IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1...

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

InSAR Time-Series Estimation of the IonosphericPhase Delay: An Extension of the Split

Range-Spectrum TechniqueHeresh Fattahi, Member, IEEE, Mark Simons, and Piyush Agram, Member, IEEE

Abstract— Repeat pass interferometric synthetic apertureradar (InSAR) observations may be significantly impacted bythe propagation delay of the microwave signal through theionosphere, which is commonly referred to as ionospheric delay.The dispersive character of the ionosphere at microwave fre-quencies allows one to estimate the ionospheric delay fromInSAR data through a split range-spectrum technique. Here,we extend the existing split range-spectrum technique to InSARtime-series. We present an algorithm for estimating a time-seriesof ionospheric phase delay that is useful for correcting InSARtime-series of ground surface displacement or for evaluatingthe spatial and temporal variations of the ionosphere’s totalelectron content (TEC). Experimental results from stacks ofL-band SAR data acquired by the ALOS-1 Japanese satelliteshow significant ionospheric phase delay equivalent to 2 m of thetemporal variation of InSAR time-series along 445 km in Chile,a region at low latitudes where large TEC variations are common.The observed delay is significantly smaller, with a maximum of10 cm over 160 km, in California. The estimation and correctionof ionospheric delay reduces the temporal variation of the InSARtime-series to centimeter levels in Chile. The ionospheric delaycorrection of the InSAR time-series reveals earthquake-inducedground displacement, which otherwise could not be detected.A comparison with independent GPS time-series demonstrates anorder of magnitude reduction in the root mean square differencebetween GPS and InSAR after correcting for ionospheric delay.The results show that the presented algorithm significantlyimproves the accuracy of InSAR time-series and should becomea routine component of InSAR time-series analysis.

Index Terms— Interferometric synthetic aperture radar(InSAR), ionospheric phase delay, split range-spectrum.

I. INTRODUCTION

INTERFEROMETRIC synthetic aperture radar (InSAR) hasbeen shown to be an effective technique for geodetic

imaging of surface ground displacement caused by naturaland anthropogenic processes, such as earthquakes, tectonics,volcanic unrest, shallow hydrological processes, landslides,and glacier flow. The accuracy of repeat-pass InSAR measure-ments of ground displacement can be significantly affected

Manuscript received February 20, 2017; revised May 2, 2017; acceptedJune 13, 2017. The work of H. Fattahi and M. Simons was supported by theNational Aeronautics and Space Administration under Grant NNX14AH80Gand Grant NNX16AK58G. (Corresponding author: Heresh Fattahi.)

H. Fattahi and P. Agram are with the Jet Propulsion Laboratory,California Institute of Technology, Pasadena, CA 91109 USA (e-mail:[email protected]).

M. Simons is with the California Institute of Technology, Pasadena, CA91125 USA.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2017.2718566

by the extra path delay of the microwave signal passingthrough a planet’s atmosphere. For SAR satellites orbitingaround earth, the atmospheric delay is largely caused bythe spatial and temporal variations of water vapor in thetroposphere [1]–[4] and of the number of free electrons in theionosphere [5], [6], [10]–[12].

In the ionosphere, highly energetic solar radiations such asextreme ultraviolet and X-ray radiation partially ionize theatmosphere’s neutral atoms and molecules forming a mixtureof free electrons, ions, and neutral gas molecules aroundearth [13]–[15]. The ionosphere extends approximately fromaltitudes of 60 to 1000 km, with a maximum electron densityat around 300 km [16]. In addition to altitude-dependentvariations, the ionosphere’s total electron content (TEC) varieswith geographic location, time of day, season, and levelsof geomagnetic and solar activities [14]. The ionosphereshows a latitudinal variation, with distinct behaviors in threemain regions including low (or equatorial), middle, and high(auroral) latitude regions [14].

In equatorial regions, the ionosphere is dominated by theequatorial (Appleton) anomaly [17] due to a fountain effectwhereby ionosphere electron density is higher on both sidesof equator rather than at the equator itself. The equator-ial anomaly is often asymmetric with a higher density onthe winter hemisphere relative to the summer hemisphere.The anomaly may also be disturbed by geomagnetic storms.Irregularities in ionospheric TEC variation that causes suddenchange to the phase or amplitude of the microwave signals,known as the scintillation effect, are also maximum at thelow latitudes. In contrast to the equatorial region, ionospherein the mid-latitude regions is less intense and least variable.The TEC variation at mid-latitudes is small, around 20–30% ofthe average value, and can be accurately predicted by differentmodels [13]. At high latitudes, the irregular variation of TEC islarger than at mid-latitudes and still smaller than at equatorialregions. At polar regions, photoionization and high energyparticles are the main sources of ionization. Energetic particlesfrom the magnetosphere are guided by the geomagnetic fieldlines through atmosphere where they collide with neutralgas atoms and molecules resulting in intense electromagneticwaves. Precipitating particles excite atmospheric elements tohigher energy levels, which result in emission of visible lightsknown as auroral lights [13].

The ionosphere is a dispersive medium with respect to themicrowave frequencies. In such a dispersive medium, the delayin the microwave signal is inversely proportional to the signal

0196-2892 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

frequency such that low-frequency signals experience a largerdelay than higher frequency signals. The dispersive mediumof ionosphere for microwave signals allows space geodeticsystems operating in two different microwave frequencies,such as the Global Navigation Satellite Systems, to directlyestimate the ionospheric delay [13]. Moreover, ionospherebecomes birefringent media in the geomagnetic field, suchthat the microwave signals propagating through the ionosphereare decomposed into two circularly propagating waves withslightly different propagating velocities, which depend on thepolarization and orientation of the propagation direction withrespect to the geomagnetic field [19]. Birefringent ionosphererotates the polarization plane of the microwave signals by anangle called Faraday rotation, which can be estimated fromfull-polarization SAR data [9].

Propagation of microwave signals through the ionospherecauses distortions in the InSAR data, including defocusing ofSAR images, Faraday rotation, phase delay, and an extra shiftbetween SAR images in the satellite along-track (azimuth)direction. When the ionospheric variation in the satellite along-track direction has a correlation length shorter than the lengthof the synthetic aperture, the resulting image will be defo-cused in the azimuth direction [18]. For polarized microwavesignals passing through ionosphere, the polarization directionwill rotate relative to the original polarization direction byFaraday rotation [16]. Ionospheric delay also introduces anextra phase component to the SAR interferograms, which if notcompensated, decreases the accuracy of InSAR measurementsof ground displacement [5], [6]. Along-track TEC gradientscause a phase gradient equivalent to an extra Doppler shift,which translates to a time shift in the azimuth direction [6].In other words, the ionospheric phase gradient introducesextra azimuth offsets between two SAR images that cannotbe predicted with geometrical coregistration techniques.

Several approaches exist to estimate the ionospheric phasedelay from InSAR data. One approach uses Faraday rotation,whereby full-polarization SAR data are used to estimate theFaraday rotation, from which the ionosphere’s TEC can beestimated [7]–[10], [16] and used to predict the expectedphase delay. However, the ionospheric phase delay estimationusing Faraday rotation is limited by the availability of full-polarization SAR data and to high-latitude regions wherethe geomagnetic field and the radar line of sight (LOS)are largely parallel. Nevertheless, when Faraday rotation isapplicable, absolute TEC at each SAR acquisition can beestimated whereas other approaches, which are explained inthe following, estimate only a differential TEC between SARacquisitions. A second approach relies on estimates of theazimuth offsets. These offsets can be integrated along theazimuth direction to estimate the ionospheric phase delay [20].The azimuth offsets may be estimated from coherent or inco-herent cross correlation of SAR images or with spectraldiversity from multiaperture interferometry [21]. Offset-basedtechniques are limited by the direction and spatial wavelengthof the ionospheric phase delay such that they are only sensitiveto the along-track ionosphere variation with short spatial wave-length. Moreover, the azimuth offsets induced by ionospherecannot be distinguished from offsets caused by large

ground displacement. A third approach uses the dispersivecharacteristic of the ionosphere for microwave signals anddivides the spectrum of the radar signal in range direction intotwo sub-bands from which two lower resolution SAR imagesat different center frequencies are formed. In this technique,known as the split range-spectrum technique (also referred toas range split-spectrum in previous studies [12], [22]), sub-band images from two acquisitions are combined to form twosub-band interferograms and to estimate the dispersive andnondispersive components of the interferometric phase. Thedispersive component represents the ionospheric phase delay.

An algorithm for the split range-spectrum technique hasbeen detailed in [23] and has been demonstrated for Sentinel-1and ALOS-2 acquisitions [24]. The split range-spectrumtechnique has already been evaluated for a limited numberof InSAR pairs. Here, we extend the split range-spectrumapproach in order to estimate a time-series of ionosphericphase delay using a stack of SAR acquisitions. The time-series of ionospheric phase delay can be used to compensatethe InSAR displacement time-series or to evaluate the spatio-temporal variation of the TEC.

In Section II, we review the ionospheric phase delay inInSAR data. We discuss the basic concept of estimatingionospheric phase delay from multifrequency SAR acquisi-tions and using the split range-spectrum technique for narrow-band SAR data. We then extend the split range-spectrumtechnique to estimate the time-series of ionospheric phasedelay. In Section III, we discuss the details of the proposedworkflow for time-series estimation of ionospheric phase delayfrom a stack of stripmap SAR acquisitions. In Section IV,we present experimental results; in Section V, we discuss thepresented algorithm and the results.

II. IONOSPHERIC PHASE DELAY

The interferometric phase of an InSAR interferogramformed from two SAR acquisitions at ti and t j containsdifferent components as

�φ = 4π

λ

(�r i j

d + �r i jgeom + �r i j

trop + �r i jiono

)(1)

where λ represents the carrier wavelength of the radar, �r i jd is

the ground displacement in radar LOS direction, �r i jgeom repre-

sents the geometrical range difference from radar to the targetcaused by a nonzero spatial baseline between the two orbits,

and �r i jtrop and �r i j

iono are tropospheric and ionospheric delay,respectively. The ionospheric delay at a given acquisition isthe difference between the length of the actual path traveledby the microwave signal through ionosphere and the geometricrange from radar to the target, given as [13]

�r iiono =

∫nds −

∫ds0 (2)

where n is the ionosphere refractive index, s is the actual pathof the signal, and s0 is the geometrical path of the signal. Thefirst term on the right-hand side of (2) denotes the traveledpath by the microwave signal and the second term denotesthe geometric path. The delay between two acquisitions isthe difference of the delay at each of the acquisitions as


FATTAHI et al.: InSAR TIME-SERIES ESTIMATION OF THE IONOSPHERIC PHASE DELAY 3

�r i j = �r j −�r i . Based on the Appleton-Hertree formula forthe ionospheric refractive index, which ignores the collisioneffects of the particles [25], and following [26], (2) can bewritten as

�r iiono = − K

f 20

∫Neds0 ± 7525c

2 f 30

× Bcos(θ)

∫Neds0 − 812.4

f 40

∫N2

e ds0 + β (3)

where K = 40.31 m3/s2 is a constant, f0 is the carrierfrequency of the microwave signal, Ne is the electron density,c is the speed of light, B is the magnitude of the earth’smagnetic field, θ is the angle between the magnetic field andthe propagation direction, and β = ∫

ds − ∫ds0 represents

the effect of bending of the microwave signal through theionosphere. Bending of the microwave signal in the ionospherefor elevation angles greater than 5° (i.e., incidence angles lessthan 85°) is negligible [27]. Since the incidence angle forcurrent and upcoming SAR missions are below 60°, bendingis ignored in our discussion in the following. The first threeterms on the right-hand side of (3) express the first-, second-,and third-order ionospheric delay, respectively. The ± signfor the second-order term in (3) represents birefringence inthe ionosphere [9]. A maximum magnitude of the earth’smagnetic field of 0.65 gauss (10−4 tesla) and a TEC variationof 20 TECU results in submillimeter delay. The third-orderdelay is even smaller. Therefore, we keep only the first-orderterm in the following. Given TEC = ∫

Neds0, the first-orderionospheric delay between two SAR acquisitions is obtainedas

�r i jiono = − K

f 20

�TECi j (4)

where �TECi j represents TEC variation in the slant rangedirection between the two acquisitions at times ti and t j .Equation (4) shows that ionospheric delay is inversely pro-portional to the square of the carrier frequency. By substitut-ing (4) into (1), the interferometric phase is expressed as thesum of the dispersive and nondispersive components

�φ = 4π f0

c�r i j

non-disp − 4π K

cf0�TECi j (5)

where the first term represents the nondispersive component,which is the sum of the ground displacement, geometricalphase, and tropospheric delay. The second term represents thedispersive component, which is the ionospheric phase delay.

A. Ionospheric Phase Delay Estimation FromMultifrequency InSAR Data

If SAR images at different carrier frequencies of f0 andf1 are available, the interferometric phase at f1 can beexpressed based on the dispersive (�φdisp) and nondispersivecomponents of the interferometric phase at f0 as

�φ f1 = f1

f0�φnon-disp + f0

f1�φdisp. (6)

For additional carrier frequencies of f1, . . . , fN , a lin-ear system of equations d = Am can be formed, whered = [�φ f0,�φ f1, . . . ,�φ fN ]T is the observation vector

of interferometric phases at different carrier frequencies,m = [�φnon-disp,�φdisp]T is the unknown vector, whichis the dispersive and nondispersive phase components atf0, and A is an incidence matrix, where A = [[1, 1]T ,[( f1/ f0), ( f0/ f1)]T , . . . , [( fN / f0), ( f0/ fN )]T ]T . This linearsystem can be solved to estimate the nondispersive and disper-sive phase components at the f0 frequency using a weightedleast squares as m̂ = (AT C−1

d A)−1AT C−1d d, where Cd rep-

resents the variance-covariance matrix of d. The variance-covariance matrix of the unknowns is therefore obtained asCm = (AT C−1

d A)−1.Currently, no space-borne radar mission operates in

multiple carrier frequencies. The L-band mode of theNASA-ISRO SAR (NISAR) mission will nominally includea 5-MHz sideband separated from a 20- or 40-MHz mainband [28], allowing to estimate the ionospheric and nondis-persive phase components. Moreover, in selected regions,NISAR will operate in an extra S-band frequency [28], whichenables ionospheric phase estimation when combined with theL-band acquisitions. We note that a dispersive phase compo-nent estimated from S and L bands may not only representthe propagation delay in ionosphere but also may containdispersive phase components caused by different scatteringproperties of S and L bands due to surface moisture content,vegetation density, or surface roughness [29]. Separating thetwo components of dispersive phase caused by surface scat-tering and propagation delay in multifrequency SAR data isbeyond the scopes of this paper.

B. Ionospheric Phase Delay Estimation From Narrow-BandInSAR Data Using Split Range-Spectrum

For narrow-band SAR images, the full range-spectrum of aradar image acquired at center frequency of f0 can be split intotwo narrower nonoverlapping sub-bands at lower and highercenter frequencies of fL and fH . Splitting the range-spectrumcan be achieved with a bandpass filter (for more details, seeSection III). The SAR images at each sub-band can be usedto form sub-band interferograms. Using interferometric phasefrom the two sub-bands, �φL and �φH , A then simplifiesto A = [[( fL/ f0), ( f0/ fL)]T , [( fH / f0), ( f0/ fH )]T ]T , andm = [�φnon-disp,�φdisp]T , which represents the nondispersiveand dispersive interferometric phase components at f0. Dueto small separation between fL and fH (usually less thantens of megahertz), the dispersive component from surfacescattering is negligible. Assuming that the dispersive compo-nent represents only the ionospheric delay, the ionospheric andnondispersive phase components are given by

�φiono = fL fH

f0(

f 2H − f 2

L

) (�φL fH − �φH fL) (7)

�φnon-disp = f0(f 2H − f 2

L

) (�φH fH − �φL fL). (8)

Assuming the same phase standard deviation for the low-band and high-band interferometric phases of σ�φL,H , the vari-ance of the ionospheric and nondispersive phase componentsand the covariance between the two components are given as

σ 2iono = f 2

L f 2H(

f 2H − f 2

L

)2

f 2L + f 2

H

f 20

σ 2�φL,H

(9)



σ 2non-disp = f 2

L f 2H(

f 2H − f 2

L

)2 f 20

(1

f 2L

+ 1

f 2H

)σ 2

�φL,H(10)

ηiono,non−dis = −2 f 2L f 2

H(f 2H − f 2

L

)2 σ 2�φL,H

. (11)

The accuracy of the estimated ionospheric and nondisper-sive phase components is therefore a function of the sub-band interferometric phase noise and the central frequencies.Assuming an L-band central frequency of 1.3 GHz andsub-band frequencies with ±10 MHz from the carrier fre-quency (i.e., fL = 1.29 GHz and fH = 1.31 GHz), basedon (9) and (10), phase noise with standard deviation of oneradian in the sub-band interferograms amplifies to 46 radi-ans in the estimated ionospheric and nondispersive phasecomponents. Note that the ionospheric and nondispersivephase components are inversely correlated. The covariance ofthe ionospheric and nondispersive phase components for thenumerical example above, equals −2112 radians2. Therefore,because of the large negative covariance, the variance ofthe sum of noisy ionospheric and nondispersive components,obtained as σ 2

iono+non−dis = σ 2iono + σ 2

non-disp + 2ηiono,non-dis,reduces to around one radian, which is of the order of thesub-band interferogram phase noise.

C. Time-Series of the Ionospheric PhaseDelay From Split Range-Spectrum

To estimate a time-series of the ionospheric phase delay,one could ideally estimate the ionospheric delay for each pairin a single master network of interferograms. However, dueto noise amplification caused mainly by the small separationbetween the low- and high-band frequencies, that is smallfH − fL , small interferometric phase noise may significantlyaffect the accuracy of ionospheric phase estimates. There-fore, geometrical and temporal baseline decorrelations limitionospheric phase delay estimation from a single master net-work of interferograms. To reduce the impact of geometricaland temporal baseline decorrelations, we use a network ofcoherent small baseline interferograms to estimate the networkof ionospheric phase delay.

Given a connected network of ionospheric phase delays,

the vector of ionospheric pairs at each pixel �φi, jiono is related

to a vector of the sequential phase differences �φk,k+1iono , here-

after called differential time-series, as �φi, jiono = G�φ

k,k+1iono ,

where G is a design matrix [30]. Assuming N SAR acqui-sitions used to estimate the network of ionospheric phasedelay, i, k ∈ [1, N) and j ∈ [2, N]. For a connected networkof small baseline pairs of ionospheric phase delay, G isfull rank and the system of equations is overdetermined.We notice that disconnected networks with small subsets, suchas those networks commonly used for displacement time-seriesanalysis [30], would bias the estimated differential time-seriesof ionospheric phase delay and should not be used.

We estimate the differential time-series of theionospheric phase delay using a weighted least-squares

as �φ̂k,k+1iono = (GT C−1

�φi, j G)−1GT C−1�φi, j �φ

i, jiono, where

C�φi, j is the variance-covariance matrix of the network of

ionospheric phase delay estimated from split range-spectrum.The variance-covariance matrix of the estimated differentialtime-series is obtained as C

�φ̂k,k+1 = (GT C−1

�φi, j G)−1.

Since each element of �φ̂k,k+1iono is differential between two

consequent acquisitions, a time-series of ionospheric phasedelay relative to a reference acquisition is obtained by

temporal integration of �φ̂k,k+1iono over its elements.

The square root of the diagonal components of C�φ̂

k,k+1

represents the uncertainty of differential time-series ofionospheric phase delay. The covariance between the elements

of �φ̂k,k+1

should be taken into account to express the uncer-tainty of the ionospheric delay time-series at each acquisitiondate relative to a reference date. For example, given �φ̂1,2

and �φ̂2,3 as the first and second elements of the differentialtime-series, the uncertainty of �φ̂1,3 in a time-series relativeto the first acquisition is given as

σ 2�φ̂1,3 = σ 2

�φ̂1,2 + σ 2�φ̂2,3 + 2η�φ̂1,2,�φ̂2,3 (12)

where η�φ̂1,2,�φ̂2,3 is the covariance between �φ̂1,2 and �φ̂2,3.

III. PROCESSING WORKFLOW FOR TIME-SERIES

ESTIMATION OF THE IONOSPHERIC PHASE DELAY

The processing workflow for the time-series estimation ofthe ionospheric phase delay from a stack of SAR data issummarized in Fig. 1. The workflow can be divided intothree main blocks that include: 1) estimating accurate time-series of offsets to coregister the stack of single-look compleximage (SLC) images to a common coordinate system; 2)splitting the range-spectrum and resampling the sub-bandSLCs using the precise offsets from the previous step; and 3)forming networks of low-band and high-band interferogramsto form a network of ionospheric phase delay and finallyestimating the ionospheric phase time-series. We explain theworkflow in more detail in the following sections.

A. Coarse Coregistration Using Geometrical OffsetsFor estimating a time-series of the ionospheric phase delay,

stacks of full-band and sub-band SLCs should be coregisteredto a common master coordinate system, here after called thestack master. We choose an arbitrary full-band SLC image asthe stack master and compute the geometrical offsets betweenall slave full-band SLCs and the stack master. The geometricaloffsets are obtained using a digital elevation model and preciseorbits of the SAR satellite [31]. Using the geometrical offsets,the stack of full-band SLCs is coregistered to the stack master.This process is the same as the first stage of geometriccoregistration in the network-based enhanced spectral diver-sity approach, which was developed to coregister a stackof SAR acquisitions acquired with Terrain Observation withProgressive Scan [32]. The geometrical offsets in the azimuthdirection usually require refinement to account for possibletiming-errors, along-track orbital errors or ionosphere-inducedazimuth offsets [33].

B. Time-Series of Azimuth OffsetsIn order to refine the azimuth offsets, we estimate a

time-series of azimuth misregistration with respect to the



Fig. 1. InSAR processing workflow for time-series estimation ofionospheric phase delay. The colors indicate different processing blocks asorange: estimating time-series of offsets to coregister the stack of SLCs,blue: splitting range-spectrum for the stack and using the time-seriesof offsets to coregister the stacks to a common coordinate system, andgreen: processing block for estimating the time-series of ionospheric phase.For the sake of simplicity, different acronyms have been used as follows.geom: geometrical. coreg: coregistered. Amp: amplitude. corr: correlation.Net: network. SB: small baseline and refers to pairs of SAR acquisitionswith small spatial and temporal baselines. Az: azimuth. Tseries: time-series.LB: low-band. HB: high-band. igrams: interferograms. iono: ionospheric. AllSB networks are connected networks.

stack master. For a stack of stripmap acquisitions, the time-series of azimuth misregistration can be obtained by ampli-tude cross correlation of the stack master with the coarsecoregistered full-band SLCs. However, the accuracy ofthe azimuth misregistration decreases with increased time-difference or spatial baseline from the stack master acquisition.To reduce the impact of the temporal and spatial baselinedecorrelations on the azimuth offsets, we use pixel-offset smallbaseline technique in which we compute the pixel-offsets fora network of small baseline pairs of full-band SLCs and theninvert the network of the azimuth offsets to estimate the time-series of azimuth offsets with respect to the stack master [34].A connected network of small baseline pixel-offsets should beused to ensure unbiased estimation of the time-series of theazimuth offsets.

C. Splitting the Range-Spectrum

Given a stack of SAR acquisitions, we focus the data toform full-band SLCs at the carrier frequency f0 and sub-bandSLCs at low-band and high-band frequencies of fL and fH .Alternatively, one may first focus the stack to the carrierfrequency and then split the range-spectrum for each image

to form the sub-band SLCs at frequencies fL and fH . Givenan SAR SLC focused to the carrier frequency with the rangebandwidth of B , the spectrum of the complex signal in rangedirection for each line of the image can be split into sub-bandsusing bandpass filtering. After bandpass filtering of the range-spectrum, each sub-band SLC is obtained by computing theinverse Fourier transforms of the sub-band spectrum. Finally,to center the low-band and high-band spectra at fL and fH ,respectively, we demodulate the sub-band SLCs as

IL = ILe− j2π f Lt , t ∈ [0, w/RSR] (13)

IH = IH e− j2π f H t , t ∈ [0, w/RSR] (14)

where IL and IH are the low-band and high-band SLCs,respectively, t is the range time, w is the number of samplesin range direction, and RSR is the range sampling rate.

D. Fine Coregistration and Interferogram Generation

Using the geometrical offsets refined with the time-seriesof azimuth offsets, the stacks of full-band and sub-band SLCsshould be coregistered and resampled to the stack master.Afterward, a connected network of small baseline full-bandand sub-band interferograms can be computed by cross mul-tiplying coregistered SLCs at each sub-band. We note thatthe sub-band frequencies should be taken into account forresampling the sub-band SLCs and for flattening the sub-bandinterferograms.

E. Ionospheric Phase Delay EstimationIn order to estimate the dispersive and nondispersive phase

components for each small baseline pair, the sub-band inter-ferograms need to be multilooked, filtered, and unwrapped.Due to the amplification of noise, the estimated dispersiveand nondispersive components need to be low-pass filtered.To mitigate possible artifacts caused by low-pass filtering,we use an iterative masking-interpolation filtering approach.

In this approach, we first create a mask for invalid regions,including areas covered by water (e.g., lakes, ocean), shadowareas, and regions with low coherence. We mask out invalidregions of the dispersive and nondispersive phase compo-nents, fill in the masked regions using a nearest neighborinterpolation and apply the low-pass filter to the maskedand interpolated data. In the second iteration, we reset areaswith good data to their original unfiltered values and fillin the masked region by interpolating the filtered data. Themasked and interpolated data are filtered again. This processis repeated until convergence. We normally use 5–6 iterations.

The filtered dispersive and nondispersive components alongwith the sub-band interferograms are used to estimate possiblephase unwrapping errors in the sub-band interferograms [23].Afterward, the sub-band interferograms corrected for unwrap-ping errors are used to re-estimate the dispersive and nondis-persive pairs. Then, the iterative filtering should be applied toreduce noise in the two components. The resulting networkof pairs of ionospheric delay is inverted to estimate the time-series of the delay, which can be used to compensate the full-band interferograms or InSAR time-series. The time-series ofdelay can also be used to produce TEC time-series with respectto a reference acquisition.



Fig. 2. Location of ALOS-1 acquisitions in Chile and California.

IV. EXPERIMENTAL RESULTS

In order to evaluate the proposed algorithm to estimatetime-series of ionospheric phase delay, we use three stacks ofL-band acquisitions in Chile and California (Fig. 2), acquiredby ALOS-1 from 2007 to 2011. ALOS-1 stacks wereacquired in two modes, fine beam dual polarization (FBD)and fine beam single polarization (FBS) with bandwidthsof 14 and 28 MHz, respectively. In order to evaluate theperformance of the algorithm with a smaller range bandwidth,we downsample the raw FBS acquisitions of each stack to14-MHz bandwidth. We then split the range-spectrum of theSLCs to form the sub-band SLCs at ±3.5 MHz from thecarrier frequency with the sub-band bandwidth of 6 MHz.We use the shuttle radar topography mission digital elevationmodel (DEM) and precise orbits to compute the geometricaloffsets for each stack and refine the azimuth offsets byamplitude cross correlations using a 64 × 64 pixel windowsize. After inverting the azimuth offsets, we compute tem-poral coherence [35] to evaluate the inversion and mask outthe estimated azimuth offset time-series using the temporalcoherence with a threshold of 0.8. We then use a nearestneighbor interpolation approach to fill the masked regions ofthe azimuth offsets and oversample the offsets to the samegrid size of the geometrical azimuth offsets. We multilookeach interferogram by 4 and 14 looks in range and azimuthdirections, respectively, filter using a Goldstein filter, andunwrap using statistical-cost network-flow algorithm for phaseunwrapping [36]. After estimating the dispersive and nondis-persive components, we use a 2-D Gaussian filter with a kernelsize of 100 pixels in both range and azimuth directions tolow-pass filter the estimated ionospheric and nondispersivephase components using the iterative filtering-interpolationapproach explained in Section III. For each stack, we alsoestimate a raw InSAR time-series, in which a network of

full-band interferograms (14-MHz interferograms) is invertedto estimate the InSAR time-series. We call this time-series,a raw InSAR time-series because the interferograms containground displacement, tropospheric and ionospheric delays, andpossible geometrical residuals (e.g., caused by DEM errors).

Fig. 3 shows the raw InSAR differential time-series,the estimated differential time-series of ionospheric phasedelay, the differential InSAR time-series after compensa-tion for the ionospheric delay, uncertainty of the estimatedionospheric phase delay, and the differential time-series ofthe azimuth offsets for track 104 in Chile. Note that the esti-mated differential phase between 2007-09-15 and 2008-01-31contains the coseismic ground displacement caused by theMw 7.7 2007-11-14 Tocopilla earthquake. Fig. 3 indicates amaximum relative ionospheric delay of 1.3 m across the265-km-long swath. The differential time-series of azimuthoffsets indicates a maximum 12.4-m azimuth offsets causedby an ionospheric phase gradient in the azimuth direc-tion. The differential InSAR time-series compensated forionospheric delay reveals coseismic ground displacement dueto the Tocopilla earthquake between 2007-09-15 and 2008-01-31 acquisitions.

Differential time-series of ionospheric delay for track 103 inChile (Fig. 4) shows that the delay varies more than 2 mbetween the acquisition dates along the 445-km azimuth extentof this track. The differential time-series of the azimuthoffsets also indicates maximum azimuth offsets of 25 mcaused by the ionospheric phase gradient in the azimuthdirection. Parts of the coseismic ground displacements causedby the 2007 Tocopilla earthquake are evident in the differ-ential phase between 2007-10-14 and 2007-11-29 acquisi-tions in the differential InSAR time-series compensated forthe ionospheric delay. Comparing the differential time-seriesof the azimuth offsets with the differential InSAR time-series compensated for ionospheric delay, reveals that afterionosphere compensation, differential phase maps with largerresiduals also show significant azimuth offsets, implying thatthe residuals are mainly caused by high-gradient ionosphericphase delay (scintillation) originating from ionospheric irreg-ularities. Two geocoded interferograms from tracks 103 and104 (Fig. 5), containing the coseismic ground displacement,are more consistent in their overlap region, after ionosphericdelay correction. The remaining inconsistency in the southernpart of the overlap of the two tracks after the correction ismost likely due to tropospheric delay.

The differential time-series for a stack of 23 ALOS-1 acqui-sitions in California (Fig. 6) shows a maximum ionosphericdelay of less than one phase cycle (11.8 cm) across 160-kmALOS-1 azimuth extent. The smaller ionospheric delay inCalifornia relative to Chile is likely due to the fact thatCalifornia is located at mid-latitudes with less intense andsmaller TEC variations as compared to Chile.

A. Comparing InSAR Time-Series With GPS Time-SeriesIn order to validate the InSAR time-series after ionospheric

delay correction, we use several GPS time-series, whoselocations are plotted in Fig. 5(b). Fig. 7 compares time-seriesof pairwise GPS positions with InSAR time-series before



Fig. 3. Differential InSAR time-series for ALOS-1 track 104 in Chile. Each map shows differential quantities between two consequent acquisition dates.First row shows differential raw InSAR time-series, second row shows differential time-series of ionospheric phase delay, third row shows differential InSARtime-series compensated for the ionospheric delay, fourth row shows uncertainty of the differential time-series of ionospheric delay, and fifth row shows thedifferential time-series of azimuth offsets.

and after ionospheric delay correction. Comparing the InSARand GPS time-series reveals that the scatter of InSAR time-series significantly reduces after ionospheric delay correction.To quantifying the improvement of the InSAR time-seriesafter ionospheric delay correction, we assume the GPS time-series as truth and compute the deviation of InSAR time-series relative to GPS time-series using a root mean squareerror (RMSE) given as

RMSE =√

∑Ni=1

(dgps

i − d InSARi

)2

N(15)

where dgpsi and d InSAR

i represent the GPS and InSAR time-series, respectively, at the i th InSAR epoch, and N is the

number of InSAR acquisitions in the stack. Note that the twotime-series are compared only at their common epochs. Beforecorrection, the RMSE between InSAR and GPS varies from14.0 cm at MCL1-VLZL stations to 48.0 cm at CRSC-SRGDstations (Table I). Correction of ionospheric delay significantlyreduces the RMSE, varying between 1.0 cm at CDLC-SRGDto 6.8 cm at CRSC-CTLR (Table I and Fig. 7).

V. DISCUSSION

A. Noise Amplification in the EstimatedIonospheric Phase Delay

The uncertainty of estimated ionospheric phase delay givenin (9) is mainly controlled by the separation of sub-bandfrequencies. Fig. 8 shows the ratio of the standard deviation



Fig. 4. Similar to Fig. 3, but for track 103.

of the ionospheric phase to that of the sub-band phase asa function of frequency separation between the two sub-bands, assuming a full-band central frequency of 1.27 GHz

that is within the L-band range of the microwave spectrum.As expected, the ratio is large for small separation betweenfL and fH implying that noise of the sub-band interferograms



Fig. 5. ALOS-1 interferograms, containing the ground displacement causedby the Tocopilla earthquake, from adjacent tracks (Left) 103 (acquisitions2007-10-14 and 2007-11-29) before ionospheric delay correction and (Right)104 (acquisitions 2007-09-15 and 2008-01-31) after ionospheric delay correc-tion. Black diamonds: location of GPS stations whose time-series has beencompared with InSAR time-series in Fig. 7.

TABLE I

RMSE BETWEEN GPS TIME-SERIES AND InSAR TIME-SERIES

BEFORE AND AFTER IONOSPHERIC DELAY CORRECTIONFOR SEVERAL STATIONS IN CHILE

significantly amplifies in the estimated ionospheric phase. Theratio decreases with increased separation between fL and fH .For two sub-bands, 7.0 MHz apart (similar to ALOS-1 FBDacquisitions), σiono is 131 times larger than σ�φL,H .

A nominal NISAR L-band mode will include main bandand sideband of 20 and 5 MHz, respectively, at the twoends of a total 85-MHz bandwidth. This acquisition moderesults in 72.5-MHz separation between the two bands. Thislarge separation will reduce the noise amplification factor toaround 13 for NISAR data. In other words, assuming thesame scene scattering properties, the estimated ionosphericphase delay from NISAR acquisitions is expected to be anorder of magnitude less noisy than the ionospheric phase delayestimated from the ALOS-1 FBD acquisitions.

Fig. 9 shows an ALOS-1 FBS interferogram covering theFeb. 27, 2010 Mw 8.8 Maule earthquake in Chile and the esti-mated ionospheric and nondispersive phase components beforeand after low-pass filtering. The ionospheric and nondispersivephase components [Fig. 9(b) and (e)] are sufficiently noisy,such that the phase fringes are not evident in the re-wrappedphase [Fig. 9(h) and (k)]. Given the nominal L-band NISARacquisition parameters [28], and assuming the same noise level

Fig. 6. Differential InSAR time-series for ALOS-1 track 216 in California.First and second rows: differential raw InSAR time-series. Third and fourthrows: differential time-series of ionospheric phase delay. Fifth and sixthrows: differential InSAR time-series compensated for the ionospheric delay.Seventh and eights rows: uncertainty of differential time-series of ionosphericdelay.

in the sub-band ALOS-1 FBS interferograms and NISAR side-band and main-band interferograms, the noise amplification inthe ionospheric and nondispersive phase components reducesby a factor of five. Fig. 9(d) shows expected ionospheric phasedelay before filtering, assuming NISAR L-band acquisitionparameters. For the expected NISAR ionospheric phase delay,we estimate noise as the difference of unfiltered [Fig. 9(b)]and filtered [Fig. 9(c)] ALOS-1 ionospheric phase delays andscaled the noise by 1/5 to simulate the expected noise inNISAR ionospheric phase. The expected NISAR ionosphericphase [Fig. 9(d)] is the sum of the scaled noise and the filteredionospheric delay [Fig. 9(c)]. Fig. 9(j) suggests that withnominal NISAR parameters, the ionospheric phase fringes areclearly visible even before low-pass filtering.

B. Residual Ionospheric DelayLow-pass filtering of the ionospheric phase delay estimated

from the split range-spectrum technique reduces noise at theexpense of spatial resolution. In other words, with the splitrange-spectrum technique, only the long spatial wavelengthionospheric phase delay can be estimated. The shortest spatialwavelength of the estimated ionospheric delay depends onthe size of the low-pass filter. This mainly depends on theseparation of sub-band center frequencies such that largerfilter sizes are required for a smaller separation of sub-bandfrequencies and smaller filter sizes for a larger sub-bandseparation. Gaussian low-pass filters with larger kernel sizes



Fig. 7. (Left) Differential GPS time-series (block circles) comparedwith InSAR time-series before (yellow squares) and after (green circles)ionospheric delay correction. Both GPS and InSAR time-series are differentialbetween the GPS sites. InSAR time-series were obtained by temporal integra-tion of the differential time-series and are relative to a reference date, which is2008-01-31 for track 104 and 2007-11-29 for track 103. All InSAR time-series are from track 103 except for MCL1-VLZL, which is from track 104.GPS time-series are referenced to the same reference date as InSAR time-series. For each GPS time-series, all three components in east, north, andvertical directions were used to project to the InSAR LOS direction. Orangevertical dashed line: 2007 Mw 7.7 Tocopilla earthquake. (Right) Residualtime-series that is the difference of GPS and InSAR after ionospheric delaycorrection. Each residual time-series is shifted to its mean. Shaded gray bars inthe residual plots for CRSC-CTLR, CDLC-CTLR, and CTLR-SRGD indicateacquisition dates with large azimuth offsets at station CTLR (see Fig. 10 fora time-series of azimuth offsets at stations CTLR and CDLC).

remove a larger spectrum of the ionospheric delay throughnoise reduction process.

The time-series of residuals between GPS and InSARafter ionospheric delay correction at different GPS stationpairs (Fig. 7) indicates a higher RMSE for CRSC-CTLR,CDLC-CTLR, and CTLR-SRGD pairs, which all share theCTLR station and higher residuals at the first and 8th epochsof the time-series. These two epochs also show significantazimuth offsets at station CTRL (Fig. 10). Azimuth off-sets are caused by high-gradients in the ionospheric phasedelay in the azimuth direction. Therefore, the correlationbetween epochs with large residuals (Fig. 7) and large azimuthoffsets (Fig. 10) imply that the residual of InSAR and GPStime-series in Fig. 7 are most likely dominated by the high-gradient ionospheric delay that is lost due to the necessarylow-pass filtering.

Fig. 8. Ratio of the ionospheric phase standard deviation to thesub-band phase standard deviation as a function of the separationof sub-bands center frequencies. For smaller values of ( fH − fL ), noise of thesub-band interferograms significantly amplifies in the estimated ionosphericphase. The noise amplification reduces with the increase in ( fH − fL ). Notethe logarithmic scale of both the horizontal and vertical axes.

Fig. 9. Noise amplification and the need for low-pass filtering of theionospheric and nondispersive phase components estimated with the splitrange-spectrum technique. (a) Full-band ALOS-1 interferogram formed fromtwo FBS (28 MHz) acquisitions, acquired on 2010-02-25 and 2010-04-12 fromtrack 116 (frames 6410 to 6460) covering the coseismic displacement causedby the Mw 8.8 2010 Maule earthquake. (b) Estimated ionospheric phase delaybefore filtering. (c) Similar to (b), but after filtering using a 2-D Gaussianlow-pass filter with a kernel size of 100 pixels in both the range and azimuthdirections. (d) Expected ionospheric phase delay before filtering if L-bandNISAR acquisition strategy is assumed with two 5- and 20-MHz bands,72.5 MHz apart from each other. The expected NISAR-like ionospheric delaywas obtained by scaling noise [difference of (b) and (c)] to one-fifth andadding it back to (c). (e) Estimated nondispersive phase before filtering.(f) Similar to (e) but after low-pass filtering. (g)–(l) Same as top row butrewrapped to ALOS-1 L-band natural fringe rate. The range-spectrum ofeach full-band ALOS-1 FBS SLC was split into two sub-bands with 14-MHzdifference between fH and fL and with a sub-band bandwidth of 12 MHz.

The high-gradient ionospheric phase variations in azimuthdirection can be potentially estimated by integrating azimuthoffsets [19], [20]. However, this approach cannot distinguishbetween ionosphere-induced azimuth offsets and those causedby large ground displacements. The expected high frequencyionospheric phase delay should also be reduced with dusk-



Fig. 10. Time-series of azimuth offsets at stations CTLR and CDLC fromtrack 103. The vertical gray bars indicate epochs with significant azimuthoffsets compared to the rest of the time-series at station CTLR.

Fig. 11. Ionospheric delay at different frequencies shown as wrapped phasefor the corresponding wavelength. (a) Observed ionospheric phase delay atL-band [the same as Fig. 9(i)] and predicted delay for the same TEC variationat different frequencies (b) S-band, (c) C-band, and (d) X-band. If shown asunwrapped phase, the difference between L- and X-bands would be about afactor of 60.

down acquisition strategy, when ionosphere scintillation is ata minimum [37]. Less noisy ionospheric delay from NISARwill require lighter low-pass filters and, therefore, a higherfrequency ionospheric delay will be preserved.

C. Expected Ionospheric Delay at DifferentCarrier Frequencies

The first-order ionospheric delay given in (4) is inverselyproportional to the square of carrier frequency of microwavesignals. Given the same variation of ionosphere TEC anda similar imaging geometry, ionospheric delay at L-bandfrequency (1.27 GHz) is 3.9, 18.1, and 57.7 times larger thanS-band (2.5 GHz), C-band (5.405 GHz), and X-band(9.65 GHz) frequencies, respectively. Fig. 11 shows estimatedionospheric delay in Chile at L-band frequency compared withexpected delay at S-, C-, and X-band frequencies assumingthe same TEC variation observed with ALOS-1 and same

Fig. 12. Impact of the ionosphere-induced azimuth offsets on the interfero-metric phase and coherence for a pair of ALOS-1 acquisitions, acquired on2007-02-26 and 2007-10-14 from track 103 over Chile. (a) Interferometricphase and (b) coherence between the two SLCs coregistered with onlygeometrical offsets. (c) and (d) Same as (a) and (b) but with azimuth offsetsadjusted with amplitude cross correlation between the two acquisitions. SeeFig. 4 for a plot of azimuth offsets between the two acquisitions.

imaging geometry as ALOS-1. A TEC variation of around10 TECU between the two SAR acquisitions (2010-02-25 and2010-04-12) and along 360-km azimuth extent of the imagedtrack, results in more than 21 interferometric phase cycles inL-band while it would only generate 10, 5, and less thanthree phase cycles in S-, C-, and X-band interferograms,respectively.

D. Impact of Azimuth Misregistration

Ionospheric phase gradient in the azimuth direction mayintroduce significant azimuth offsets, causing misalignment ofSAR images and resulting in noisy interferograms [6], [20].Fig. 12 shows an interferogram and the associated coher-ence map obtained with only geometric coregistration com-pared with the same interferogram and coherence map afteraccounting for the azimuth offsets induced by the ionosphericphase variation. The azimuth offsets for this pair can beseen in Fig. 4. If not accounted for, the large ionosphere-induced azimuth offsets reduce coherence, as well as introducenoise to and bias the interferometric phase. We note that theazimuth offsets are induced by the gradient of the ionosphericphase delay in the azimuth direction and not by the absolute



magnitude of TEC. For example, the spatially low-frequencylarge ionospheric delay variation of around 1.5 m (6.1 TECU)between 2007-11-29 and 2008-04-15 acquisitions in Fig. 4,does not introduce significant azimuth offsets. In contrast,the spatially high frequency ionospheric phase delay between2007-02-26 and 2007-08-29 acquisitions in Fig. 4 introducelarge phase gradients that cause significant azimuth offsets.

E. Phase Ramps in InSAR DataLong-wavelength phase ramps in InSAR data have been

traditionally attributed to residual geometrical phase mainlycaused by inaccuracy of satellite orbits. However, based onreported accuracies of the orbits of SAR satellites, the residualphase caused by orbital errors even for older SAR missions,such as European remote sensing satellite and environmentalsatellite, is expected to be smaller than a phase cycle overaround 100 km [1]. The expected uncertainty of orbital errorsin ground displacement velocity fields obtained from InSARtime-series is of the order of 1-2 mm/yr over 100 km for oldersatellites and should reach below 1 mm/yr over 100 km formodern satellites with precise orbits [38]. Here we found thatlong-wavelength phase ramps in L-band SAR data acquiredover Chile in the equatorial belt are dominated by ionosphericdelay. The evaluated stack in California is affected by smallerionospheric delay, such that the magnitude and temporalvariation of the ionospheric delay is of the order of expectedtropospheric delay in this region. After ionospheric delaycorrection, the residuals are most likely due to troposphericdelay, DEM error, and residual ionospheric delay caused byhigh-gradient TEC variation. The contribution from orbitalerrors is most likely negligible.

VI. CONCLUSION

We presented an algorithm based on the split range-spectrum technique for time-series estimation of ionosphericphase delay from a stack of SAR acquisitions. We appliedthe algorithm to three 14-MHz ALOS-1 stacks in Chile andCalifornia with different ionospheric delay characteristics.Estimated time-series of ionospheric delay shows significantvariation of ionospheric delay of up to 2 m along 445 km inChile with both low and high spatial frequencies. The temporalvariation of the delay in California reaches maximum 10 cmover 160 km with only low spatial frequencies. Correctionfor ionospheric delay in regions with high TEC variationreduces the temporal variation of the InSAR time-seriesfrom meter levels before the correction to centimeter levelsafter correction for ionospheric delay. Comparing independentGPS time-series to InSAR time-series demonstrated significantreduction in deviation of InSAR from GPS with an RMSEof 14.0 to 48.0 cm before correction to 1.0 to 6.8 cm aftercorrection.

Uncertainty in estimates of the ionospheric delay time-seriesis a function of the separation between low-band and high-band frequencies and the coherence of the interferograms.For highly coherent stacks in arid areas of Chile, stacks ofL-band SAR data with small full-bandwidth of 14 MHzresulted in uncertainties of less than 1 cm for most acquisitiondates. For the California stack, with less coherence between

the SAR acquisitions, uncertainties were larger (around 2-3 cmfor most acquisitions). Larger range bandwidth and separationbetween low-band and high-band center frequencies, shorterspatial baselines, and more frequent acquisitions will all reducethe uncertainty in estimates of the ionospheric delay time-series. Large separation between main band and sideband ofNISAR L-band data is expected to improve the accuracy ofionospheric phase delay estimation by an order of magnitudecompared to ALOS-1 FBD and by a factor of five comparedto ALOS-1 FBS data.

ACKNOWLEDGMENT

The authors would like to thank the Alaska Satellite Facilityand the Japanese Aerospace Exploration Agency for providingthe ALOS-1 data, P. Rosen from the Jet Propulsion Laboratory,NASA, F. Meyer from the University of Alaska–Fairbanks,and G. Gomba from the German Aerospace Center for helpfuldiscussions on ionospheric phase delay in InSAR data. U.S.Government sponsorship acknowledged.

REFERENCES

[1] R. F. Hanssen, Radar Interferometry: Data Interpretation and ErrorAnalysis. Dordrecht, The Netherlands: Kluwer, 2001.

[2] Z. Li, E. J. Fielding, P. Cross, and J.-P. Muller, “Interferometric syntheticaperture radar atmospheric correction: Medium Resolution ImagingSpectrometer and Advanced Synthetic Aperture Radar integration,”Geophys. Res. Lett., vol. 33, no. 6, pp. 1–4, 2006.

[3] R. Jolivet et al., “Improving InSAR geodesy using Global AtmosphericModels,” J. Geophys. Res. Solid Earth, vol. 119, no. 3, pp. 2324–2341,2014.

[4] H. Fattahi and F. Amelung, “InSAR bias and uncertainty due to thesystematic and stochastic tropospheric delay,” J. Geophys. Res. SolidEarth, vol. 120, no. 12, pp. 8758–8773, 2015.

[5] A. L. Gray, K. E. Mattar, and G. Sofko, “Influence of ionosphericelectron density fluctuations on satellite radar interferometry,” Geophys.Res. Lett., vol. 27, no. 10, pp. 1451–1454, 2000.

[6] K. E. Mattar and A. L. Gray, “Reducing ionospheric electron densityerrors in satellite radar interferometry applications,” Can. J. RemoteSens., vol. 28, no. 4, pp. 593–600, 2002.

[7] X. Pi, A. Freeman, B. Chapman, P. Rosen, and Z. Li, “Imagingionospheric inhomogeneities using spaceborne synthetic aperture radar,”J. Geophys. Res. Space Phys., vol. 116, no. A4, pp. 1–13, 2011.

[8] X. Pi, “Ionospheric effects on spaceborne synthetic aperture radar and anew capability of imaging the ionosphere from space,” Space Weather,vol. 13, no. 11, pp. 737–741, 2015.

[9] J. S. Kim, K. P. Papathanassiou, R. Scheiber, and S. Quegan, “Correctingdistortion of polarimetric SAR data induced by ionospheric scintillation,”IEEE Trans. Geosci. Remote Sens., vol. 53, no. 12, pp. 6319–6335,Dec. 2015.

[10] E. J. M. Rignot, “Effect of Faraday rotation on L-band interferometricand polarimetric synthetic-aperture radar data,” IEEE Trans. Geosci.Remote Sens., vol. 38, no. 1, pp. 383–390, Jan. 2000.

[11] F. Meyer, R. Bamler, N. Jakowski, and T. Fritz, “The potential of low-frequency SAR systems for mapping ionospheric TEC distributions,”IEEE Geosci. Remote Sens. Lett., vol. 3, no. 4, pp. 560–564, Oct. 2006.

[12] P. A. Rosen, S. Hensley, and C. Chen, “Measurement and mitigationof the ionosphere in L-band interferometric SAR data,” in Proc. IEEERadar Conf., May 2010, pp. 1459–1463.

[13] J. Böhm and H. Schuh, Eds., Atmospheric Effects in Space Geodesy.Berlin, Germany: Springer, 2013.

[14] J. S. Shim, “Analysis of total electron content (TEC) variations in thelow- and middle-latitude ionosphere,” Ph.D. dissertation, Dept. Phys.,Utah State Univ., Logan, UT, USA, 2009.

[15] J. S. Shim, L. Scherliess, R. W. Schunk, and D. C. Thompson, “Spatialcorrelations of day-to-day ionospheric total electron content variabilityobtained from ground-based GPS,” J. Geophys. Res. Space Phys.,vol. 113, no. A9, pp. 1–14, 2008.



[16] P. A. Wright, S. Quegan, N. S. Wheadon, and C. D. Hall, “Faradayrotation effects on L-band spaceborne SAR data,” IEEE Trans. Geosci.Remote Sens., vol. 41, no. 12, pp. 2735–2744, Dec. 2003.

[17] E. V. Appleton, “Two anomalies in the ionosphere,” Nature, vol. 157,p. 691, May 1946.

[18] G. Gomba, M. Eineder, A. Parizzi, and R. Bamler, “High-resolution esti-mation of ionospheric phase screens through semi-focusing processing,”in Proc. IEEE Geosci. Remote Sens. Symp., Jul. 2014, pp. 17–20.

[19] J. S. Kim, “Development of ionosphere estimation techniques forthe correction of SAR data,” Ph.D. dissertation, ETH Zürich, Zürich,Switzerland, 2013.

[20] A. C. Chen and H. A. Zebker, “Reducing ionospheric effects in InSARdata using accurate coregistration,” IEEE Trans. Geosci. Remote Sens.,vol. 52, no. 1, pp. 60–70, Jan. 2014.

[21] H.-S. Jung, D.-T. Lee, Z. Lu, and J.-S. Won, “Ionospheric correction ofSAR interferograms by multiple-aperture interferometry,” IEEE Trans.Geosci. Remote Sens., vol. 51, no. 5, pp. 3191–3199, May 2013.

[22] R. Brcic, A. Parizzi, M. Eineder, R. Bamler, and F. Meyer, “Estimationand compensation of ionospheric delay for SAR interferometry,” in Proc.IEEE IGARSS, Jul. 2010, pp. 2908–2911.

[23] G. Gomba, A. Parizzi, F. De Zan, M. Eineder, and R. Bamler, “Towardoperational compensation of ionospheric effects in SAR interferograms:The split-spectrum method,” IEEE Trans. Geosci. Remote Sens., vol. 54,no. 3, pp. 1446–1461, Mar. 2016.

[24] G. Gomba, F. R. González, and F. De Zan, “Ionospheric phase screencompensation for the Sentinel-1 TOPS and ALOS-2 ScanSAR modes,”IEEE Trans. Geosci. Remote Sens., vol. 55, no. 1, pp. 223–235,Jan. 2017.

[25] K. G. Budden, The Propagation of Radio Waves: The Theory of RadioWaves of Low Power in the Ionosphere and Magnetosphere. Cambridge,U.K.: Cambridge Univ. Press, 1985.

[26] F. K. Brunner and M. Gu, “An improved model for the dual frequencyionospheric correction of GPS observations,” Manuscripta Geodaetica,vol. 16, no. 3, pp. 205–214, 1991.

[27] A. El-Rabbany, Introduction to GPS: The Global Positioning System.Norwood, MA, USA: Artech House, 2002.

[28] P. A. Rosen et al., “The NASA-ISRO SAR mission—An internationalspace partnership for science and societal benefit,” in Proc. IEEE RadarConf., May 2015, pp. 1610–1613.

[29] P. A. 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. Planets,vol. 101, no. E10, pp. 23109–23125, 1996.

[30] P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, “A new algorithmfor surface deformation monitoring based on small baseline differentialSAR interferograms,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11,pp. 2375–2383, Nov. 2002.

[31] E. Sansosti, P. Berardino, M. Manunta, F. Serafino, and G. Fornaro,“Geometrical SAR image registration,” IEEE Trans. Geosci. RemoteSens., vol. 44, no. 10, pp. 2861–2870, Oct. 2006.

[32] H. Fattahi, P. Agram, and M. Simons, “A network-based enhancedspectral diversity approach for TOPS time-series analysis,” IEEE Trans.Geosci. Remote Sens., vol. 55, no. 2, pp. 777–786, Feb. 2017.

[33] N. Yague-Martinez, M. Eineder, R. Brcic, H. Breit, and T. Fritz,“TanDEM-X mission: SAR image coregistration aspects,” in Proc. 8thEur. Conf. Synth. Aperture Radar (EUSAR), 2010, pp. 576–579.

[34] F. Casu, A. Manconi, A. Pepe, and R. Lanari, “Deformation time-series generation in areas characterized by large displacement dynamics:The SAR amplitude pixel-offset SBAS technique,” IEEE Trans. Geosci.Remote Sens., vol. 49, no. 7, pp. 2752–2763, Jul. 2011.

[35] A. Pepe and R. Lanari, “On the extension of the minimum cost flowalgorithm for phase unwrapping of multitemporal differential SARinterferograms,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 9,pp. 2374–2383, Sep. 2006.

[36] C. W. Chen and H. A. Zebker, “Two-dimensional phase unwrapping withuse of statistical models for cost functions in nonlinear optimization,”J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 18, no. 2, pp. 338–351, 2001.

[37] F. J. Meyer, K. Chotoo, S. D. Chotoo, B. D. Huxtable, andC. S. Carrano, “The influence of equatorial scintillation on L-band SARimage quality and phase,” IEEE Trans. Geosci. Remote Sens., vol. 54,no. 2, pp. 869–880, Feb. 2016.

[38] H. Fattahi and F. Amelung, “InSAR uncertainty due to orbital errors,”Geophys. J. Int., vol. 199, no. 1, pp. 549–560, 2014.

Heresh Fattahi (M’12) received the M.S. degreein remote sensing engineering from the K. N. ToosiUniversity of Technology, Tehran, Iran, in 2007, andthe Ph.D. degree in geosciences from the Universityof Miami, Coral Gables, FL, USA, in 2015.

He was a Postdoctoral Scholar at the CaliforniaInstitute of Technology from 2015 until June 2017.Since then he has joined the Radar Algorithmsand Processing Group, Jet Propulsion Laboratory,Pasadena, CA, USA. His research interests includealgorithm development for SAR, InSAR, and InSAR

time-series analysis.

Mark Simons received the B.Sc. degree in geo-physics and space physics from the University ofCalifornia, Los Angles, Los Angles, CA, USA,in 1989, and the Ph.D. degree in geophysics from theMassachusetts Institute of Technology, Cambridge,MA, USA, in 1996.

He has been with the California Institute of Tech-nology, Pasadena, CA, USA, since 1996, wherehe is currently a Professor of geophysics withthe Seismological Laboratory. His research interestsinclude studying processes that deform the solid

earth including those associated with the seismic cycle, migration of magmaand water in the subsurface, tides, and glacial rebound; tectonics and the rela-tionship between short and long time scale processes; glaciology, particularlybasal mechanics and ice rheology; tools and applications using space geodesy,particularly GNSS and SAR; Bayesian methods for large geophysical inverseproblems; and application of space geodesy for monitoring and rapid responseto natural disasters.

Piyush Agram (M’10) received the B.Tech. degreein electrical engineering from IIT Madras, Chennai,India, in 2004, and the Ph.D. degree in electricalengineering from Stanford University, Stanford, CA,USA, in 2010.

He was a Keck Institute of Space Studies Post-Doctoral Scholar with the Caltech’s SeismologicalLaboratory, Pasadena, CA, USA, until 2013, andthen joined the Radar Algorithms and ProcessingGroup, Jet Propulsion Laboratory, Pasadena, CA,USA. His research interests include algorithm devel-

opment for SAR focusing, radar interferometry for deformation time-seriesapplications, and geospatial big data analysis.

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1...

Documents

Transcript of IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1...