research article gps and insar time series analysis...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 601209 11 pageshttpdxdoiorg1011552013601209

Research ArticleGPS and InSAR Time Series Analysis DeformationMonitoring Application in a Hydraulic EngineeringResettlement Zone Southwest China

Ruya Xiao and Xiufeng He

Institute of Satellite Navigation amp Spatial Information System Hohai University Nanjing 210098 China

Correspondence should be addressed to Xiufeng He xfhehhueducn

Received 10 October 2013 Accepted 25 November 2013

Academic Editor Ting-Hua Yi

Copyright copy 2013 R Xiao and X He This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Booming development of hydropower in China has resulted in increasing concerns about the related resettlement issues Bothglobal positioning system (GPS) and persistent scatterer interferometric synthetic aperture radar (InSAR) time series analysis areapplied to measuring the magnitude and monitoring the spatial and temporal variations of land surface displacement in Hanyuana hydraulic engineering resettlement zone southwest China The results from the GPS monitoring system established in Hanyuanmatch well the digital inclinometer results suggesting that the GPS monitoring system can be employed as a complement to thetraditional groundmovementmonitoringmethodsThe InSAR time series witness various patterns andmagnitudes of deformationin the resettlement zone Combining the two complementary techniques will overcome the limitations of the single method

1 Introduction

Pubugou Hydropower Station with a 186m high core wallrock-fill dam located in the middle reaches of Dadu Riversouthwest China is built for power generation flood controland sediment retaining retention Several towns have beeninundated by the backwater and the population in thewhole area needs to relocate involving more than 100000residents which in resettlement scale is next only to theThreeGorges and Xiaolangdi water control project among modernhydraulic engineering projects in China

The resettlement zone new Hanyuan County located onLuobogang hillock consists of unstable broken limestoneweathered shale and schist shone with laminated loess In2009 and 2010 two landslide failures occurred in Hanyuanresulting in great loss of lives and properties Thus to detectearly indications of catastrophic movements monitoring isessential to predict landslides

However the current conventional deformation mon-itoring techniques are always time-consuming and costlyIn addition even if taken regularly the monitoring pointsare not usually dense enough to assist in understanding themechanisms of the landslide Therefore in this paper we

address deformationmonitoring applications through severalgeodetic techniques that is global positioning system (GPS)and interferometric synthetic aperture radar (InSAR) in thereservoir resettlement county

The remainder of the paper is organized as followsSection 2 briefly introduces the principles of GPS and InSARtime series analysis Site conditions and SAR data usedare described in Section 3 In Section 4 we present theGPS monitoring system established in the study area andcomparison between GPS and digital inclinometers in alandslide case Then time series results obtained by bothGPS and InSAR are also displayed Finally conclusions of thepaper are drawn in Section 5

2 Method

Two modern geodetic techniques developed since the late1980s global positioning system (GPS) and interferometricsynthetic aperture radar (InSAR) have revolutionized theway we observe the Earth surface GPS can provide 3Dinformation at each GPS observation points while InSARcan image the line of sight (LOS) component of deformation

2 Mathematical Problems in Engineering

middot middot middot


RF switch

GPSOEM receiver

Antenna array

Low noiseamplifier

Micro‐processor

Powersupply

Data processingcontrol center

GPSreceiver

Basestation

Datacommunication

Monitoringreport

Databasemanagement

Modelanalysis

Alarm device

Figure 1 Outline of multiantenna GPS system for deformation monitoring

over a large area at spatial resolution of tens of meters [1ndash4]The technology using GPS tomonitor deformation is maturethus we just briefly introduce the multiantenna monitoringsystem aiming at decreasing the device investment

21 GPSMultiantennaMonitoring System GPS is consideredas one of the best techniques for deformation monitoringthanks to its higher automation and lower labor consumingthan that of traditional geodetic survey techniques [5ndash8]Depending on density of the GPS antenna the spatialresolution is low Therefore GPS does have disadvantageswith the major drawback being the high cost associated withplacing a permanent GPS receiver at each monitoring point

The approach of linking a single GPS receiver with multi-ple antennas mounted at several monitoring points has beenimplemented We use a dedicated electronic timed switchingdevice theGPSmultiantenna switch (GMAS) to connect onereceiver with individual antennas This significantly reducesthe number of receivers required thus decreasing hardwareinvestment GMAS has been patented in China (Patent no002198916 Owners Xiufeng He Xiaoli Ding Yongrong SunYongqi Chen et al) The receiver conducts standard pseudo-range and carrier-phase observations for each antenna [9ndash12] It takes efficient advantage of the characteristics ofdeformation survey such as the position of a surveyedpoint which changes relatively little between two consecutive

survey epochs Figure 1 shows the outline of multiantennaGPS system

22 Persistent Scatterers InSAR Time Series InSAR can pro-vide measurements of surface movements at a considerablyimproved spatial resolution with quite high accuracy thatis centimeter or even millimeter level over the whole areaThus repeat-pass satellite InSAR is a rapidly evolving remotesensing technology for observing the Earth surface and nowwell developed with many applications [13ndash18]

Due to the slow surface displacements rate phaseambiguity problems related to temporal and geometricaldecorrelations and strong tropospheric effects it is difficultto obtain reliable measurements of subsidence in denselyvegetated areas using conventional InSAR techniques In thelate 1990s it is noticed that some radar targets maintainstable backscattering characteristics for a period of monthor years and the phase information from these stable targets(hereafter called Persistent Scatterers PS) can be used evenover a long time period This led to the development of PSInSARmethodologies adopting both amplitude stability andcoherence stability (ie correlation) as pixel selection criteria[19ndash21] The persistent scatterers technique is a powerful toolthat overcomes the above-said limitation of routine InSARby simultaneously exploiting all the available SAR imagesgathered during repeated satellite passes

Mathematical Problems in Engineering 3

The deformation was modeled in time and a temporalmodel of evolution was fitted to the double difference phaseduring the process as the phase is unwrapped By takingthe phase difference between nearby persistent scatterercandidates atmospheric and orbit errors are mainly reducedBesides signals lacking in consistency in both space and timedimension are always considered as the atmospheric errorrather than the deformation signal By high-pass filteringthe unwrapped phase in time and low-pass filtering in spacewe estimate the spatially correlated errors Deformation andDEM error contributing to the double difference phase arelatermodeled for thewhole time seriesThe residuals betweenthe model and the double phase signal were considered asthe noise level Then for each persistent scatterer candidatesnetwork adjustment is applied to estimating the noise

Stanford method for persistent scatterers (StaMPS) isused for analyzing crustal deformation in nonurban envi-ronments in this paper Unlike Ferretti method StaMPSproduces a time series of deformation with no prior assump-tions about the temporal nature of deformation Thereforeit can get better performance and be more reliable underthe circumstances of unknown or not readily parameterizeddeformation Here only PS identification and selection stepsof the innovative PS processing method are discussed moredetailed information about the algorithm such as the phaseunwrapping and spatially correlated terms removal can befound in [22]

221 Amplitude Analysis Ferretti et al [19] defined theamplitude dispersion index as

119863119860equiv120590119860

119898119860

(1)

where120590119860and119898

119860are respectively the standard deviation and

the mean of the amplitude values For a constant signal andhigh signal to noise ratio (SNR) 119863

119860asymp 120590Φ where 120590

Φis the

phase standard deviation As lower119863119860indicates higher phase

stability consideration of amplitude is useful both to reducethe number of pixels for phase analysis and to better estimatethe probability of a pixel being a PS The pixels selected as PScandidates have119863

119860le 04 [23]

222 Phase Analysis The residual phase (with flat earth andDEM reference phase removal) Φint of the 119909th pixel in the119894th interferogram can be written as

Φint119909119894 = Φdef 119909119894 + ΔΦ120576119909119894 + Φatm119909119894 + ΔΦorb119909119894 + Φ119899119909119894(2)

where Φdef is the phase change due to the deformation ofthe pixel in the satellite line-of-sight (LOS) direction ΔΦ

120576is

the residual topographic phase due to DEM errorΦatm is thephase equivalent of the difference in atmospheric retardationbetween passes ΔΦorb is the residual phase due to orbitinaccuracies and Φ

119899is the noise term due to variability in

scattering from the pixel thermal noise and coregistrationerrors

The spatially correlated phase is estimated through low-pass adaptive filtering A 5th order Butterworth filter 119871(119909 119910)

with a typical cutoff wavelength of 800m was used as anarrow low-pass filter response The adaptive part of thecombined filter determines the pass band based on thedominant frequencies present in the phase of the pixelsthemselves [20] The response is calculated as

119867(119909 119910) =1003816100381610038161003816119885 (119909 119910)

1003816100381610038161003816 (3)

where 119885 is the smoothed intensity of the 2D FFT Combine119867(119909 119910) with 119871(119909 119910) to form the new filter response

119866 (119909 119910) = 119871 (119909 119910) + 120573(119867(119909 119910)

119867(119909 119910)

minus 1)

120572

(4)

where119867(119909 119910) is the median value of119867(119909 119910) 120572 (typically 1)and 120573 (typically 03) are adjustable weighting parameters

Subtracting the filtered phase value Φint119909119894 from Φint119909119894leaves

Φint119909119894 minus Φint119909119894 = ΔΦ120598119909119894 + Φ119899119909119894 minus Φ1015840

119899119909119894 (5)

The phase error caused by DEM inaccuracies is propor-tional to the perpendicular baseline 119861

perp so

ΔΦ120598119909119894

= 119861perp119909119894

119870120598119909 (6)

where 119870120598is a proportionality constant Substituting this

expression into (6) gives

Φint119909119894 minus Φint119909119894 = 119861perp119909119894119870120598119909 + Φ119899119909119894 minus Φ1015840

119899119909119894 (7)

Using all the available interferograms we can estimate119870120598

for pixel 119909 in a least square sense as this is the only term thatcorrelates with baseline

A measure based on the temporal coherence of pixel 119909 isdefined as

120574119909=1

119873

1003816100381610038161003816100381610038161003816100381610038161003816

119873

sum

119894=1

exp 119895 (Φint119909119894 minus Φint119909119894 minus ΔΦ120576119909119894)

1003816100381610038161003816100381610038161003816100381610038161003816

(8)

where119873 is the number of available interferograms andΔΦ120576119909119894

is the estimate of Φint119909119894 Assuming that Φ1015840119899119909119894

values aresmall 120574

119909is a measure of the phase stability of the pixel and

hence an indicator of whether the pixel is a PS

223 PS Probability The 120574119909values are binned and normal-

ized to get a probability density All pixels are divided into twosets PS pixels and non-PS pixels 119901(120574

119909) is then a weighted

sum of the probability density for the PS pixels 119901PS(120574119909) andthe probability density for the non-PS pixels 119901

119877(120574119909) that is

119901 (120574119909) = 120572119901PS (120574119909) + (1 minus 120572) 119901119877 (120574119909) (9)

where 0 le 120572 le 1 To derive 119901119877(120574119909) 106 pseudo-pixels with

randomphase are simulated that is119882120595119909119894minus119909119894 = exp(119895119877)

where 119877 is a random variable in the interval [minus120587 120587] andfollow the steps described above to arrive at a value of 120574

119909

for each pseudo-pixel We bin these values and normalize


Figure 2 Cracks found on the retaining walls in Hanyuan

the distribution to obtain an estimate for 119901119877(120574119909) For low

values of 120574119909 that is lt03 119901PS(120574119909) asymp 0 which implies that

int

03

0

119901 (120574119909) 119889120574119909= (1 minus 120572)int

03

0

119901119877(120574119909) 119889120574119909 (10)

We use the data to evaluate the integral on the left andthe simulation to evaluate the integral on the right Thus weare able to estimate a conservative value of 120572 For pixel 119909 theprobability that it is a PS is

119875 (119909 isin PS) = 1 minus(1 minus 120572) 119901119877 (120574119909)

119901 (120574119909)

(11)

224 PS Selection After every iteration the new 120574119909

iscompared to the old value to see the changes of 120574

119909 The root-

mean-square of the change are calculated Once the RMS fallsbelow the RMS threshold for example 0005 the solutionshould have converged The selection of PS pixels is based onthe PS probability [21]Theprobability can be calculatedmoreaccurately by considering the amplitude dispersion of thepixels119863

119860119909 as well as 120574

119909 Pixels are binned by119863

119860119909 ensuring

that there are at least 104 pixels in every bin resulting ina number of data probability distributions 119901(120574

119909 119863119860119909) For

each distribution 119901(120574119909 119863119860119909) we estimate 120572(119863

119860119909) If only

pixels with 120574119909above a threshold value 120574thresh(119863

119860119909) are

selected the number of those pixels that are non-PS pixelsis given by

(1 minus 120572 (119863119860119909))int

1

120574thresh

119875119877(120574119909) 119889120574119909 (12)

We choose 120574thresh(119863119860119909) such that the fraction of non-PS

pixels to the total number of chosen pixels is acceptable forour particular application that is

(1 minus 120572 (119863119860119909)) int1

120574thresh 119875119877 (120574119909) 119889120574119909

int1

120574thresh 119875 (120574119909 119863119860119909) 119889120574119909

= 119902 (13)

where 119902 is the maximum fraction of all the selected pixelsthat we will accept to be non-PS pixels (false positives)

We expect 120574119909to decrease with increasing 119863

119860119909 This implies

that as 119863119860119909

increases 119875(120574119909 119863119860119909) will skew more to lower

values of 120574119909 The net effect on 120574thresh(119863

119860119909) is to increase with

increasing 119863119860 Empirically we find that the relationship is

approximately linear that is 120574thresh = 120581119863119860 where 120581 is a

constantWe find the best-fitting 120581 by least-squares inversionand select pixels for which 120574

119909gt 120581119863119860119909

as PS

3 Study Area

31 Site Conditions Three ancient landslides namely Luan-shigang Futang and Kangjiaping were identified by geolo-gists on Luobogang hillock The stability of the hill slopes isadversely affected by the water surface rising and fluctuationin the reservoir Large-scale catastrophic movements may betriggered when the shear stress exceeds the shear resistanceof the material

Hundreds of retaining walls were built to minimizelarge movement of the landslides But cracks were soonobserved on the retaining walls (Figure 2)The displacementsof landslides cause continuous damage to buildings andinfrastructures

32 SAR Data Set The present study used a data set com-posed of 34 images produced by ENVISATASAR systemsspanning the time from September 20 2003 to August14 2010 The ENVISAT ASAR data (descending orbitstrack 61) were provided under the European Space Agency(ESA)-National Remote Sensing Center of China (NRSCC)Dragon cooperation project collected with a nominal radarlook angle of 23∘ DORIS precise orbits data provided bythe ESRIN help desk of ESA were applied to calculat-ing ENVISAT interferometric baselines The 3 arcsecond (sim90m) shuttle radar topography mission (SRTM) DEM datawere used to correct the interferometric phase for topographyat the first step and then for geocoding the C-band SAR data(transforming Range-Doppler coordinates into UniversalTransverse Mercator map geometry system)

The size of the test area is about 12lowast 12 km covering about2926∘ to 2940∘Nand 10253∘ to 10272∘E (Figure 3)The sceneacquired on May 31 2008 is selected as the ldquomasterrdquo image


101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

0 1000 2000 3000 4000 5000

(m)

Figure 3 Location map of Hanyuan County Sichuan The bigger black rectangle indicates the ENVISAT scene footprint (descending orbitstrack 61) used in the PS analysis and the smaller one represents the region of interest in this paper

minus700

minus600

minus500

minus400

minus300

minus200

minus100

0

Perp

endi

cula

r bas

eline

(m)

2003 2004 2005 2006 2007 2008 2009 2010

Year (temporal baseline)

700

800

600

500

400

300

200

100

Figure 4 Perpendicular baseline relative to the ldquomasterrdquo scene plot for the interferometric stack

The maximum temporal baseline is 1715 days and the max-imum normal baseline is about 746m Figure 4 and Table 1show more details about the temporal and perpendic-u-lar baselines

4 Results and Analysis

41 GPS Monitoring System More than 100 monitoringstations are installed in the whole county The 28 continuous

monitoring stations operate 7 lowast 24 hours per week andengineers will periodically check the other 90 stations In keyareas with more buildings the density of GPS monitoringstations is also higher Detailed information about the GPSmonitoring network can be found in [24]

The power to the GPS receivers and data transmissiondevices is supplied by the uninterruptible power system(UPS) at the monitoring sites Although solar panels are allemployed at each site power from the city electricity grid isalways the preferred option when it is available


Table 1 ENVISAT ASAR data set used in the PS time series analysis

Date Temporal baseline (day) Perp baseline (m) Date Temporal baseline (day) Perp baseline (m)20-Sep-2003 minus1715 3545 13-Sep-2008 105 351525-Oct-2003 minus1680 6448 27-Dec-2008 210 minus28429-Nov-2003 minus1645 1723 31-Jan-2009 245 23043-Jan-2004 minus1610 7459 7-Mar-2009 280 351813-Mar-2004 minus1540 7169 11-Apr-2009 315 minus66617-Apr-2004 minus1505 4168 16-May-2009 350 84226-Jun-2004 minus1435 3732 20-Jun-2009 385 403713-Nov-2004 minus1295 6827 25-Jul-2009 420 minus58718-Dec-2004 minus1260 1843 3-Oct-2009 490 minus88526-Feb-2005 minus1190 1181 12-Dec-2009 560 398718-Nov-2006 minus560 6828 16-Jan-2010 595 145827-Jan-2007 minus490 3697 20-Feb-2010 630 118621-Jul-2007 minus315 minus56 27-Mar-2010 665 27723-Nov-2007 minus210 2514 1-May-2010 700 193331-May-2008 0 0 5-Jun-2010 735 23255-Jul-2008 35 2468 10-Jul-2010 770 minus439-Aug-2008 70 2574 14-Aug-2010 805 minus53

Each site needs to transfer massive amount of data to thecontrol center which is located within a town area A publicwireless phone network or other media may be used In thiscase we chose the wireless transmission and 3rd generationtelecommunication technologies

The central servers housed inside the control center areconnected with a local area network (LAN) The controlcenter serves two main functions Firstly it receives themonitoring data verifies the integrity of the data assessesthe status of all the devices and issues control commands tothe field stations Secondly the control center is responsiblefor data analysis storage of processed data deformationmodeling forecast and transmission of information

42 GPS versus Digital Inclinometer in a Landslide CaseThe GPS monitoring system is designed to detect mm levelmovements Figure 5 illustrates the movements on the threecomponents captured by the system in August 2011 Theresult for site TP6-1 showed a significant displacement whichoccurred in August and it became stable again in SeptemberThe site moves by almost 15mm to the north as well as 5mmto the west within 20 days

The engineers periodically collect subsurface deforma-tion data using RST MEMS digital inclinometer system atGPS monitoring stations Measurements were taken alongtwo perpendicular directions both 119860 and 119861 axes from thedepth of 05m to 285m at 05m intervals Figure 6 showsthe comparison between the GPS and digital inclinometerresults on TP6-1 during the unstable period The totaldisplacements at the depth of 05m from inclinometer (whichis the measurement point closest to the ground surface) werecompared with the results obtained from GPS Generally thedisplacement amplitude on the ground surface will be largerthan that in subsurfaceTherefore themagnitude fromdigitalinclinometer is smaller than that from GPS monitoring The

Def

orm

atio

n (m

m)

minus10

minus5

0

5

10

15

612011 712011 812011 912011 1012011Time

TP6-1

X

Y

Z

Figure 5 The movements captured by the landslide monitoringsystem during August 2011

displacement trend and time of occurrence captured by bothmethods match well

Field investigations were conducted shortly after thedisplacement was discovered Construction activities nearsite TP6-1 influenced the stability of the local ground Amound of soil heaped in the south results in much more loadand pressure to the retaining wall We believe that this is themain reason for the monitoring site moving north

Due to page limit detailed information about the GPSmonitoring system established in Hanyuan and the resulttime series is omitted here in this paperThe exhaustive reportand analysis can be found in [24]

43 Time Series InSARResults PubugouHydropower Stationstarted to impound water for the first time on November


Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1

GPSDigital inclinometer

Figure 6 GPS versus digital inclinometer results for the displacement on TP6-1 in August 2011

2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)

Figure 7The new resettlement county Luobogang hillock in the SAR image After completing the hydropower project and water storage areservoir was formed and the old Hanyuan County is now under water

1 2009 The old county no longer existed from then on Inthe mean SAR amplitude image (Figure 7) we can clearlysee the Dadu River and the Luobogang resettlement zone Areservoir named Hanyuan Lake was formed at the locationof the old Hanyuan County

With StaMPS the density of PS identified overmost of theregion was about 20 per km2 (1794 PSs in total excluding thewater area) No PSs were identified in the densely vegetatedarea due to the seasonal cultivation flood irrigation and cropgrowth Even in some parts of urban area (on Luobogang)relatively rare PSs were identified because of the constructionactivities in the resettlement zone which lead to local inter-ferometric phase decorrelation In addition due to the side-looking radar signals the slope and aspect in the mountainareas also have considerable influence on PS detection

Unlike other PS algorithms StaMPS extracts the LOSdeformation via phase unwrapping rather than assuming amodel for how displacement rates vary with time Figure 8demonstrates the LOS deformation time series at Hanyuanduring the period from 2003 to 2010 For the scene predat-ing the ldquomasterrdquo image positive phase implies movementtowards the satellite and vice versa

Based on the unwrapped phase time series mean LOSvelocity of PSs was calculated As shown in Figure 9 thedensity of PS in the southern part of the new county reachedmore than 40 per km2 Due to the construction activitiesrare PSs were detected in downtown Scatterers appearing onall the images were accepted as PS and the ones existed inonly a subset of the data stack were rejected Therefore noscattererswere identified in the old countywhich disappeared


Figure 8 Time series of LOS deformation at Hanyuan spanning from September 2003 to August 2010 referenced temporally to the ldquomasterrdquoscene (May 31 2008) and superimposed on the mean amplitude image

after the water storage Standard deviation of the mean LOSvelocity shows the precision of the linear regression

Overall the mean LOS velocity of the PSs is relativelyslow Several PSs in two typical regions displayed in Figure 10are selected for further analysis

The deformation histories of the PSs (4 PSs in Figure 10upper case and 5 PSs in the lower case) in such a smallregion match well This to a certain degree verified thereliability of the phase unwrapping The average velocities ofthe adjacent PSs in the two cases are about 3mmyear andminus4mmyear respectively It should be noted that the signof the deformation and the velocity implies the movementtowards or away from the satellite on the LOS direction

Without the information of the look angle and aspects of theslope we cannot determine the movement direction (upliftor subsidence) only from the InSAR results This is alsothe main limitation of the InSAR technique which can beimproved by integrating ascendingdescending orbits datafrom multiplatform satellite sensors

The real-time GPS landslide monitoring system of newHanyuan county began trial operation in May 2011 TheENVISAT satellite was brought to a new lower orbit inOctober 2010 The orbital change ends the PS time seriesanalysis using ASAR data Unfortunately no synchronousdata can be collected from the two sources thus verificationbetween GPS and InSAR is impossible

Mathematical Problems in Engineering 9La

titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)

Mean LOS velocity map35

minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)

Standard deviation of mean LOS velocity

04

17

2928

293

2932

2934

2936

2938

(b)

Figure 9 Mean LOS deformation velocity map of the PSs and the standard deviation of mean LOS velocity The units are mmyear withpositive values being towards the satellite along the LOS direction

Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)

Location of selected PSs


minus50

minus40

minus30

minus20

minus10

0

10

20

Jan 03 Jan 04 Dec 04 Dec 05 Dec 08 Dec 09Jan 07 Jan 08Time (mmmyy)

Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371

Figure 10 LOS deformation time series of the selected PSs The red lines indicate linear trends

5 Concluding Remarks

The measurement of ground surface movements overHanyuan is one of the important field monitoring activitieswhich would provide advance warning against sudden fail-ures A real-time landslide monitoring system using GPS in

new Hanyuan County is now in normal operation The com-parison between GPS and digital inclinometer results showsa high consistency in respect of the displacement trend Thissuggests that the GPS monitoring system can be employed asa complement to the traditional ground movement monitor-ing methods


New Hanyuan County is not an ideal environment forthe application of conventional InSAR technique becauseof its dense vegetation cover high soil moisture contentand humidity and the active constructions over the pastyears However the persistent scatterer InSAR approachcan overcome the problems and the time series of surfacedisplacements show various patterns and magnitudes ofdeformation in the resettlement zone

GPS provides 3D information at relatively sparse obser-vation points while InSAR captures LOS deformation on asurface (in effect as for PS approach the ldquosurfacerdquo refers todenser points) with wide coverage Therefore it is obviousthat the two techniques are complementary Unfortunatelyneither ENVISAT ASAR nor ALOS PALSAR satellite datacan be synchronous with the ground GPSmonitoring resultsNevertheless the historical information obtained via InSARtechnique using archived scenes cannot be replicated

Acknowledgments

Thiswork is supported by theNational Natural Science Foun-dation of China (Grant nos 41274017 41204002 4130144940974001 and 50579013) the Key Technology RampD Programof Jiangsu Province (Grant no BE2010316) FundamentalResearch Funds for the Central Universities (Grant no2010B14714) Jiangsu Graduate Student Research InnovativeProjects (Grant no CXZZ11 0451) and Open Research Fundof Key Laboratory of Disaster Reduction and EmergencyResponse Engineering of the Ministry of Civil Affairs (Grantno LDRERE20120102) The ENVISAT scenes are obtainedfrom the European Space Agency (ESA) under a Category-1 Proposal no 2774 Ms Zhu Jialursquos help in polishing thelanguage is highly appreciatedmeanwhile the authors wouldlike to thank the anonymous reviewers for their constructivecomments that helped in improving the quality of this paper

References

[1] X He H Luo Q Huang andM He ldquoIntegration of InSAR andGPS for hydraulic engineeringrdquo Science in China E vol 50 no1 pp 111ndash124 2007

[2] M Peyret Y Djamour M Rizza et al ldquoMonitoring of the largeslow Kahrod landslide in Alborz mountain range (Iran) by GPSand SAR interferometryrdquo Engineering Geology vol 100 no 3-4pp 131ndash141 2008

[3] Y Yin W Zheng Y Liu J Zhang and X Li ldquoIntegration ofGPSwith InSAR tomonitoring of the Jiaju landslide in SichuanChinardquo Landslides vol 7 no 3 pp 359ndash365 2010

[4] T-H Yi H-N Li andMGu ldquoRecent research and applicationsof GPS-based monitoring technology for high-rise structuresrdquoStructural Control andHealthMonitoring vol 20 no 5 pp 649ndash670 2013

[5] P PsimoulisM Ghilardi E Fouache and S Stiros ldquoSubsidenceand evolution of the Thessaloniki plain Greece based onhistorical leveling and GPS datardquo Engineering Geology vol 90no 1-2 pp 55ndash70 2007

[6] E M D Souza J F GMonico and A Pagamisse ldquoGPS satellitekinematic relative positioning analyzing and improving thefunctional mathematical model using waveletsrdquo Mathematical

Problems in Engineering vol 2009 Article ID 934524 18 pages2009

[7] T H Yi H N Li and M Gu ldquoExperimental assessment ofhigh-rate GPS receivers for deformation monitoring of bridgerdquoMeasurement vol 46 no 1 pp 420ndash432 2013

[8] T Yi H Li and M Gu ldquoFull-scale measurements of dynamicresponse of suspension bridge subjected to environmental loadsusing GPS technologyrdquo Science China Technological Sciencesvol 53 no 2 pp 469ndash479 2010

[9] Y Chen X Ding D Huang and J Zhu ldquoA multi-antenna GPSsystem for local area deformation monitoringrdquo Earth Planetsand Space vol 52 no 10 pp 873ndash876 2000

[10] X L Ding Development a et al ldquond field testing of a multi-antenna GPS system for deformation monitoringrdquo WuhanUniversity Journal of Natural Sciences vol 8 no 2 pp 671ndash6762003

[11] X He G Yang X Ding and Y Chen ldquoApplication andevaluation of a GPSmulti-antenna system for dam deformationmonitoringrdquo Earth Planets and Space vol 56 no 11 pp 1035ndash1039 2004

[12] XHeD Jia andW Sang ldquoMonitoring steep slopemovement atxiaowan damwith GPSmulti-antennamethodrdquo Survey Reviewvol 43 no 323 pp 462ndash471 2011

[13] P Lu N Casagli F Catani and V Tofani ldquoPersistent scatterersinterferometry hotspot and cluster analysis (PSI-HCA) fordetection of extremely slow-moving landslidesrdquo InternationalJournal of Remote Sensing vol 33 no 2 pp 466ndash489 2012

[14] A M Lubis N Isezaki and T Sato ldquoTwo-dimensional coseis-mic deformation field of the Sumatra-Andaman earthquake2004 Mw 92 derived from synthetic aperture radar observa-tionrdquo Remote Sensing Letters vol 2 no 2 pp 107ndash116 2011

[15] X Ding and W Huang ldquoD-InSAR monitoring of crustaldeformation in the eastern segment of the Altyn Tagh FaultrdquoInternational Journal of Remote Sensing vol 32 no 7 pp 1797ndash1806 2011

[16] W Fu H Guo Q Tian and X Guo ldquoLandslide monitoring bycorner reflectors differential interferometry SARrdquo InternationalJournal of Remote Sensing vol 31 no 24 pp 6387ndash6400 2010

[17] Z Li E J Fielding P Cross and R Preusker ldquoAdvancedInSAR atmospheric correction MERISMODIS combinationand stacked water vapour modelsrdquo International Journal ofRemote Sensing vol 30 no 13 pp 3343ndash3363 2009

[18] Z Li E J Fielding and P Cross ldquoIntegration of InSARtime-series analysis and water-vapor correction for emappingpostseismicmotion after the 2003Bam (Iran) earthquakerdquo IEEETransactions onGeoscience andRemote Sensing vol 47 no 9 pp3220ndash3230 2009

[19] A Ferretti C Prati and F Rocca ldquoPermanent scatterers in SARinterferometryrdquo IEEE Transactions on Geoscience and RemoteSensing vol 39 no 1 pp 8ndash20 2001

[20] A Hooper H Zebker P Segall and B Kampes ldquoA newmethod for measuring deformation on volcanoes and othernatural terrains using InSAR persistent scatterersrdquo GeophysicalResearch Letters vol 31 no 23 pp 1ndash5 2004

[21] A Hooper P Segall and H Zebker ldquoPersistent scattererinterferometric synthetic aperture radar for crustal deformationanalysis with application to Volcan Alcedo Galapagosrdquo Journalof Geophysical Research B vol 112 no 7 Article IDB07407 2007

[22] A J Hooper Persistent Scatterer Radar Interferometry forCrustal Deformation Studies andModeling of Volcanic Deforma-tion Stanford University 2006


[23] A J Hooper ldquoA multi-temporal InSAR method incorporatingboth persistent scatterer and small baseline approachesrdquo Geo-physical Research Letters vol 35 no 16 Article ID L16302 2008

[24] R Xiao and X He ldquoReal-time landslidemonitoring of Pubugouhydropower resettlement zone using continuous GPSrdquo NaturalHazards vol 69 no 3 pp 1647ndash1660 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of




RF switch

GPSOEM receiver

Antenna array

Low noiseamplifier

Micro‐processor

Powersupply

Data processingcontrol center

GPSreceiver

Basestation

Datacommunication

Monitoringreport

Databasemanagement

Modelanalysis

Alarm device

Figure 1 Outline of multiantenna GPS system for deformation monitoring

over a large area at spatial resolution of tens of meters [1ndash4]The technology using GPS tomonitor deformation is maturethus we just briefly introduce the multiantenna monitoringsystem aiming at decreasing the device investment

21 GPSMultiantennaMonitoring System GPS is consideredas one of the best techniques for deformation monitoringthanks to its higher automation and lower labor consumingthan that of traditional geodetic survey techniques [5ndash8]Depending on density of the GPS antenna the spatialresolution is low Therefore GPS does have disadvantageswith the major drawback being the high cost associated withplacing a permanent GPS receiver at each monitoring point

The approach of linking a single GPS receiver with multi-ple antennas mounted at several monitoring points has beenimplemented We use a dedicated electronic timed switchingdevice theGPSmultiantenna switch (GMAS) to connect onereceiver with individual antennas This significantly reducesthe number of receivers required thus decreasing hardwareinvestment GMAS has been patented in China (Patent no002198916 Owners Xiufeng He Xiaoli Ding Yongrong SunYongqi Chen et al) The receiver conducts standard pseudo-range and carrier-phase observations for each antenna [9ndash12] It takes efficient advantage of the characteristics ofdeformation survey such as the position of a surveyedpoint which changes relatively little between two consecutive

survey epochs Figure 1 shows the outline of multiantennaGPS system

22 Persistent Scatterers InSAR Time Series InSAR can pro-vide measurements of surface movements at a considerablyimproved spatial resolution with quite high accuracy thatis centimeter or even millimeter level over the whole areaThus repeat-pass satellite InSAR is a rapidly evolving remotesensing technology for observing the Earth surface and nowwell developed with many applications [13ndash18]

Due to the slow surface displacements rate phaseambiguity problems related to temporal and geometricaldecorrelations and strong tropospheric effects it is difficultto obtain reliable measurements of subsidence in denselyvegetated areas using conventional InSAR techniques In thelate 1990s it is noticed that some radar targets maintainstable backscattering characteristics for a period of monthor years and the phase information from these stable targets(hereafter called Persistent Scatterers PS) can be used evenover a long time period This led to the development of PSInSARmethodologies adopting both amplitude stability andcoherence stability (ie correlation) as pixel selection criteria[19ndash21] The persistent scatterers technique is a powerful toolthat overcomes the above-said limitation of routine InSARby simultaneously exploiting all the available SAR imagesgathered during repeated satellite passes





119863119860equiv120590119860

119898119860

(1)

where120590119860and119898



119860asymp 120590Φ where 120590

Φis the



119860le 04 [23]




120576is






119867(119909 119910) =1003816100381610038161003816119885 (119909 119910)

1003816100381610038161003816 (3)


119866 (119909 119910) = 119871 (119909 119910) + 120573(119867(119909 119910)

119867(119909 119910)

minus 1)

120572

(4)




119899119909119894 (5)


perp so

ΔΦ120598119909119894

= 119861perp119909119894

119870120598119909 (6)




119899119909119894 (7)




120574119909=1

119873

1003816100381610038161003816100381610038161003816100381610038161003816

119873

sum

119894=1


1003816100381610038161003816100381610038161003816100381610038161003816

(8)










119877(120574119909) that is

119901 (120574119909) = 120572119901PS (120574119909) + (1 minus 120572) 119901119877 (120574119909) (9)




119909






int

03

0

119901 (120574119909) 119889120574119909= (1 minus 120572)int

03

0

119901119877(120574119909) 119889120574119909 (10)



119901 (120574119909)

(11)



119909 The root-


119860119909 as well as 120574


119860119909 ensuring


119909 119863119860119909) For


119860119909) If only


119860119909) are


(1 minus 120572 (119863119860119909))int

1

120574thresh

119875119877(120574119909) 119889120574119909 (12)



(1 minus 120572 (119863119860119909)) int1

120574thresh 119875119877 (120574119909) 119889120574119909

int1

120574thresh 119875 (120574119909 119863119860119909) 119889120574119909

= 119902 (13)




that as 119863119860119909







119909gt 120581119863119860119909

as PS

3 Study Area






101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

0 1000 2000 3000 4000 5000

(m)


minus700

minus600

minus500

minus400

minus300

minus200

minus100

0

Perp

endi

cula

r bas

eline

(m)

2003 2004 2005 2006 2007 2008 2009 2010


700

800

600

500

400

300

200

100














Def

orm

atio

n (m

m)

minus10

minus5

0

5

10

15

612011 712011 812011 912011 1012011Time

TP6-1

X

Y

Z







Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1



2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)














titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119863119860equiv120590119860

119898119860

(1)

where120590119860and119898



119860asymp 120590Φ where 120590

Φis the



119860le 04 [23]




120576is






119867(119909 119910) =1003816100381610038161003816119885 (119909 119910)

1003816100381610038161003816 (3)


119866 (119909 119910) = 119871 (119909 119910) + 120573(119867(119909 119910)

119867(119909 119910)

minus 1)

120572

(4)




119899119909119894 (5)


perp so

ΔΦ120598119909119894

= 119861perp119909119894

119870120598119909 (6)




119899119909119894 (7)




120574119909=1

119873

1003816100381610038161003816100381610038161003816100381610038161003816

119873

sum

119894=1


1003816100381610038161003816100381610038161003816100381610038161003816

(8)










119877(120574119909) that is

119901 (120574119909) = 120572119901PS (120574119909) + (1 minus 120572) 119901119877 (120574119909) (9)




119909






int

03

0

119901 (120574119909) 119889120574119909= (1 minus 120572)int

03

0

119901119877(120574119909) 119889120574119909 (10)



119901 (120574119909)

(11)



119909 The root-


119860119909 as well as 120574


119860119909 ensuring


119909 119863119860119909) For


119860119909) If only


119860119909) are


(1 minus 120572 (119863119860119909))int

1

120574thresh

119875119877(120574119909) 119889120574119909 (12)



(1 minus 120572 (119863119860119909)) int1

120574thresh 119875119877 (120574119909) 119889120574119909

int1

120574thresh 119875 (120574119909 119863119860119909) 119889120574119909

= 119902 (13)




that as 119863119860119909







119909gt 120581119863119860119909

as PS

3 Study Area






101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

0 1000 2000 3000 4000 5000

(m)


minus700

minus600

minus500

minus400

minus300

minus200

minus100

0

Perp

endi

cula

r bas

eline

(m)

2003 2004 2005 2006 2007 2008 2009 2010


700

800

600

500

400

300

200

100














Def

orm

atio

n (m

m)

minus10

minus5

0

5

10

15

612011 712011 812011 912011 1012011Time

TP6-1

X

Y

Z







Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1



2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)














titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













int

03

0

119901 (120574119909) 119889120574119909= (1 minus 120572)int

03

0

119901119877(120574119909) 119889120574119909 (10)



119901 (120574119909)

(11)



119909 The root-


119860119909 as well as 120574


119860119909 ensuring


119909 119863119860119909) For


119860119909) If only


119860119909) are


(1 minus 120572 (119863119860119909))int

1

120574thresh

119875119877(120574119909) 119889120574119909 (12)



(1 minus 120572 (119863119860119909)) int1

120574thresh 119875119877 (120574119909) 119889120574119909

int1

120574thresh 119875 (120574119909 119863119860119909) 119889120574119909

= 119902 (13)




that as 119863119860119909







119909gt 120581119863119860119909

as PS

3 Study Area






101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

0 1000 2000 3000 4000 5000

(m)


minus700

minus600

minus500

minus400

minus300

minus200

minus100

0

Perp

endi

cula

r bas

eline

(m)

2003 2004 2005 2006 2007 2008 2009 2010


700

800

600

500

400

300

200

100














Def

orm

atio

n (m

m)

minus10

minus5

0

5

10

15

612011 712011 812011 912011 1012011Time

TP6-1

X

Y

Z







Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1



2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)














titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

101∘36

998400102

∘00

998400102

∘24

998400102

∘48

998400103

∘12

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

30∘00

998400

29∘36

998400

29∘12

998400

28∘48

998400

0 1000 2000 3000 4000 5000

(m)


minus700

minus600

minus500

minus400

minus300

minus200

minus100

0

Perp

endi

cula

r bas

eline

(m)

2003 2004 2005 2006 2007 2008 2009 2010


700

800

600

500

400

300

200

100














Def

orm

atio

n (m

m)

minus10

minus5

0

5

10

15

612011 712011 812011 912011 1012011Time

TP6-1

X

Y

Z







Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1



2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)














titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Def

orm

atio

n (m

m)

minus10

minus5

0

5

10

15

612011 712011 812011 912011 1012011Time

TP6-1

X

Y

Z







Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1



2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)














titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Tota

l def

orm

atio

n (m

m)

0

5

10

15

20

5252011 6242011 7242011 8232011 9222011 10222011Time

TP6-1



2926

2940

Latit

ude (

∘N

)

10253 10272

Longitude (∘E)














titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















titud

e (∘N

)

10255 1026 10265 1027

Longitude (∘E)


minus48

(mm

yr)

2928

293

2932

2934

2936

2938

(a)

Latit

ude (

∘N

)

10255 1026 10265 1027

Longitude (∘E)

(mm

yr)


04

17

2928

293

2932

2934

2936

2938

(b)


Latit

ude (

∘N

)La

titud

e (∘N

)

1026445 102645 1026455

Longitude (∘E)

Longitude (∘E)



minus50

minus40

minus30

minus20

minus10

0

10

20


Def

orm

atio

n (m

m)

Def

orm

atio

n (m

m)

minus40

minus30

minus20

minus10

10

0

20

30

40


29291

292914

292918

292922

292926

102678 1026785 102679

293361

293363

293365

293367

293369

293371








Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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