Vaníček P, Krakiwsky EJ (1986) Geodesy: the Concepts (2nd edn). Elsevier Science. https://doi.org/10.1016/C2009-0-07552-7

Contents

Part I: Introduction

Chapter 1 - History of geodesy

1.1 Historical beginning of geodesy

1.2 Scientific beginning of geodesy

1.3 Geodesy in the service of mapping

1.4 Geodesy of the modern era

Chapter 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

Chapter 3 - Mathematics and geodesy

3.1 Algebra

3.2 Analysis

3.3 Geometry

3.4 Statistics

Chapter 4 - Structure of geodesy

4.1 Functions of geodesy

4.2 Geodetic theory

4.3 Geodetic practice

4.4 Geodetic profession

Part 1 - References

Part II: The Earth

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 9 - Earth and its atmosphere

9.1 Some physical propersities 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

Part II - References

Part III: Methodology

Chapter 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

Chapter 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

Chapter 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

Chapter 13 - Assessment of results

13.1 Hilbert 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

Chapter 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

Part III - References

Part IV: Positioning

Chapter 15 - Point positioning

15.1 Fundamentals of geodetic astronomy

15.2 Astronomical positioning

15.3 Satellite positioning

15.4 Transformations of terrestrial positions

Chapter 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

Chapter 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 Assessmen and merger of three-dimensional networks

Chapter 18 - Horizontal networks

18.1 Horizontal datumn

18.2 Mathematical models and their solution

18.3 Assessment, expansion, and merger of horizontal networks

18.4 Marine positioning

Chapter 19 - Height networks

19.1 Vertical datum

19.2 Mathematical models for levelling

19.3 Assessment and design of height networks

19.4 Other heighting concepts

Part IV - References

Part V: Earth’s gravity field

Chapter 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

Chapter 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

Chapter 22 - Determination of the gravity field from gravity observations

22.1 Stoke’s concept

22.2 Molodenskij’s concept

22.3 Gravimetry

22.4 Evaluation of the surface integrals

Chapter 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

Chapter 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 paramters

24.3 Densification and refinement of deflections of the vertical

24.4 Solutions for the geoid from heterogeneous data

Part V - References

Part VI: Temporal variations

Chapter 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

Chapter 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 modelling of vertical movements

Chapter 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

Part VI - References