# Geodesy

## 2nd Edition

### The Concepts

**Authors:**P. Vanícek E.J. Krakiwsky

**eBook ISBN:**9781483290799

**Imprint:**Elsevier Science

**Published Date:**1st November 1986

**Page Count:**714

## Description

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

## Details

- No. of pages:
- 714

- Language:
- English

- Copyright:
- © Elsevier Science 1986

- Published:
- 1st November 1986

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9781483290799