Rise times of earthquake moment release influence the spectra of seismic waves. For example, slow fault movements in tsunami earthquakes excite larger tsunamis than expected from intensities of short-period seismic waves. Here we compare amplitudes of two different atmospheric waves, long-period internal gravity waves and short-period acoustic waves, excited by coseismic vertical crustal movements. We observe them as coseismic ionospheric disturbances by measuring ionospheric electrons using global navigation satellite systems. Four regular megathrust earthquakes M_w 8.0-9.0 showed that the internal gravity waves become ten times stronger as the magnitude increases by one. We found that the 2010 Mentawai earthquake, a typical tsunami earthquake, excited internal gravity waves stronger than those expected by this empirical relationship. On the other hand, amplitudes of acoustic waves excited by tsunami earthquakes were normal. This suggests that slow fault ruptures excite long-period atmospheric waves efficiently, leaving a slow earthquake signature in ionospheric disturbances.