Free oscillations of the Earth: 1. Toroidal oscillations

The free periods of toroidal oscillations of the earth have been computed for two earth models. The lowest period for the Gutenberg model earth is 2651 sec and for the Jeffreys-Bullen model 2732 sec. The surface amplitudes of the oscillations have been computed for three kinds of delta function stress sources—a unit force, a unit couple, and a unit torque—at depths of 600, 250, 100, and 30 km. The amplitudes decrease with increasing depth of the source. For a unit couple at 600 km the maximum amplitude of the lowest period for the Gutenberg model is 1.59×10−25 cm, and for the Jeffreys-Bullen model it is 0.70×10−25 cm. By using the free periods of oscillation we have extended Love wave phase velocity and group velocity dispersion curves to include long-period Love waves. The method used to compute the periods and amplitudes of the free oscillations is an extension of the Thomson-Haskell matrix method used in plane layered media. An example is presented to show the correspondence between the free oscillations and ray theory.