Syllabus
Surface data sources on the gravity potential of the Earth's. Information on the gravitational potential from space geodetic methods.
General formulation of boundary value problems of potential theory in physical geodesy. Choice of the system of coordinates and the representation of the figure of the Earth as an embedding of the unit sphere in Euclidean three-dimensional space. Geodetic fixed, free and mixed boundary value problems - Stokes' and Molodensky's problem, gravimetric boundary value problem, altimetry-gravimetry boundary value problems. A note on problems in airborne gravimetry and satellite gradiometry.
The linearization of geodetic boundary value problems, infinitesimal and finite perturbations of an initial model of the figure and gravity field of the Earth - position anomaly, deflections of the vertical, telluroid, quasi-geoid, geoid and the tie to systems of heights. The loss of smoothness in iteration solutions.
Classical and modern methods in the solution of linear geodetic boundary value problems - integral equations method, Green's function method, principle of methods based on the concept of Hilbert spaces - function bases, variational and collocation methods. Successive approximations in the representation of topography effects.
Geodetic and geophysical importance of the subject, its history and present state, international co-operation in the field.
Annotation
Data sources on the Earth's surface and in its exterior. General formulation of boundary value problems of potential theory in physical geodesy. Categories of problems. Perturbations of an initial model of the gravitational field and figure of the Earth. Classical and modern methods in the solution of linear geodetic boundary value problems.
Geodetic interpretation of the results, history and the importance of the subject.