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A new technology to derive analytical models of the Earth's gravity field without application of spherical functions

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This project will focus on the development of a new computing technology for global and regional analytical approximations of the Earth's gravity field. Numerical algorithms and computer programmes will be designed to realise a new approach to approximating gravity fields without the application of spherical functions. The mathematical theory will, to some extent, undergo further development.

A software package will be produced that will provide linear approximations of the Earth's gravity and magnetic fields with a resolution of 1:1,000,000 to 1:200,000 from gravimetric and magnetic observation data. The present analytical approximations have a resolution on a scale of about 1:10,000 000 to 1:5,000,000. Here the theory as well as the computer programmes should provide approximations in two variants: everywhere outside the Earth's surface on the base of global data; on territories with a surface area of 1 to 5 million km{2} - where it is impossible to neglect the sphericity of the Earth - by using regional data. In both cases, exact data will be used from a set of arbitrarily distributed sampling points.

The theory and the numerical algorithms are based on the classical representation of functions that are harmonic outside a given sphere by a truncated series of spherical functions (in special definitions of associated Legendre functions and of spherical functions given by V.N. Strakhov); a new approximation obtained by V.N. Strakhov from classical Whittaker's integral representation. This is more flexible and may be used for global and regional data. Regional approximations of the anomalous gravity potential and its radial derivative for the European part of Russia and for central and northern Europe will be established. Initially this will include the acquisition and preparation of respective data and subsequently will yield new coefficient sets as an outcome of the data analysis. By means of these coefficients it will be possible to approximate the regional gravity fields with a much higher resolution than it is currently possible.

An additional result of the project will be the development of new iterative methods to solve huge systems of linear algebraic equations (with 10{6} to 10{8} unknowns). These methods should be specially efficient for those systems which arise from approximating functions that are harmonic outside a given sphere. On the other hand these methods may be applied also in case of arbitrary systems and hence will be important in geophysics/geodesy as a whole.

Furthermore, by means of global gravity and magnetic field approximations, even on a scale of about 1:1,000,000 it becomes possible to solve many problems in geophysics, geodesy and geology on a qualitatively new level.

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Institut für Angewandte Geodäsie
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Adresse
Michendorfer Chaussee 23
14473 Potsdam
Deutschland

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Letzte Aktualisierung: 19 September 1996

Mein Booklet

Permalink: https://cordis.europa.eu/project/id/INTAS-93-1779/de

European Union, 2024