Rigidity of the Earth's core and fundamental oscillations of the Earth

Varying parametrically the rigidity of the earth's core, i.e. µo of the Gutenberg model of the earth, we calculate free periods of spheroidal and toroidal oscillations of the earth for n = 2. For a fixed µo, we get an infinite number of periods for the spheroidal and toroidal modes. Normalizing their surface oscillation amplitudes, we pick up from among them an oscillation of the minimum total kinetic energy. This may be considered to be the most easily excitable oscillation for the µo by surface origins. The periods of both spheroidal and toroidal oscillations thus picked up are plotted against the corresponding µo, and from this we may conclude that the maximum rigidity of the earth's core compatible with the observations of spheroidal or toroidal oscillations is 1010 or 1012 dynes/cm2 for n = 2.