Please use this identifier to cite or link to this item: http://hdl.handle.net/2122/1617
AuthorsMoritz, H. 
TitleThe sand grain and the butterfly. Instability in geodesy and geophysics
Issue DateOct-1997
Series/Report no.40/5
URIhttp://hdl.handle.net/2122/1617
KeywordsGeodesy
geophysics
gravity field
instability
chaos theory
Subject Classification04. Solid Earth::04.02. Exploration geophysics::04.02.99. General or miscellaneous 
AbstractThe 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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