Measuring 3-D Ground Movement by Differential Interferometry: Technique and
Validation.
S.Sircar1, 2, C.Randell1, D.Power1, J.Youden1 and E.Gill2
Remote Sensing Group C-CORE1 / Faculty of Engineering and Applied Science2
Memorial University
St. Johns NF Canada.
email:- sircar@engr.mun.ca
Abstract
Interferometry is a phase-based technique, which
uses a coherent imaging system to extract
topographical information from image pairs.
This paper will derive a technique for extracting
lateral ground displacement using interferometry
with data from satellite Synthetic Aperture Radar
(SAR). Ground movement derived from a single
look direction (e.g., subsidence only) will
contain errors if it is incorrectly assumed that
the other two components (i.e., East-West and
North-South) are zero. The advanced technique
presented can be used to improve the accuracy
of single-pair subsidence estimates by fusing two
non-parallel pass images and measuring the
lateral movement and subsidence. It is shown
that three dimensional movement estimates can
be derived from two satellite look directions by
combining the look geometry with standard least
squares estimation technique.
range change in two or more SAR images of the
same scene.
A single SAR image does not contain enough
information to say anything about the movement
or relative height change of the imaged scene [2].
InSAR combines two complex and co-registered
images of the same scene from almost identical
perspectives into a so-called interferogram. The
phase difference for each picture element (pixel)
in the interferogram is a measure of relative
change in distance between the ground
(scatterer) and the SAR antenna as shown in
Figure 1. A Digital Elevation Model (DEM) can
be obtained from this if there is no large-scale
ground deformation between image acquisition
times.
1. Introduction
SAR (Synthetic Aperture Radar) interferometry
is a relatively new technique for remote sensing
applications. InSAR (interferometric SAR) was
first introduced for topographic mapping by
researchers Zebker and Goldstein in 1986 and its
usefulness for precise terrain mapping has been
validated [1]. Interferometry, by definition, is a
technique that utilizes interference of waves for
precise determination of distance. In SAR
interferometry, the phase of the received
backscattered signal from two images of the
same scene are used to measure path length
differences with millimeter accuracies [1]. These
path length differences can be related to
parameters such as terrain height and
deformation of the earth’s surface. What
distinguishes SAR from other typical radar is
that it is a coherent imaging system which
records and processes both amplitude and phase
information of the radar echo. The phase
recordings can be used to measure differential
D
 2  1 
360 °
x
2
SAR Beam Width
  j
After Movement
Before Movement
Figure 1. Image acquisition geometry of SAR. 1 and 2 are
the phase differences obtained from the two image scenes
related to slant range change D and  is the wavelength. +j
is the Cartesian representation of amplitude and phase
recorded by the SAR.
In general, the phases corresponding to
differential range change in the interferogram
will contain topographical information as well as
movement information. Thus, there is a need for
two interferometric pairs (4 images), so that the
first two images can be used to generate an
accurate topographical model or Digital
Elevation Model (DEM) and then this model can
be used to remove the topographical phases from
1
the subsequent pair to obtain movement
information. This technique is called differential
interferometry. In principle, phase relating to
range change can be written as
derived from a series of SAR images using
DInSAR over the same period.
The DEM required to remove topographical
information with the DInSAR technique was
obtained from a tandem mode ERS-1 and ERS-2
pair. The time interval between interferometric
acquisitions of ERS-1/2 is only one day and is
suitable for DEM, since decorrelation in the
phase due to changes in the scattering properties
of the ground is limited over that period. The
interferogram shown in Figure 3 is obtained after
processing ERS-1/2 interferometric pair, which
contains only topographical information. Five
RADARSAT-1 both ascending and descending
scenes were obtained over a 7 month period
during 2001 for application of differential
interferometry. The area of interest containing
the 65 monuments is well contained by the
coverage region of all the obtained scenes.
  (Topography )  (displacement )  (error )
The two interferometric pairs (4 images) are
required to generate the movement-only
interferogram, assuming there is no other way to
get the topographical information of the scene
[3].
2. Experimental Methodology
North Belridge Oil Field located in San Joaquin
Valley in southern California is known to be
experiencing significant ground movement due
to oil production based on historical surveys.
This ground movement has resulted in
significant problems for companies operating in
the region. For example, one gas pipeline
company has experienced several ruptures to a
pipeline that runs directly through the subsiding
region.
2.1 Processing Steps
The ERS-1/2 and RADARSAT-1 SAR
processing used is detailed in [4,5]. An output
product of the SAR processing is called the
Single Look Complex (SLC), which is required
for interferometric processing. A SLC image
forms the basis for interferometry, and contains
both magnitude and phase of the radar echoes.
InSAR/D-InSAR processing includes coregistration of SLC images and generation of a
coherence image, interferogram generation
(Figure 3), flat earth phase removal, elevation
phase removal, differential interferogram
generation, phase unwrapping and conversion
from phase to range change maps. When the
phase is converted to a change map, the output is
“change in slant range”.
The measurements of ground position via global
positioning satellites or GPS is a popular and
convenient method for measuring ground
movement. Although it does not achieve the
same accuracy as a rigorous theodolite derived
survey, differential GPS measurements with a
fixed and moving station can achieve reasonably
accurate positional estimates. The accuracy of
these estimates increase with the amount of time
the roving station collects its data at a single
point and accuracies of 1-2 cm in x, y and 2-5
cm in z are achieved respectively if data is
collected for greater than 20 minutes or so.
GPS surveys were made of 65 monuments
during the period of 2000 to 2001, with six
surveys conducted in 2000 and four surveys
conducted in the year 2001. The area of
coverage for this survey was approximately
~10km2 where measurements from these 65
monuments were recorded. The recording of
these GPS surveys was not periodic and there
were some instances where the interval of
readings exceeded many months. To normalize
these inconsistencies in the GPS survey, standard
slope fitting techniques were used to estimate a
general movement trend for each monument
from the GPS measured data set. These data
were used to validate ground movement data
Figure 2. Interferogram or fringe image. Every cycle from
red to red is (half wavelength) shift of the propagation path.
Coherence measures correlation of the two
image pairs and varies in the range of 0 to 1. The
2
degree of coherence can be used as a quality
measure because it significantly influences the
accuracy of phase differences and hence slant
range change measurements [4]. Some of the
factors that influence loss in coherence are steep
slopes (surface slope > SAR incidence angles),
major ground movement, extended period
between the two passes (e.g. temporal
decorrelation due to vegetation growth) and long
baseline [3]. Baseline is the separation of
satellite orbits for the two image acquisition
times [4].
In principle, only one component of the
displacement vector can be obtained from a
single interferometric pair of similar viewing
geometry (either ascending or descending). To
measure three components of displacement one
must have three sets of interferometric pair each
of which have different look directions, unless
additional information (e.g., from ground
observations) are available to determine the full
three-dimensional displacement field. To extract
the third component of movement some
assumptions have to be made in the absence of a
third pair of differential interferogram with
unique
look
direction.
With
Satellite
interferometry, it is not possible to obtain this
third unique pair. However, under certain
conditions it may be possible to estimate three
dimensional ground movement using least
squares techniques. These conditions include
regions experiencing well-behaved ground
movement, in which the movement is generally
homogeneous over many resolution cells of the
SAR sensor.
Typically DEM contains spatial elevation change
information. A 3-D perspective of the area under
investigation is shown in Figure 5, which is a
DEM.
Consider a small area on ground viewed by a
varying incidence angle  to  +  where
the surface change is a small-scale coherent
change common to several adjacent pixels.
Figure 3 (DEM San Joaquin Valley. InSAR processing of
ERS-1/2 data)

The synthesis equations that were derived in [7]
for extracting ground movement from the two
non-parallel passes can, in general, be used to
derive two dimensional ground movement. The
equation derived in [7] for extracting 2-D ground
movement is as follows:
 sin( d ) cos( d )
 sin( ) cos( )

a
a
sin( d ) sin( d )
 sin( a ) sin( a )
Variation in look angle
n pixels in a square over each column
patch
Figure 4: Bounded region of n pixels that coherently move
together.
cos( d ) 
cos( a )

Region
coherently
moves together
3. Fusion of Ascending and Descending Passes
for estimating 3-D ground movement.
In other words, the deformation is well behaved
with no discontinuities. With this assumption,
the under-determined system can be restructured
into an over-determined system for pixels within
the region bounded by (  ,  +  ) as
illustrated in Figure 4. Consider n pixels in that
neighbourhood where the position of the radar
scatter has not changed substantially however,
the ensemble of the scatter has moved up, down,
or sideways in some correlated fashion. This
implies an area on the ground experienced
homogenous movement and can be collectively


 x 
   d  , and is clearly underdetermined.
. y = 
   a 
 z 
It is possible to estimate Subsidence z and
East-West x by neglecting North-South
y movement.
3
grouped by those n pixels. For the ith pixel in that
n pixel region (Figure 4), the 3-D movement
xi , y i and zi can now be estimated. The
Change ind
n pixel
neighborhood
of the overlapping
region
conversion matrix for each ith pixel is given as:
 sin( di ) cos( d )

 sin( ai ) cos( a )
sin( d ) sin( d )
i
 sin( a ) sin( a )
i
w 
 x i   x i    d 
 w  .  y i  =  i  ,
 y i      a i 
 w   z i 
 zi 
 d
cos( d ) 
i
cos( a )
i
.

[1]
 a
Change in a
where w x , w y and w z are
the
constraints
i
i
i
imposed on the solution xi , yi and z i . The
Figure 5: Ascending and Descending pass grid with varying
incidence angle. The n neighbourhood identifies region of
continuous displacement field used for the least squares
solution.
constrained least squared solution would
estimate ground movement in all three
directions. The constrained matrix can be derived
from the knowledge of sensitivity of InSAR in
each individual direction. InSAR is insensitive to
changes in the y direction compared to x and
z directions. As a consequence, the estimated
movement in the y direction would be large
compared to x and z . This would require
further constraints to the obtained solution in y
direction. The gradient vector of SRC over a
small grid will be proportional with respect to
the amount of lateral ground movement of that
region. Thus more lateral movement is likely to
occur when the rate of change of SRC with
respect to distance is observed in a particular
region. The solution can be adjusted according to
the gradient of the SRC vector.
4 Verification and Results
For verification of the fusion least squares
technique presented in section 3, an area
experiencing ground movement must be first
selected. North Belridge Oil Field located in San
Joaquin Valley in southern California is known
to be experiencing significant ground movement
due to oil production based on historical surveys.
GPS data were processed of the area to verify the
technique. D-InSAR data were processed over
the same time frame as that of the GPS survey
data. Five satellite scenes February 2001 to
September 2001 from ascending and descending
were processed. All pairs exhibited excellent
coherence, thus DInSAR results were expected
to be of very good quality.
The grid for the over determined system of
equations with overlapping ascending and
descending pass images is illustrated in Figure 5.
The variation of  a and  d over a small area
i
i
on ground is insignificant thus a relatively large
area has to be chosen to provide a meaningful
result from the least squares estimation. The
rationale for this is based on the convergence of
a least squares solution. However, it also reduces
the likelihood of having a region of
homogeneous ground movement with no
discontinuities. To mitigate these potential
problems, an optimization routine can be
employed to determine the region of most
suitable size.
The comparison of results between InSAR and
GPS illustrate the following:
1.
Subsidence, East-West and North-South
movements derived from D-InSAR correlate
very favourably to GPS.
2.
The average variance (scatter of the
data) from the trend line achieved in East-West,
North-South and Subsidence are <0.22, 0.35 and
0.34>cm respectively and are well with in the
expected measurement error. Achieved slope for
East-West and Subsidence is close to 1 and a
strong correlation indicates validation of the
technique.
The estimated North-South movement with the
aid of constrained least squares technique seems
to work very well.
4
noted difference is seen in the East-West
displacement, which seems to have improved
appreciably from the previous work in [7]. More
precise measurements of the monuments with a
theodolite would have helped demonstrate better
results.
Lateral Movement (East-West) [Feb-Sept 2001] Averaged
InSAR Measured East-West Movement (unts: cm)
1
Correlation = 0.87
Scatter about Slope Line = 0.22 cm
0.5
0
5.Conclusion
-0.5
In the context of deriving 3-D ground movement
from Synthetic Aperture Radar, the possibility of
fusing ascending/descending pass SAR images
in order to extract ground movement is shown.
The results give a satisfactory indication of the
capability of D-InSAR to measure 3-D ground
movement. The objective of this paper was to be
able to show that there exists a trend between DInSAR estimated lateral ground movements with
respect to GPS estimated ground movements.
The excellent correlation between the two
suggests the success of this technique. Overall it
can be said that the technique provides a much
improved subsidence estimate and a very
favourable lateral movement estimate.
-1
-1.5
-1.5
-1
-0.5
0
0.5
1
GPS Measured East-West Movement (units : cm)
1.5
Figure 5-21: D-InSAR versus GPS East-West movement
normalized to 24 days from February – September 2001.
Lateral Movement (North-South) [Feb-Sept 2001] Averaged
InSAR Measured North-South Movement (unts: cm)
2
Scatter about Slope Line = 0.35 cm
Correlation = 0.64
1.5
1
0.5
6. References
0
[1] Zebker, H. A., and R.M. Goldstein, Topographic
Mapping From Interferometric Synthetic Aperture Radar
Observations, J. Geophys. Res., 91, 4993-4999,1986.
-0.5
-1
-1.5
-1.5
-1
-0.5
0
0.5
1
GPS Measured North-South Movement (units : cm)
[2] Soren, N.M, H.A. Zebker, and J.Martin, Topographic
mapping using radar interferometric processing techniques,
IEEE Trans. Geosci. Remote. Sens., 30(3),560-567,1992.
1.5
Figure 5-22: InSAR versus GPS North-South movement
normalized to 24 days from February – September 2001.
[3] Gabriel, A.K., R.M. Goldstein, and H.A. Zebker,
Mapping small elevation changes over large areas:
differential radar interferometry, J.Geophys.Res., 94(B7),
9183-9191, 1989.
Subsidence [Feb-Sept 2001] Averaged
InSAR Measured Subsidence Movement (unts: cm)
1
0
Correlation = 0.98
Scatter about Slope Line = 0.34 cm
[4] Gabriel, A.K., and R.M. Goldstein, Crossed orbit
interferometry theory and experimental results from SIR-B,
Int. J. Remote Sens., 9(5),857-872,1988.
-1
-2
[5] Qian, L., J.F. Vesecky, and H.A. Zebker, New
Approaches in Interferometric SAR data processing, IEEE
Trans. Geosci. Remote. Sens., 30(5),950 - 959,1992.
-3
-4
[6] Prati, C., Report on ERS-1 SAR Interferometric
Techniques and Applications, June 1994.
-5
-6
-6
-5
-4
-3
-2
-1
0
GPS Measured Subsidence Movement (units : cm)
[7] Sircar, S., Power, D., Youden, J., Gill, E. and Han, P.,
2002. Lateral Movement Estimation from Space-borne Radar
by Differential Interferometry, IEEE NECEC 2002, St.
John's, Newfoundland, Canada.
1
Figure 5-20: InSAR versus GPS Subsidence movement
normalized to 24 days from February – September 2001.
Carefully observing the plots it can be seen that
the correlation between InSAR measured
movement and GPS measured movements have
improved over results published in [7] earlier. A
5