Hofmann-Wellenhof and Moritz (2006) Physical Geodesy (2nd edn)
Hofmann-Wellenhof B, Moritz H (2006) Physical geodesy (2nd edn). https://doi.org/10.1007/978-3-211-33545-1
Heiskanen WA, Moritz H (1967) Physical geodesy.
Content
1 Fundamentals of potential theory
1.1 Attraction and potential
1.2 Potential of a solid body
1.3 Harmonic functions
1.4 Laplace’s equation in spherical coordinates
1.5 Spherica harmonics
1.6 Surface spherical harmonics
1.7 Legendre’s functions
1.8 Legendre’s functions of the second kind
1.9 Expansion theorem and orthogonality relations
1.10 Fully normalized spherical harmonics
1.11 Expansion of the reciprocal distance into zonal harmonics and decomposition formula
1.12 Solution of Dirichlet’s problem by means of spherical harmonics and Poisson’s integral
1.13 Other boundary-value problems
1.14 The radial derivative of a harmonic function
1.15 Laplace’s equation in ellipsoidal-harmonic coordinates
1.16 Ellipsoidal harmonics
2 Gravity field of the earth
2.1 Gravity
2.2 Level surfaces and plumb lines
2.3 Curvature of level surfaces and plumb lines
2.4 Natural coordinates
2.5 The potential of the earth in terms of spherical harmonics
2.6 Harmonics of lower degree
2.7 The gravity field of the level ellipsoid
2.8 Normal gravity
2.9 Expansion of the normal potential in spherical harmonics
2.10 Series expansions for the normal gravity field
2.11 Reference ellipsoid – numerical values
2.12 Anomalous gravity field, geoidal undulations, and deflections of the vertical
2.13 Spherical approximation and expansion of the disturbing potential in spherical harmonics
2.14 Gravity anomalies outside the earth
2.15 Stokes’ formula
2.16 Explicit form of Stokes’ integral and Stokes’ function in spherical harmonics
2.17 Generalization to an arbitrary reference ellipsoid
2.18 Gravity disturbances and Koch’s formula
2.19 Deflections of the vertical and formula of Vening Meinesz
2.20 The vertical gradient of gravity
2.21 Practical evaluation of the integral formulas
3 Gravity reduction
3.1 Introduction
3.2 Auxiliary formulas
3.3 Free-air reduction
3.4 Bouguer reduction
3.5 Poincare and Prey reduction
3.6 Isostatic reduction
- 3.6.1 Isostasy
- 3.6.2 Topographic-isostatic reductions
3.7 The indirect effect
3.8 The inversion reduction of Rudzki
3.9 The condensation reduction of Helmert
4 Heights 157
4.1 Spirit leveling
4.2 Geopotential numbers and dynamic heights
4.3 Orthometric heights
4.4 Normal heights
4.5 Comparison of different height systems
4.6 GPS leveling
5 The geometry of the earth
5.1 Overview
Part I: Global reference systems after GPS
5.2 Introduction
5.3 The Global Positioning System
- 5.3.1 Basic concept
- 5.3.2 System architecture
- 5.3.3 Satellite signal and observables
- 5.3.4 System capabilities and accuracies
- 5.3.5 GPS modernization concept
5.4 From GPS to coordinates
- 5.4.1 Point positioning with code pseudoranges
- 5.4.2 Relative positioning with phase pseudoranges
5.5 Projection onto the ellipsoid
5.6 Coordinate transformations
- 5.6.1 Ellipsoidal and rectangular coordinates
- 5.6.2 Ellipsoidal, ellipsoidal-harmonic, and spherical coordinates
5.7 Geodetic datum transformations
- 5.7.1 Introduction
- 5.7.2 Three-dimensional transformation in general form
- 5.7.3 Three-dimensional transformation between WGS 84 and a local system
- 5.7.4 Differential formulas for other datum transformations
Part II: Three-dimensional geodesy: a transition
5.8 The three-dimensional geodesy of Bruns and Hotine
5.9 Global coordinates and local level coordinates
5.10 Combining terrestrial data and GPS
- 5.10.1 Common coordinate system
- 5.10.2 Representation of measurement quantities
Part III: Local geodetic datums
5.11 Formulation of the problem
5.12 Reduction of the astronomical measurements to the ellipsoid
5.13 Reduction of horizontal and vertical angles and of distances
5.14 The astrogeodetic determination of the geoid
5.15 Reduction for the curvature of the plumbline
5.16 Best-fitting ellipsoids and the mean earth ellipsoid
6 Gravity field outside the earth
6.1 Introduction
6.2 Normal gravity vector
6.3 Gravity disturbance vector from gravity anomalies
6.4 Gravity disturbances by upward continuation
6.5 Additional considerations
6.6 Gravity anomalies and disturbances compared
7 Space methods 255
7.1 Introduction
7.2 Satellite orbits
7.3 Determination of zonal harmonics
7.4 Rectangular coordinates of the satellite and perturbations
7.5 Determination of tesseral harmonics and station positions
7.6 New satellite gravity missions
- 7.6.1 Motivation and introductory considerations
- 7.6.2 Measurement concepts
- 7.6.3 The CHAMP mission
- 7.6.4 The GRACE mission
- 7.6.5 The GOCE mission
8 Modern views on the determination of the figure of the earth
8.1 Introduction
Part I: Gravimetric methods
8.2 Gravity reductions and the geoid
8.3 Geodetic boundary-value problems
8.4 Molodensky’s approach and linearization
8.5 Thesphericalcase
8.6 Solution by analytical continuation
- 8.6.1 The idea
- 8.6.2 First-order solution
- 8.6.3 Higher-order solution
- 8.6.4 Problems of analytical continuation
- 8.6.5 Another perspective
8.7 Deflections of the vertical
8.8 Gravity disturbances:the GPS case
8.9 Gravity reduction in the modern theory
8.10 Determination of the geoid from ground-level anomalies
8.11 A first balance
Part II: Astrogeodetic methods according to Molodensky
8.12 Some background
8.13 Astronomical leveling revisited
8.14 Topographic-isostatic reduction of vertical deflections
8.15 The meaning of the geoid
9 Statistical methods in physical geodesy
9.1 Introduction
9.2 The covariance function
9.3 Expansion of the covariance function in spherical harmonics
9.4 Interpolation and extrapolation of gravity anomalies
9.5 Accuracy of prediction methods
9.6 Least-squares prediction
9.7 Correlation with height
10 Least-squares collocation
10.1 Principles of least-squares collocation
10.2 Application of collocation to geoid determination
11 Computational methods
11.1 The remove-restore principle
11.2 Geoid in Austria by collocation
11.3 Molodensky corrections
11.4 The geoid on the internet