A Hamiltonian theory for an elastic earth: Elastic energy of deformation

In this paper we study only the perturbation due to the deformation of the elastic mantle by a tidal body force. In a previous publication (Getino and Ferrándiz, 1989a) we defined two canonical systems of variables - we gave them the names ofelastic variables of Euler and Andoyer respectively. Next, using them, we obtained the canonical expression of rotational kinetic energy. In the present paper, using the same variables, we build up the elastic energy which is produced by the deformation of the elastic mantle. We show that the three termsm = 0, 1, 2 corresponding to the second order of the development in spherical harmonics of the perturbing potential, a tidal potential, are of the same order of magnitude. In addition, the numerical integration for a particular Earth Model (Takeuchi's Model 2) is performed, with the aim of obtaining a numerical estimate of the coefficients which intervene in both this energy and the previously mentioned kinetic energy.