Sneeuw N. (2006). Physical geodesy. Lecture notes, Institute of Geodesy, University of Stuttgart. https://www.gis.uni-stuttgart.de/lehre/LectureNotes/LNErdmSS06.pdf

Content

1. Introduction

1.1. Physical Geodesy

1.2. Links to Earth sciences

1.3. Applications in engineering

2. Gravitation

2.1. Newtonian gravitation

• 2.1.1. Vectorial attraction of a point mass
• 2.1.2. Gravitational potential
• 2.1.3. Superposition discrete
• 2.1.4. Superposition continuous

2.2. Ideal solids

• 2.2.1. Solid homogeneous sphere
• 2.2.2. Spherical shell
• 2.2.3. Solid homogeneous cylinder

2.3. Tides 2.4. Summary

3. Rotation

3.1. Kinematics: acceleration in a rotating frame

3.2. Dynamics: precession, nutation, polar motion

3.3. Geometry: defining the inertial reference system

• 3.3.1. Inertial space
• 3.3.2. Transformations
• 3.3.3. Conventional inertial reference system
• 3.3.4. Overview

4. Gravity and Gravimetry

4.1. Gravity attraction and potential

4.2. Gravimetry

• 4.2.1. Gravimetric measurementlespendulum
• 4.2.2. Gravimetric measurement principles: spring
• 4.2.3. Gravimetric measurement principles: free fall

4.3. Gravity networks

• 4.3.1. Gravity observation procedures
• 4.3.2. Relative gravity observation equation

5. Elements from potential theory

5.1. Some vector calculus rules

5.2. Divergence Gauss

5.3. Special cases and applications

5.4. Boundary value problems

6 Solving Laplace’s equation

6.1. Cartesian coordinates

• 6.1.1. Solution of Dirichlet and Neumann BVPs in `x`, `y`, `z`

6.2. Spherical coordinates

• 6.2.1. Solution of Dirichlet and Neumann BVPs in `r`, `\theta`, `\lambda`

6.3. Properties of spherical harmonics

• 6.3.1. Orthogonal and orthonormal base functions
• 6.3.2. Calculating Legendre polynomials and Legendre functions
• 6.3.3. The addition theorem

6.4. Physical meaning of spherical harmonic coefficients

6.5. Tides revisited

7. The normal field

7.1. Normal potential

7.2. Normal gravity

7.3. Adopted normal gravity

• 7.3.1. Formulae
• 7.3.2. GRS80 constants

8. Linear model of physical geodesy

8.1. Two-step linearization

8.2. Disturbing potential and gravity

8.3. Anomalous potential and gravity

8.4. Gravity reductions

• 8.4.1. Free air reduction
• 8.4.2. Bouguer reduction
• 8.4.3. Isostasy

9. Geoid determination9.

9.1. The Stokes approach

9.2. Spectral domain solutions

• 9.2.1. Local: Fouriere
• 9.2.2. Global: spherical harmonics

9.3. Stokes integration

9.4. Practical aspects of geoid calculation

• 9.4.1. Discretization
• 9.4.2. Singularity at `\psi` = 0
• 9.4.3. Combination method
• 9.4.4. Indirect effects

A. Reference Textbooks

B. The Greek alphabet