The first estimate of magnitude (magnitude 7.9 in the case of the March 2011 Tohoko earthquake) for a major earthquake in the Pacific is made by the USGS and the tsunami warning centers in the Pacific, based on limited data, within minutes of the earthquake. That estimate is made as soon as possible to give maximum warning time for possible tsunamis, and happens before the waves from the earthquake have even arrived at many seismic stations. As the waves reach distant stations, the additional data are combined with the original and re-analyzed to produce a revised magnitude (an 8.9 in our example), which is then released by the USGS. After even more analysis, which requires looking at very low frequency recordings of the seismic waves from many seismic stations, the USGS may update their magnitude estimate again (to a 9.0 in our example). Generally the magnitude in the USGS earthquake catalog remains fixed at this point.
If your students are interested in the timeline of how the USGS and other organizations work together to release information, the following clip shows a timeline for the March 2011 Tohoku quake.