Sciences of Geodesy – I

Guochang XuEditor

Sciences of Geodesy – I

Advances and Future Directions

123

EditorDr. Guochang XuGFZ German Research Centre for GeosciencesDepartment 1: Geodesy and Remote SensingTelegrafenberg14473 PotsdamGermanyxu@gfz-potsdam.de

ISBN 978-3-642-11740-4 e-ISBN 978-3-642-11741-1DOI 10.1007/978-3-642-11741-1Springer Heidelberg Dordrecht London New York

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Preface

This series of reference books describes sciences of different fields in and aroundgeodesy with independent chapters. Each chapter covers an individual field anddescribes the history, theory, objective, technology, development, highlights ofresearch and applications. In addition, problems as well as future directions arediscussed. The subjects of this reference book include Absolute and RelativeGravimetry, Adaptively Robust Kalman Filters with Applications in Navigation,Airborne Gravity Field Determination, Analytic Orbit Theory, Deformation andTectonics, Earth Rotation, Equivalence of GPS Algorithms and its Inference, MarineGeodesy, Satellite Laser Ranging, Superconducting Gravimetry and SyntheticAperture Radar Interferometry. These are individual subjects in and around geodesyand are for the first time combined in a unique book which may be used for teachingor for learning basic principles of many subjects related to geodesy. The material issuitable to provide a general overview of geodetic sciences for high-level geodeticresearchers, educators as well as engineers and students. Some of the chapters arewritten to fill literature blanks of the related areas. Most chapters are written bywell-known scientists throughout the world in the related areas.

The chapters are ordered by their titles. Summaries of the individual chapters andintroductions of their authors and co-authors are as follows.

Chapter 1 “Absolute and Relative Gravimetry” provides an overview of thegravimetric methods to determine most accurately the gravity acceleration at givenlocations. The combination of relative and absolute gravimeters allows the survey-ing of local, regional and global networks which can be used to monitor short-termand long-term gravity variations. As an example of the present state-of-the-art abso-lute and relative gravimeters, the main characteristics and accuracy estimates for theHannover instruments are presented. The observational g-values are reduced for thetime-dependent and position-dependent gravity variations due to Earth’s body andocean tides, atmospheric mass redistributions and polar motion. Usually hydrologi-cal effects are not reduced but they may become a target signal to monitor changes inaquifers and deep water reservoirs. The gravimetric surveying of the crustal defor-mation in northern Europe is still a main focus of the ongoing absolute gravimetryactivities. It serves to study the postglacial isostatic adjustment of Fennoscandia.

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The author of Chap. 1 is Dr. Ludger Timmen. Ludger Timmen works atthe Leibniz Universität Hannover (LUH), Germany, where he has lectured ingravimetry since 2005 (since 1996 as a guest lecturer). He holds a Dipl.-Ing. degreein surveying engineering and obtained a Ph.D. from the University of Hannover(now LUH) in 1994. As a research assistant at the Institut für Erdmessung (IfE)of LUH, he specialised in precise gravimetry and its application to geodynamicresearch (tectonics, Earth tides). From 1995 to 1999, he held a scientist position atGFZ Potsdam, the German geoscience research center, focussing on airborne gravi-metric techniques and coordinating the international airborne gravimetry projectsof GFZ. Back at IfE since 2002, his main research interest is the improvement andapplication of relative and absolute gravimetry to measure small temporal gravityvariations on the timescale from some days to a few decades. He organized and per-formed various gravimetry campaigns in China, South America and northern Europeand participated in two German Antarctic expeditions.

In Chap. 2 “Adaptively Robust Kalman Filters with Applications in Navigation”,the main achievements of the adaptively robust filter are summarized from the pub-lished papers in recent years. In Sect. 2.1, the background and developments ofadaptive filters are summarized. The principle of the adaptively robust filter is pre-sented and the estimators are derived in Sect. 2.2. The special cases of the newadaptively filter are also given. In Sect. 2.3, the properties of the adaptive Kalmanfilter are analysed. After that the establishment of four kinds of learning statistics forjudging the kinematic model errors, which include state discrepancy statistic, pre-dicted residual statistic, variance component ratio statistic and velocity discrepancystatistic are given in Sect. 2.4. And in Sect. 2.5, four adaptive factors for balancingthe contribution of kinematic model information and measurements are presented,which include three-segment function, two-segment function, exponential functionand zero and one function for state component adaptation. In Sect. 2.6, two fad-ing filters and adaptively robust filter are compared and computation examples areincluded. In Sect. 2.7, the Sage adaptive filter and an adaptively robust filter are alsocompared; the problems of the Sage adaptive filter are analysed. The last sectionpresents some application examples of the adaptively robust filter.

The author of Chap. 2 is Prof. Yuanxi Yang. Yuanxi Yang, Academician ofChinese Academy of Science, is a professor. He graduated in Geodesy in 1980 and1987 from the Zhengzhou Institute of Surveying and Mapping (ZISM) with BSc andMSc degrees. He obtained his doctorate from Institute of Geodesy and Geophysics,the Chinese Academy of Science, in 1991. He worked as associate professor andprofessor in ZISM from 1990 to 1992 and from 1992 to 1998, respectively. He hasbeen a deputy director and chief engineer of Xi’an RISM since 1998. He was a vis-iting scholar of Center for Space Research of University of Texas, USA in 1995.From 1996 to 1997 he was a scientist in Institute of Theoretical Geodesy of BonnUniversity in Germany under a Humboldt fellowship. He is a member of ChineseUnion of Geodesy and Geophysics since 1997, second secretary of Section IV, IAGfrom 1999 to 2003, and member of ICCT, IAG since 1999. His main research fieldincludes geodetic data processing, navigation and geodetic coordinate system, etc.

Preface vii

He has published more than 100 papers on robust estimation and adaptive Kalmanfiltering.

Chapter 3 “Airborne Gravity Field Determination” outlines some of the basicprinciples of airborne gravimetry, with special focus on geodetic applications, andgives some examples from recent large-scale surveys. For geodesy, the main focusis more on absolute accuracy and long-wavelength stability, since long-wavelengtherrors in gravity transforms to large geoid errors; for geophysical exploration focusis mainly on the short-wavelength performance and ultimately making reliabledetection and mapping of small, elusive gravity signatures. The chapter starts withan introduction and describes principles of airborne gravimetry and filtering tech-nique of airborne gravity. Some results of large-scale government airborne surveysare given in Sect. 3.4 and downward continuation of airborne gravimetry are dis-cussed in Sect. 3.5. Geoid determination and conclusions are given in the sixthsection and the last, respectively.

The author and co-author of Chap. 3 are state scientist Rene Forsberg andDr. Arne V. Olesen.

Rene Forsberg is the state geodesist and head of the Department of Geodynamicsof the National Space Institute of Denmark, formerly known as the Danish NationalSpace Center. He obtained MSc degrees in both geophysics and geodesy fromUniversity of Copenhagen during 1980s before joining the Danish Geodetic Instituteas research geodesist with working fields as gravimetry, satellite geodesy andGreenland survey projects. From 1983 to 1984 he was a visiting scientist of OhioState University and University of Calgary (1984–1985). Rene Forsberg has beenan external lecturer at University Copenhagen since 1989. He is a project coordina-tor or participant in numerous ESA, EU and research council projects, focusing ongravity field determination or cryosphere measurement. In addition, he is a mem-ber of the scientific advisory board for the ESA Cryosat mission, chairman of theIAG International Gravity Field Service, the vice president of the InternationalGravity and Geoid Commission and a member of the International Associationof Geodesy Restructuring Committee since 1999. He was elected as the chair-man of IAG Special Working Group “Local Gravity Field Modelling” (1987–1995)and appointed as section president (Gravity field Determination) of IAG (1995–1999). Rene Forsberg is a world-renowned scientist in the field of aerogravimetry.Several PhD studies were completed under his supervision and he is the author andco-author of more than 250 scientific papers in journals, proceedings and reports.

Arne V. Olesen is a senior scientist in National Space Institute of Denmark.He obtained his doctorate 2001 in University of Copenhagen and worked as sci-entist in National Survey and Cadastre, Denmark, since 1997. He has been workingvery intensively on aerogravimetry research and field campaigns as well as GPSinvestigation since many years and authored and co-authored many scientific papers.

The Chap. 4 “Analytic Orbit Theory” describes the satellite orbit theory in a con-densed way. The perturbed equations of satellite motion are discussed first. Thensingularity-free and simplified equations are given. The solutions of extraterrestrial

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disturbances such as solar radiation pressure, atmospheric drag and the disturbanceof the sun, the moon and planets are then outlined. Solutions of geopotential dis-turbances are given with examples. Numerical and analytical orbit determination isdealt with before the summary and discussions.

I (Guochang Xu) am the author of Chap. 4. After graduating in mathemat-ics and geodesy from Wuhan University and the Chinese Academy of Sciences(CAS) in 1982 and 1984, respectively, I obtained Dr.-Ing. degree from the TechnicalUniversity (TU) Berlin in 1992. Having worked as a research associate at the TUBerlin from 1986 to 1993, as a scientist at the GeoForschungsZentrum (GFZ)Potsdam from 1993 to 1998 and as a senior scientist at the National Survey andCadastre, Denmark, from 1998 to 1999, I returned to the GFZ as a senior scientistin 1999. I have been involved in geodetic research since 1983 and have authored andco-authored several scientific books and software. From 2003 to 2008 I was an over-seas assessor, adjunct professor and winner of overseas outstanding scholar fund ofCAS. I am an adjunct professor of ChangAn University since 2003, overseas com-munication assessor of Education Ministry China since 2005, an adjunct professorof National Time Service Center, CAS, since 2009 and national distinguished expertof China Academy of Space Technology since 2010.

The Chap. 5 “Deformation and Tectonics” addresses some aspects of the useof the GPS system in the study of plate tectonics. After a short summary on theevolution of models of the angular velocities of plate tectonics using geophys-ical, geological and geodetic data, the best methodologies to define a referenceframe using GPS base stations are explained and the problem of mapping theGPS solutions to accurately obtain the position of a station with respect to themost recent International Terrestrial Reference Frame solution (ITRFxxxx) is dis-cussed in Sect. 5.3. In the next section, the geophysical signals that need to besubtracted from the GPS observations to clearly distinguish the secular tectonicplate motion are referred. In Sect. 5.5 the problem of estimating the plate motionusing those preprocessed GPS time-series is described. The contribution of theGPS technique to unravel the geodynamics features of a plate boundary zone isexemplified using research carried out in the Azores Triple Junction region. Theimportance of a full integration of all available GPS data, both continuous andepisodic, possible evolutions in the exploitation of the GNSS technology, includingthe benefits of a multi-technique approach, as well as the need for a proper inte-gration of geodetic, geophysical and geological information are stressed in the lastsection.

The author and co-authors of Chap. 5 are Dr. Luisa Bastos, Dr. Machiel Bos andDr. Rui Manuel Fernandes.

Luisa Bastos is a senior researcher at the University of Porto and since 1997director of the Astronomical Observatory of the Faculty of Sciences. Since 2002she is a member of CIIMAR (Centre of Marine and Environmental Research of theUniversity of Porto). She graduated as surveying engineer in 1976 at the Universityof Porto where she received a Ph.D. degree in 1991 with a work focused on GPSapplication to geodynamics. Her main interest is on precise GNSS applications and

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in the last 20 years she has been involved not only in projects related with geody-namics studies, but also in the development of applications based in the integrationof GNSS with other sensors and its exploitation for airborne, terrestrial and marineapplications, namely airborne gravimetry and mobile mapping. She has been super-vising or co-supervising M.Sc. and Ph.D. thesis on these topics. From 1999 to 2004she acted as president of the WEGENER project and is presently a member of theWEGENER inter-commission. She is currently working on research projects thatinvolve the exploitation of satellite-based systems and multi-sensor integration forgeodynamics studies, environmental monitoring and coastal dynamics.

Machiel Bos studied aerospace engineering at Delft University of Technology,The Netherlands. After his graduation in 1996 he performed his Ph.D. researchat Proudman Oceanographic Laboratory, Liverpool, United Kingdom. In 2001 hespent 7 months as post-doc at Onsala Space Observatory, Sweden. From 2001 to2003 he worked as a post-doc at the Faculty of Geodesy of Delft University ofTechnology. From 2003 to 2008 he held a post-doc position at the AstronomicalObservatory of Porto, Portugal, and he is working at CIIMAR since 2008 (Centre ofMarine and Environmental Research of the University of Porto). His main scientificinterests are ocean tide loading, GPS time-series analysis and the geoid.

Rui Manuel Fernandes has a doctoral degree in earth and space sciences fromTechnical University of Delft (The Netherlands). He is assistant professor in theUniversity of Beira Interior (UBI), Covilhã, Portugal, and associated researcherof Institute Geophysical Infante D. Luíz (IDL), Lisbon, Portugal. He is the headof SEGAL (Space & Earth Geodetic Analysis Laboratory), a collaborative projectbetween UBI and IDL. He has been an active researcher in the use of GNSS for mon-itoring geophysical signals and for the definition of reference frames. In this respect,he has published several papers at peer-reviewed international journals and he ismember of technical and scientific committees of EUREF and AFREF (Europeanand African Reference Frames).

Chapter 6 “Earth Rotation” provides an overview of the state-of-the-art theoret-ical and observational aspects on Earth rotation. It is organised in five parts. Thefirst section describes theoretical foundations of space-fixed and Earth-fixed refer-ence systems, their mutual relation and the consequences of the implementation ofthe new IAU2000 resolutions. The second and third sections describe the results ofastrometric and space geodetic observations of polar motion and length-of-day vari-ations, respectively. The presented time-series are analysed in time and space withregard to signatures of gravitational and other geophysical processes in the Earthsystem. The fourth section deals with the physical foundations of Earth rotationmodels that are based on the balance of angular momentum in the Earth system.After theoretical considerations, various approaches for numerical Earth rotationmodels are presented. In Sect. 6.5, the chapter concludes with a discussion of therelation between modelled and observed variations of Earth rotation.

The author and co-author of Chap. 6 are Prof. Florian Seitz and Prof. HaraldSchuh.

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Florian Seitz studied geodesy at the Technische Universität München (TUM),Germany. After his graduation in the year 2000 he joined the DeutschesGeodätisches Forschungsinstitut (DGFI) in Munich, where he collaborated in var-ious projects in the fields of Earth rotation, gravity field and surface geometry. Inaddition to theoretical studies, his main focus during his time at DGFI was the devel-opment of a numerical Earth system model for the simulation of atmospheric andhydrospheric effects on Earth rotation and gravity field, for which he obtained hisdoctorate from the TUM with distinction in 2004. During 2006 he joined NASA’sJet Propulsion Laboratory, Pasadena, USA, for a research visit for several months.He returned to the TUM as a professor for Earth Oriented Space Science andTechnology in 2007. His main scientific interest is the integrated analysis of dataof Earth observation satellites and space geodetic techniques and their applicationfor numerical studies and models of the Earth system. At present he is chair of thestudy group SG-3 “Configuration Analysis of Earth Oriented Space Techniques” ofIAG’s Inter-commission Committee on Theory (2007–2011) and secretary of IAUCommission 19 ‘Rotation of the Earth’ (2009–2012).

Harald Schuh is a full professor and Director of the Institute of Geodesy andGeophysics, Vienna University of Technology, Austria. Major areas of scientificinterest are very long baseline interferometry (VLBI), Earth rotation, investigationsof the troposphere and ionosphere. He graduated in 1979 from Bonn University,Germany and received his PhD in 1986. He occupied the following positions:Scientific assistant and associate professor at Bonn University (1980–1988); pro-gram scientist at the German Air and Space Agency (1989–1995); senior scientistand head of the Earth Rotation Division at DGFI, Munich (1995–2000); chair ofthe IVS Directing Board since 2007; president of IAU Commission 19 “Rotationof the Earth” (2009–2012); president of the Austrian Geodetic Commission since2008 and president of the Austrian National Committee of the IUGG since 2009;member of the IAG executive committee and of various directing and governingboards; editorial board of the Journal of Geodesy (2003–2007); served as president,chair, member or consultant of various commissions, sub-commissions and workinggroups in geodesy (IAG) and astronomy (IAU); coordinator of the German ResearchGroup on Earth Rotation (1999–2003); supervisor, co-supervisor, or examinator ofmore than 20 dissertations.

Chapter 7 is entitled “Equivalence of GPS Algorithms and its Inference”. Theequivalence principle of differential and un-differential GPS algorithms, combinedand un-combined GPS algorithms as well as their mixtures are discussed. The prin-ciple can be alternatively argued as follows. As soon as the GPS data are measured,the information contents of the data are definitive ones. If the model used is the sameand the principle of the adjustment and filtering is also the same, the obtained resultsshould be equivalent. Advantages and disadvantages of different algorithms are rel-ative and balanced. Based on the equivalence principle, the topic of independentparameterisation of the GPS observation model is discussed which points out wherethe singularity problem comes from. The consequences of the equivalence principleare important beyond the principle itself. The diagonalisation algorithm could be

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extremely useful even for classic adjustment for reducing parameters. Separabilityof any observation equation and its normal equation may lead to an apparentlyunsolvable problem to be solvable or an accumulated one and later solvable one.Optimal criterion for ambiguity search may clear a decade-long confusion of theambiguity searching criterion caused by the so-called LSSA method.

The author and co-authors of Chap. 7 are Dr. Guochang Xu (see Chap. 4), Prof.Yunzhong Shen, Prof. Yuanxi Yang (see Chap. 2), Prof. Heping Sun, Prof. QinZhang, Dr. Jianfeng Guo and Prof. Ta-Kang Yeh.

Yunzhong Shen is a professor in Department of Surveying and Geo-informaticsEngineering of Tongji University. He received his Ph.D. from the Institute ofGeodesy and Geophysics, Chinese Academy of Sciences in 2001. He is now aneditor of “Acta Geodetica et Cartographica Sinica”. His main research interests aretheory of geodetic data processing, satellite positioning and satellite gravimetry.

Heping Sun graduated in geophysics from University of Science and Technologyof China in 1980. He obtained his doctorate from Catholique University of Louvainin Belgium in 1995. Having worked as a research assistant at the Institute ofSeismology of the China Earthquake Prediction Administration in Wuhan from1980 to 1991, Royal Observatory of Belgium from 1991 to 1996, he is a researchprofessor in Institute of Geodesy and Geophysics, Chinese Academy of Sciencessince 1997, and is director of the Institute since February 2005. He has been involvedin gravity research, including theoretical study, data process and its application inGeodynamics; he has authored and co-authored more than 30 research papers.

Qin Zhang graduated in geodesy and survey engineering from Wuhan Universityin 1982 and 1994, respectively. She obtained her doctorate from Wuhan Universityin 2002. Having worked as a lecturer at the Wuhan University from 1982 to 1984and as an associate professor at the Chang’an University, Xian, from 1984 to 2000,she works as a professor and vice dean at the Chang’an University since 2000.Prof. Zhang has been involved in GPS research since 1991 and has authored andco-authored several books. She is also an adjunct professor at Tianjin Institute ofUrban Construction and an editor of some Chinese core journals. Several part-timepositions are held by her, for example, as commissioner for Chinese Society forGeodesy, Photogrammetry and Cartography, executive commissioner and directorfor Society for Geodesy Photogrammetry and Cartography of Shaanxi province.

Jianfeng Guo is an associate professor at Information Engineering University(IEU), China. He obtained a B.Sc. in Mathematics from Xi’an Jiaotong University(XJTU) and an M.Sc. in Geodesy from IEU and a Ph.D. in Geodesy from Instituteof Geodesy & Geophysics, Chinese Academy of Sciences (CAS). His researchinterests include geodesy and GNSS positioning and navigation.

Ta-Kang Yeh graduated in civil engineering and surveying engineering fromNational Chiao Tung University at Taiwan in 1997 and 1999, respectively. Healso obtained his doctorate in geomatics from National Chiao Tung University atTaiwan in 2005. Having worked as an associate engineer at Industrial TechnologyResearch Institute from 2000 to 2005, he has been an assistant professor at ChingYun University since 2005. After working for 4 years he passed the promotion appli-cation and has been an associate professor since 2009. Moreover, he is the CEO of

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e-GPS research center of Ching Yun University from 2008. He has been involvedin GPS research since 1997 and has authored and co-authored several books andpapers. He is also a member of International GNSS Service (IGS), InternationalAssociation of Geodesy (IAG) and American Geophysical Union (AGU).

Chapter 8 “Marine Geodesy” presents an overview of geodetic contributions tothe scope of the marine environment. After a brief introduction to the acquisitionand use of hydrographic data the basic principles of hydroacoustics are presented.The importance of precise navigation is discussed and some examples are explained.The focus is put on the estimation of ship dynamic parameters and the contributionof geodesy to ship dynamics. A newly developed method for ship squat observa-tion is described in detail which provides high precise data that allow discussingthe correlation of trim and squat and furthermore the optimisation of ship under-keel clearance by considering the static trim and the squat-related dynamic trimchange.

The author of Chap. 8 is Prof. Joerg Reinking. Joerg Reinking studied geode-tic engineering at the Technical University (TU) Berlin, Germany, and received hisdiploma in 1988. Since 1988 he has worked as a research associate at TU Berlin andTechnical University (TU) Braunschweig, Germany. He obtained his doctorate fromTU Braunschweig in 1993 and worked as a scientist at the GeoForschungsZentrum(GFZ) Potsdam from 1993 to 1997. Since 1997 he has been a professor of geodesy,adjustment techniques and hydrographic surveying at the Jade University of AppliedSciences in Oldenburg, Germany. During the last decade he was engaged in thedevelopment of geodetic observation and analysis strategies for ship dynamic anal-ysis (squat, trim and roll) and founded the Institute of Metrology and AdjustmentTechniques and is a member of the Institute of Martime Studies in Elsfleth,Germany’s largest nautical school.

Chapter 9 “Satellite Laser Ranging” introduces the reader to this space geodetictechnique and covers the basics of instrumentation, error sources both in the mea-sured and in calculated range, leading up to determination of observed-computedresiduals, which provides an indication of “best-fit” orbit to the observations.Initially a range model is developed, which includes additional signal delays expe-rienced by the transmitted laser pulse due to the atmosphere and general relativity.A description of centre-of-mass correction is given using LAGEOS as an example.Station range and time bias are discussed, highlighting the reasons for range biasvariability while cautioning its application or interpretation as a station error with-out consideration of its diverse constituents. Following the measured range model,a simple orbit and force model are described, which includes the effects of gravityand its temporal changes, n-body perturbations, general relativity, atmospheric drag,solar and Earth radiation pressure as well as empirical forces. A calculated rangemodel is then described, which makes allowance for station position variations dueto solid Earth processes as well as other necessary adjustments. A brief overviewof a typical SLR station is given, using MOBLAS-6 as an example. Operationalaspects are covered with reference to the important role of the International

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Laser Ranging Service (ILRS) and the global network of participating SLRstations.

The author of Chap. 9 is Dr. Ludwig Combrinck. Ludwig Combrinck is emp-loyed at the Hartebeesthoek Radio Astronomy Observatory (HartRAO) locatednear Krugersdorp, South Africa. HartRAO is a facility of the National ResearchFoundation (NRF). Ludwig was awarded a PhD by the University of Cape Townin 2000, his thesis focussed on GNSS applications for precise positioning. Heis responsible for the Space Geodesy Programme at HartRAO, which includesthe NASA satellite laser ranging station, MOBLAS-6. In 2009 he was appointedprofessor-extraordinaire at the University of Pretoria and research associate at theUniversity of South Africa where he lectures part-time. His main research inter-ests currently include applications of space geodetic techniques, reference framedevelopment for Africa and the development of a new high-accuracy satellite andlunar laser ranger for South Africa. His diverse interests in the applications of spacegeodesy have resulted in the establishment of geodetic stations throughout Africa,Marion Island and Antarctica, in collaboration with international partners.

Chapter 10 “Superconducting Gravimetry” is related to measuring, evaluationand interpretation of superconducting gravimeter data. It gives an overview ofthe instrument, the data processing techniques including pre-processing and Earthtide analysis and its application in geodynamics, combined with the correction ofenvironmental influences (atmosphere, hydrosphere and ocean). The correspondingsections of this chapter include the description of the instrument, site selection andobservatory design, calibration of the gravity sensor, noise characteristics, descrip-tion and modelling of the principal constituents of the gravity signal, analysis ofdifferent surface gravity effects, combination of ground-and satellite-derived gravityvariations, co-seismic gravity changes, up to future applications.

The author of Chap. 10 is Dr. Jürgen Neumeyer. Jürgen Neumeyer graduatedin electrical engineering at Technical University Ilmenau in 1965. He obtainedhis first Ph.D. in electrical engineering at University of Ilmenau in 1971 and hissecond Ph.D. in geophysical measurement technique at Academy of Sciences ofGDR in 1989. Since 1978 he has been dealing with geo-sciences. He worked from1978 to 1991 at “Central Institute Physics of the Earth” Potsdam in the fields ofgravimetry, seismology and remote sensing. From 1992 to 2007 he was workingat “GeoForschungZentrum Potsdam” in the field of superconducting- and airborne-gravimetry and GPS. During this time he published his scientific results in severalpapers.

Chapter 11 “Synthetic Aperture Radar Interferometry” introduces the principlesand data processing of the SAR interferometry including differential SAR interfer-ometry, corner reflector SAR interferometry (CR-INSAR) and some of the practicalapplications. In Sect. 11.2 the basics of the SAR imaging are briefly reviewedto understand the SAR imaging process and SAR image feature, which also isthe background of the SAR interferometry. Section 11.3 describes the principleand data processing of the SAR interferometry for digital elevation model (DEM)

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generation. Section 11.4 deals with the differential SAR interferometry. InSect. 11.5 the differential interferometry of the persistent coherent is discussed.

The author of Chapter 11 is Dr. Ye Xia. Ye Xia received the Dr.-Ing. degreein navigation from the University of Stuttgart, Germany, in 1995, the M.S. degreein electrical engineering from Hunan University, China, in 1982, and the B.A.degree in electrical engineering from Shanghai Jiao Tong University, China, in 1968.He is currently a senior scientist at the Geo-Research Center Potsdam, Germany.His research interests include electrocircuit theory, active filter design, imagingand interferometry of the synthetic aperture radar and the INSAR applications ingeography survey and geological disasters monitoring.

The book has been subjected to an individual review of chapters. I am grate-ful to reviewers Prof. Aleksander Brzezinski of the Space Research Centre of thePolish Academy of Sciences, Prof. Wu Chen of HongKong Polytech University,Prof. Alexander Härting of the University of Applied Sciences Oldenburg,Prof. Urs Hugentobler of Technical University Munich, Dr. Corinna Kroner,Dr. Svetozar Petrovic and Dr. Ludwig Grunwaldt of GFZ, Prof. Xiaohui Liof National Time Service Center in Xi’an, Prof. Zhiping Lü and Dr. JianfengGuo of Information Engineering University (IEU) in Zhengzhou, Prof. YunzhongShen of Tonji University in Shanghai, Prof. Heping Sun and Prof. Jikun Ou of theInstitute of Geodesy and Geophysics (IGG) in Wuhan, Dr. Tianhe Xu of GFZ andthe Institute of Surveying and Mapping (ISM) in Xi’an, Prof. Ta-Kang Yeh of ChingYun University of Taiwan, Dr. Walter Zürn of University Karlsruhe. As editor of thisbook I made a general review of the whole book. A grammatical check of technicalEnglish writing has been performed by Springer Heidelberg.

I wish to thank sincerely the key authors of the individual chapters: Dr. LudgerTimmen of University Hannover, Prof. Yuanxi Yang of ISM in Xi’an, state scien-tist Rene Forsberg and Dr. Arne V. Olesen of Danish Space Center in CopenhagenUniversity, Dr. Luisa Bastos and Dr. Machiel Bos of University of Porto, Dr.Rui Manuel Fernandes of University of Beira Interior (UBI), Prof. Florian Seitzof Technische Universität München, Prof. Harald Schuh of Vienna University ofTechnology, Prof. Yunzhong Shen of Tonji University in Shanghai, Prof. HepingSun of IGG in Wuhan, Prof. Qin Zhang of ChangAn University in Xi’an, Dr.Jianfeng Guo of IEU in Zhengzhou, Prof. Ta-Kang Yeh of Ching Yun University ofTaiwan, Prof. Joerg Reinking of University of Applied Sciences in Oldenburg, Dr.Ludwig Combrinck of Hartebeesthoek Radio Astronomy Observatory, Dr. JürgenNeumeyer of Potsdam, Dr. Ye Xia of GFZ. Without their consistent efforts sucha book will be never available. I also wish to thank sincerely scientists who madegreat efforts for enriching this book. They are Prof. Jürgen Kusche of UniversityBonn, Dr. Oscar Colombo of NASA and Prof. Tianyuan Shih of Central Universityof Taiwan.

I wish to thank sincerely the former directors Prof. Dr. Ch. Reigber and Prof.Dr. Markus Rothacher of GFZ for their support and trust during my research activ-ities at the GFZ and for granting me special freedom of research. I also wish tothank sincerely Prof. Yuanxi Yang of ISM in Xi’an, Prof. Qin Zhang of ChangAn

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University in Xi’an, Prof. Heping Sun, Prof. Jikun Ou and Prof. Yunbin Yuan ofIGG in Wuhan for their friendly support by organising the International GeodeticForum Xi’an 2006, which is the origin of the idea to write and edit such a scientificbook. The Chinese Academy of Sciences is thanked for the Outstanding OverseasChinese Scholars Fund, which supported greatly the valuable scientific activities.

Special thanks goes to Springer, Heidelberg; their support and their evaluationfor such a book are preconditions for successfully organizing this publication. I amalso grateful to Dr. Chris Bendall of Springer, Heidelberg, for his valuable advice.

Potsdam, Germany Guochang XuJune 2009

Contents

1 Absolute and Relative Gravimetry . . . . . . . . . . . . . . . . . . 1Ludger Timmen1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Characteristics of Absolute Gravimetry . . . . . . . . . . . . . 2

1.2.1 General Aspects . . . . . . . . . . . . . . . . . . . . 21.2.2 Objectives of Geo-scientific and

State-geodetic Surveys . . . . . . . . . . . . . . . . . 31.3 Measurements with Free-Fall Absolute Gravimeters . . . . . . 5

1.3.1 Principles of FG5 Gravimeters . . . . . . . . . . . . 61.3.2 Observation Equation . . . . . . . . . . . . . . . . . 71.3.3 Operational Procedures with FG5-220 . . . . . . . . 91.3.4 Accuracy and Instrumental Offset . . . . . . . . . . . 12

1.4 Relative Gravimetry . . . . . . . . . . . . . . . . . . . . . . . 181.4.1 Principles of Spring Gravimeters . . . . . . . . . . . 191.4.2 Observation Equation . . . . . . . . . . . . . . . . . 211.4.3 Regional and Local Surveys with Scintrex SC-4492 . 221.4.4 Microgravimetric Measurements . . . . . . . . . . . 261.4.5 Instrumental Drift . . . . . . . . . . . . . . . . . . . 28

1.5 Reduction of Non-tectonic Gravity Variations . . . . . . . . . 301.5.1 Earth’s Body and Ocean Tides . . . . . . . . . . . . . 311.5.2 Polar Motion . . . . . . . . . . . . . . . . . . . . . . 341.5.3 Atmospheric Mass Movements . . . . . . . . . . . . 371.5.4 Groundwater Variations . . . . . . . . . . . . . . . . 38

1.6 Gravity Changes: Examples . . . . . . . . . . . . . . . . . . . 391.6.1 Hydrology: Groundwater Variations in Hannover . . . 391.6.2 Tectonics: Isostatic Land Uplift in Fennoscandia . . . 40

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2 Adaptively Robust Kalman Filters with Applications in Navigation 49Yuanxi Yang2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.2 The Principle of Adaptively Robust Kalman Filtering . . . . . 532.3 Properties of the Adaptive Kalman Filter . . . . . . . . . . . . 56

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xviii Contents

2.3.1 Difference of State Estimate . . . . . . . . . . . . . . 562.3.2 The Expectation of the State Estimate of the

Adaptive Filter . . . . . . . . . . . . . . . . . . . . . 572.3.3 Posterior Precision Evaluation . . . . . . . . . . . . . 58

2.4 Three Kinds of Learning Statistics . . . . . . . . . . . . . . . 602.4.1 Learning Statistic Constructed by State Discrepancy . 602.4.2 Learning Statistic Constructed by Predicted

Residual Vector . . . . . . . . . . . . . . . . . . . . 612.4.3 Learning Statistic Constructed by the Ratio of

Variance Components . . . . . . . . . . . . . . . . . 622.4.4 Learning Statistic Constructed by Velocity . . . . . . 63

2.5 Four Kinds of Adaptive Factors . . . . . . . . . . . . . . . . . 632.5.1 Adaptive Factor by Three-Segment Function . . . . . 632.5.2 Adaptive Factor by Two-Segment Function . . . . . . 642.5.3 Adaptive Factor by Exponential Function . . . . . . . 642.5.4 Adaptive Factor by Zero and One . . . . . . . . . . . 652.5.5 Actual Computation and Analysis . . . . . . . . . . . 66

2.6 Comparison of Two Fading Filters and AdaptivelyRobust Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.6.1 Principles of Two Kinds of Fading Filters . . . . . . . 692.6.2 Comparison of Fading Filter and Adaptive Filter . . . 712.6.3 Actual Computation and Analysis . . . . . . . . . . . 72

2.7 Comparison of Sage Adaptive Filter and AdaptivelyRobust Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 742.7.1 IAE Windowing Method . . . . . . . . . . . . . . . . 742.7.2 RAE Windowing Method . . . . . . . . . . . . . . . 752.7.3 The Problems of the Windowing Estimation

for Covariance Matrix of Kinematic Model . . . . . . 762.8 Some Application Examples . . . . . . . . . . . . . . . . . . 77References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3 Airborne Gravity Field Determination . . . . . . . . . . . . . . . 83Rene Forsberg and Arne V. Olesen3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.2 Principles of Airborne Gravimetry . . . . . . . . . . . . . . . 863.3 Filtering of Airborne Gravity . . . . . . . . . . . . . . . . . . 893.4 Some Results of Large-Scale Government Airborne Surveys . 913.5 Downward Continuation of Airborne Gravimetry . . . . . . . 933.6 Use of Airborne Gravimetry for Geoid Determination . . . . . 96

3.6.1 Case Story of Mongolian Geoid . . . . . . . . . . . . 973.7 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . 102References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4 Analytic Orbit Theory . . . . . . . . . . . . . . . . . . . . . . . . 105Guochang Xu4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Contents xix

4.2 Perturbed Equation of Satellite Motion . . . . . . . . . . . . . 1074.2.1 Lagrangian-Perturbed Equation of Satellite Motion . . 1084.2.2 Gaussian-Perturbed Equation of Satellite Motion . . . 1104.2.3 Keplerian Motion . . . . . . . . . . . . . . . . . . . 112

4.3 Singularity-Free and Simplified Equations . . . . . . . . . . . 1134.3.1 Problem of Singularity of the Solutions . . . . . . . . 1134.3.2 Disturbed Equations in the Case of Circular Orbit . . 1144.3.3 Disturbed Equations in the Case of Equatorial Orbit . 1154.3.4 Disturbed Equations in the Case of Circular

and Equatorial Orbit . . . . . . . . . . . . . . . . . . 1154.3.5 Singularity-Free Disturbed Equations of Motion . . . 1164.3.6 Simplified Singularity-Free Disturbed

Equations of Motion . . . . . . . . . . . . . . . . . . 1174.3.7 Singularity-Free Gaussian Equations of Motion . . . . 117

4.4 Solutions of Extraterrestrial Disturbances . . . . . . . . . . . 1184.4.1 Key Notes to the Problems . . . . . . . . . . . . . . . 1184.4.2 Solutions of Disturbance of Solar Radiation Pressure . 1194.4.3 Solutions of Disturbance of Atmospheric Drag . . . . 1264.4.4 Solutions of Disturbance of the Sun . . . . . . . . . . 1294.4.5 Solutions of Disturbance of the Moon . . . . . . . . . 1344.4.6 Solutions of Disturbance of Planets . . . . . . . . . . 1364.4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . 136

4.5 Solutions of Geopotential Perturbations . . . . . . . . . . . . 1364.6 Principle of Numerical Orbit Determination . . . . . . . . . . 1414.7 Principle of Analytic Orbit Determination . . . . . . . . . . . 1444.8 Summary and Discussions . . . . . . . . . . . . . . . . . . . 147References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

5 Deformation and Tectonics: Contribution of GPSMeasurements to Plate Tectonics – Overview and RecentDevelopments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155Luisa Bastos, Machiel Bos and Rui Manuel Fernandes5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2 Plate Tectonic Models . . . . . . . . . . . . . . . . . . . . . . 1585.3 Mapping Issues . . . . . . . . . . . . . . . . . . . . . . . . . 1625.4 Geophysical Corrections for the GPS-Derived Station Positions 1675.5 Time-Series Analysis . . . . . . . . . . . . . . . . . . . . . . 1695.6 GPS and Geodynamics – An Example . . . . . . . . . . . . . 1745.7 Further Developments . . . . . . . . . . . . . . . . . . . . . . 179References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

6 Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Florian Seitz and Harald Schuh6.1 Reference Systems . . . . . . . . . . . . . . . . . . . . . . . 1866.2 Polar Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.3 Variations of Length-of-Day and �UT . . . . . . . . . . . . . 195

xx Contents

6.4 Physical Model of Earth Rotation . . . . . . . . . . . . . . . . 1986.4.1 Balance of Angular Momentum in the Earth System . 1986.4.2 Solid Earth Deformations . . . . . . . . . . . . . . . 2036.4.3 Solution of the Euler–Liouville Equation . . . . . . . 212

6.5 Relation Between Modelled and Observed Variationsof Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . . 218

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

7 Equivalence of GPS Algorithms and Its Inference . . . . . . . . . 229Guochang Xu, Yunzhong Shen, Yuanxi Yang, Heping Sun,Qin Zhang, Jianfeng Guo and Ta-Kang Yeh7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2307.2 Equivalence of Undifferenced and Differencing Algorithms . . 231

7.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2327.2.2 Formation of Equivalent Observation Equations . . . 2327.2.3 Equivalent Equations of Single Differences . . . . . . 2347.2.4 Equivalent Equations of Double Differences . . . . . 2377.2.5 Equivalent Equations of Triple Differences . . . . . . 2397.2.6 Method of Dealing with the Reference Parameters . . 2407.2.7 Summary of the Unified Equivalent Algorithm . . . . 241

7.3 Equivalence of the Uncombined and Combining Algorithms . 2427.3.1 Uncombined GPS Data Processing Algorithms . . . . 2427.3.2 Combining Algorithms of GPS Data Processing . . . 2447.3.3 Secondary GPS Data Processing Algorithms . . . . . 2467.3.4 Summary of the Combining Algorithms . . . . . . . 249

7.4 Parameterisation of the GPS Observation Model . . . . . . . . 2497.4.1 Evidence of the Parameterisation Problem of

the Undifferenced Observation Model . . . . . . . . . 2507.4.2 A Method of Uncorrelated Bias Parameterisation . . . 2517.4.3 Geometry-Free Illustration . . . . . . . . . . . . . . . 2577.4.4 Correlation Analysis in the Case of

Phase–Code Combinations . . . . . . . . . . . . . . 2587.4.5 Conclusions and Comments on Parameterisation . . . 259

7.5 Equivalence of the GPS Data Processing Algorithms . . . . . 2607.5.1 Equivalence Theorem of GPS Data Processing

Algorithms . . . . . . . . . . . . . . . . . . . . . . . 2607.5.2 Optimal Baseline Network Forming and Data Condition 2637.5.3 Algorithms Using Secondary GPS Observables . . . . 2647.5.4 Non-equivalent Algorithms . . . . . . . . . . . . . . 266

7.6 Inferences of Equivalence Principle . . . . . . . . . . . . . . 2667.6.1 Diagonalisation Algorithm . . . . . . . . . . . . . . . 2667.6.2 Separability of the Observation Equation . . . . . . . 2687.6.3 Optimal Ambiguity Search Criteria . . . . . . . . . . 269

7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Contents xxi

8 Marine Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Joerg Reinking8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2758.2 Bathymetry and Hydrography . . . . . . . . . . . . . . . . . . 276

8.2.1 Scope of Work . . . . . . . . . . . . . . . . . . . . . 2768.2.2 Hydroacoustic Measurements . . . . . . . . . . . . . 281

8.3 Precise Navigation . . . . . . . . . . . . . . . . . . . . . . . 2888.3.1 Maps of Coastal Waters and Approach Channels . . . 2888.3.2 ENC and ECDIS . . . . . . . . . . . . . . . . . . . . 2888.3.3 Ship’s Attitude . . . . . . . . . . . . . . . . . . . . . 2898.3.4 Hydrodynamics of Ships . . . . . . . . . . . . . . . . 291

8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 298References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

9 Satellite Laser Ranging . . . . . . . . . . . . . . . . . . . . . . . . 301Ludwig Combrinck9.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

9.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 3029.1.2 Basic Principles . . . . . . . . . . . . . . . . . . . . 303

9.2 Range Model . . . . . . . . . . . . . . . . . . . . . . . . . . 3069.2.1 Atmospheric Delay Correction . . . . . . . . . . . . 3089.2.2 Centre-of-Mass Correction . . . . . . . . . . . . . . 3119.2.3 SLR Station Range and Time Bias . . . . . . . . . . 3139.2.4 Relativistic Range Correction . . . . . . . . . . . . . 316

9.3 Force and Orbital Model . . . . . . . . . . . . . . . . . . . . 3179.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 3179.3.2 Orbital Modelling . . . . . . . . . . . . . . . . . . . 3189.3.3 Force Model . . . . . . . . . . . . . . . . . . . . . . 318

9.4 Calculated Range . . . . . . . . . . . . . . . . . . . . . . . . 3279.5 SLR System and Logistics . . . . . . . . . . . . . . . . . . . 329

9.5.1 System Configuration . . . . . . . . . . . . . . . . . 3299.6 Network and International Collaboration . . . . . . . . . . . . 334

9.6.1 Tracking Network . . . . . . . . . . . . . . . . . . . 3359.6.2 International Laser Ranging Service . . . . . . . . . . 335

9.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

10 Superconducting Gravimetry . . . . . . . . . . . . . . . . . . . . 339Jürgen Neumeyer10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 34010.2 Description of the Instrument . . . . . . . . . . . . . . . . . . 343

10.2.1 Gravity Sensing Unit . . . . . . . . . . . . . . . . . . 34410.2.2 Tilt Compensation System . . . . . . . . . . . . . . . 34610.2.3 Dewar and Compressor . . . . . . . . . . . . . . . . 34610.2.4 Gravimeter Electronic Package . . . . . . . . . . . . 34710.2.5 SG Performance . . . . . . . . . . . . . . . . . . . . 347

xxii Contents

10.3 Site Selection and Observatory Design . . . . . . . . . . . . . 34810.4 Calibration of the Gravity Sensor . . . . . . . . . . . . . . . . 351

10.4.1 Calibration Factor . . . . . . . . . . . . . . . . . . . 35110.4.2 Phase Shift . . . . . . . . . . . . . . . . . . . . . . . 354

10.5 Noise Characteristics . . . . . . . . . . . . . . . . . . . . . . 35510.5.1 Noise Magnitude . . . . . . . . . . . . . . . . . . . . 35510.5.2 Noise Caused by Misaligned Instrumental Tilt . . . . 357

10.6 Modelling of the Principal Constituents of the Gravity Signal . 35810.6.1 Theoretical Earth Tides and Tidal Acceleration . . . . 36010.6.2 Gravity Variations Induced by the Atmosphere . . . . 36410.6.3 Hydrology-Induced Gravity Variation . . . . . . . . . 37210.6.4 Ocean Tide Loading Gravity Effect . . . . . . . . . . 37810.6.5 Polar Motion . . . . . . . . . . . . . . . . . . . . . . 38110.6.6 Instrumental Drift . . . . . . . . . . . . . . . . . . . 383

10.7 Analysis of Surface Gravity Effects . . . . . . . . . . . . . . . 38310.7.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . 38410.7.2 Earth Tides . . . . . . . . . . . . . . . . . . . . . . . 38510.7.3 Nearly Diurnal-Free Wobble . . . . . . . . . . . . . . 39110.7.4 Polar Motion . . . . . . . . . . . . . . . . . . . . . . 39310.7.5 Free Oscillation of the Earth . . . . . . . . . . . . . . 39310.7.6 Translational Oscillations of the Inner Core

(Slichter Triplet) . . . . . . . . . . . . . . . . . . . . 39510.7.7 Co-seismic Gravity Change . . . . . . . . . . . . . . 39610.7.8 Gravity Residuals . . . . . . . . . . . . . . . . . . . 398

10.8 Combination of Ground (SG) and Space Techniques . . . . . . 39910.8.1 Combination of SG and GPS Measurements . . . . . 40010.8.2 Comparison of SG, GRACE and Hydrological

Models-Derived Gravity Variations . . . . . . . . . . 40010.9 Future Applications . . . . . . . . . . . . . . . . . . . . . . . 405References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

11 Synthetic Aperture Radar Interferometry . . . . . . . . . . . . . 415Ye Xia11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 41611.2 Synthetic Aperture Radar Imaging . . . . . . . . . . . . . . . 417

11.2.1 Radar Transmitted and Received Signal . . . . . . . . 41811.2.2 Impulse Response of SAR . . . . . . . . . . . . . . . 42011.2.3 Pulse Compression (Focus) and Doppler Frequency . 42111.2.4 Spotlight Mode . . . . . . . . . . . . . . . . . . . . 42311.2.5 ScanSAR Mode . . . . . . . . . . . . . . . . . . . . 426

11.3 SAR Interferometry . . . . . . . . . . . . . . . . . . . . . . . 42811.3.1 Principle of SAR Interferometry . . . . . . . . . . . . 42911.3.2 Phase Unwrapping . . . . . . . . . . . . . . . . . . . 43211.3.3 Image Registration . . . . . . . . . . . . . . . . . . . 43811.3.4 Coherence of SAR Images . . . . . . . . . . . . . . . 439

Contents xxiii

11.4 Differential SAR Interferometry . . . . . . . . . . . . . . . . 44011.4.1 Principle of D-INSAR . . . . . . . . . . . . . . . . . 44011.4.2 Persistent Scatterer SAR Interferometry . . . . . . . . 44111.4.3 Example: Coseismic Deformation

Measurement of Bam Earthquake . . . . . . . . . . . 44511.4.4 Example: Subsidence Monitoring in Tianjin Region . 452

11.5 SAR Interferometry with Corner Reflectors (CR-INSAR) . . . 45311.5.1 Orientation of the Corner Reflectors . . . . . . . . . . 45511.5.2 Interpolation Kernel Design and Co-registration . . . 45511.5.3 Phase Pattern of Flat Terrain . . . . . . . . . . . . . . 45611.5.4 Elevation-Phase-Relation Matrix Ch and

Phase Unwrapping . . . . . . . . . . . . . . . . . . . 45811.5.5 Differential Interferogram Modelling . . . . . . . . . 45911.5.6 CR-INSAR Example: Landslide Monitoring

in Three Gorges Area . . . . . . . . . . . . . . . . . 46111.6 High-Resolution TerraSAR-X . . . . . . . . . . . . . . . . . 468References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

Contributors

Luisa Bastos Observatório Astronómico, Faculdade de Ciências, Universidade doPorto, Alameda do Monte da Virgem, 4420-146 V. N. Gaia, Portugal,lcbastos@fc.up.pt

Machiel Bos Centro Interdisciplinar de Investigação Marinha e Ambiental,Universidade do Porto, Rua dos Bragas 289, 4050-123 Porto, Portugal,mbos@ciimar.up.pt

Ludwig Combrinck Space Geodesy Programme, Hartebeesthoek RadioAstronomy Observatory, Krugersdorp 1740, South Africa, ludwig@hartrao.ac.za

Rui Manuel Fernandes Universidade da Beira Interior, Covilhã, Portugal andInstituto Geofísico Infante D. Luíz Lisboa, Portugal, rmanuel@di.ubi.pt

Rene Forsberg National Space Institute, Technical University of Denmark,Juliane Maries Vej 30, Copenhagen 2100, Denmark, rf@space.dtu.dk

Jianfeng Guo Information Engineering University of Zhengzhou, Zhengzhou,P.R. China, jianfeng.guo@gmail.com

Jürgen Neumeyer GeoForschungZentrum Potsdam, Potsdam, GermanyJuergen_Neumy@yahoo.de

Arne V. Olesen National Space Institute, Technical University of Denmark,Juliane Maries Vej 30, Copenhagen 2100, Denmark avo@space.dtu.dk

Joerg Reinking Jade University of Applied Sciences,Wilhelmshaven/Oldenburg/Elsfleth, Germany, reinking@jade-hs.de

Harald Schuh Institute of Geodesy and Geophysics, Vienna Universityof Technology, Wien, Austria, harald.schuh@tuwien.ac.at

Florian Seitz Earth Oriented Space Science and Technology, TechnischeUniversität München (TUM), Arcisstr. 21, D-80333 Munich, Munich, Germany,seitz@bv.tum.de

Yunzhong Shen Department of Surveying and Geomatics, TongJi University,Shanghai 200092, P.R. China, yzshen@mail.tongji.edu.cn

xxv

xxvi Contributors

Heping Sun Institute of Geodesy and Geophysics, CAS, Wuhan 430077, P.R.China, heping@asch.whigg.ac.cn

Ludger Timmen Institut für Erdmessung (IfE), Leibniz Universität Hannover(LUH), Schneiderberg 50, Hannover 30167, Germany,timmen@ife.uni-hannover.de

Ye Xia German Research Centre for Geosciences, Telegrafenberg A17, PotsdamD-14473, Germany, xia@gfz-potsdam.de

Guochang Xu GFZ German Research Centre for Geosciences, Department 1:Geodesy and Remote Sensing, Telegrafenberg, 14473 Potsdam, Germany,xu@gfz-potsdam.de

Yuanxi Yang Xian Research Institute of Surveying and Mapping, Xian 710054,China, yuanxi@pub.xaonline.com

Ta-Kang Yeh Institute of Geomatics and Disaster Prevention Technology, ChingYun University, Jhongli 320, Taiwan, bigsteel@cyu.edu.tw

Qin Zhang Department of Geology and Surveying, ChangAn University, XiAn710054, P.R. China, zhangqinle@263.net.cn