The Concepts

2nd Edition - November 1, 1986

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  • Authors: P. Vanícek, E.J. Krakiwsky
  • eBook ISBN: 9781483290799

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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


    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


    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


    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


    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


    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


    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

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  • 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.