Ensemble averages of spectra on seismically quiet days exhibit fundamental spheroidal modes of Earth's free oscillations from 3 to 7 mHz at 14 stations. We obtain acceleration amplitudes for these modes of ~0.4 ngal (1ngal=10-11 ms-2) by fitting a spectral model to the ensemble averages of the spectra. The following three statistical features are characteristic to these spectra: (1) standard deviations of the spectra show that the amplitude of each mode fluctuates with time, (2) total modal signal power of the spectra shows that the oscillations are excited continuously, and (3) cross-correlation coefficients between the modal amplitudes show that the modes do not correlate even with adjacent modes. These features suggest a random excitation mechanism. Assuming random excitation, we estimate the correlation length of the source to be shorter than 600 km, the source area to extend over the whole Earth's surface, and the repeat time of excitation to be shorter than the damping time of mode. Thus the sources must be incessant random disturbances on the whole surface of the Earth. On the basis of these results, four possible mechanisms are discussed. Atmospheric turbulent motions are efficient in exciting the oscillations and explains the statistical features, whereas the efficiencies of processes in the ocean remain questionable. The cumulative effects of earthquakes with seismic moments smaller than 1017 Nm cannot explain the observed amplitudes because the observed amplitudes at 3 mHz would require a moment release rate of 1019 Nm d-1. We also argue that slow earthquakes cannot explain the stochastic properties of the source. ¿ 1999 American Geophysical Union