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Extra resources for Tidal Phenomena (Lecture Notes in Earth Sciences 66)

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Astrophys. 190:342 - 352. A. 1993. Effect of the Earth's ellipticity on the lunar potential. Geophys. J. Int. 113: 250- 251. H. 1883. Report of a committee for the harmonic analysis of tidal observations. Brit. Ass. : 48 - 118. T. 1921. The harmonic development of the tide generating potential. Proc. Royal Soc. London A 100:306 - 328. Reprint in Int. Hydrogr. Rev. 31 Hartmann, T. -G. Wenzel. 1994a. Catalogue of the earth tide generating potential due to the planets. Bull. Inf. Mardes Terre~tre~ 119:8847 - 8880.

R - . , = po(,: = po(r) t) . ) + p'L(r - - - u, ~) u(~,t) • vpo(~) - poCr) v . ( ~ , ~ ) = po(r) v . ), we find that the incremental Eulerian density can be expressed by - 05) Solid Earth Response p~(r,t) = - V . (poU). 33 (16) Here we see a difference of u . Vpo between the two incremental densities p~ and p~. This difference is understandable when we keep in mind that in the definition of the Lagrangian and Eulerian incrementais in (12) and (14), respectively, two different reference positions for the initial density have been considered.

T'L =-Po [ ~ + 2 0 ] × /1], / (44) V~¢s = 4 r G V . (poU). Dahlen (1972) derived the equations of motion under a more general assumption on the initial static equilibrium. In case of the hydrostatic pre-stress, the equations of motion given by Dahlen are identical with (44). In order to determine the tidal deformations, however, the equation system (40), (43) or (44) is not enough. , 3 displacement components, 1 potential and 6 independent components of the stress tensor. We need therefore an additional relationship between the incremental stress and strain, for example, Hooke's law for an isotropie material: T'L : A (V- u)I + # [Vu + (Vu) t ], (45) where ~ and # are Lam6 constants.

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