Phase Correction of Single-Look Complex Radar Images for User-Friendly Efficient Interferogram Formation

Abstract

We present a new interferometric synthetic aperture radar processing approach that removes topography–dependent phase from single-look complex (SLC) radar images, making interferogram formation more efficient. We first adopt motion compensation techniques to resample SLC images with respect to an ideal reference orbit and then separate the residual topographic phase contributions into parts dependent only on individual SLC acquisitions, and generate topography-compensated images directly in latitude–longitude coordinates. Since the number of interferograms is typically much larger than the number of SLC images, our approach greatly reduces needed computational resources. Furthermore, we move the need for precise knowledge of imaging geometry upstream from the end user to the data provider. We demonstrate our approach for both preprocessed SLC images and raw data using COSMO-SkyMed L1A and ALOS L0 products. The performance of our method depends on the quality of the digital elevation model (DEM) used—DEM error affects the correction phase proportionally to the baseline between radar scenes and the reference orbital path. With a 1000-m baseline and a nominal 30° incidence angle, we find that the uncertainty of estimated deformation increases by approximately 1 cm with every 3 m increase in the DEM error.

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Abstract—We present a new InSAR processing approach that
removes topography dependent phase from single look complex
(SLC) radar images, making interferogram formation more
efficient. We first adopt motion compensation techniques to
resample SLC images with respect to an ideal reference orbit and
then separate the residual topographic phase contributions into
parts dependent only on individual SLC acquisitions, and
generate topography-compensated images directly in latitude-
longitude coordinates. Since the number of interferograms is
typically much larger than the number of SLC images, our
approach greatly reduces needed computational resources.
Further, we move the need for precise knowledge of imaging
geometry upstream from the end-user to the data provider. We
demonstrate our approach for both preprocessed SLC images
and raw data using COSMO-SkyMed L1A and ALOS L0
products. The performance of our method depends on the quality
of the digital elevation model (DEM) used – DEM error affects
the correction phase proportionally to the baseline between radar
scenes and the reference orbital path. With a 1000 m baseline and
a nominal 30° incidence angle, we find that the uncertainty of
estimated deformation increases by approximately 1 cm with
every 3 m increase in the DEM error.
Index Terms—Interferometric synthetic aperture radar,
synthetic aperture radar processing, radar interferometry.
I. INTRODUCTION
NTERFEROMETRIC synthetic aperture radar (InSAR),
with which we measure mm-cm level surface deformation
over large areas at fine spatial detail, has been extensively
applied in studies as diverse as earthquake and volcano
modeling [1]–[4], glacier mechanics [5]–[7], hydrology [8]–
[9], and topographic mapping [10]–[11]. The InSAR technique
combines interferometry and conventional synthetic aperture
radar (SAR) to compute the phase differences between two
complex valued, single look (SLC) SAR images. The
resulting interferometric phase contains signals from i) the
local topography due to the spatial separation of the sensor
locations and ii) any radar line of sight (LOS) displacements
of the target occurring between the two SAR acquisitions.
Despite its applicability to a diverse set of problems, InSAR
Y. Zheng and H.A. Zebker are with the Dept. of Geophysics, Stanford
University, Stanford, CA 94305 USA (e-mail: yjzheng@stanford.edu). This
work was supported by a graduate fellowship from the School of Earth,
Energy, and Environmental Sciences at Stanford University.
remains a challenging technique for non-specialists, which
significantly limits its potential for widespread use. The need
for familiarity with methods of radar processing, acquisition
coordinate systems, and detailed metadata describing imaging
geometry, satellite orbit state vectors, and instrumental
configuration often limits studies by scientists who are mainly
concerned with measurements of geophysical processes and
their interpretation. Furthermore, with modern sensors now
acquiring data at weekly intervals or faster the number of
radar interferograms available for analysis over any area of
interest can be in the thousands, so even downloading the data
over electronic networks remains a bottleneck.
Here we propose a method that enables delivery of data
products that can be easily reduced to the desired observations
and are less constrained by the sheer volume of data that must
be transferred to an end user. Our approach addresses the
limitations of specialized knowledge and data volume,
delivering products that are identical in accuracy to existing
processors’ capabilities but are easy to use.
II. APPLICABILITY AND ADVANTAGES
For many applications, we are primarily interested in
mapping the surface deformation over time and therefore need
to remove topography-related signals from interferograms.
Fig. 1 (a) shows a typical InSAR processing and product
delivery flow. InSAR users first acquire SAR data in the form
of either raw data or an SLC image from data providers and
then process the acquired data into topography corrected and
geocoded interferograms, which can then be used in various
geophysical applications. Even with sophisticated InSAR
software such as ROI_PAC (the Repeat Orbit Interferometry
PACkage) or ISCE (InSAR Scientific Computing
Environment), the additional InSAR processing needed to
form the deformation history is not always an easy task. The
complexity of InSAR processing can make a single successful
run of the processing flow unlikely. More often than not,
InSAR users have to stop the flow at various points to either
modify parameters or fix errors. Consequently, InSAR data
users, most of whom are not InSAR experts, are required to be
considerably familiar with the detailed imaging geometry for
each SAR acquisition, and also to be experienced in InSAR
processing techniques. Here we show that an alternative
Phase Correction of Single Look Complex Radar
Images for User Friendly, Efficient Interferogram
Formation
Yujie Zheng and Howard A. Zebker, Fellow, IEEE
I

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InSAR processing approach moves the need for precise
knowledge of imaging geometry and radar techniques
upstream from the end-users to the data providers, so users
need only be concerned with common GIS-style data analysis
(Fig. 1 (b)). We facilitate this by correcting topography-related
signals from each SLC image, and resampling the
compensated SLC images into latitude-longitude coordinates
for easy ingestion to image processing packages.
Interferograms generated by simple cross-multiplication of
pairs of these processed SLC images are thus automatically
topography corrected and can be readily used for subsequent
geophysical modeling. In this way, we separate InSAR
processing from InSAR application, thus making the use of
InSAR data easier for non-expert InSAR users.
The other major advantage of our alternative approach is
that it greatly reduces the computational resources needed to
compute deformation time-series. For N SLC radar images,
𝑁(𝑁−1)/2 interferograms can be formed and hence
𝑁(𝑁−1)/2 topography correction computations are needed
in the traditional processing approach. Common analyses
widely used today for investigating temporal evolution of
surface deformation, such as the small baseline subset (SBAS)
[12] and persistent scatterer (PS) [13]–[14], typically use as
many SAR interferograms as possible. Each of these requires
the detailed metadata described above plus the software and
computer resources to compute the correction. In contrast, in
our new approach the data provider applies the topography
compensation rather than the end user, and further only N
topography correction steps are needed. With more and more
SAR data available nowadays and in the foreseeable future,
our approach can significantly improve the efficiency of
interferogram formation.
Many technical paths to compensate radar interferograms
and SLC images for geometry and topography are possible,
and we propose one such flow here. If applied properly, all of
these will produce similarly accurate data sets. Our method
has the advantage of delivering low volume and readily
ingestible images, greatly increasing the number of persons
who can feasibly use the observations. Here we demonstrate
one such method and show how it can be applied to either raw
radar data or to SLC products as now produced by many of the
international constellation of radar satellites.
This is not the first time that the idea of correcting SLC
images for topographic effects has been proposed. Ferreti et al.
[13] introduced “zero-baseline steering” in order to
compensate slave SLC images with respect to a chosen master
SLC image for topographic effects, however the correction is
applied to interferograms rather than the SLCs directly.
Schmitt and Stilla [15] used the absolute signal phase in a
single SLC image as a function of topography to infer
scatterer height in SAR tomography. We combine and extend
the above ideas by first adopting motion-compensation
techniques to propagate actual radar echoes to a virtual ideal
orbit as suggested by [16], and then, with an external digital
elevation model (DEM), compensating each SLC image for
the residual topographic phase contribution. The advantage of
using a common ideal orbit rather than a master orbit is that
the imaging geometry equations are particularly simple and
therefore topographic correction is efficient to implement. The
motion compensation techniques can equally well be applied
either to the generation of the SLC images, or to the zero-
Doppler SLC products produced by many sensors today (e.g.,
Sentinel-1A/B, Radarsat-2, COSMO-SkyMed or ALOS-II).
We present results from data acquired by the Italian COSMO-
SkyMed satellites and the Japanese ALOS satellite to
demonstrate the use of our method for preprocessed SLC
images and raw data products, respectively. Since our method
needs topography information for phase correction, its
performance depends on the quality of the DEMs used. Thus
the new processing method may not work well over areas
where only poor-quality DEMs are available.
Since we have the precisely coregistered DEM along with
each SLC product, we also geocode the SLCs prior to
distribution. Each end-user is thus presented data in a well-
understood latitude/longitude system rather than in a radar-
specific and varying set of range/Doppler coordinates,
relieving the user again of a task that requires a metadata
analysis in order to generate useful observations.
The remainder of this paper is organized as follows. We
begin by describing our processing method in Section III.
Next, in Section IV we apply our approach to COSMO-
SkyMed and ALOS data. Then, we discuss the phase noise
due to errors in the DEMs in Section V. Finally we present
conclusions in Section VI.
III. PROCESSING
Our processing approach removes topography-related
signals from individual SAR scenes. This makes interferogram
formation not only simpler and possible by non-experts, but
much more computationally efficient when large SLC stacks
are analyzed.
A. Topographic Correction Review
Uncompensated interferograms contain topography-
dependent phase terms [17]. Fig. 2 shows the geometry of an
InSAR system. The radar path length difference 𝛿𝜌, which we
observe as interferometric phase 𝜙 between the two SAR
scenes, consists of two parts: 𝜙!"#" and 𝜙!"#$ . The first part,
𝜙!"#", is due to the difference in geometrical path length from
each of two sensor locations to the imaging point and depends
on the spatial baseline 𝐵. The other part, 𝜙!"#$, is due to any
surface displacement 𝐷 that occurs between radar
observations. For a narrowband signal in the far field of the
antenna, the observed interferometric phase is [10], [18]
𝜙=𝜙!"#" +𝜙!"#$ =4𝜋
𝜆−𝑢⋅𝐵+𝑢∙𝐷, (1)

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where 𝑢 is a unit vector representing the radar look direction.
For displacement mapping, we need to remove the
topographic phase term 𝜙!"#" =−!!
!(𝑢∙𝐵).
We adopt coordinates defined by a virtual perfectly circular
orbit above a nonrotating planet [16] for easy calculations of 𝑢
and 𝐵. This coordinate system greatly simplifies the equations
describing the imaging geometry. We then use a motion
compensation approach to translate raw radar echoes from
their actual positions to what would be observed if the satellite
were traveling in the ideal reference orbit [16]. We then co-
register the SLC images. Since motion compensation has
already resampled all SLC images with respect to the
reference orbit geometry, the co-registration step is very
efficient.
Motion compensation essentially sets the effective InSAR
baselines 𝐵 to zero such that the topographic phase term is
zero for points located on the surface. However, the
topographic phase contribution is still present for any non-zero
topography; it can be evaluated from [16]
𝜙!"#" =4π
λu!"!# −u!"# ∙B, (2)
where the multiple 𝑢 are the unit vectors representing radar
look directions from the sensor location to the pixel at actual
elevation and on the zero-elevation reference sphere,
respectively. We must calculate the remaining topographic
phase term and remove it from the interferogram before
interpreting the deformation signals.
B. Separation of Topographic Correction Term
We compensate the individual SLC images before
interferogram formation, so that the computed interferogram
does not include the topographic phase term from each SAR
scene. To do so, we divide the baseline vector into two parts
B=P
!−P
! (3)
where 𝑃
!,! are the position vectors of the actual locations of
the SAR sensors in the reference coordinate system. The
difference in radar LOS vectors can be expressed as
𝑢!"!# −𝑢!"# =!!!!"!#
!!!!"!# −!!!!"#
!!!!"# , (4)
where 𝑃=1
2(𝑃1+𝑃2), the midpoint between the two antenna
locations. Since |𝑃−𝑇!"!#|≈𝑃−𝑇!"# ≈𝜌, where 𝜌 is the
range from the reference sensor position to the imaged point
we can approximate the above equation as
𝑢!"!# −𝑢!"# ≈1
ρT!"# −T!"!# . (5)
The approximation is valid since all InSAR measurements are
made far field. Because the target locations 𝑇 depend only on
the reference geometry, the term 𝑢!"!# −𝑢!"# is independent of
individual sensor locations, and
𝜙!"#" =𝜙!"#"
!!−𝜙!"#"
!! (6)
where
𝜙!"#"
!!= 4π
λu!"!# −u!"# ∙P
!, i =1,2. (7)
This yields the topography-related phase for each individual
SLC image, so we can generate topography-corrected SLC
images that no longer contain a topography dependent phase
signature. Interferograms formed by simple cross-
multiplication do not require further baseline corrections.
It is worth noting that in principle we are able to separate
the topographic correction phase into parts dependent only on
each orbit’s imaging geometry as long as a common reference
coordinate system is defined. Motion compensation is not a
prerequisite to our approach, but it makes processing easily
implemented and efficient by co-registering the SLCs to a
common coordinate system.
C. Comparison with traditional methods
The biggest difference between our proposed processing
approach and the traditional method is where we apply the
topography correction in the InSAR processing flow (Fig. 1).
Our method separates the topography correction term into
parts that depend only on individual SLC images and hence
moves topography correction step upstream from
interferogram-level to SLC-level. By doing so, InSAR data
users can avoid complicated InSAR processing and start
straight from compensated SLC images that directly produce
topography corrected and geocoded interferograms. Moreover,
since topography correction steps are needed fewer times at
the SLC-level than at the interferogram-level, the overall
efficiency of InSAR processing is improved.
Our approach also moves geocoding step upstream from
interferogram-level to SLC-level. Therefore we resample SLC
images into latitude-longitude coordinates before forming
interferograms. Since multi-looked interferograms are used for
most geophysical applications, errors that may be introduced
by the additional resampling step before interfering are
insignificant. Even if single-look interferograms are required
for some special applications, SLC images that are topography
corrected but not geocoded can still be provided.
Our proposed approach in the end generates, in principle,
interferograms with the same accuracy as produced by
traditional methods -- we only alter the sequence of processing
steps. Therefore, interferograms generated using our approach
are still subject to InSAR phase noise such as orbital ramps,
atmospheric noise and decorrelation. However, correction of
these noise terms is often either empirical or based on
stochastic models and hence, less demanding for users’
knowledge of InSAR processing techniques and detailed

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InSAR imaging geometry.
The inclusion of motion compensation techniques in our
approach makes InSAR processing faster and more accurate.
Most importantly, motion compensation facilitates efficient
image co-registration [16] as we seek to produce co-registered,
geocoded and topography-corrected SLC images. Motion
compensation techniques are also implemented in the existing
InSAR software ISCE.
IV. DEMONSTRATION APPLICATIONS
In this section, we present several images using our new
processing method and data from both the Italian COSMO-
SkyMed X-band satellites (Level 1 zero-Doppler SLC images)
and the Japanese ALOS L-band satellite (Level 0 raw data
products). The focus of this section is to show the range of
applicability of our approach for different data formats and to
demonstrate how our new approach may be used for
geophysical modeling by computing SBAS time-series
analyses in both product format cases. We also conducted the
same analysis using the traditional method and compare the
results between our proposed processing workflow and the
traditional flow.
A. COSMO-SkyMed dataset, Central Valley of California
We begin with data delivered in zero-Doppler SLC format.
We processed 37 COSMO-SkyMed Level 1A products
acquired from June 20, 2012 until May 25, 2014 over the city
of Fresno in the Central Valley of California. Due to the
ongoing drought in California, intensive pumping of
groundwater has resulted in land subsidence that can be easily
detected using InSAR [9], [19]. We formed 62 topography
corrected interferograms with baseline values smaller than 100
m -- Fig. 3 shows their average phase. Location C exhibits an
exceptionally high phase value, indicating that the region may
be sinking relative to its surrounding areas. A sequence of six
interferograms generated with respect to one common SAR
scene (Fig. 4) shows the deformation pattern grows with time.
To further investigate the temporal evolution of the detected
deformation, we used an SBAS approach [12] to generate
displacement time series. As shown in Fig. 5, location A
exhibits no apparent deformation during the observation time.
Location C, in contrast, sinks almost 3 cm (in radar LOS
direction) during the time period between January 2013 and
October 2013. Location B also has subsided in the same time
period of about 1 cm in radar LOS direction. We speculate
that perhaps a well started to pump water near location C
around January 2013 and caused the subsidence seen in this
area.
B. ALOS dataset, Kilauea, Hawaii
Next, we compute a time series using raw radar data
products. Dense spatial and temporal sampling has made
InSAR an incredibly useful tool for volcano studies. We
generated 66 topography-corrected interferograms from an
ALOS Level 0 dataset comprising 25 acquisitions from May
28, 2006 to March 11, 2011, over the Kilauea region, Hawaii.
The interferograms generated have a maximum baseline of
500 m and their average phase (Fig. 6) shows significant
deformation in three areas: Kilauea caldera, Makaopuhi crater
and Pu‘u ‘Ō‘ō. We used the SBAS approach to compute the
temporal evolution of deformation in these regions (Fig. 7).
We find that the Makaopuhi crater region uplifted
significantly between 15 March 2007 and 8 August 2007.
Around the same time, Kilauea caldera and Pu‘u ‘Ō‘ō started
to subside. Temporally the observed deformation is associated
with the 17 June 2007 “Father’s Day” intrusion/eruption at
Kilauea. The summit caldera likely deflated as magma was
transported from Kilauea caldera to the Makaopuhi crater
region. It is posited [20] that Pu‘u ‘Ō‘ō’s magma supply was
disrupted, causing that region to subside as well. The
displacement time-series readily shows uplift in the
Makaopuhi crater region (Fig. 7b). The similarity in
deformation patterns between the Kilauea caldera and Pu‘u
‘Ō‘ō suggests a strong link between the summit magma
system and volcanic activities near the Pu‘u ‘Ō‘ō region.
Starting 21 July 2007, the lava eruption on the east flank of
Pu‘u ‘Ō‘ō resulted in eastward deformation of the region.
Kilauea caldera continued to deflate after July 2007 as well,
most likely due to supplying magma to the fissure eruption
site on the east flank of Pu‘u ‘Ō‘ō [20]. These events are
observed as an approximately 50 cm LOS deformation in both
Kilauea caldera and Pu‘u ‘Ō‘ō from July 2007 to January
2009, after which volcanic activity was less frequent and all
three regions remained relatively stable.
C. Comparison with traditional flow
We conducted the same SBAS time-series analysis in both
product format cases using the traditional method in order to
assess the influence of reversing the order of resampling and
interferometry. We find that there is no significant difference
between these as the root-mean-square difference of
deformation time-series between the two workflows is around
2 mm, as shown in Fig. 8.
V. EFFECTS OF AN IMPERFECT DEM
Our approach relies on the availability of digital topography
data, thus any errors in the DEM used will generate
imperfections in the derived products. In this section, we
quantify the relationship between DEM errors and
interferometric phase. DEMs always contain errors and in
most cases the resolution of the DEM does not match the
resolution of radar images, requiring interpolation.
Interpolating a DEM to match the fine resolution of radar
images often works well, but this step may also introduce
noise into the DEM. As a result, errors are introduced in the
estimated topographic phase, and hence the interferograms.
Starting with (2) and (5), and taking 𝑇
!
!"# =0
!
!!𝜙𝑡𝑜𝑝𝑜 ≈
T
elev
−T
ref
𝜌
∙𝐵≈
!
!
!"!#!!!!
!
!"!#!!
!
!"# !!!!!,!
!, (8)
where subscripts s,c,h stand for the SCH coordinate system

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axes used here. The SCH coordinate system is a special
coordinate system that aligns with the radar geometry [16].
The s and c coordinates are along-track and across-track
ground coordinates respectively and the h coordinate measures
the height of the point above the surface. Since the SCH
coordinate system is not an orthogonal coordinate system, the
vector subtraction in (8) is not exact. However, since 𝑇!"!# and
𝑇!"# are very similar, a direct-subtraction approximation
works reasonably well and is sufficient for the present
analysis.
The noise in the DEM enters though the term 𝑇!"!#, the
target position on the surface, which depends on both the
imaging geometry and topography. Letting ∆𝑧 be the error in
the DEM, and ∆𝑇!"!# the error in the position vector, then the
corresponding error in the computed phase is:
!
!!
∆𝜙𝑡𝑜𝑝𝑜 =!
!
∆𝑇
!
!"!#𝐵!!!!,!,! , (9)
where
∆𝑇
!
!"!# ≈0;∆𝑇
!
!"!# ≈∆!
!"# !;∆𝑇
!
!"!# =∆𝑧, (10)
and 𝜃 is the incidence angle of the radar wave. Combining (9)
and (10), we can write ∆𝜙!"#" in terms of ∆𝑧
!
!!
∆𝜙!"#" ≈∆!
!
!!
!"# !+𝐵!. (11)
The baseline 𝐵=𝐵!
!+𝐵!
!+𝐵!
!. Since 𝐵! is typically much
smaller than 𝐵! and 𝐵!, we can approximate B as
𝐵=
2𝐵!≈2𝐵!, 𝐵!≈𝐵!
𝐵!, 𝐵!≫𝐵!
𝐵!, 𝐵!≪𝐵!
. (12)
Combining (11) and (12), ∆𝜙!!"! as a function of DEM error
∆𝑧 and the baseline B becomes
!
!!
∆𝜙𝑡𝑜𝑝𝑜 =
!
!!
!
!"# !+1𝐵∆𝑧, 𝐵𝑐≈𝐵ℎ
!
!
!
!"# !
𝐵∆𝑧, 𝐵𝑐≫𝐵ℎ
!
!
𝐵∆𝑧, 𝐵𝑐≪𝐵ℎ
. (13)
For spaceborne satellite geometries, the three conditions in
(13) are all possible. Since the first, 𝐵!≈𝐵!, typically yields
the largest estimation errors, we use the following
!
!!
∆𝜙𝑡𝑜𝑝𝑜 =
!
!!
!
!"# !+1𝐵∆𝑧 (14)
to bound the uncertainty in interferometric phase introduced
by DEM error.
Note that the right hand side of (14) does not depend on
wavelength, and the left hand side of (14) is the uncertainty in
estimated LOS surface deformation caused by DEM error. The
deformation uncertainty is proportional to DEM error with a
scale solely determined by imaging geometry — the larger the
baseline B, the more sensitive the system is to DEM error. Fig.
9 illustrates the dependence of deformation uncertainty on
both DEM error and baseline in the COSMO-SkyMed case.
For our application to the Central Valley of California, we
used SLC pairs with baseline smaller than 100 m. Since DEM
error ∆𝑧 is typically smaller than 3 m for flat areas like the
Central Valley, the error introduced by DEM error in our
derived surface deformation is less than 0.1 cm. As shown in
Fig. 9, for SLC pairs with baselines smaller than 1000 m we
obtain cm-level accurate surface displacement given no other
significant error sources are present. In the Hawaii case, the
DEM error is about 7–10 m and we used SLC pairs with
baseline smaller than 500m. The ALOS satellite has a greater
range and slightly larger look angle than COSMO-SkyMed
satellite, and as a result, a smaller multiplier on DEM error. In
this case, the uncertainty level in our final estimation is about
1 cm. Since the observed deformation is about 50 – 70 cm, the
effects of DEM error can be safely ignored. Both cases have
shown that with some knowledge of the DEM error level in
the study region, we can use Fig. 9 or (14) to find an upper
bound for baseline in order to choose SLC pair selections. For
example, for the COSMO-SkyMed case, the maximum
baseline we can use is about 600 m if the uncertainty caused
by DEM error need be under 0.5 cm.
VI. CONCLUSIONS
Here we describe a new InSAR processing approach that
generates products meeting the needs of a wider than
traditional InSAR user community, is both efficient and robust,
and is especially useful for time-series analysis that requires a
large number of SAR acquisitions. These goals are reached by
altering the data flow such that detailed and needed phase
corrections are done by experts at the data provider level,
relieving users of the need to attain a high degree level of
specialization in InSAR proficiency and of the need for vast
amounts of compute resources. We demonstrate our approach
using both preprocessed SLC image products and raw data
products to derive time-series analyses over the Central Valley
of California and Kilauea Volcano in Hawaii. We further
quantify a major error source, phase errors due to
imperfections in the digital elevation model of an area,
showing that deformation artifacts grow linearly with DEM
errors and InSAR baseline. For regions with poor DEMs,
sufficiently accurate estimation of LOS deformation can yet
be achieved with SLC pairs that have small baselines.
Current imaging radar satellites acquire SAR data for
almost every point on Earth at least once every six days [21].
Currently planned radar satellites, including the SAOCOM L-
band system, Radarsat constellation, and the upcoming
NASA-ISRO SAR mission will provide additional rich
sources of high quality interferometric data. While the wide
coverage of current and future SAR missions in both space

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and time will open up the possibility of using InSAR for near
real-time monitoring, the high rates and large volumes of data
still pose challenges to existing InSAR processing algorithms.
The work presented here will significantly improve the
efficiency of interferogram formation when analyzing a large
stack of SAR acquisitions.
In addition to separating InSAR product processing from
many InSAR applications – the former requires knowledge of
detailed SAR acquisition geometries and complicated InSAR
processing techniques, and the latter is mostly about
geophysical modeling – enhanced computational efficiency
results from our new processing approach. The separated
InSAR processing approach delivers compensated SLC
images that simply need to be cross-multiplied to yield
products that can be readily used in the geophysical modeling.
If InSAR data users can acquire these compensated SLC
products from data providers, the use of InSAR data for
geophysical applications can become much simpler and easier
than it is today.
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Fig. 1. (a) Traditional InSAR processing workflow, (b) The proposed InSAR
processing workflow.
Fig. 2. Radar imaging geometry and the SCH coordinate system. P1 and P2
represent two satellite locations at distinct SAR acquisition times. T is the
imaged point on the ground, 𝑢 is the unit radar line of sight vector, and 𝜌!, 𝜌! are
the distance that radar signals travelled in the two acquisitions. The difference
δρ between the two radar path lengths is related to 1) baseline B between the
sensor locations P1 and P2, and 2) any surface motion D of the target T between
radar observations. The SCH coordinates are aligned with the reference orbit path.
The curvature of the Earth is considered in the study but not shown in this figure.
Fig. 3. Interferogram over Fresno, California constructed from 62 topography
corrected interferograms formed by 37 COSMO-SkyMed Level 1A products
from June 20, 2012 to May 25, 2014. Deformation series at locations A, B and C
are shown in Fig. 4. The reference phase is an average of the areas marked by
white circles where little deformation is apparent.
Fig. 4. Unwrapped interferograms over Fresno, showing time-progressive
fringes at location C. Interferograms show change between June 20, 2012,
and (a) August 7, 2012, spanning 47 days, (b) September 8, 2012, 78 days, (c)
August 10, 2013, 415 days, (d) September 27, 2013, 462 days, (e) November
14, 2013, 509, days (f) February 2, 2014, 592 days. All interferograms are
corrected for orbital errors by deramping.
Fig. 5. Displacement time series at locations A, B and C (Fig. 3). Location A
remained stable during the observation time while locations B and C subsided
between 2013.01 and 2013.10 by ~1 cm and ~4 cm in radar LOS, respectively.

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Fig. 6. Interferogram of Kilauea, Hawaii, constructed by averaging 66
topography corrected interferograms created from 25 ALOS Level 0 products
acquired from May 28, 2006 to March 11, 2011. Details of the deformation in
Kilauea Caldera, Makaopuhi Crater and Puʻu ʻŌʻō region are shown in Fig. 7.
Fig. 7. Displacement time series at Kilauea caldera, Makaopuhi crater and Pu‘u
‘Ō‘ō. All three regions show active deformation from mid-2007 to early 2009
and have remained relatively stable afterwards. The June 2007 Father’s Day
event can be clearly identified as the abrupt rapid uplift in the Makaopuhi crater
region with corresponding subsidence in both Kilauea caldera and Pu‘u ‘Ō‘ō
region between observation points at 2007.03 and 2007.07.
Fig. 8. Difference in estimated displacement time-series using the traditional
workflow and the proposed workflow with (a) COSMO-SkyMed dataset and
(b) ALOS dataset. The root-mean-square of differences in both cases are around
2 mm.
Fig. 9. Effects of DEM error on estimation of surface displacements in LOS
direction calculated using COSMO-SkyMed imaging geometry. The
uncertainty in LOS deformation estimation grows linearly with both baseline
and DEM errors. For example, if the DEM has a 10 m uncertainty, then the
uncertainty in LOS deformation estimation will increase by 1 cm with every
300 m increase in baseline. Or, if a pair of SLC images has a 1000 m baseline,
then the uncertainty of estimated deformation increases by 1 cm with every 3
m increase in DEM error.