Abstract: In this paper the coseismic horizontal displacements and strains of the Mw9.0 Tohoku earthquake on March 11,2011 in Japan are obtained from continuous GPS observations at 245 stations in the Crustal Movement Observation Network of China (CMONOC) and other stations based on the dislocation reference frame with 7 core stations that are much more far away from the earthquake epicenter according to the elastic dislocation theory. The far field horizontal displacements at stations further away from the epicenter are close to zero and in good agreement with the theoretical elastic dislocation model. More reasonable elastic dislocation models can be inverted from the coseismic horizontal displacements observed by GPS in this reference frame. In addition, the influence area of this earthquake can be reasonably estimated from these displacements.#br#Time series of far field displacements in the regional reference frame at continuous GPS observation stations show that the coseismic horizontal displacements are not only the result of the rupture of the earthquake fault but also the elastic rebound of the displacements accumulated during several months or even several years before the earthquake. Therefore the preseismic displacements at these stations wereprecursory anomalous before the Tohoku earthquake in Japan and they contained at least the coseismic displacements at these stations in opposite sense. So the elastic dislocation model is one of the theoretical models that can also be used in qualitative studies on anomalous displacements before similar great earthquakes. Therefore,it is even more important that comprehensive studies on the coseismic horizontal displacements in the dislocation reference frame, their elastic dislocation model and the time series of horizontal displacements in the regional reference frame are instrumental to explaining and understanding of anomalous crustal movements before this giant event. The anomalous elastic displacements with a duration of several months or several years could be used in mid or short term earthquake predictions.