An integrated wavelet concept of physical geodesy |
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| Authors: | W Freeden F Schneider |
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| Institution: | (1) University of Kaiserslautern, Geomathematics Group, P.O. Box 3049, D-67653 Kaiserslautern, Germany Tel: +49 631 205 3867; fax: +49 631 29081; e-mail: freeden@mathematik.uni-kl.de, DE |
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| Abstract: | For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial
gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection
between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept
of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can
be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical
geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an
integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing
the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential
outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of
band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding
to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique
derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking
and gradiometry.
Received: 28 February 1997 / Accepted: 17 November 1997 |
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| Keywords: | Integrated wavelet concept Scaling function Band-limited harmonic wavelets Exact fully discrete wavelet transform Runge-Walsh approximation Dirichlet's Neumann's and Stokes' problem SST SGG |
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