Abstract: the coseismic and the preseismic displacements in the regional reference frame were obtained for the M7.8 earthquake on Nov. 13, 2016 in New Zealand based on time series of coordinates at continuous GPS observation stations, available from http://geodesy.unr.edu, in New Zealand and Australia. horizontal displacement time series vectors at CMBL and KAIK in New Zealand and at USUD and TSKB in Japan are shown. The vector time series show clearly with direct visual effect that the coseismic horizontal displacements were sudden and dramatic, and opposite to the accumulated preseismic horizontal displacements. These represent a rebound or elastic rebound of the accumulated preseismic horizontal displacements. Therefore, the accumulated preseismic horizontal displacements were precursors to the earthquakes. Results produced from the abundant GPS observations are used to discuss the rebound and elastic rebound models. Detailed reanalysis on the results of GPS observations of the M9.0 Tohoku earthquake in Japan shows that one principal strain in the region at and around the epicenter was dominated by compression in the east direction before the earthquake. Moreover, the earthquake and the coseismic displacements were the result of shear rupture at the earthquake faults. This agrees with test of rock failure results, strain analysis, and consistent with earthquake mechanisms.