## Abstract

Physical geodesy studies the large-scale figure and gravity field of the Earth, which are closely related. Our understanding of the gravity field is based on Newton’s theory of gravitation. We present field theory, with partial differential equations describing the behaviour of the field throughout space. Techniques for solving these equations using boundary conditions on the Earth’s surface are explained. A central concept is the geopotential.

The figure of the Earth is approximated by an ellipsoid of revolution, after which the precise figure is described by small deviations from this ellipsoid. Vertical reference systems are discussed in this context. Extending the approach to the Earth’s gravity field yields small difference quantities, such as the disturbing potential and gravity anomalies.

Approaches to modelling the gravity field explained are spectral development of the field using spherical harmonics, the Stokes equation, numerical techniques based on the Fast Fourier Transform, the remove-restore technique, and least-squares collocation. Gravity measurement techniques are discussed, as are the multiple links with geophysics, such as terrain effects, isostasy, mean sea level and the sea level equation, and the tides.

The figure of the Earth is approximated by an ellipsoid of revolution, after which the precise figure is described by small deviations from this ellipsoid. Vertical reference systems are discussed in this context. Extending the approach to the Earth’s gravity field yields small difference quantities, such as the disturbing potential and gravity anomalies.

Approaches to modelling the gravity field explained are spectral development of the field using spherical harmonics, the Stokes equation, numerical techniques based on the Fast Fourier Transform, the remove-restore technique, and least-squares collocation. Gravity measurement techniques are discussed, as are the multiple links with geophysics, such as terrain effects, isostasy, mean sea level and the sea level equation, and the tides.

Original language | English |
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Publisher | AALTO-YLIOPISTO |

Number of pages | 516 |

ISBN (Electronic) | 978-952-60-8940-9 |

Publication status | Published - 2020 |

MoE publication type | D4 Published development or research report or study |

### Publication series

Name | Aalto University publication series SCIENCE + TECHNOLOGY |
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Publisher | Aalto University |

No. | 2 |

Volume | 2020 |

ISSN (Electronic) | 1799-490X |

## Keywords

- figure of the Earth
- gravity field
- geopotential
- reference ellipsoid
- normal field
- disturbing potential
- gravity anomaly
- geoid
- height system
- spherical harmonics
- Stokes equation
- remove-restore
- least-squares collocation
- gravimetry
- isostasy
- mean sea level
- tides