Gravity field refinement by radial basis functions from in-situ satellite data:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
München
Verlag der Bayerischen Akademie der Wissenschaften
2008
Bonn Univ. Bonn, Inst. für Geodäsie und Geoinformation |
| Series: | Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften
Reihe C, Dissertationen ; 676 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zsfassung in dt. Sprache |
| Physical Description: | 137 S. Ill., graph. Darst. Kt. |
| ISBN: | 9783769650884 |
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| adam_text | UNIVERSITATBONN INSTITUT FIIR GEODASIE UND GEOINFORMATION SCHRIFTENREIHE
10 ANNETTE EICKER GRAVITY FIELD REFINEMENT BY RADIAL BASIS FUNCTIONS
FROM IN-SITU SATELLITE DATA CONTENTS 1 INTRODUCTION 7 2 REGIONAL GRAVITY
FIELD RECOVERY USING NEW SATELLITE MISSIONS 9 2.1 OVERVIEW OF THE
SATELLITE MISSIONS CHAMP, GRACE, AND GOCE 9 2.1.1 CHAMP 9 2.1.2 GRACE 10
2.1.3 GOCE 11 2.2 REGIONAL GRAVITY FIELD RECOVERY 12 2.2.1 NEW ANALYSIS
TECHNIQUES FOR THE NEW SATELLITE MISSIONS 12 2.2.2 MOTIVATION FOR
REGIONAL ANALYSIS 14 2.2.3 EXISTING APPROACHES TO REGIONAL GRAVITY FIELD
MODELING 15 3 MODELING OF THE REGIONAL GRAVITY FIELD 17 3.1 FUNDAMENTALS
OF POTENTIAL THEORY 17 3.2 REPRODUCING KERNEL HILBERT SPACE 18 3.3
SPHERICAL HARMONICS 21 3.3.1 MATHEMATICAL DESCRIPTION . . . 21 3.3.2 THE
USE OF SPHERICAL HARMONICS IN GEODESY 23 3.3.3 COVARIANCE FUNCTION ON
THE SPHERE 24 3.3.4 RKHS ON THE SPHERE 26 3.3.5 UPWARD CONTINUATION 28
3.4 SPACE LOCALIZING BASIS FUNCTIONS 28 3.4.1 RADIAL BASIS FUNCTIONS 29
3.4.2 SPHERICAL SPLINES 30 3.4.3 BANDLIMITED SPLINE FUNCTIONS 31 3.4.4
ARRANGEMENT OF THE BASIS FUNCTIONS ON THE SPHERE 32 3.4.5 CONVERGENCE
ISSUES: SUMMARY 34 3.5 POINT DISTRIBUTIONS ON THE SPHERE 36 3.5.1 GRIDS
36 3.5.2 APPLICABILITY AS NODAL POINTS FOR SPLINES 42 3.5.3 RESOLUTION
52 CONTENTS 4 SETTING UP THE OBSERVATION EQUATIONS 54 4.1 LEAST SQUARES
APPROXIMATION 54 4.2 THE GRAVITY FIELD AND ITS FUNCTIONALS IN TERMS OF
SPLINES 55 4.2.1 GRAVITATIONAL POTENTIAL 56 4.2.2 GRAVITY 56 4.2.3
GRAVITY GRADIENT 57 4.3 FUNCTIONAL MODEL 59 4.3.1 PRECISE ORBIT
DETERMINATION 60 4.3.2 LOW-LOW SATELLITE-TO-SATELLITE TRACKING 63 4.3.3
SATELLITE GRAVITY GRADIOMETRY (GOCE) 64 5 SOLVING THE SYSTEM OF
OBSERVATION EQUATIONS 65 5.1 INVERSE PROBLEMS, EL-POSED PROBLEMS 65
5.1.1 EL-POSEDNESS OF THE DOWNWARD CONTINUATION PROCESS 66 5.1.2
SINGULAR VALUE DECOMPOSITION OF THE DESIGN MATRIX 66 5.2 REGULARIZATION
68 5.2.1 TIKHONOV REGULARIZATION 68 5.2.2 REGULARIZATION IN THE FINITE
DIMENSIONAL MODEL 69 5.2.3 REGULARIZATION AND SPLINES 70 5.2.4 VARIANCE
COMPONENT ESTIMATION 73 5.2.5 REGIONALLY ADAPTED REGULARIZATION 74 5.3
RELATIONSHIP BETWEEN SPLINE APPROXIMATION AND COLLOCATION 76 6 FROM
REGIONAL TO GLOBAL GRAVITY FIELDS 78 6.1 CONVERSION FROM A GLOBAL SPLINE
REPRESENTATION TO SPHERICAL HARMONICS 78 6.2 PATCHING OF INDIVIDUAL
REGIONAL SOLUTIONS 79 6.2.1 QUADRATURE METHODS 79 7 CALCULATIONS AND
RESULTS 88 7.1 (REAL) DATA ANALYSIS WITH THE PROGRAMMING SYSTEM GROOPS
88 7.1.1 BACKGROUND MODELS 92 7.2 SIMULATION STUDY: BASIS FUNCTIONS 93
7.3 GRAVITY FIELD SOLUTIONS 95 7.3.1 CHAMP 98 7.3.2 GRACE 103 7.3.3
COMBINATION OF GRACE AND GOCE 108 CONTENTS 8 SUMMARY AND OUTLOOK 113 A
MATHEMATICAL FUNDAMENTALS 116 A.I FUNCTION SPACES 116 A.2 LINEAR
FUNCTIONALS AND LINEAR OPERATORS 118 B DERIVATION OF THE WEIGHTS FOR THE
GAUSS-LEGENDRE QUADRATURE 122 ABBREVIATIONS 124 LIST OF FIGURES 125 LIST
OF TABLES 128 REFERENCES 120
|
| adam_txt |
UNIVERSITATBONN INSTITUT FIIR GEODASIE UND GEOINFORMATION SCHRIFTENREIHE
10 ANNETTE EICKER GRAVITY FIELD REFINEMENT BY RADIAL BASIS FUNCTIONS
FROM IN-SITU SATELLITE DATA CONTENTS 1 INTRODUCTION 7 2 REGIONAL GRAVITY
FIELD RECOVERY USING NEW SATELLITE MISSIONS 9 2.1 OVERVIEW OF THE
SATELLITE MISSIONS CHAMP, GRACE, AND GOCE 9 2.1.1 CHAMP 9 2.1.2 GRACE 10
2.1.3 GOCE 11 2.2 REGIONAL GRAVITY FIELD RECOVERY 12 2.2.1 NEW ANALYSIS
TECHNIQUES FOR THE NEW SATELLITE MISSIONS 12 2.2.2 MOTIVATION FOR
REGIONAL ANALYSIS 14 2.2.3 EXISTING APPROACHES TO REGIONAL GRAVITY FIELD
MODELING 15 3 MODELING OF THE REGIONAL GRAVITY FIELD 17 3.1 FUNDAMENTALS
OF POTENTIAL THEORY 17 3.2 REPRODUCING KERNEL HILBERT SPACE 18 3.3
SPHERICAL HARMONICS 21 3.3.1 MATHEMATICAL DESCRIPTION . . . 21 3.3.2 THE
USE OF SPHERICAL HARMONICS IN GEODESY 23 3.3.3 COVARIANCE FUNCTION ON
THE SPHERE 24 3.3.4 RKHS ON THE SPHERE 26 3.3.5 UPWARD CONTINUATION 28
3.4 SPACE LOCALIZING BASIS FUNCTIONS 28 3.4.1 RADIAL BASIS FUNCTIONS 29
3.4.2 SPHERICAL SPLINES 30 3.4.3 BANDLIMITED SPLINE FUNCTIONS 31 3.4.4
ARRANGEMENT OF THE BASIS FUNCTIONS ON THE SPHERE 32 3.4.5 CONVERGENCE
ISSUES: SUMMARY 34 3.5 POINT DISTRIBUTIONS ON THE SPHERE 36 3.5.1 GRIDS
36 3.5.2 APPLICABILITY AS NODAL POINTS FOR SPLINES 42 3.5.3 RESOLUTION
52 CONTENTS 4 SETTING UP THE OBSERVATION EQUATIONS 54 4.1 LEAST SQUARES
APPROXIMATION 54 4.2 THE GRAVITY FIELD AND ITS FUNCTIONALS IN TERMS OF
SPLINES 55 4.2.1 GRAVITATIONAL POTENTIAL 56 4.2.2 GRAVITY 56 4.2.3
GRAVITY GRADIENT 57 4.3 FUNCTIONAL MODEL 59 4.3.1 PRECISE ORBIT
DETERMINATION 60 4.3.2 LOW-LOW SATELLITE-TO-SATELLITE TRACKING 63 4.3.3
SATELLITE GRAVITY GRADIOMETRY (GOCE) 64 5 SOLVING THE SYSTEM OF
OBSERVATION EQUATIONS 65 5.1 INVERSE PROBLEMS, EL-POSED PROBLEMS 65
5.1.1 EL-POSEDNESS OF THE DOWNWARD CONTINUATION PROCESS 66 5.1.2
SINGULAR VALUE DECOMPOSITION OF THE DESIGN MATRIX 66 5.2 REGULARIZATION
68 5.2.1 TIKHONOV REGULARIZATION 68 5.2.2 REGULARIZATION IN THE FINITE
DIMENSIONAL MODEL 69 5.2.3 REGULARIZATION AND SPLINES 70 5.2.4 VARIANCE
COMPONENT ESTIMATION 73 5.2.5 REGIONALLY ADAPTED REGULARIZATION 74 5.3
RELATIONSHIP BETWEEN SPLINE APPROXIMATION AND COLLOCATION 76 6 FROM
REGIONAL TO GLOBAL GRAVITY FIELDS 78 6.1 CONVERSION FROM A GLOBAL SPLINE
REPRESENTATION TO SPHERICAL HARMONICS 78 6.2 PATCHING OF INDIVIDUAL
REGIONAL SOLUTIONS 79 6.2.1 QUADRATURE METHODS 79 7 CALCULATIONS AND
RESULTS 88 7.1 (REAL) DATA ANALYSIS WITH THE PROGRAMMING SYSTEM GROOPS
88 7.1.1 BACKGROUND MODELS 92 7.2 SIMULATION STUDY: BASIS FUNCTIONS 93
7.3 GRAVITY FIELD SOLUTIONS 95 7.3.1 CHAMP 98 7.3.2 GRACE 103 7.3.3
COMBINATION OF GRACE AND GOCE 108 CONTENTS 8 SUMMARY AND OUTLOOK 113 A
MATHEMATICAL FUNDAMENTALS 116 A.I FUNCTION SPACES 116 A.2 LINEAR
FUNCTIONALS AND LINEAR OPERATORS 118 B DERIVATION OF THE WEIGHTS FOR THE
GAUSS-LEGENDRE QUADRATURE 122 ABBREVIATIONS 124 LIST OF FIGURES 125 LIST
OF TABLES 128 REFERENCES 120 |
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| discipline | Physik |
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| series2 | Schriftenreihe / Institut für Geodäsie und Geoinformation Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften : Reihe C, Dissertationen |
| spelling | Eicker, Annette 1978- Verfasser (DE-588)134215257 aut Gravity field refinement by radial basis functions from in-situ satellite data Annette Eicker München Verlag der Bayerischen Akademie der Wissenschaften Bonn Univ. Bonn, Inst. für Geodäsie und Geoinformation 2008 © 2012 137 S. Ill., graph. Darst. Kt. txt rdacontent n rdamedia nc rdacarrier Schriftenreihe / Institut für Geodäsie und Geoinformation 10 Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften : Reihe C, Dissertationen 676 Zsfassung in dt. Sprache Zugl.: Bonn, Univ., Diss., 2008 Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf Satellitengeodäsie (DE-588)4051744-5 gnd rswk-swf Gravitationsfeld (DE-588)4072014-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Gravitationsfeld (DE-588)4072014-7 s Satellitengeodäsie (DE-588)4051744-5 s Mehrgitterverfahren (DE-588)4038376-3 s DE-604 Institut für Geodäsie und Geoinformation Schriftenreihe 10 (DE-604)BV023109775 10 Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften Reihe C, Dissertationen ; 676 (DE-604)BV000004312 676 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016738220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eicker, Annette 1978- Gravity field refinement by radial basis functions from in-situ satellite data Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften Mehrgitterverfahren (DE-588)4038376-3 gnd Satellitengeodäsie (DE-588)4051744-5 gnd Gravitationsfeld (DE-588)4072014-7 gnd |
| subject_GND | (DE-588)4038376-3 (DE-588)4051744-5 (DE-588)4072014-7 (DE-588)4113937-9 |
| title | Gravity field refinement by radial basis functions from in-situ satellite data |
| title_auth | Gravity field refinement by radial basis functions from in-situ satellite data |
| title_exact_search | Gravity field refinement by radial basis functions from in-situ satellite data |
| title_exact_search_txtP | Gravity field refinement by radial basis functions from in-situ satellite data |
| title_full | Gravity field refinement by radial basis functions from in-situ satellite data Annette Eicker |
| title_fullStr | Gravity field refinement by radial basis functions from in-situ satellite data Annette Eicker |
| title_full_unstemmed | Gravity field refinement by radial basis functions from in-situ satellite data Annette Eicker |
| title_short | Gravity field refinement by radial basis functions from in-situ satellite data |
| title_sort | gravity field refinement by radial basis functions from in situ satellite data |
| topic | Mehrgitterverfahren (DE-588)4038376-3 gnd Satellitengeodäsie (DE-588)4051744-5 gnd Gravitationsfeld (DE-588)4072014-7 gnd |
| topic_facet | Mehrgitterverfahren Satellitengeodäsie Gravitationsfeld Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016738220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT eickerannette gravityfieldrefinementbyradialbasisfunctionsfrominsitusatellitedata |