We have constructed a theory for standing Alfven waves driven in the magnetosphere by a monochromatic source localized in the ionosphere. It is shown that a dominant role in such oscillations is played by harmonics with large azimuthal wave numbers with m≫1. We explore the possibility of such oscillations being excited during active experiments on periodic (with the period of Alfven eigenmodes of the magnetosphere) ionospheric modifications. Our study has made it apparent that the measured distance between local maxima of the amplitude of oscillations excited in such an experiment can be used to infer the value of the polarization splitting of the spectrum between poloidal and toroidal eigenmodes of the magnetosphere. ¿ 1999 American Geophysical Union