more
than one measurement looking in different
directions to completely measure the
movement of the surface.
EE/Ge 157 b, Week 4

y

Horizontal Movement
4-6
DIFFERENTIAL INTERFEROMETRY
Typical Applications
•
•
•
•
Tectonic deformations (pre-, co- and post-seismic deformations)
Ground subsidence due to oil or groundwater extraction
Volcanic inflation and deflation due to magma movement
Glacier movement, both regular ice stream movement and tidal flexing of glaciers
The major advantage of differential interferometry is the spatial patterns that are
measured, as opposed to single point measurements that are typically measured
with GPS receivers.
EE/Ge 157 b, Week 4
4-7
DIFFERENTIAL INTERFEROMETRY
Provides Dense Spatial Sampling
EE/Ge 157 b, Week 4
4-8
DIFFERENTIAL INTERFEROMETRY
Example of Co-Seismic Deformation – Eureka Valley
•
•
•
On 17 May, 1993, a M6.1 earthquake occurred in the Eureka on the border between California and
Nevada.
This earthquake occurred at a depth of 13 km along the west side of the Eureka Valley.
The focal mechanism of the main shock indicates that the earthquake ruptured a north-northeaststriking fault, steeply dipping to the west.
EE/Ge 157 b, Week 4
4-9
DIFFERENTIAL INTERFEROMETRY
Example of Co-Seismic Deformation – Eureka Valley
•
•
•
•
•
•
The aftershocks define a north-northwest
trend, and include two shocks of M~5 and
several of M>4.
Small surface ruptures formed in the central
part of the Eureka valley (arrow A1 on right).
Arrow A1 shows location of surface breaks
recognized in the field after the earthquake
Arrow A2 points to fault segment where
seismic rupture reached the surface, as
inferred from the radar data.
Large star indicates location of main shock,
small stars, locations of aftershocks of
magnitude greater than 4.5, and circles
smaller aftershocks
Dashed line delineates area shown in radar
interferograms
EE/Ge 157 b, Week 4
4 - 10
DIFFERENTIAL INTERFEROMETRY
Example of Co-Seismic Deformation – Eureka Valley
14 Sep. 1992 - 23 Nov. 1992
EE/Ge 157 b, Week 4
23 Nov. 1992 - 8 Nov. 1993
Difference
4 - 11
DIFFERENTIAL INTERFEROMETRY
Example of Co-Seismic Deformation – Eureka Valley
•
•
ERS-1, 3-pass interferograms show that the
Eureka Valley earthquake produced an
elongated subsidence basin oriented northnorthwest, parallel to the trend defined by the
aftershock distribution, whereas the source
mechanism of the earthquake implies a northnortheast striking normal fault.
These observations suggest that the rupture
initiated at depth and propagated diagonally
upward and southward on a west dipping,
north-northeast fault plane, reactivating the
largest escarpment in the Saline Range
EE/Ge 157 b, Week 4
4 - 12
DIFFERENTIAL INTERFEROMETRY
Example of Co-Seismic Deformation – Eureka Valley
•
The ±3 mm accuracy of the radar observed displacement map over short spatial scales, allowed
identification of the main surface rupture associated with the event.
Reference: Peltzer and Rosen, Surface displacement of the 17 May 1993 Eureka Valley
earthquake observed by SAR interferometry, Science, 268, 1333-1336, 1995.
EE/Ge 157 b, Week 4
4 - 13
DIFFERENTIAL INTERFEROMETRY
June 28, 1992, M 7.3, Landers, California Earthquake
EE/Ge 157 b, Week 4
4 - 14
DIFFERENTIAL INTERFEROMETRY
Example: 1995 North Sakhalin Earthquake (M 7.6)
Radar
Differential
Interferogram
Deformation Model
Predictions
EE/Ge 157 b, Week 4
4 - 15
Reference: Tobita, et al., Earth Planets Space, 50, 1998
DIFFERENTIAL INTERFEROMETRY
Example of Post-Seismic Deformation – Landers
•
•
GPS, trilateration, strainmeter, and SAR
interferometry (InSAR) data revealed patterns
of various scales in the surface deformation
field associated with post-seismic processes
after the 1992 Landers earthquake.
A large scale pattern consistent with after-slip
on deep sections of the fault was observed in
all data sets
–
•
After-slip models imply vertical movements of up to 4
cm in the 10-20 km range from the fault, which are
inconsistent with the range change observed in the
InSAR data spanning 1-4 years after the earthquake.
InSAR data revealed several centimeters of
post-seismic rebound in step-overs of the
1992 break with a characteristic decay time
of 0.7 years.
–
Such a rebound can be explained by shallow crustal
fluid flow associated with the dissipation of pore
pressure gradients caused by co-seismic stress changes
EE/Ge 157 b, Week 4
4 - 16
DIFFERENTIAL INTERFEROMETRY
Example of Post-Seismic Deformation – Landers
EE/Ge 157 b, Week 4
4 - 17
DIFFERENTIAL INTERFEROMETRY
Example of Strain Accumulation – California
EE/Ge 157 b, Week 4
4 - 18
DIFFERENTIAL INTERFEROMETRY
Example of Strain Accumulation – California
Satellite synthetic aperture radar interferometry revealed an undiscovered transient strain pattern along the
Blackwater-Little Lake fault system within the Eastern California Shear Zone (See map). The surface strain
map obtained by averaging eight years (1992-2000) of ERS (1) radar data shows a 120 km-long, ~20 kmwide zone of concentrated shear between the southern end of the 1872 Owens Valley earthquake surface
break and the northern end of the 1992 Landers earthquake surface break. The observed shear zone is
continuous through the Garlock fault, which does not show any evidence of localized left-lateral slip during
the same time period. A dislocation model of the observed shear indicates that the Blackwater-Little Lake
fault is currently creeping below the depth of ~5 km at a rate of 7±3 mm/yr in a right-lateral direction. This
rate is about 3 times larger than the long-term geological rate estimated for the Blackwater fault(2) and takes
up more than 50% of the entire right-lateral shear distributed across the Eastern California Shear Zone.
This transient slip rate observed in the 1992-2000 ERS radar data and the absence of resolvable slip on the
Garlock fault during the same time period may be the manifestation of an oscillatory strain pattern between
interacting, conjugate fault systems. Such a cycle provides a possible explanation for the observed clustering
of large earthquakes in the ECSZ and on the Garlock fault. In this interpretation, the recent seismicity in the
ECSZ (Owens Valley 1872, Landers 1992) may have been triggered by accelerated, localized strain
accumulation within the shear zone in the last several hundred years as it is now observed along the
Blackwater-Little Lake fault system.
Alternatively the fast, localized shear observed along the Blackwater-Little Lake fault system may have been
triggered by the recent large earthquakes at both ends (Owens Valley, 1872 and Landers, 1992) but the
mechanism by which these earthquakes may have triggered the observed shallow creep is not understood.
EE/Ge 157 b, Week 4
4 - 19
DIFFERENTIAL INTERFEROMETRY
Example of Strain Accumulation – California
EE/Ge 157 b, Week 4
4 - 20
DIFFERENTIAL INTERFEROMETRY
Example of Strain Accumulation – California
EE/Ge 157 b, Week 4
4 - 21
DIFFERENTIAL INTERFEROMETRY
Example of Ground Subsidence – LA Basin
•
•
Regions of ground subsidence include the
Pomona (P) area (water), the Beverly Hills
(BH) oil field (oil) and localized spots in the
San Pedro and Long Beach airport (LBA)
area (probably oil industry activity).
Noticeable surface uplift is observed in Santa
Fe Springs oil field (SFS) and east of Santa
Ana (SA). Surface uplift in these areas may
result from the recharge of aquifers or oil
fields with water, or from the poro-elastic
response of the ground subsequent to water or
oil withdrawal.
EE/Ge 157 b, Week 4
4 - 22
DIFFERENTIAL INTERFEROMETRY
Example of Magma Movement – Darwin Volcano, Galapagos
Interferogram 1992-1998
Predicted deformation
The best fitting point source is 3 km deep
EE/Ge 157 b, Week 4
4 - 23
DIFFERENTIAL INTERFEROMETRY
Example of Magma Movement – Sierra Negra Volcano, Galapagos
EE/Ge 157 b, Week 4
4 - 24
DIFFERENTIAL INTERFEROMETRY
Example of Magma Movement – Sierra Negra Volcano, Galapagos
Point source
Magma sill
EE/Ge 157 b, Week 4
Reference:
Amelung, F., S. Jonsson, H. A. Zebker, and P. Segall,, Nature, 407, No.6807, 993-996, 2000.
4 - 25
DIFFERENTIAL INTERFEROMETRY
Example of Glacier Movement: Ryder Glacier, Greenland
21-22 September 1995
EE/Ge 157 b, Week 4
26-27 October 1995
Reference:Joughin et al., Science, 1996
4 - 26
DIFFERENTIAL INTERFEROMETRY
Measuring Tidal Displacements on Glaciers
•
•
•
•
For most glaciers, the underlying movement
of the glacier can be considered constant over
extended periods of time.
– The exceptions are mini surges of
glaciers as illustrated on the previous
page
The floating “tongue” of the glacier moves up
and down because of sea-level changes
associated with tides
If two different velocity maps are constructed
as shown in the previous slide, changes
between the two differential interferograms
are associated with tidal flexture of the
glacier
The position of the grounding (or hinge) line
is a sensitive indicator of the mass of the
glacier tongue
EE/Ge 157 b, Week 4
Grounding Line
Glacier Movement
Tongue Movement
Tidal
Movement
Glacier
Ocean
Bedrock
4 - 27
DIFFERENTIAL INTERFEROMETRY
Example of Glacier Tidal Flexing: Nioghalvfjerdsbrae Glacier,
Greenland
Reference: Rignot, ESA SP-414, 1997
EE/Ge 157 b, Week 4
4 - 28
DIFFERENTIAL INTERFEROMETRY
Example of Glacier Recession, Pine Island Glacier, Antarctica
Reference: Rignot, Science, 1998
EE/Ge 157 b, Week 4
4 - 29
West Antarctic Ice Streams from InSAR
The time evolution of ice
stream flow variability
is uniquely imaged by
InSAR. Complete
coverage by InSAR is
needed to understand
flow dynamics of the
potentially unstable
marine ice sheet.
Joughin et al , 1999
EE/Ge 157 b, Week 4
4 - 30
DIFFERENTIAL INTERFEROMETRY
ERROR SOURCES
•
•
•
•
Uncompensated differential motion
– Any residual error in position of the radar will appear as surface deformations
Atmospheric effects
– The expressions derived earlier assumes that the radar signal propagates through a
medium with index of refraction equal to 1. Water vapor in the atmosphere, for
example, could modify the index of refraction slightly, leading to an observed
differential phase. These artifacts change on relatively small time and spatial
scales.
Temporal decorrelation
– If objects move too much, the phase becomes random, and we cannot generate an
interferogram to begin with. This happens in vegetated areas, especially for shorter
wavelengths, but could also occur as a result of changing surface conditions
(freezing, snow, etc). Also happened for glaciers that move too far between
observations.
Layover
– Cannot unwrap the phase to begin with
EE/Ge 157 b, Week 4
4 - 31
Atmospheric Effects
EE/Ge 157 b, Week 4
4 - 32
Atmospheric Effects
Reference: Hansen et al., 1999, Science
EE/Ge 157 b, Week 4
4 - 33
Atmospheric Effects
Reference: Hansen et al., 1999, Science
EE/Ge 157 b, Week 4
4 - 34
Atmospheric Effects
Reference: Hansen et al., 1999, Science
EE/Ge 157 b, Week 4
4 - 35
Temporal Decorrelation
L-band (left) and C-band absolute phase (modulo 2 pi) assuming scattering centers are at the
center of each pixel. Pixel size is 10m
EE/Ge 157 b, Week 4
4 - 36
Temporal Decorrelation
L-band (left) and C-band absolute phase (modulo 2 pi) assuming scattering centers are distributed
uniformly randomly within each pixel. Pixel size is 10m
EE/Ge 157 b, Week 4
4 - 37
Temporal Decorrelation
L-band (left) and C-band interferometric phase (modulo 2 pi) assuming scattering centers are
distributed uniformly randomly within each pixel. Pixel size is 10m, baseline is 5 m
EE/Ge 157 b, Week 4
4 - 38
Temporal Decorrelation
L-band (left) and C-band interferometric phase (modulo 2 pi) assuming scattering centers are
distributed uniformly randomly within each pixel. Pixel size is 10m, baseline is 5 m. We further
assume a uniformly random movement of 5 mm of the scattering centers between acquisitions.
EE/Ge 157 b, Week 4
4 - 39
Temporal Decorrelation
L-band (left) and C-band interferometric phase (modulo 2 pi) assuming scattering centers are
distributed uniformly randomly within each pixel. Pixel size is 10m, baseline is 5 m. We further
assume a uniformly random movement of 5 cm of the scattering centers between acquisitions.
EE/Ge 157 b, Week 4
4 - 40
Scatterer Motion - Temporal Decorrelation
• Motion of scatterers within the resolution cell from one observation
to the next will lead to randomly different coherent backscatterphase
from one image to another, i.e. “temporal” decorrelation.
EE/Ge 157 b, Week 4
4 - 41
Form of Motion Correlation Function
• The Fourier Transform relation can be evaluated if Gaussian probability distributions for the
motions are assumed
†
where y,z is the standard deviation of
the scatterer displacements crosstrack and vertically
Note correlation goes to 50% at about
1/4 wavelength displacements
EE/Ge 157 b, Week 4
† The
is valid if the x and y motions are uncorrelated.
4 - 42
Temporal Decorrelation from Random Disturbance
1æ 4 p ö 2
- ç
÷ s los
2è l ø
2
g t (l ) = e
æ l1 ö2
ç ÷
è l2 ø
g t (l2 ) = g t (l1 )
• Assuming that temporal correlation primarily results from random movement of scatterers
between observations and that L-band and P-band backscatter results from scattering off the
EE/Ge 157 b, Week 4
4 - 43
same objects then we would expect the temporal correlations to scale by the square of the ratio
of wavelengths.