Theory of the Earth's Shape, Volume 13
1st Edition
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Table of Contents
Preface
First Part Physical Geodesy
1. Origin, Structure and Form of the Earth
1.1 The Earth as a Planet of the Solar System
1.2 The Earth's Physical Structure
1.3 Brief Historical Survey of the Ideas Concerning the Earth's Form and Size
2 Elements of Potential Theory
2.1 Principles of Field Theory
2.2 Harmonic Functions
2.3 Newtonian Potential
2.4 Boundary-Value Problems of Potential Theory
3 Reference Surfaces. Coordinate Systems
3.1 Level Surfaces
3.2 The Level Spheroid
3.3 The Level Ellipsoid
3.4 Coordinate Systems
3.5 Altitude Systems
4 The Perturbing Potential
4.1 Bruns' Formula. The Third Boundary-Value Problem for the Geoid
4.2 The Third Boundary-Value Problem for the Earth's Physical Surface
4.3 Expansion of the Perturbing Potential in Spherical Harmonics. The Spherical Approximation of the Boundary Condition for the Geoid
4.4 The Gravity Anomaly in External Space
5 The Determination of the Geoid by Gravity Methods
5.1 Stokes' Formula
5.2 Generalization of Stokes' Formula
5.3 Determination of the Gravimetric Deflection of the Vertical
5.4 The Gravity Reduction
5.5 Types of Reductions Used in Physical Geodesy
5.6 Practical Determination of the Components of the Deflection of the Vertical and of the Geoid Undulations
6 Determination of the Geoid by Astro-Gravimetric Methods
6.1 The Astro-Geodetic Levelling
6.2 The Astro-Gravimetric Levelling
7 Determination of the Earth's Physical Surface
7.1 Molodenski's Problem
7.2 Determination of the Perturbing Potential by Using Green's Formulae
7.3 Solving the Main Integral Equation
7.4 Geometrical Interpretation of the Solution of Molodenski's Equation
7.5 The Deflection of the Vertical on the Earth's Physical Surface
Second Part Ellipsoidal Geodesy
8 The Rotation Ellipsoid as Reference Surface in Geodesy
8.1 The Parameters of the Reference Ellipsoid
8.2 The Parametric Equations of the Rotation Ellipsoid
9 Curves on the Surface of the Reference Ellipsoid
9.1 The Coordinate Lines
9.2 Normal Sections
9.3 The Geodetic Line
10 The Reduction of the Geodetic Observations on the Reference Ellipsoid's Surface
10.1 The Reduction of the Astronomical Observations
10.2 The Reduction of the Azimuthal Observations
10.3 The Reduction of the Zenithal Observations to the Normal to the Ellipsoid
10.4 The Reduction of the Distances on the Ellipsoid
11 Solving the Geodetic Triangles on the Reference Ellipsoid
11.1 The Spherical Excess
11.2 Solving Small Geodetic Triangles by Means of Legendre's Theorem
11.3 Solving Small Geodetic Triangles by the Additament Method
12 Calculation of the Geodetic Coordinates on the Reference Ellipsoid
12.1 Solving the Basic Geodetic Problems for Small Geodetic Distances
12.2 Gauss' Method (Method of the Mean Arguments) for Solving the Basic Geodetic Problems for Medium Geodetic Distances
12.3 Solving the Basic Geodetic Problems for Large Geodetic Distances
12.4 Differential Formulae
Third Part Astro-Geodetic Triangulation
13 The Notion of Performing Astro-Geodetic Triangulation
13.1 General Considerations
13.2 Error Propagation in the Astro-Geodetic Triangulation
14 Measurements in Astro-Geodetic Triangulation
14.1 Angle Measurements
14.2 Distance Measurements
14.3 Relative Measurements of Gravity
14.4 Levelling Measurements
14.5 Determinations of Geodetic Astronomy
15 Adjustment of the Astro-Geodetic Triangulation
15.1 General Considerations
15.2 Adjustment of the Triangulation Network by Means of the Method of Conditioned Observations
15.3 Adjustment of the Triangulation Network by Means of the Method of Indirect Observations
15.4 Weight Determination After Adjustment
15.5 Processing of the Observations in Free Geodetic Networks
16 The 1st-Order Astro-Geodetic Triangulation Network of the Socialist Republic of Romania
16.1 The Network Layout
16.2 Marking and Constructing the Station Points of the Network
16.3 Angle and Distance Measurements as well as Astro-Geodetic Determinations Carried out at the Station Points of the Network
16.4 The Network Adjustment
Fourth Part Three-Dimensional Geodesy
17 Basic Equations of Three-Dimensional Geodesy
17.1 Coordinate Systems Used in Three-Dimensional Geodesy
17.2 Origin, Methodology and Purpose of Three-Dimensional Geodesy
17.3 Basic Equations of Three-Dimensional Geodesy
18. Elementary Calculations in Three-Dimensional Geodesy
18.1 The Calculation Principle in the Local System
18.2 Choice of the Local Geodetic Trihedron
18.3 Calculating the Coordinates of a Point
18.4 Determining the Local Astronomical Vertical
18.5 Orientation Calculation in the Local System
18.6 Calculation of a Geodetic Traverse
18.7 Triangulation Calculations
19 Basic Methods for Developing the Geodetic Networks by Means of the Earth's Artificial Satellites
19.1 General Considerantions
19.2 Elements of an Artificial Satellite's Orbit
19.3 Geodetic Artificial Satellites
19.4 Methods of Observing Artificial Satellites
19.5 Spatial Triangulation
19.6 Spatial Trilateration
19.7 Vector Network
20 Triangulation Calculations Using Artificial Satellites
20.1 Identification of the Recorded Stars
20.2 Calculation of the Coordinates on the Photographic Plate of the Recorded Stars
20.3 Comparison of the Measured and Calculated Values
20.4 Linearization of the Satellite's Position on the Photographic Plate
20.5 Returning to the Global System
20.6 General Adjustment of a Spatial Triangulation by Means of Artificial Satellites
21 Some Examples of Spatial Triangulation Operations
21.1 The France — Algeria Connexion
21.2 The European Continent — Azores Islands Connexion
21.3 The World Network of Triangulation by Means of Artificial Satellites
21.4 Western European Triangulation by Means of Satellites (West)
21.5 Brief Survey of Other Triangulation Operations by Means of Artificial Satellites
22 General Survey of Other Geometrical Methods of Spatial Geodesy by Means of Artificial Satellites
22.1 The 4-Laser Method
22.2 The Optical-Telemetric Method
22.3 The Orbital Method
22.4 The Method of the Simultaneity Circle
22.5 Experiment of Using Laser Measurements
Fifth Part Methods for Determining the Terrestrial Ellipsoid and the Geoid
23 The Determination of the Reference Ellipsoid by Using Astro-Geodetic Methods
23.1 Determining the Reference Ellipsoid from Measurements of Meridian and Parallel Arcs
23.2 Determining the Reference Ellipsoid by Using the Method of Surfaces
23.3 Determining the Reference Ellipsoid by Using Differential Relations
24 The Determination of the Earth's Form from Astro-Geodetic and Gravity Measurements
24.1 Global Determination of the Geoid
24.2 Determining the Earth's Physical Constants
24.3 Determining the Gravity Field and the Parameters of the General Terrestrial Ellipsoid
25 Dynamic Geodesy
25.1 Non-Perturbed Orbits
25.2 Relationships Between the Elements of the Satellite Orbit and the Geocentric, Topocentric and Rectangular Coordinate Systems
25.3 Perturbed Orbits
25.4 The Luni — Solar Perturbation
25.5 Perturbations of the Artificial Satellites' Orbits Caused by the Resistance of the Atmosphere and by Radiation Pressure
25.6 Determining the Parameters of the Earth's Gravitational Field by Using Artificial Satellites
25.7 The Geoid Determination
25.8 Satellite Altimetry
25.9 Interpretation of the Results of Satellite Geodesy
26 The Geodetic Reference System
Sixth Part Determination of the Recent Movements of the Earth's Crust
27 Geodetic Methods for Determining the Recent Movements of the Earth's Crust
27.1 Introductory Remarks
27.2 Repeated Geometrical Levelling
27.3 Triangulation-Trilateration Networks for Determining the Horizontal Movements of the Earth's Crust
27.4 Astro-Geodetic Methods for Determining the Movements of the Continents
27.5 Other Methods Used for Determining the Crustal Movements
28 Processing the Geodetic Observations Carried Out for Determining the Recent Crustal Movements
28.1 A Functional-Stochastic Model for the Three-Dimensional Determination of the Recent Movements of the Earth's Crust within Areas of Limited Size
28.2 Particular Functional-Stochastic Models for Determining the Recent Crustal Movements
28.3 Possibilities of Adjusting the Repeated Geodetic Observations
28.4 Accuracy Estimation and Statistical Analysis of the Determinations of Recent Crustal Movements
29 Examples of Daterminations of Recent Movements of the Earth's Crust
29.1 Map of the Recent Crustal Movements in Eastern Europe
29.2 Map of the Vertical Crustal Movements on the Territory of the Socialist Republic of Romania
29.3 Utilization of Some Improved Functional-Stochastic Models for Determining the Vertical Crustal Movements
29.4 Other Examples of Determining Recent Movements of the Earth's Crust
Future Prospects in the Light of Present Geodetic Achievements
References
Abbreviations
Index
Description
Theory of the Earth's Shape considers the physical-mathematical problems raised by the determination of the form of the planet, thereby making a significant contribution to the technological scientific literature in this field. This book is organized into six parts encompassing 29 chapters. The first part, entitled Physical Geodesy, presents the theory of the determination of the gravitational field, in the definition of which preference was given to the method of expansion in spherical harmonics recommended by the International Union of Geodesy and Geophysics in establishing the international "Geodetic Reference System 1967". Part II deals with the principal aspects of Ellipsoidal Geodesy, such as the methods of solving the geodetic problems on the reference ellipsoid. Part III considers the main problems associated with Astro-geodetic Triangulation, particularly with the conception of materialization and the necessary measurements as the required adjustment procedures. This part also provides approaches regarding the controlled analysis of angular measurements and the description of some original calculation and measurement methods. Part IV concerns one of the methods of determining the spatial coordinates of the geodetic points in a unitary system, such as the three-dimensional geodesy, which has had more concrete applications since the launching of the Earth's first artificial satellites. Part V describes the methods for determining the terrestrial ellipsoid and the geoid, as well as the conventional methods and the methods of Dynamical Geodesy. Part VI discusses the geodetic methods for the determination of the movements of the Earth's crust, along with an overall examination of the theoretical and practical aspects which in principle constitute the object of such activities. This book will prove useful to geophysicists, astronomers, Earth scientists, and researchers.
Details
- Language:
- English
- Copyright:
- © Elsevier Science 1982
- Published:
- 1st January 1982
- Imprint:
- Elsevier Science
- eBook ISBN:
- 9781483291895