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http://hdl.handle.net/2122/1617| Authors: | Moritz, H. | Title: | The sand grain and the butterfly. Instability in geodesy and geophysics | Issue Date: | Oct-1997 | Series/Report no.: | 5/40 (1997) | URI: | http://hdl.handle.net/2122/1617 | Keywords: | Geodesy geophysics gravity field instability chaos theory |
Subject Classification: | 04. Solid Earth::04.02. Exploration geophysics::04.02.99. General or miscellaneous | Abstract: | The problems of convergence of series in celestial mechanics and of certain series in geodesy (Molodensky's series and spherical harmonics) show similar features, involving a curious instability. This is imaginatively expressed as the « butterfly effect» in chaos theory and the «sand-grain effect» for spherical harmonics. Similarly, the geodetic boundary-value problem (M.S. Molodensky, L. Hormander) and the KAM problem in nonlinear dynamics have a common mathematical structure: a «hard» inverse function problem. Such interrelations are reviewed in the present paper. |
| Appears in Collections: | Annals of Geophysics |
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|---|---|---|---|---|
| 33 moritz.pdf | 1.76 MB | Adobe PDF | View/Open |
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