An integrated wavelet concept of physical geodesy
- For the determination of the earth" s gravity field many types of observations are available nowadays, e.g., terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradiometry etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other hand, 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.
Verfasser*innenangaben: | Willi Freeden, F. Schneider |
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URN: | urn:nbn:de:hbz:386-kluedo-5770 |
Schriftenreihe (Bandnummer): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (173) |
Dokumentart: | Preprint |
Sprache der Veröffentlichung: | Englisch |
Jahr der Fertigstellung: | 1998 |
Jahr der Erstveröffentlichung: | 1998 |
Veröffentlichende Institution: | Technische Universität Kaiserslautern |
Datum der Publikation (Server): | 03.04.2000 |
Bemerkung: | Altdaten, kein Volltext verfügbar ; Printversion in Bereichsbibliothek Mathematik vorhanden: MAT 144/620-173 |
Quelle: | Journal of Geodesy (1998) |
Fachbereiche / Organisatorische Einheiten: | Kaiserslautern - Fachbereich Mathematik |
DDC-Sachgruppen: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Lizenz (Deutsch): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |