FREE OSCILLATIONS OF ELASTICALLY ANISOTROPIC SPHERES AND ELLIPSOIDS

The free oscillations of elastically anisotropic spheres are computed here using a Rayleigh-Ritz method developed by Mochizuki (1988). The c omputation of eigenfrequencies was made for elastic spheres with ortho rhombic, tetragonal, cubic and isotropic crystal symmetries, and how t he degenerate eigenfrequencies split due to the elastic anisotropy has been shown. A perturbation theory combined with the Rayleigh-Ritz met hod was presented to compute shifts in and splits of eigenfrequencies due to deformation of an elastic sphere into an ellipsoid. The frequen cy shifts are expressed by delta omega = Phi(x) epsilon(x) + Phi(y) ep silon(y) + Phi(z) epsilon(z), where epsilon(j) and Phi(j) (j = x, y, z ) are, respectively, asphericities and aspherical coefficients of the ellipsoid. This equation was used not only to compute the free-oscilla tion frequencies of an elastically anisotropic ellipsoid, but also to determine the asphericities of an olivine ellipsoid from observed reso nant frequencies.