A Theory of Toroidal Core Oscillations of the Earth

A rotating incompressible fluid bounded by two concentric spherical rigid surfaces can exhibit purely toroidal free oscillations. The eigenfrequencies are fractions of the angular frequency of rotation. If the bounding surfaces are slightly ellipsoidal, secondary spheroidal fields become existent, and in general, a free mode splits into a doublet with one of which exists only when the inner bounding surface is present.
For the real earth, the compressibility of the outer core, the elasticity of the solid earth, and the self-gravitation of the entire earth modify the toroidal core oscillations. The present treatment gives explicitly the effects of these parameters on the eigenfrequencies.