Sansò F., Sideris M.G. (eds.) Geoid Determination: Theory and Methods

Springer, 2013. - 734 pp.
This book is based on the material of the lecture noties in several International Schools for the Determination and Use of the Geoid, organized by the International Geoid Serivice of the International Association of Geodesy. It consolidates, unifies, and streamlines this material in a unique way not covereed by the few other books that exist on this subjext. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level).
The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.Theory
The Forward Modelling of the Gravity Field.
Observables of Physical Geodesy and Their Analytical Representation.
Harmonic Calculus and Global Gravity Models.
The Local Modelling of the Gravity Field: The Terrain Effects.
The Local Modelling of the Gravity Field by Collocation.
Methods and Applications
Global Gravitational Models.
Geoid Determination by 3D Least-Squares Collocation.
Topographic Reductions in Gravity and Geoid Modeling.
Marine Gravity and Geoid from Satellite Altimetry.
Geoid Determination by FFT Techniques.
Combination of Heights.
Advanced Analysis Methods
Hilbert Spaces and Deterministic Collocation.
On Potential Theory and HS of Harmonic Functions.
A Quick Look to Classical Boundary Value Problems (BVP) Solutions.
The Analysis of Geodetic Boundary Value Problems in Linear Form.