Distortion of the ground-based spatial structure of ULF waves is described in detail using analytical and numerical models of the resonant Alfven wave transmission through the thin ionosphere. The numerical calculations have been done for geophysical conditions corresponding to the midlatitude Borok Observatory and the low-latitude L'Aquila Observatory. As compared with a resonant field-aligned oscillation above the ionosphere, the ground spatial structure has the following additional features which have not been described by existing models: the amplitude peak is shifted northward, the width of it is changed, and amplitude and phase are modified. The effect is most evident when the resonant frequency and ionospheric conductivity are high. From a physical point of view the effect is caused by two reasons: (1) excitation of a diffusive-like surface-type mode in the ionosphere and (2) finite Earth's conductivity. The possible influence of the predicted distortion of the ULF field on various ground-based methods for the determination of the magnetospheric resonant frequency is discussed. ¿ 2000 American Geophysical Union