Geodetic boundary value problems in view of the one centimeter geoid: with 37 tables
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1997
|
| Schriftenreihe: | Lecture notes in earth sciences
65 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 592 S. graph. Darst. |
| ISBN: | 3540626360 |
Internformat
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Datensatz im Suchindex
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| adam_text | FERNANDO SANSO REINER RUMMEL (EDS.) GEODETIC BOUNDARY VALUE PROBLEMS IN
VIEW OF THE ONE CENTIMETER GEOID WITH 83 FIGURES AND 37 TABLES SPRINGER
TABLE OF CONTENTS INTRODUCTION R. KLEES AND B. HECK PART I : BOUNDARY
VALUE PROBLEMS 17 POTENTIAL THEORY E. MARTENSEN AND S. RITTER 1.
REPRESENTATION THEOREMS 19 1.1 SCALAR REPRESENTATION 20 1.2 FIRST ORDER
VECTOR REPRESENTATION 22 1.3 THE LORENTZ CONDITION 23 1.4 SECOND ORDER
VECTOR REPRESENTATION 25 2. LIMITING RELATIONS AND INTEGRAL OPERATORS 26
2.1 LIMITING RELATIONS FOR THE SCALAR POTENTIAL 26 2.2 LIMITING
RELATIONS FOR THE DIPOLE POTENTIAL 27 2.3 THE SCALAR INTEGRAL OPERATORS
T AND X 28 2.4 THE OPERATORS T AND V FOR THE SPHERE 29 2.5 THE
EIGENVALUES -1, 1 FOR T, V 30 2.6 LIMITING RELATIONS FOR THE VECTOR
POTENTIAL 32 2.7 THE VECTOR INTEGRAL OPERATORS U AND U 33 2.8 THE
EIGENVALUES -1, 1 FOR U, U 35 3. BOUNDARY VALUE PROBLEMS, THE BOUNDARY
INTEGRAL METHOD 37 3.1 THE SCALAR DIRICHLET PROBLEM 38 3.2 THE SCALAR
NEUMANN PROBLEM 40 3.3 THE ROBIN PROBLEM ., 42 3.4 THE VECTOR DIRICHLET
AND NEUMANN PROBLEMS 44 3.5 THE VECTOR POISSON EQUATION 45 4. THE
BOUNDARY ELEMENT METHOD (BEM) 46 4.1 GENERAL CONSIDERATIONS 46 4.2 THE
COLLOCATION METHOD 49 4.3 THE GALERKIN METHOD , 54 5. SOBOLEV SPACES -
THE MODERN APPROACH TO BEM 57 5.1 SOBOLEV SPACES ON THE SPHERE 57 5.2
MAPPING PROPERTIES OF SOME INTEGRAL OPERATORS IN POTENTIAL THEORY 60 5.3
THE CONCEPT OF STRONG ELLIPTICITY 61 5.4 GALERKIN METHOD IN SOBOLEV
SPACES , 63 REFERENCES 65 VIII BOUNDARY VALUE PROBLEMS FOR HARMONIC
RANDOM FIELDS Y. ROZANOV AND F. SANSO 1. INTRODUCTION 67 2. THE
STOCHASTIC LAPLACE EQUATION 71 3. DIRECT COMPLEMENTS TO LAPLACE EQUATION
74 4. GENERAL SOLUTION OF THE LAPLACE EQUATION 79 5. BOUNDARY VALUES
CHARACTERIZATION 82 6. THE STOCHASTIC DIRICHLET PROBLEM 83 7. NEGLIGIBLE
SINGULARITIES 86 8. EXPECTATION AND CORRELATION 87 9. A FILTERING
PROBLEM 90 10. GENERALIZED LEAST SQUARE METHOD 94 REFERENCES 97 FREE
BOUNDARY PROBLEMS M. BIROLI 1. INTRODUCTION 98 2. THE WEIERSTRASS
THEOREM REVISITED 100 3. THE OBSTACLE PROBLEM 104 4. THE RECTANGULAR DAM
PROBLEM, [2] 106 5. THE IMAGE SEGMENTATION PROBLEM, [1] ILL 6. THE SHAPE
OPTIMIZATION FOR DIRICHLET PROBLEMS, [4] 114 REFERENCES 118 PART II :
GEODETIC BOUNDARY VALUE PROBLEM (GBVP) 119 FORMULATION AND LINEARIZATION
OF BOUNDARY VALUE PROBLEMS: FROM OBSERVABLES TO A MATHEMATICAL MODEL B.
HECK 1. INTRODUCTION 121 2. THE BOUNDARY CONDITIONS IN THE CLASSICAL
GBVPS 122 2.1 BASIC MODEL AND ASSUMPTIONS 122 2.2 THE FIXED GRAVIMETRIC
GBVP 127 2.3 THE VECTORIAL FREE GBVP 128 2.4 THE SCALAR FREE GBVP 129 IX
3. LINEARIZATION OF THE BOUNDARY CONDITIONS 131 3.1 APPROXIMATE AND
DIFFERENCE QUANTITIES 131 3.2 LINEARIZATION OF THE FIXED GBVP 134 3.3
LINEARIZATION OF THE VECTORIAL FREE GBVP 136 3.4 LINEARIZATION OF THE
SCALAR FREE GBVP 140 3.5 EVALUATION OF LINEARIZATION ERRORS 142 4.
FURTHER APPROXIMATIONS OF THE BOUNDARY CONDITIONS 144 4.1 SPECIFICATION
OF THE BOUNDARY CONDITIONS IN SEVERAL COORDINATE SYSTEMS 144 4.2
SPHERICAL APPROXIMATION 147 4.3 CONSTANT RADIUS APPROXIMATION 150 5.
SOLUTION OF THE NON-SPHERICAL GBVP IN TERMS OF SPHERICAL HARMONICS 153
6. CONCLUDING REMARKS 157 REFERENCES 157 EXERCISES 160 THE HIERARCHY OF
GEODETIC BVPS F. SANSO ON WIENER MEASURES AND THE CONTINUOUS FORMULATION
OF OBSERVATION EQUATIONS 161 1. WIENER MEASURES AND WIENER INTEGRAL 161
2. CONTINUOUS OBSERVATION EQUATIONS 168 WHAT IS A GEODETIC B.V.P.? 177
3. PURELY GRAVITATIONAL B.V.P S OF GEODESY 177 4. THE PHYSICAL SURFACE
OF THE EARTH 182 5. ERRORS FROM THE DTM 184 AUXILIA MATHEMATICA 190 6.
THE LEGENDRE TRANSFORM . 190 7. THE HODOGRAPH-LEGENDRE TRANSFORM 192
8. HOLDER SPACES AND SCHANDER ESTIMATES FOR THE DIRICHLET PROBLEM 194 9.
ON THE LOCAL SOLVABILITY OF NON-LINEAR FUNCTIONAL EQUATIONS : 197 THE
ANALYSIS OF GEODETIC B.V.P S ;* 201 10. THE VECTOR MOLODENSKY S PROBLEM
AND THE GRAVITY SPACE APPROACH 201 11. SEVERAL TRANSFORMATIONS OF THE
BASIC PROBLEM ! 205 12. THEOREMS OF EXISTENCE AND UNIQUENESS 208 13. THE
QUASI-LINEAR SCALAR MOLODENSKY PROBLEM 211 REFERENCES 217 GBVP -
CLASSICAL SOLUTIONS AND IMPLEMENTATION H. SIINKEL 1. THE STOKES SOLUTION
219 1.1 THE STOKES OPERATOR 220 1.2 SPHERICAL AND PLANAR APPROXIMATION
222 1.3 ELLIPSOIDAL CORRECTIONS 223 1.4 STOKES INTEGRATION BY 2D-FFT 225
1.5 STOKES INTEGRATION BY 1D-FFT 228 1.6 STOKES INTEGRATION BY FHT 228
1.7 PRACTICAL EXAMPLES AND EXPERIENCE 229 2. THE MOLODENSKY SOLUTION 231
2.1 THE MOLODENSKY OPERATOR 231 2.2 SOLUTION BY ANALYTICAL CONTINUATION
233 2.3 MOLODENSKY SOLUTION BY FFT 235 2.4 PRACTICAL EXAMPLES AND
EXPERIENCE 236 REFERENCES 237 PART III : FROM THE GBVP TOWARDS A LCM
GEOID 239 TOPOGRAPHIC EFFECTS IN GRAVITY FIELD MODELLING FOR BVP R.
FORSBERG AND C.C. TSCHERNING 1. INTRODUCTION .-... 241 2. BASICS OF THE
GRAVITY FIELD AND TERRAIN REDUCTIONS 243 2.1 GEOID, QUASIGEOID AND
HARMONIC CONTINUATION 245 2.2 DENSITY ANOMALIES AND CONVENTIONAL GRAVITY
TERRAIN REDUCTIONS 248 2.3 RESIDUAL DENSITY ANOMALIES AND RTM GRAVITY
ANOMALIES 251 2.4 GENERAL REMOVE-RESTORE TERRAIN REDUCTIONS 252 2.5
DIRECT OR INDIRECT USE OF TERRAIN REDUCTIONS 254 2.6 TERRAIN REDUCTIONS
AND MOLODENSKY : S THEORY 255 2.7 HELMERT CONDENSATION 256 2.8 REFERENCE
FIELDS IN ROUGH TOPOGRAPHY 259 3. THE PRACTICAL COMPUTATION OF TERRAIN
EFFECTS 260 3.1 TERRAIN EFFECT INTEGRATION BY PRISMS 261 3.2 TERRAIN
EFFECTS BY FOURIER TRANSFORMATION METHODS 264 REFERENCES 268 XI GLOBAL
MODELS FOR THE LCM GEOID - PRESENT STATUS AND NEAR TERM PROSPECTS R.H.
RAPP 1. INTRODUCTION 273 2. PRELIMINARY EQUATIONS 274 3. POTENTIAL
COEFFICIENT ESTIMATION 275 3.1 THE SATELLITE MODEL 275 3.2 THE LOW
DEGREE COMBINATION MODEL 276 3.3 HIGH DEGREE MODEL - QUADRATURE APPROACH
280 3.4 HIGH DEGREE MODEL - BLOCK DIAGONAL APPROACH 283 3.5 SUMMARY 284
4. GEOID UNDULATION DETERMINATION 284 5. GEOSTROPHIC VELOCITIES AND
ACCURACY USING SATELLITE ALTIMETER DATA AND GEOID UNDULATION MODELS 290
6. PAST AND CURRENT GEOPOTENTIAL MODELS 291 7. GEOID UNDULATION ACCURACY
- RESULTS FROM OSU91A AND JGM-3 292 8. THE GSFC/DMA JOINT GRAVITY AND
GEOID IMPROVEMENTS PROJECT 295 8.1 THE JGP95E 5 GLOBAL TOPOGRAPHIC
DATABASE 297 8.2 THE TERRESTRIAL GRAVITY ANOMALY FILES 297 8.3 THE
ALTIMETRY DERIVED GRAVITY ANOMALY FILES 300 8.4 THE MERGED 30 FILE 301
8.5 THE PRELIMINARY POTENTIAL COEFFICIENT MODELS 301 8.6 EVALUATION OF
SOME TEST MODELS AT OHIO STATE 303 8.7 FORMAL ACCURACY ESTIMATES OF THE
NEW GEOPOTENTIAL MODELS 306 9. HOW ACCURATELY DO WE KNOW THE GEOID
UNDULATIONS * FROM POTENTIAL COEFFICIENT MODELS? 306 10. SHOULD WE BE
CONSIDERING GEOID SLOPE ACCURACIES? 307 11. CONCLUSIONS 308 REFERENCES
308 AN INTRODUCTION TO AIRBORNE GRAVIMETRY AND ITS BOUNDARY VALUE
PROBLEMS K.-P. SCHWARZ AND ZUOFA LI ABSTRACT 312 PART ONE: INTRODUCTION
TO SYSTEM CONCEPTS 313 1. INTRODUCTION 313 2. THE CONCEPT OF AIRBORNE
GRAVIMETRY 315 XII PART TWO: MODELLING OF OBSERVABLES AND ESTIMATION
METHODS 323 3. THE MEASUREMENT MODEL OF AIRBORNE GRAVIMETRY 323 4. THE
ERROR MODEL OF AIRBORNE GRAVIMETRY 325 5. THE ESTIMATION PROBLEM 332
PART THREE: THE BOUNDARY VALUE PROBLEMS OF AIRBORNE GRAVIMETRY 338 6.
BVPS USING AIRBORNE GRAVIMETRIC DATA ONLY 339 7. BVPS COMBINING AIRBORNE
GRAVITY DATA WITH GROUND DATA 343 8. MULTIRESOLUTION BVPS 347 PART FOUR:
ASSESSMENT OF CURRENT TRENDS IN AIRBORNE GRAVIMETRY 352 9. APPLICATION
AREAS 352 REFERENCES 355 SPHERICAL SPECTRAL PROPERTIES OF THE EARTH S
GRAVITATIONAL POTENTIAL AND ITS FIRST AND SECOND DERIVATIVES R. RUMMEL
1. INTRODUCTION 359 2. SATELLITE GRADIOMETRY AND THE MEISSL SCHEME 361
3. SPECTRAL ANALYSIS OF SATELLITE GRADIOMETRY 378 3.1 SIGNAL CONTENT OF
SATELLITE GRADIOMETRY ,. 378 3.2 NOISE MODEL 385 3.3 SPECTRAL ESTIMATION
390 4. REGULARIZATION 395 REFERENCES 401 SATELLITE ALTIMETRY, OCEAN
DYNAMICS AND THE MARINE GEOID E.J.O. SCHRAMA 1. INTRODUCTION 405 2.
SATELLITE ALTIMETRY 407 2.1 ALTIMETRIC MEASUREMENTS 407 2.2 RADAR
CORRECTION ALGORITHMS 408 2.3 PRECISE ORBIT DETERMINATION 411 3. TIDES
413 3.1 TIDE GENERATING POTENTIAL 413 XIII 3.2 LOVE S THEORY OF THE
DEFORMING EARTH 419 3.3 OCEAN TIDES 423 3.4 LOAD TIDES 427 3.5 OTHER
TIDAL PHENOMENA 430 3.6 ALTIMETRY AND TIDES _., 431 4. OCEAN DYNAMICS
433 4.1 EQUATIONS OF MOTION 433 4.2 OBSERVING OCEAN CIRCULATION 437 4.3
TEMPORAL VARIATIONS IN THE OCEANS 444 5. SOME CLOSING REMARKS 448
APPENDIX 451 A. LAPLACE TIDAL EQUATIONS 451 REFERENCES 452 PART IV :
SEMINARS 455 STOCHASTIC BOUNDARY VALUE PROBLEM THEORY : AN ELEMENTARY
EXAMPLE F. SACERDOTE 457 1. INTRODUCTION 457 2. SOME REMARKS ON SOBOLEV
SPACES 459 3. SOME PROPERTIES OF WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL
EQUATIONS 461 4. APPLICATION TO STOCHASTIC BOUNDARY VALUE PROBLEMS 465
5. CONCLUDING REMARKS 466 REFERENCES 467 VARIATIONAL METHODS FOR
GEODETIC BOUNDARY VALUE PROBLEMS P. HOLOTA 468 1. INTRODUCTION 468 2.
ELEMENTARY NOTIONS AND TOOLS 470 2.1 SOBOLEV WEIGHT SPACE : 470 2.2
LIPSCHITZ BOUNDARY 470 2.3 TRACE THEOREM 471 2.4 EQUIVALENT NORMS 473 3.
GEODETIC BOUNDARY VALUE PROBLEMS 474 XIV 3.1 MOLODENSKY PROBLEM - AN
ELEMENTARY EXPOSITION 474 3.2 LINEAR GRAVIMETRIC BOUNDARY VALUE PROBLEM
476 4. GENERALIZED OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM 477 5.
LAX-MILGRAM THEOREM AND THE ELLIPTICITY 479 6. CONCLUSION 480 REFERENCES
481 TOPICS ON BOUNDARY ELEMENT METHODS R. KLEES 482 1. INTRODUCTION 482
2. MATHEMATICAL MODEL 485 3. REPRESENTATION FORMULAE 488 4. JUMP
RELATIONS AND BOUNDARY INTEGRAL EQUATIONS 492 5. CONSTRUCTION OF THE
APPROXIMATING SUBSPACE 496 6. DISCRETIZATION OF THE INTEGRAL EQUATION
498 7. LINEAR SYSTEM OF EQUATIONS 501 8. FAST NUMERICAL ALGORITHMS 501
8.1 PANEL CLUSTERING 502 8.2 MULTISCALE METHODS 508 8.3 NUMERICAL
INTEGRATION 516 9. SOLUTION IN THE DOMAIN 517 10. ERROR ESTIMATES 522
10.1 DISCRETIZATION ERROR 522 10.2 INTEGRATION ERROR 526 REFERENCES 527
SOLVING GEODETIC BOUNDARY VALUE PROBLEMS WITH PARALLEL COMPUTERS R.
LEHMANN 532 1. INTRODUCTION 532 2. HARDWARE ISSUES 533 3. PROGRAMMING
ISSUES 535 4. GEODETIC PROBLEMS OF PARALLEL NUMERICAL INTEGRATION 536 5.
GEODETIC PROBLEMS OF PARALLEL LINEAR ALGEBRA 538 6. RESULTS 540
REFERENCES 540 XV APPLICATION OF BOUNDARY VALUE TECHNIQUES TO SATELLITE
GRADIOMETRY W. KELLER 542 1. INTRODUCTION 542 2. MATHEMATICAL MODEL 543
2.1 FUNCTIONAL MODEL 544 2.2 STOCHASTIC MODEL 547 2.3 OVERDETERMINED
PROBLEMS 550 3. SATELLITE GRADIOMETRY 553 3.1 ARISTOTELES MISSION 553
REFERENCES 558 THE POLAR GAP N. SNEEUW AND M. VAN GELDEREN 559 1.
INTRODUCTION 559 2. DISTORTION OF THE SPHERICAL HARMONIC SPECTRUM 560 3.
A SIMPLE APPROACH 561 4. A TIME-WISE APPROACH: LUMPED COEFFICIENTS 563
5. A LEAST-SQUARES FORMULATION 565 6. ERROR PROPAGATION ONTO THE SPHERE
566 7. CONCLUSIONS 567 REFERENCES 568 EUROPEAN CAPABILITIES AND
PROSPECTS FOR A SPACEBORNE GRAVIMETRIC MISSION M. SCHUYER : 569 1.
INTRODUCTION 569 2. SCIENCE BACKGROUND AND MISSION OBJECTIVES 570 3. THE
GRAVITY FIELD AND STEADY-STATE OCEAN CIRCULATION EXPLORER (GOCE) SPACE
MISSION CONCEPT 571 4. SCIENTIFIC INSTRUMENTS 573 4.1 PRINCIPLES OF
GRAVIMETRIC MEASUREMENTS FROM SPACE 573 4.2 THE GNSS RECEIVER 575 4.3
THE GRAVITY GRADIOMETER 576 5. THE GOCE SATELLITE 580 5.1 SPECIFIC
REQUIREMENTS 580 XVI 5.2 ORBIT MAINTENANCE AND DFC 582 5.3 ATTITUDE
CONTROL 584 5.4 THE GOCE SATELLITE SUBSYSTEMS 584 5.5 LAUNCH AND ORBIT
OPERATIONS 586 6. EVALUATION OF THE EXPECTED MISSION PERFORMANCE 587 7.
CONCLUSION 588 LIST OF ACRONYMS 589 INDEX 591
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| indexdate | 2024-07-09T18:07:50Z |
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| isbn | 3540626360 |
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| series | Lecture notes in earth sciences |
| series2 | Lecture notes in earth sciences |
| spelling | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables Fernando Sansò ... (ed.) Berlin [u.a.] Springer 1997 XIX, 592 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in earth sciences 65 Geodätisches Randwertproblem (DE-588)4020209-4 gnd rswk-swf Como (DE-588)4085313-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift gnd-content Geodätisches Randwertproblem (DE-588)4020209-4 s Como (DE-588)4085313-5 g DE-604 Sansò, Fernando 1945- Sonstige (DE-588)1082398675 oth Lecture notes in earth sciences 65 (DE-604)BV023550940 65 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007609143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables Lecture notes in earth sciences Geodätisches Randwertproblem (DE-588)4020209-4 gnd |
| subject_GND | (DE-588)4020209-4 (DE-588)4085313-5 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables |
| title_auth | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables |
| title_exact_search | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables |
| title_full | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables Fernando Sansò ... (ed.) |
| title_fullStr | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables Fernando Sansò ... (ed.) |
| title_full_unstemmed | Geodetic boundary value problems in view of the one centimeter geoid with 37 tables Fernando Sansò ... (ed.) |
| title_short | Geodetic boundary value problems in view of the one centimeter geoid |
| title_sort | geodetic boundary value problems in view of the one centimeter geoid with 37 tables |
| title_sub | with 37 tables |
| topic | Geodätisches Randwertproblem (DE-588)4020209-4 gnd |
| topic_facet | Geodätisches Randwertproblem Como Aufsatzsammlung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007609143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023550940 |
| work_keys_str_mv | AT sansofernando geodeticboundaryvalueproblemsinviewoftheonecentimetergeoidwith37tables |