There were few follow-up studies for decades. Then the 1995 launch of the Solar and Heliospheric Observatory led to observation of coronal waves, which cause Moreton waves. Moreton waves were a research topic again. (SOHO's EIT instrument discovered another, different wave type called 'EIT waves'.) The reality of Moreton waves (aka fast-mode MHD waves) has also been confirmed by the two STEREO spacecraft. They observed a 100,000-km-high wave of hot plasma and magnetism, moving at 250 km/second, in conjunction with a big coronal mass ejection in February 2009.
Moreton waves propagate at a speed of 500–1500 km/s (this range does not agree with the just-quoted STEREO observation of a 250 km/second speed). Yutaka Uchida interpreted Moreton waves as MHD fast mode shock waves propagating in the corona.  He links them to type II radio bursts, which are radio wave discharges created when coronal mass ejections accelerate shocks. 
Moreton waves can be observed primarily in the Hα band.
^Moreton, G. E. & Ramsey, H. E. (1960). "Recent Observations of Dynamical Phenomena Associated with Solar Flares". Publications of the Astronomical Society of the Pacific72 (428): 357. Bibcode:1960PASP...72..357M. doi:10.1086/127549.
^Athay, R. Grant; Moreton, Gail E. (1961). "Impulsive Phenomena of the Solar Atmosphere. I. Some Optical Events Associated with Flares Showing Explosive Phase". Astrophysical Journal133: 935. Bibcode:1961ApJ...133..935A. doi:10.1086/147098.