The sand grain and the butterfly. Instability in geodesy and geophysics

H. Moritz

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.

Keywords


Geodesy;geophysics;gravity field;instability;chaos theory

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References


DOI: https://doi.org/10.4401/ag-3871

Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X