Content uploaded by Yujie Zheng

Author content

All content in this area was uploaded by Yujie Zheng on Feb 06, 2019

Content may be subject to copyright.

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

1

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

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

2

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)

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

3

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

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

4

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

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

5

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

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

6

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.

REFERENCES

[1] D. Massonnet, M. Rossi, C. Carmona, F. Adragna, G. Peltzer, K. Feigl,

and T. Rabaute, “The displacement field of the Landers earthquake

mapped by radar interferometry,” Nature, vol. 364, no. 6433, pp. 138–

142, July 1993.

[2] H. A. Zebker, P. A. Rosen, R. M. Goldstein, A. Gabriel, and C. Werner,

“On the derivation of coseismic displacement fields using differential

radar interferometry: The Landers earthquake,” J. Geophys. Res.—Solid

Earth, vol. 99, no. B10, pp. 19 617–19 634, Oct. 1994.

[3] C.Wicks,W. Thatcher, and D. Dzurisin, “Migration of fluids beneath

Yellowstone Caldera inferred from satellite radar interferometry,”

Science, vol. 282, no. 5388, pp. 458–462, Oct. 1998.

[4] F. Amelung, S. Jonsson, H. A. Zebker, and P. Segall, “Widespread uplift

and trapdoor faulting on Galapagos volcanoes observed with radar

interferometry,” Nature, vol. 407, no. 6807, pp. 993–996, Oct. 2000.

[5] R. M. Goldstein, H. Engelhardt, B. Kamb, and R. M. Frolich, “Satellite

radar interferometry for monitoring ice sheet motion: Application to an

Arctic ice stream,” Science, vol. 262, no. 5139, pp. 1525–1530, Dec.

1993.

[6] D. R. Fatland and C. S. Lingle, “InSAR observations of the 1993-95

Bering Glacier (Alaska, USA) surge and a surge hypothesis,” J. Glaciol,

vol. 48, no. 162, pp. 439-451, June 2002

[7] I. Joughin, B. E. Smith, and W. Abdalati, “Glaciological advances made

with interferometric synthetic aperture radar,” J. Glaciol, vol. 56, no.

200, pp. 1026–1042, Dec. 2010.

[8] J. Hoffmann, H. A. Zebker, D. L. Galloway, and F. Amelung, “Seasonal

subsidence and rebound in Las Vegas Valley, Nevada, observed by

synthetic aperture radar interferometry,” Water Resour. Res., vol. 37, no.

6, pp. 1551–1566, June 2001.

[9] D. L. Galloway and J. Hoffmann, “The application of satellite

differential SAR interferometry-derived ground displacements in

hydrogeology, ” Hydrogeol. J, vol. 15, no. 1, pp. 133-154, Feb. 2007

[10] H. A. Zebker and R. M. Goldstein, “Topographic mapping from

interferometric synthetic aperture radar observations,” J. Geophys. Res.,

vol. 91, no. B5, pp. 4993–4999, Apr. 1986.

[11] T. G. Farr, P. A. Rosen, E. Caro, R. Crippen, R. Duren, S. Hensley, M.

Kobrick, M. Paller, E. Rodriguez, L. Roth, D. Seal, S. Shaffer, J.

Shimada, J. Umland, M.Werner,M. Oskin, D. Burbank, and D. Alsdorf,

“The Shuttle Radar Topography Mission,” Rev. Geophys., vol. 45, no. 2,

p. RG2004, May 2007.

[12] P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, “A new algorithm

for surface deformation monitoring based on small baseline differential

SAR interferograms,” IEEE Trans. Geosci. Remote Sens., vol. 40, no.

11, pp. 2375–2383, Nov. 2002.

[13] A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR

interferometry,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 1, pp.

8–20, Jan. 2001.

[14] A. Hooper, P. Segall, and H. Zebker, “Persistent scatterer interferometric

synthetic aperture radar for crustal deformation analysis, with

application to Volcan Alcedo, Galapagos,” J. Geophys. Res., vol. 112,

no. B7, p. B07 407, July 2007.

[15] M. Schmitt and U. Stilla, "Maximum-likelihood-based approach for

single-pass synthetic aperture radar tomography over urban areas," IET

Radar Sonar Nav, vol. 8, pp. 1145-1153, Dec. 2014.

[16] H. A. Zebker, S. Hensley, P. Shanker, and C. Wortham, “Geodetically

accurate InSAR data processor. Geoscience and Remote Sensing,” IEEE

Trans Geosci. Remote Sens., vol. 48, no. 12, pp.4309-4321, July 2010

[17] P. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N Madsen, E.

Rodriguez, and R. M. Goldstein, “Synthetic aperture radar

interferometry,” Proc. IEEE, vol. 88, no. 3, pp. 333-382, Mar. 2000

[18] P. Rosen, S. Hensley, H. A. Zebker, F. H. Webb and E. J. Fielding,

“Surface deformation and coherence measurements of Kilauea Volcano,

Hawaii, from SIR-C radar interferometry,” J. Geophys. Res., vol. 101,

no. E10, pp 23109-23225, Oct. 1996.

[19] J. W. Bell, F. Amelung, A. Ferretti, M. Bianchi, and F. Novali,

“Permanent scatterer InSAR reveals seasonal and long-term aquifer-

system response to groundwater pumping and artificial recharge,” Water

Resour. Res., vol. 44, no. 2, Feb. 2008.

[20] M. Poland, A. Miklius, T. Orr, J. Sutton, C. Thornber, and D. Wilson,

“New episodes of volcanism at Kilauea Volcano, Hawaii,” EOS Trans.

AGU, vol. 89, no. 5, pp. 37–38, Jan. 2008.

[21] A. Hooper, D. Bekaert, K. Spaans, and M. Arıkan, “Recent advances in

SAR interferometry time series analysis for measuring crustal

deformation,” Tectonophysics, vol. 514-517, pp. 1-13, Jan. 2012.

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

7

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.

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

8

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.