A magnetospheric cavity with a two-dimensional profile in Alfv¿n speed has been driven with a nonmonochromatic source. Detailed numerical results show that the magnetospheric cavity filters the random driving signal and excites preferentially the fast modes whose eigenfrequencies lie within the driving spectrum. These fast modes may also couple to the Alfv¿n mode, provided ky≠0 and their eigenfrequencies lie within the Alfv¿n continuum. The resulting Alfv¿n modes and the position of the resonant field lines can be predicted to high accuracy by calculating the natural fast and Alfv¿n frequencies of the undriven system. A preliminary investigation into the seismology of the magnetosphere has also been undertaken. The ratio of the energy density in the two resonant field lines depends only on the equilibrium of the cavity and not on the nature of the driving source (e.g., initial condition, impulsive excitation, or random forcing). Good agreement is found with the ratio predicted by an approximate analytical treatment based upon the eigenfunctions of the equilibrium magnetosphere. The new seismological technique may prove to be a useful diagnostic tool in future studies. ¿ 1998 American Geophysical Union