Handbook Of Geodesy

Handbook of Geodesy

Handbook of Mathematical Geodesy

Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.

Geometrical Geodesy

Surveying a Century Ago As it was based on the principles of geometry and trigonometry, surveying may be may be looked upon as a branch of practical mathematics. Hence, it was necessary that land surveyors and hydrographers should have a fair general knowledge, not only of these subjects, but also of all the subjects comprised by the term mathemat ics. In addition, the knowledge of mathematics required in ordinary chain surveying and levelling was not very extensive but in geodetical work, the highest mathematical ability and great organising power were required for a proper conception and supervision of the operations (Threlfall, 1940). Only small area of a few hundred square kilometres can be accurately mapped and surveyed without a frame work, since no difficulty is encountered because of Earth-curvature. In the past, especially in hydrography due to the type of work, surveying was carried out on the principles of ordinary practice, but in a very rough man ner, rapidity of execution being of paramount importance, the permissible error was sometimes large. The relative positions of the main surface features were obtained by aid of portable instruments, such as sextants and lead lines, tide poles, and logships. Sketching, just like military surveying was often filling in the smaller detail. In contrary, survey works done by the national mapping agencies (NMAs) were of a higher-level, and comprised the delimitation of boundaries as well as topographical surveys.