Since 2001, 3 earthquakes of magnitudes of 7.1 to 7.7 and 4 earthquakes of magnitudes over 8.0 occurred offshore Chile and its neighborhood. There are at least one or several GPS stations of continuous observations near these events and they detected crustal movements for these earthquakes. Based on the time series of displacements in the regional reference frame of South America (SA) at more than 70 stations of continuous GPS observations, downloaded from the website http://geodesy.unr.edu
, the accumulated preseismic horizontal displacements, coseismic and post seismic displacements of these earthquakes are obtained. Therefore, more earthquake cases with GPS observations have been collected in this study for the benefit of exploring earthquake predictions. The study shows that the coseismic horizontal displacements of these events are rebound or elastic rebound of the accumulated horizontal displacements at the GPS stations and they are the evidences of the precursory crustal deformations. There were no significant accumulated vertical displacements at or near the epicenters before these events. These facts demonstrate that the earthquakes were originated from plate motion of horizontal crustal movements. Both the 9.0 earthquake in 2011 in Japan and the 8.8 earthquake in Chile in 2010 showed clearly the spreading of the bottom of the Pacific Ocean. Though the tectonics in both countries are quite different, the rebound or elastic rebound shown by coseismic horizontal displacements of the 2 earthquakes are of the same pattern and they were the results of horizontal compression. It should be noted that the coseismic horizontal displacements of the 8.8 eathquake in 2010 were significantly smaller and in almost same abnormal direction at GPS stations north of the 8.3 earthquake in 2015. This was the most obvious and particular case from the GPS observations for the earthquakes in Chile and may be considered as the crustal motion precursory to the 8.3 event. The area near Chile in South America is one of the areas in the world, most favorable for the exploration of earthquake predictions.