Geodesy
The Concepts
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Geodesy: The Concepts, Second Edition focuses on the processes, approaches, and methodologies employed in geodesy, including gravity field and motions of the earth and geodetic methodology. The book first underscores the history of geodesy, mathematics and geodesy, and geodesy and other disciplines. Discussions focus on algebra, geometry, statistics, symbolic relation between geodesy and other sciences, applications of geodesy, and the historical beginnings of geodesy. The text then ponders on the structure of geodesy, as well as functions of geodesy and geodetic theory and practice. The publication examines the motions, gravity field, deformations in time, and size and shape of earth. Topics include tidal phenomena, tectonic deformations, actual shape of the earth, gravity anomaly and potential, and observed polar motion and spin velocity variations. The elements of geodetic methodology, classes of mathematical models, and formulation and solving of problems are also mentioned. The text is a dependable source of data for readers interested in the concepts involved in geodesy.
Table of Contents
Foreword
Foreword to the Second Edition
Part I. Introduction
1. History of Geodesy
1.1. Historical Beginnings of Geodesy
1.2. Scientific Beginnings of Geodesy
1.3. Geodesy in the Service of Mapping
1.4. Geodesy of the Modern Era
2. Geodesy and Other Disciplines
2.1. Applications of Geodesy
2.2. Symbiotic Relation Between Geodesy and some Other Sciences
2.3. Theoretical Basis of Geodesy
3. Mathematics and Geodesy
3.1. Algebra
3.2. Analysis
3.3. Geometry
3.4. Statistics
4. Structure of Geodesy
4.1. Functions of Geodesy
4.2. Geodetic Theory
4.3. Geodetic Practice
4.4. Geodetic Profession
References
Part II. The Earth
5. Earth and its Motions
5.1. Earth's Annual Motion
5.2. Earth's Spin, Precession, and Nutation
5.3. Earth's Free Nutation
5.4. Observed Polar Motion and Spin Velocity Variations
6. Earth and its Gravity Field
6.1. Gravity Field
6.2. Gravity Anomaly
6.3. Gravity Potential
6.4. Geoid and Deflections of the Vertical
7. Earth and its Size and Shape
7.1. Actual Shape of the Earth
7.2. Geoid as a Figure of the Earth
7.3. Biaxial Ellipsoid as a Figure of the Earth
7.4. Other Mathematical Figures of the Earth
8. Earth and its Deformations in Time
8.1. Tidal Phenomena
8.2. Crustal Loading Deformations
8.3. Tectonic Deformations
8.4. Man-Made and Other Deformations
9. Earth and its Atmosphere
9.1. Some Physical Properties of the Atmosphere
9.2. Wave Propagation Through the Atmosphere and Water
9.3. Temporal Variations of the Atmosphere
9.4. Gravitational Field of the Atmosphere
References
Part III. Methodology
10. Elements of Geodetic Methodology
10.1. General Procedure
10.2. Formulation of the Mathematical Model
10.3. Observables and their Properties
10.4. Vector of Observables
11. Classes of Mathematical Models
11.1. Classification of Models
11.2. Models with a Unique Solution
11.3. Models with an Underdetermined Solution
11.4. Models with an Overdetermined Solution
12. Least-Squares Solution of Overdetermined Models
12.1. Formulation of the Least-Squares Problem
12.2. Solution of the Least-Squares Problem
12.3. Covariance Matrices of the Results
13. Assessment of Results
13.1. Hubert Space and Statistics
13.2. Statistical Testing
13.3. Assessment of Observations of One Observable
13.4. Simultaneous Assessment of Observations and Mathematical Models
13.5. Assessment of the Determined Parameters
14. Formulation and Solving of Problems
14.1. Optimal Accuracy Design
14.2. Analysis of Trend
14.3. Adjustment of Observations
14.4. Problems with a Priori Knowledge About the Parameters
14.5. Problems with Constraints and Singularities
14.6. Step-by-Step Procedures in Dynamic and Static Problems
References
Part IV. Positioning
15. Point Positioning
15.1. Fundamentals of Geodetic Astronomy
15.2. Astronomical Positioning
15.3. Satellite Positioning
15.4. Transformations of Terrestrial Positions
16. Relative Positioning
16.1. Relative Three-Dimensional Positioning
16.2. Relative Horizontal Positioning on Reference Ellipsoid
16.3. Relative Horizontal Positioning on Conformal Map
16.4. Relative Vertical Positioning
17. Three-Dimensional Networks
17.1. Three-Dimensional Networks Using Terrestrial Observations
17.2. Photogrammetrical Networks
17.3. Three-Dimensional Networks Using Extraterrestrial Observations
17.4. Assessment and Merger of Three-Dimensional Networks
18. Horizontal Networks
18.1. Horizontal Datum
18.2. Mathematical Models and their Solution
18.3. Assessment, Expansion, and Merger of Horizontal Networks
18.4. Marine Positioning
19. Height Networks
19.1. Vertical Datum
19.2. Mathematical Models for Leveling
19.3. Assessment and Design of Height Networks
19.4. Other Heighting Concepts
References
Part V. Earth's Gravity Field
20. Global Treatment of the Gravity Field
20.1. Fundamental Equations for Gravity Potential
20.2. Eigenfunction Development of Gravitational Potential
20.3. Model Gravity Field
20.4. Disturbing Potential
21. Local Treatment of the Gravity Field
21.1. Conversion of Disturbing Potential into Other Field Parameters
21.2. Vertical Gradient of Gravity
21.3. Curvature of the Plumb Line
21.4. Topographical and Isostatic Effects
22. Determination of the Gravity Field from Gravity Observations
22.1. Stokes's Concept
22.2. Molodenskij's Concept
22.3. Gravimetry
22.4. Evaluation of the Surface Integrals
23. Determination of the Gravity Field from Observations to Satellites
23.1. Satellites and the Gravitational Field
23.2. Prediction of Orbits
23.3. Analysis of Orbital Perturbations
23.4. Evaluation of Gravity Field Parameters
24. Determination of the Gravity Field from Deflections and from Heterogeneous Data
24.1. Geometrical Solution for the Geoid
24.2. Transformation of Gravity Field Parameters
24.3. Densification and Refinement of Deflections of the Vertical
24.4. Solutions for the Geoid from Heterogeneous Data
References
Part VI. Temporal Variations
25. Corrections for Temporal Variations
25.1. Elastic Response to Tidal Stress
25.2. Tidal Corrections
25.3. Corrections Due to Sea Tide Effects
25.4. Corrections Due to Polar Motion Deformations, and Other Causes
26. Detection of Vertical Movements
26.1. Sources of Information on Vertical Movements
26.2. Interdependence of Temporal Variations of Gravity and Heights
26.3. Vertical Displacement Profiles
26.4. Areal Modeling of Vertical Movements
27. Detection of Horizontal Movements
27.1. Sources of Information on Horizontal Movements
27.2. Comparison of Horizontal Positions
27.3. Direct Evaluation of Horizontal Displacements
27.4. Strain, Shear, and Other Models
References
Author Index
Subject Index
Product details
- No. of pages: 714
- Language: English
- Copyright: © Elsevier Science 1986
- Published: November 1, 1986
- Imprint: Elsevier Science
- eBook ISBN: 9781483290799
About the Authors
P. Vanícek
E.J. Krakiwsky
Ratings and Reviews
Latest reviews
(Total rating for all reviews)
Sajjad S. Thu Jun 30 2022
Part V - "Earth Gravity Field" is very well defined in components.
This work is worthy of admiration, it shows the potential to influence and inspire fellow researchers and scholars.