Geometrical geodesy: using information and computer technology
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| 245 | 1 | 0 | |a Geometrical geodesy |b using information and computer technology |c Maarten Hooijberg |
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Datensatz im Suchindex
| _version_ | 1804137211404222464 |
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| adam_text | Contents
Preface V
Contents XII
Index of Authors XVI
List of Figures XXI
Time and Reference Systems
1.1 Earth in Space Time Metric__________________________________________________________________1
1.2 Frequency and Time________________________________________________________________________2
1.3 Principal Time Scales in Brief________________________________________________________________6
1.4 Definitions of the Figure of the Earth or Geoid___________________________________________________9
1.5 Fundamental Polyhedron___________________________________________________________________12
1.6 Celestial and Terrestrial Reference Systems ____________________________________________________14
1.6.1 Orbital Systems______________________________________________________________________15
1.6.2 Inertial Reference Systems_____________________________________________________________15
1.6.3 Reference Systems and Frames__________________________________________________________16
2. Dealing with Geoscience Branches________________________________________________________ 27
2.1 Continental Drift Hypothesis________________________________________________________________27
2.2 Concept of Earth s Wobbling Movements_______________________________________________________30
2.2.1 Tidal Deformation of the Earth__________________________________________________________32
2.2.2 Polar Motion________________________________________________________________________34
2.2.3 Orbit Perturbations___________________________________________________________________35
3. The Figure of Earth_____________________________________________________________________ 37
3.1 Astronomic and Geodetic Research___________________________________________________________37
3.2 Horizontal Control Datum__________________________________________________________________39
3.2.1 Specification of Size and Shape_________________________________________________________41
3.2.2 Combining Local Reference Datums_______________________________________________________43
3.3 Vertical Control Datum____________________________________________________________________43
3.4 Stellar Triangulation Network_______________________________________________________________47
3.5 Toward a Worldwide 3D Geodetic Reference System______________________________________________49
3.6 Fundamental Parameters in Astronomy Geodesy Geodynamics______________________________________50
3.6.1 Estimated Parameters for the 2000s ______________________________________________________50
3.6.2 Primary Geodetic Parameters and Discussion________________________________________________54
3.6.3 Consistent Set of Fundamental Constants (1997)_____________________________________________55
3.6.4 SC 3 Appendices_____________________________________________________________________56
4. 3D Positioning and Mapping____________________________________________________________ 59
4.1 At the Dawn of the Space Age_______________________________________________________________59
4.2 Geometric and Dynamic Satellite Geodesy_____________________________________________________59
4.2.1 Geometrical Satellite Surveying Systems___________________________________________________61
4.2.2 Dynamical Satellite Surveying Systems____________________________________________________65
4.3 Global Navigation Satellite System___________________________________________________________67
4.3.1 TRANSIT System____________________________________________________________________68
4.3.2 GPS System_________________________________________________________________________69
4.3.3 Global Differential GPS_______________________________________________________________76
4.3.4 GLONASS System___________________________________________________________________79
4.3.5 GALILEO System____________________________________________________________________80
4.3.6 Combined GALILEO, GPS and GLONASS Systems in Differential Mode_________________________81
4.3.7 eLORAN Systems____________________________________________________________________82
4.3.8 Uncorrected Errors due to System Time Drift________________________________________________83
4.4 Acoustic 3D positioning___________________________________________________________________83
4.5 Global Geographic Information Systems_______________________________________________________84
5. Plane and Spherical Earth Systems_______________________________________________________ 87
5.1 Plane Trigonometry_______________________________________________________________________87
5.2 Plane Coordinate System___________________________________________________________________89
5.3 Distance Measurement Techniques___________________________________________________________93
Contents xiii
5.3.1 Baseline Crossing____________________________________________________________________96
5.4 Spherical Trigonometry___________________________________________________________________99
5.4.1 Formulae in Spherical Trigonometry_____________________________________________________ 100
5.5 Area Calculation_____________________________________________________________________ 104
6. Classical Datums and Reference Systems_________________________________________________113
6.1 Standard Units of Linear Measure___________________________________________________________113
6.2 Spheres and Ellipsoids____________________________________________________________________115
6.3 Basic Control Surveys for Reference Systems__________________________________________________119
6.3.1 Classical Geodesy___________________________________________________________________120
6.3.2 Satellite Geodesy____________________________________________________________________127
6.3.3 Information in European Standards______________________________________________________129
6.3.4 On the Meaning of Geodetic Orientation__________________________________________________130
6.4 Formulae for Various Types of Latitude______________________________________________________130
7. Spatial Coordinate Calculations__________________________________________________________133
7.1 Using Bi linear Interpolation_______________________________________________________________133
7.2 S transformation_________________________________________________________________________13 8
7.3 Cartesian Coordinates_____________________________________________________________________152
8. Geodetic Arc Calculations ______________________________________________________________153
8.1 Great Elliptic Arc________________________________________________________________________153
8.2 Normal Section__________________________________________________________________________154
8.3 Geodesies up to 20 000 km________________________________________________________________15 5
8.3.1 Using Kivioja s Method_______________________________________________________________155
8.3.2 Using Vincenty s Method_____________________________________________________________158
8.4 The Meridional Arc______________________________________________________________________164
8.4.1 Recasting Algorithms________________________________________________________________166
8.4.2 Accuracy and Precision_______________________________________________________________168
8.5 Arc of Parallel__________________________________________________________________________170
9. Conversions and Zone Systems__________________________________________________________173
9.1 Scope and Terminology___________________________________________________________________174
9.2 Projection Zone Systems__________________________________________________________________175
9.3 Computation Zone Systems________________________________________________________________178
9.4 Conversions and Transformations___________________________________________________________178
10. Conformal Projections Using Reference Ellipsoids_______________________________________183
10.1 Lambert s Conformal Conical Projection______________________________________________________183
10.2 Gauss Schreiber Conformal Double Projection_________________________________________________194
10.3 Normal Mercator Projection________________________________________________________________200
10.4 Gauss Kruger Conformal Projection_________________________________________________________207
10.5 Hotine s Oblique Mercator Projection_____________________________________________^__^_____214
10.6 Rosenmund s Oblique Mercator Projection_________________________________________.___________222
10.7 Oblique Stereographic Conformal Projection___________________________________________________227
10.8 Polyeder Mapping_______________________________________________________________________232
10.9 Conversions between Grid Systems__________________________________________________________236
11. Astrolabe Observations_______________________________________________________________245
11.1 Reduction of Astrolabe Observations_________________________________________________________245
11.2 Derivation of the Method__________________________________________________________________245
12. About History A Bird s Eye View______________________________________________________249
12.1 In Antiquity____________________________________________________________________________249
12.1.1 Trigonometrical Surveys______________________________________________________________250
12.1.2 Prolate or Oblate Ellipsoid_____________________________________________________________251
12.2 A Quarter of a Millennium Ago_____________________________________________________________252
12.2.1 Principle of Gauss Least Squares adjustment_______________________________________________254
12.2.2 Frameworks for Mapping_____________________________________________________________255
12.2.3 Radar and Velocity of Light in Vacuo_____________________________________________________256
xiv Contents
12.2.4 Electronic Surveying Systems___________________________________________________________257
12.3 About Mathematics______________________________________________________________________258
12.3.1 Topology__________________________________________________________________________260
12.3.2 Maxwell s Electromagnetic Wave________________________________________________________263
12.3.3 Albert Einstein s Vision_______________________________________________________________264
13. Tools and Topics_____________________________________________________________________ 265
13.1 History of Tables________________________________________________________________________265
13.1.1 Dividing Circumference of the Circle_____________________________________________________265
13.2 Trigonometrical Tables___________________________________________________________________265
13.3 Trigonometric Approximation Techniques_____________________________________________________268
13.3.1 CORDIC Trigonometric Functions_______________________________________________________269
14. Computing Techniques________________________________________________________________ 275
14.1 Logarithms and Slide Rules________________________________________________________________275
14.2 Mechanical Calculators___________________________________________________________________276
14.3 Mathematical Functions for Use in Subroutines_________________________________________________277
14.4 Electronic Computers_____________________________________________________________________277
14.5 Supercomputers_________________________________________________________________________279
14.6 Scaleable Parallelism_____________________________________________________________________279
14.6.1 SP Hardware_______________________________________________________________________280
14.6.2 SP Software________________________________________________________________________282
14.6.3 Parallel Applications for SP Platforms____________________________________________________283
14.7 Operating Systems_______________________________________________________________________284
14.8 Programming Languages___________________________________________________________________285
14.9 Timeline of Calculating___________________________________________________________________286
15. Information and Computer Technology_________________________________________________ 289
15.1 Relational Databases_____________________________________________________________________290
15.2 Spatial 3D or 4D Databases________________________________________________________________293
15.3 ICT Human Resources____________________________________________________________________295
16. ICT Applied to Sea Surveying_________________________________________________________ 297
16.1 Navigation and Positioning at Sea____________________________________________________________299
16.1.1 Underwater Acoustic Positioning________________________________________________________301
16.1.2 Chart Datum_______________________________________________________________________306
16.1.3 Electronic Chart Systems _____________________________________________________________307
16.2 Geo Marine Surveying____________________________________________________________________309
16.2.1 Multi Frequency Signal Processing_______________________________________________________311
16.2.2 Acoustic Geo Sensors________________________________________________________________312
16.2.3 Underwater Acoustic Systems___________________________________________________________314
16.2.4 Sub Bottom Profiling________________________________________________________________315
16.2.5 Parametric Echosounders_____________________________________________________________315
16.2.6 Hydrographical Literature______________________________________________________________318
17. Using Computers__________________________________________________________^^_ 321
17.1 Using FORTRAN Programs________________________________________________________________321
17.1.1 Installation of FORTRAN ___________________________________________________322
17.1.2 Compilation________________________________________________________________________322
17.1.3 FORTRAN Application Program Modules_________________________________________________322
17.1.4 Program Execution___________________________________________________________________325
17.1.4.1 Error Messages__________________________________________________________________325
17.1.4.2 Detailed Information______________________________________________________________326
18. FORTRAN Application Programs________________________________________________327
18.1 Using Flat Earth Applications_______________________________________________________________328
18.2 Baseline Crossing Application_______________________________________________________________329
18.3 Bi Axial Meridional Arcs___________________________________________________________________329
18.4 Ellipsoid Constants Arcs Radii____________________________________________________________331
18.5 Quadrilateral Ellipsoidal Area_______________________________________________________________333
Contents xv
18.6 Polygonal Area on a Sphere or Bi Axial Ellipsoid_______________________________________________334
18.7 Length of Parallel________________________________________________________________________336
18.8 Geodetic Reference System________________________________________________________________3 3 7
18.9 Bi Linear Interpolation____________________________________________________________________339
18.10 S Transformation________________________________________________________________________340
18.11 Forward Long Line Kivioja s Method_______________________________________________________344
18.12 Inverse Long Line Kivioja s Method________________________________________________________346
18.13 Forward Long Line Vincenty s Method______________________________________________________348
18.14 Inverse Long Line Vincenty s Method_______________________________________________________349
18.15 Polyeder Mapping System_________________________________________________________________351
18.16 Gaussian Ellipsoid to Sphere_______________________________________________________________353
18.17 Normal Mercator Projection________________________________________________________________356
18.18 Gauss Kruger Projection__________________________________________________________________3 60
18.19 Lambert s Conical Conformal Projection______________________________________________________363
18.20 Hotine s Oblique Mercator Projection________________________________________________________368
18.21 Rosenmund s Oblique Mercator Projection____________________________________________________372
18.22 Stereographic Conformal Projection_________________________________________________________375
18.23 I/O Subroutines_________________________________________________________________________378
19. International Organisations____________________________________________________________383
19.1 International Union of Geodesy and Geophysics________________________________________________383
19.2 International Association of Geodesy_________________________________________________________384
19.3 Federation Internationale des Geometres______________________________________________________388
19.4 International Hydrographic Organisation______________________________________________________389
19.5 International Earth Rotation Service_________________________________________________________389
19.6 Participants in National Geodetic Satellite Program_______________________________________________391
Bibliography_________________________________________________________________________393
Index of Subjects_____________________________________________________________________425
Appendix ^^_____________________________________________________________________438
List of Figures
Figure 1: A four dimensional path (spiral) of a planet in space time is a geodesic______________________________1
Figure 2: Part of the Astronomical Clock at the Cathedral of Strasbourg__________________________________3
Figure 3: Time Verdi s clock____________________________________________________________________4
Figure 4: NASA/GSFC GEM4 Global Detailed Gravimetric Geoid in the Miller projection____________________11
Figure 5: Geoid undulations 15000 x enlarged _______________________________________________________11
Figure 6: The geoid and three reference ellipsoids_____________________________________________________12
Figure 7: Ecliptic and Equator____________________________________________________________________14
Figure 8: Parametry Zemli System of 1990 definition__________________________________________________18
Figure 9: World Geodetic System of 1984 definition___________________________________________________19
Figure 10: Wegener s Vision of Pangaea_____________________________________________________________27
Figure 11: Classification of Earth s depths____________________________________________________________28
Figure 12: Tectonic plates and its boundaries_________________________________________________________30
Figure 13: Celestial sphere with intersection of the Equator by ecliptics______________________________________30
Figure 14: Rotation of axis due to precession (1) and nutation (2) in 25 850 years______________________________31
Figure 15: Effect of the Moon on the Earth___________________________________________________________3 2
Figure 16: Coriolis Force_________________________________________________________________________32
Figure 17: Polar heights as surveyed by Marcuse and Preston_____________________________________________34
Figure 18: Path of polar motion between 1909.0 and 1915.0______________________________________________35
Figure 19: Flare triangulation of the connection Denmark and Norway______________________________________41
Figure 20: Comparison of various Datums along the 30° meridian from Finland to South Africa__________________42
Figure 21: One example of various reference levels and vertical datums in use Spain / Gibraltar__________________45
Figure 22: Vaisala s flare triangulation application_____________________________________________________47
Figure 23: View on the Earthsphere and the Hydrosphere________________________________________________59
Figure 24: Principle of VLBI with a short base________________________________________________________66
Figure 25: Principle of VLBI with a line base_________________________________________________________67
Figure 26: Time shift of signals____________________________________________________________________67
Figure 27: One of the first GPS satellites_____________________________________________________________69
Figure 28: Measuring pseudo ranges________________________________________________________________74
Figure 29: C Nav Starfire GcDGPS World Receiver in the foreground on a barge lifting a Hurricane Katrina
damaged platform_____________________________________________________________________77
Figure 30: Distorted filtered transformed corrected grids______________________________________________78
Figure 31: Spherical Earth________________________________________________________________________87
Figure 32: Space curvature illustrated in 2D__________________________________________________________87
Figure 33: Plane triangle_________________________________________________________________________88
Figure 34: Bearing and distance____________________________________________________________________89
Figure 35: Area calculation in four quadrants_________________________________________________________92
Figure 36: Airborne and shipbome baseline crossing___________________________________________________93
Figure 37: Shipborne baseline crossing technique______________________________________________________94
Figure 38: Determination of the shortest LS sum distance of Baseline Al ____________________________________98
Figure 39: Determination of the shortest LS sum distance of Baseline A2____________________________________98
Figure 40: General spherical triangle________________________________________________________________99
Figure 41: Rectangular spherical triangle____________________________________________________________99
Figure 42: Total and zonal area determination________________________________________________________105
Figure 43: Ellipsoidal quadrilateral area____________________________________________________________108
Figure 44: Spherical polygonal area________________________________________________________________108
Figure 45: Hydrosphere between 1200 1500 AD______________________________________________________115
Figure 46: Bessel ellipsoids in legal metres and international metres_______________________________________123
Figure 47: European 52° arc of parallel between Feaghmain and Warsaw________________________________125
Figure 48: Radii of curvature in Prime Vertical and in the Reference Meridian_______________________________126
Figure 49: ED50 corrections for AE________________________________________________________________134
Figure 50: ED50 corrections for AN _______________________________________________________________134
Figure 51: Location of a grid square for interpolation__________________________________________________13 5
Figure 52: Cross sections of the bi linear interpolation surface are defined by straight line elements________________137
Figure 53: Translated and rotated 3D coordinate system________________________________________________139
Figure 54: Geoid separation of the old and the new Datum______________________________________________143
Figure 55: Ellipsoidal and physical Earth____________________________________________________________143
Figure 56: Calculated differences for the 6 parameter transformation solution_______________________________ 146
Figure 57: Calculated differences for the 7 parameter transformation solution________________________________146
xxii List of Figures
Figure 58: Calculated differences for the 9 parameter transformation solution 146
Figure 59: Datum transformation round trip error of latitude 150
Figure 60: Datum transformation round trip error of longitude 150
Figure 61: Datum transformation round trip error of height 151
Figure 62: The great elliptic arc and the reference ellipsoid 153
Figure 63: Normal sections and the reference ellipsoid 154
Figure 64: Geodetic triangle 155
Figure 65: Geodesic divided into dS line elements 156
Figure 66: The geodesic and the reference ellipsoid 157
Figure 67: Different positions of the geodesic A B 164
Figure 68: Time to calculate a rectifying sphere 166
Figure 69: Comparison of computing time to calculate the Meridional arc 167
Figure 70: Round trip error of the meridional arc in degrees 168
Figure 71: Round trip error of the meridional arc in m 168
Figure 72: An LCC algorithm shows that iterating is not always successful 170
Figure 73: Tangencv or secancy of various map projection surfaces 173
Figure 74: Figure 75: Outline shows the four quadrants as used for computing correct signs using Flags (i|j ... Azimuth and convergence .in) 178 180
Figure 76: Normal Mercator and Lambert projection projected geodetic vs. grid angles 181
Figure 77: Transverse Mercator vs. grid angles 182
Figure 78: Lambert s conformal conical projection 184
Figure 79: Lambert s grid system 185
Figure 80: Lambert s conical IGN zone 188
Figure 81: Lambert s conformal conical projection of France 190
Figure 82: Gaussian sphere / ellipsoid mapping system 194
Figure 83: Gauss Schreiber grid of the Hannover schen Landesvermessung 1866 196
Figure 84: Perspective projection of the sphere 201
Figure 85: Mercator projection of the sphere 201
Figure 86: Scale factor as a function of 8° latitudinal zone width 205
Figure 87: Scale factor as a function of 75° latitudinal zone width 205
Figure 88: Normal Mercator with two secant lines 206
Figure 89: UM and UTM grid zones for the equatorial territory of Indonesia 207
Figure 90: Transverse Mercator grid zone system 211
Figure 91: Borneo Rectified Skew Orthomorphic grid 219
Figure 92: Initial Line of the Borneo RSO grid 219
Figure 93: Oblique Mercator Grid of Switzerland 222
Figure 94: Rosenmund s Oblique Mercator system 222
Figure 95: Construction of the stereographic projection 227
Figure 96: Stereographic grid of the Netherlands 230
Figure 97: Polyeder mapping system 232
Figure 98: Polyeder conical construction AB 232
Figure 99: Parallel bursts 233
Figure 100: Meridian bursts 233
Figure 101: Part of the Indonesian Polyeder mapping system 235
Figure 102: Conversion between 3° 6° zone systems and 6° 6° zone systems 238
Figure 103: Cover 3rd amended edition of the Principia 250
Figure 104: Pendulum observations in Newton s De Mundi Svstemate 251
Figure 105: Cover of the Theorie de la Figure de la Terre 253
Figure 106: Carl F. Gauss 260
Figure 107: Formulating a hierarchy of geometries 261
Figure 108: Hamilton s multiplication table for quaternions 262
Figure 109: Non Commutative Algebra 262
Figure 110: Vector rotation 270
Figure 111: Forward vector rotation 271
Figure 112: Inverse vector rotation 273
Figure 113: Part of the Aristo Geodat slide rule in Gon 275
Figure 114: Overview IBM RS/6000 SP Nodes 281
Figure 115: SP Switch Circuitry 281
Figure 116: IBM RISC System / 6000 SP Massively Parallel Processors 281
List of Figures xxiii
Figure 117: Electronic Teleconferencing Facility Centre fed by 1024 servers Each server is equipped with
two SCSI discs____________________________________________________________________292
Figure 118: Sketch of spatial dataflow using multi dimensional Databases and data Overlays in brief______________294
Figure 119: Ultra short baseline (USBL) configuration________________________________________________301
Figure 120: Super short baseline (SSBL) configuration________________________________________________301
Figure 121: Long baseline (LBL) configuration______________________________________________________302
Figure 122: Multi user Long Baseline (MuLBL) configuration__________________________________________302
Figure 123: Kongsberg HiPAP using an array of 241 elements assembled into one sphere__________________303
Figure 124: Kongsberg HUGIN 1000 Mine hunting survey_________________________________________309
Figure 125: Hugin 3000 AUV using GNSS and Doppler log__________________________________________309
Figure 126: Single beam ceramic transducer_______________________________________________________311
Figure 127: Kongsberg BM 636 dual beam ceramic transducer_______________________________________312
Figure 128: Simultaneous deployment of multi single beam echosounders__________________________________313
Figure 129: Hull mounted multibeam echosounder geometry___________________________________________313
Figure 130: Hull mounted multibeam echosounder geometry___________________________________________313
Figure 131: Towed Fish mounted sidescan sonar_____________________________________________________314
Figure 132: Sketch of DGPS surveying by parametric echosounder_______________________________________316
Figure 133: Laptop PC with Innomar SES 2000 Compact parametric sub bottom profiler________________317
Figure 134: Innomar SES 2000 Compact parametric transducer with cable_____________________________317
Figure 135: Recovering HUGIN 3000 AUV from deep sea operations___________________________________318
Figure 136: C C side scan sonar survey pattern for the German U 166 submarine in the Gulf of Mexico___________319
Figure 137: Side scan sonar 410 kHz image of the German U 166 submarine discovered at 1100 m depth__________319
Figure 138: Baeyer s design of the Mittel Europaischen Gradmessung_____________________________________385
Related Topics On_CD contains some corresponding figures in a colour block. In the list mentioned above are
these figures indicated in bold
|
| adam_txt |
Contents
Preface V
Contents XII
Index of Authors XVI
List of Figures XXI
Time and Reference Systems
1.1 Earth in Space Time Metric_1
1.2 Frequency and Time_2
1.3 Principal Time Scales in Brief_6
1.4 Definitions of the Figure of the Earth or Geoid_9
1.5 Fundamental Polyhedron_12
1.6 Celestial and Terrestrial Reference Systems _14
1.6.1 Orbital Systems_15
1.6.2 Inertial Reference Systems_15
1.6.3 Reference Systems and Frames_16
2. Dealing with Geoscience Branches_ 27
2.1 Continental Drift Hypothesis_27
2.2 Concept of Earth's Wobbling Movements_30
2.2.1 Tidal Deformation of the Earth_32
2.2.2 Polar Motion_34
2.2.3 Orbit Perturbations_35
3. The Figure of Earth_ 37
3.1 Astronomic and Geodetic Research_37
3.2 Horizontal Control Datum_39
3.2.1 Specification of Size and Shape_41
3.2.2 Combining Local Reference Datums_43
3.3 Vertical Control Datum_43
3.4 Stellar Triangulation Network_47
3.5 Toward a Worldwide 3D Geodetic Reference System_49
3.6 Fundamental Parameters in Astronomy Geodesy Geodynamics_50
3.6.1 Estimated Parameters for the 2000s _50
3.6.2 Primary Geodetic Parameters and Discussion_54
3.6.3 Consistent Set of Fundamental Constants (1997)_55
3.6.4 SC 3 Appendices_56
4. 3D Positioning and Mapping_ 59
4.1 At the Dawn of the Space Age_59
4.2 Geometric and Dynamic Satellite Geodesy_59
4.2.1 Geometrical Satellite Surveying Systems_61
4.2.2 Dynamical Satellite Surveying Systems_65
4.3 Global Navigation Satellite System_67
4.3.1 TRANSIT System_68
4.3.2 GPS System_69
4.3.3 Global Differential GPS_76
4.3.4 GLONASS System_79
4.3.5 GALILEO System_80
4.3.6 Combined GALILEO, GPS and GLONASS Systems in Differential Mode_81
4.3.7 eLORAN Systems_82
4.3.8 Uncorrected Errors due to System Time Drift_83
4.4 Acoustic 3D positioning_83
4.5 Global Geographic Information Systems_84
5. Plane and Spherical Earth Systems_ 87
5.1 Plane Trigonometry_87
5.2 Plane Coordinate System_89
5.3 Distance Measurement Techniques_93
Contents xiii
5.3.1 Baseline Crossing_96
5.4 Spherical Trigonometry_99
5.4.1 Formulae in Spherical Trigonometry_ 100
5.5 Area Calculation_ 104
6. Classical Datums and Reference Systems_113
6.1 Standard Units of Linear Measure_113
6.2 Spheres and Ellipsoids_115
6.3 Basic Control Surveys for Reference Systems_119
6.3.1 Classical Geodesy_120
6.3.2 Satellite Geodesy_127
6.3.3 Information in European Standards_129
6.3.4 On the Meaning of Geodetic Orientation_130
6.4 Formulae for Various Types of Latitude_130
7. Spatial Coordinate Calculations_133
7.1 Using Bi linear Interpolation_133
7.2 S transformation_13 8
7.3 Cartesian Coordinates_152
8. Geodetic Arc Calculations _153
8.1 Great Elliptic Arc_153
8.2 Normal Section_154
8.3 Geodesies up to 20 000 km_15 5
8.3.1 Using Kivioja's Method_155
8.3.2 Using Vincenty's Method_158
8.4 The Meridional Arc_164
8.4.1 Recasting Algorithms_166
8.4.2 Accuracy and Precision_168
8.5 Arc of Parallel_170
9. Conversions and Zone Systems_173
9.1 Scope and Terminology_174
9.2 Projection Zone Systems_175
9.3 Computation Zone Systems_178
9.4 Conversions and Transformations_178
10. Conformal Projections Using Reference Ellipsoids_183
10.1 Lambert's Conformal Conical Projection_183
10.2 Gauss Schreiber Conformal Double Projection_194
10.3 Normal Mercator Projection_200
10.4 Gauss Kruger Conformal Projection_207
10.5 Hotine's Oblique Mercator Projection_^_^_214
10.6 Rosenmund's Oblique Mercator Projection_._222
10.7 Oblique Stereographic Conformal Projection_227
10.8 Polyeder Mapping_232
10.9 Conversions between Grid Systems_236
11. Astrolabe Observations_245
11.1 Reduction of Astrolabe Observations_245
11.2 Derivation of the Method_245
12. About History A Bird 's Eye View_249
12.1 In Antiquity_249
12.1.1 Trigonometrical Surveys_250
12.1.2 Prolate or Oblate Ellipsoid_251
12.2 A Quarter of a Millennium Ago_252
12.2.1 Principle of Gauss' Least Squares adjustment_254
12.2.2 Frameworks for Mapping_255
12.2.3 Radar and Velocity of Light in Vacuo_256
xiv Contents
12.2.4 Electronic Surveying Systems_257
12.3 About Mathematics_258
12.3.1 Topology_260
12.3.2 Maxwell's Electromagnetic Wave_263
12.3.3 Albert Einstein's Vision_264
13. Tools and Topics_ 265
13.1 History of Tables_265
13.1.1 Dividing Circumference of the Circle_265
13.2 Trigonometrical Tables_265
13.3 Trigonometric Approximation Techniques_268
13.3.1 CORDIC Trigonometric Functions_269
14. Computing Techniques_ 275
14.1 Logarithms and Slide Rules_275
14.2 Mechanical Calculators_276
14.3 Mathematical Functions for Use in Subroutines_277
14.4 Electronic Computers_277
14.5 Supercomputers_279
14.6 Scaleable Parallelism_279
14.6.1 SP Hardware_280
14.6.2 SP Software_282
14.6.3 Parallel Applications for SP Platforms_283
14.7 Operating Systems_284
14.8 Programming Languages_285
14.9 Timeline of Calculating_286
15. Information and Computer Technology_ 289
15.1 Relational Databases_290
15.2 Spatial 3D or 4D Databases_293
15.3 ICT Human Resources_295
16. ICT Applied to Sea Surveying_ 297
16.1 Navigation and Positioning at Sea_299
16.1.1 Underwater Acoustic Positioning_301
16.1.2 Chart Datum_306
16.1.3 Electronic Chart Systems _307
16.2 Geo Marine Surveying_309
16.2.1 Multi Frequency Signal Processing_311
16.2.2 Acoustic Geo Sensors_312
16.2.3 Underwater Acoustic Systems_314
16.2.4 Sub Bottom Profiling_315
16.2.5 Parametric Echosounders_315
16.2.6 Hydrographical Literature_318
17. Using Computers_^^_ 321
17.1 Using FORTRAN Programs_321
17.1.1 Installation of FORTRAN _322
17.1.2 Compilation_322
17.1.3 FORTRAN Application Program Modules_322
17.1.4 Program Execution_325
17.1.4.1 Error Messages_325
17.1.4.2 Detailed Information_326
18. FORTRAN Application Programs_327
18.1 Using Flat Earth Applications_328
18.2 Baseline Crossing Application_329
18.3 Bi Axial Meridional Arcs_329
18.4 Ellipsoid Constants Arcs Radii_331
18.5 Quadrilateral Ellipsoidal Area_333
Contents xv
18.6 Polygonal Area on a Sphere or Bi Axial Ellipsoid_334
18.7 Length of Parallel_336
18.8 Geodetic Reference System_3 3 7
18.9 Bi Linear Interpolation_339
18.10 S Transformation_340
18.11 Forward Long Line Kivioja's Method_344
18.12 Inverse Long Line Kivioja's Method_346
18.13 Forward Long Line Vincenty's Method_348
18.14 Inverse Long Line Vincenty's Method_349
18.15 Polyeder Mapping System_351
18.16 Gaussian Ellipsoid to Sphere_353
18.17 Normal Mercator Projection_356
18.18 Gauss Kruger Projection_3 60
18.19 Lambert's Conical Conformal Projection_363
18.20 Hotine's Oblique Mercator Projection_368
18.21 Rosenmund's Oblique Mercator Projection_372
18.22 Stereographic Conformal Projection_375
18.23 I/O Subroutines_378
19. International Organisations_383
19.1 International Union of Geodesy and Geophysics_383
19.2 International Association of Geodesy_384
19.3 Federation Internationale des Geometres_388
19.4 International Hydrographic Organisation_389
19.5 International Earth Rotation Service_389
19.6 Participants in National Geodetic Satellite Program_391
Bibliography_393
Index of Subjects_425
Appendix ^^_438
List of Figures
Figure 1: A four dimensional path (spiral) of a planet in space time is a geodesic_1
Figure 2: Part of the Astronomical Clock at the Cathedral of Strasbourg_3
Figure 3: Time Verdi's clock_4
Figure 4: NASA/GSFC GEM4 Global Detailed Gravimetric Geoid in the Miller projection_11
Figure 5: Geoid undulations 15000 x enlarged _11
Figure 6: The geoid and three reference ellipsoids_12
Figure 7: Ecliptic and Equator_14
Figure 8: Parametry Zemli System of 1990 definition_18
Figure 9: World Geodetic System of 1984 definition_19
Figure 10: Wegener's Vision of Pangaea_27
Figure 11: Classification of Earth's depths_28
Figure 12: Tectonic plates and its boundaries_30
Figure 13: Celestial sphere with intersection of the Equator by ecliptics_30
Figure 14: Rotation of axis due to precession (1) and nutation (2) in 25 850 years_31
Figure 15: Effect of the Moon on the Earth_3 2
Figure 16: Coriolis Force_32
Figure 17: Polar heights as surveyed by Marcuse and Preston_34
Figure 18: Path of polar motion between 1909.0 and 1915.0_35
Figure 19: Flare triangulation of the connection Denmark and Norway_41
Figure 20: Comparison of various Datums along the 30° meridian from Finland to South Africa_42
Figure 21: One example of various reference levels and vertical datums in use Spain / Gibraltar_45
Figure 22: Vaisala's flare triangulation application_47
Figure 23: View on the Earthsphere and the Hydrosphere_59
Figure 24: Principle of VLBI with a short base_66
Figure 25: Principle of VLBI with a line base_67
Figure 26: Time shift of signals_67
Figure 27: One of the first GPS satellites_69
Figure 28: Measuring pseudo ranges_74
Figure 29: C Nav Starfire GcDGPS World Receiver in the foreground on a barge lifting a Hurricane Katrina
damaged platform_77
Figure 30: Distorted filtered transformed corrected grids_78
Figure 31: Spherical Earth_87
Figure 32: Space curvature illustrated in 2D_87
Figure 33: Plane triangle_88
Figure 34: Bearing and distance_89
Figure 35: Area calculation in four quadrants_92
Figure 36: Airborne and shipbome baseline crossing_93
Figure 37: Shipborne baseline crossing technique_94
Figure 38: Determination of the shortest LS sum distance of Baseline Al _98
Figure 39: Determination of the shortest LS sum distance of Baseline A2_98
Figure 40: General spherical triangle_99
Figure 41: Rectangular spherical triangle_99
Figure 42: Total and zonal area determination_105
Figure 43: Ellipsoidal quadrilateral area_108
Figure 44: Spherical polygonal area_108
Figure 45: Hydrosphere between 1200 1500 AD_115
Figure 46: Bessel ellipsoids in legal metres and international metres_123
Figure 47: European 52° arc of parallel between Feaghmain and Warsaw_125
Figure 48: Radii of curvature in Prime Vertical and in the Reference Meridian_126
Figure 49: ED50 corrections for AE_134
Figure 50: ED50 corrections for AN _134
Figure 51: Location of a grid square for interpolation_13 5
Figure 52: Cross sections of the bi linear interpolation surface are defined by straight line elements_137
Figure 53: Translated and rotated 3D coordinate system_139
Figure 54: Geoid separation of the old and the new Datum_143
Figure 55: Ellipsoidal and physical Earth_143
Figure 56: Calculated differences for the 6 parameter transformation solution_ 146
Figure 57: Calculated differences for the 7 parameter transformation solution_146
xxii List of Figures
Figure 58: Calculated differences for the 9 parameter transformation solution 146
Figure 59: Datum transformation round trip error of latitude 150
Figure 60: Datum transformation round trip error of longitude 150
Figure 61: Datum transformation round trip error of height 151
Figure 62: The great elliptic arc and the reference ellipsoid 153
Figure 63: Normal sections and the reference ellipsoid 154
Figure 64: Geodetic triangle 155
Figure 65: Geodesic divided into dS line elements 156
Figure 66: The geodesic and the reference ellipsoid 157
Figure 67: Different positions of the geodesic A B 164
Figure 68: Time to calculate a rectifying sphere 166
Figure 69: Comparison of computing time to calculate the Meridional arc 167
Figure 70: Round trip error of the meridional arc in degrees 168
Figure 71: Round trip error of the meridional arc in m 168
Figure 72: An LCC algorithm shows that iterating is not always successful 170
Figure 73: Tangencv or secancy of various map projection surfaces 173
Figure 74: Figure 75: Outline shows the four quadrants as used for computing correct signs using Flags (i|j . Azimuth and convergence .in) 178 180
Figure 76: Normal Mercator and Lambert projection projected geodetic vs. grid angles 181
Figure 77: Transverse Mercator vs. grid angles 182
Figure 78: Lambert's conformal conical projection 184
Figure 79: Lambert's grid system 185
Figure 80: Lambert's conical IGN zone 188
Figure 81: Lambert's conformal conical projection of France 190
Figure 82: Gaussian sphere / ellipsoid mapping system 194
Figure 83: Gauss Schreiber grid of the Hannover'schen Landesvermessung 1866 196
Figure 84: Perspective projection of the sphere 201
Figure 85: Mercator projection of the sphere 201
Figure 86: Scale factor as a function of 8° latitudinal zone width 205
Figure 87: Scale factor as a function of 75° latitudinal zone width 205
Figure 88: Normal Mercator with two secant lines 206
Figure 89: UM and UTM grid zones for the equatorial territory of Indonesia 207
Figure 90: Transverse Mercator grid zone system 211
Figure 91: Borneo Rectified Skew Orthomorphic grid 219
Figure 92: Initial Line of the Borneo RSO grid 219
Figure 93: Oblique Mercator Grid of Switzerland 222
Figure 94: Rosenmund's Oblique Mercator system 222
Figure 95: Construction of the stereographic projection 227
Figure 96: Stereographic grid of the Netherlands 230
Figure 97: Polyeder mapping system 232
Figure 98: Polyeder conical construction AB 232
Figure 99: Parallel bursts 233
Figure 100: Meridian bursts 233
Figure 101: Part of the Indonesian Polyeder mapping system 235
Figure 102: Conversion between 3° 6° zone systems and 6° 6° zone systems 238
Figure 103: Cover 3rd amended edition of the Principia 250
Figure 104: Pendulum observations in Newton's De Mundi Svstemate 251
Figure 105: Cover of the Theorie de la Figure de la Terre 253
Figure 106: Carl F. Gauss 260
Figure 107: Formulating a hierarchy of geometries 261
Figure 108: Hamilton's multiplication table for quaternions 262
Figure 109: Non Commutative Algebra 262
Figure 110: Vector rotation 270
Figure 111: Forward vector rotation 271
Figure 112: Inverse vector rotation 273
Figure 113: Part of the "Aristo Geodat" slide rule in Gon 275
Figure 114: Overview IBM RS/6000 SP Nodes 281
Figure 115: SP Switch Circuitry 281
Figure 116: IBM RISC System / 6000 SP Massively Parallel Processors 281
List of Figures xxiii
Figure 117: Electronic Teleconferencing Facility Centre fed by 1024 servers Each server is equipped with
two SCSI discs_292
Figure 118: Sketch of spatial dataflow using multi dimensional Databases and data Overlays in brief_294
Figure 119: Ultra short baseline (USBL) configuration_301
Figure 120: Super short baseline (SSBL) configuration_301
Figure 121: Long baseline (LBL) configuration_302
Figure 122: Multi user Long Baseline (MuLBL) configuration_302
Figure 123: Kongsberg HiPAP using an array of 241 elements assembled into one sphere_303
Figure 124: Kongsberg HUGIN 1000 Mine hunting survey_309
Figure 125: Hugin 3000 AUV using GNSS and Doppler log_309
Figure 126: Single beam ceramic transducer_311
Figure 127: Kongsberg BM 636 dual beam ceramic transducer_312
Figure 128: Simultaneous deployment of multi single beam echosounders_313
Figure 129: Hull mounted multibeam echosounder geometry_313
Figure 130: Hull mounted multibeam echosounder geometry_313
Figure 131: Towed Fish mounted sidescan sonar_314
Figure 132: Sketch of DGPS surveying by parametric echosounder_316
Figure 133: Laptop PC with Innomar SES 2000 Compact parametric sub bottom profiler_317
Figure 134: Innomar SES 2000 Compact parametric transducer with cable_317
Figure 135: Recovering HUGIN 3000 AUV from deep sea operations_318
Figure 136: C C side scan sonar survey pattern for the German U 166 submarine in the Gulf of Mexico_319
Figure 137: Side scan sonar 410 kHz image of the German U 166 submarine discovered at 1100 m depth_319
Figure 138: Baeyer's design of the Mittel Europaischen Gradmessung_385
Related Topics On_CD contains some corresponding figures in a colour block. In the list mentioned above are
these figures indicated in bold |
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| discipline | Physik Bauingenieurwesen Vermessungswesen Geographie |
| discipline_str_mv | Physik Bauingenieurwesen Vermessungswesen Geographie |
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| id | DE-604.BV022963354 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:05:39Z |
| indexdate | 2024-07-09T21:08:41Z |
| institution | BVB |
| isbn | 9783540254492 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016167703 |
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| physical | XXIII,439 S. Ill., graph. Darst. 270 mm x 193 mm 1 CD-ROM (12 cm) |
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| spelling | Hooijberg, Maarten 1945- Verfasser (DE-588)115539603 aut Geometrical geodesy using information and computer technology Maarten Hooijberg Berlin Springer 2008 XXIII,439 S. Ill., graph. Darst. 270 mm x 193 mm 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Geodesia - Matematicas Geodesia - Procesamiento de datos Geodäsie (DE-588)4020202-1 gnd rswk-swf Computerunterstütztes Verfahren (DE-588)4139030-1 gnd rswk-swf Geodäsie (DE-588)4020202-1 s Computerunterstütztes Verfahren (DE-588)4139030-1 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2603438&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016167703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hooijberg, Maarten 1945- Geometrical geodesy using information and computer technology Geodesia - Matematicas Geodesia - Procesamiento de datos Geodäsie (DE-588)4020202-1 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd |
| subject_GND | (DE-588)4020202-1 (DE-588)4139030-1 |
| title | Geometrical geodesy using information and computer technology |
| title_auth | Geometrical geodesy using information and computer technology |
| title_exact_search | Geometrical geodesy using information and computer technology |
| title_exact_search_txtP | Geometrical geodesy using information and computer technology |
| title_full | Geometrical geodesy using information and computer technology Maarten Hooijberg |
| title_fullStr | Geometrical geodesy using information and computer technology Maarten Hooijberg |
| title_full_unstemmed | Geometrical geodesy using information and computer technology Maarten Hooijberg |
| title_short | Geometrical geodesy |
| title_sort | geometrical geodesy using information and computer technology |
| title_sub | using information and computer technology |
| topic | Geodesia - Matematicas Geodesia - Procesamiento de datos Geodäsie (DE-588)4020202-1 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd |
| topic_facet | Geodesia - Matematicas Geodesia - Procesamiento de datos Geodäsie Computerunterstütztes Verfahren |
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