The Effect of A General Aspherical Perturbation on the Free Oscillations of the Earth

The Lagrangian governing the infinitesimal elastic-gravitational oscillations of a completely general earth model with interior fluid—solid boundaries is given. Rayleigh's principle is then used to derive a formula for calculating the first-order perturbations in the eigenfrequencies due to an arbitrary slight perturbation of a spherically symmetric, non-rotating, isotropic starting model. The perturbations considered include rotation, asphericity, elastic anisotropy, and a deviatoric initial stress, as well as a change in the positions of both welded and fluid—solid boundaries.