## 2 Materials and Methods
### GNSS-Measured Motions and Stress-Deformation Cycle in Subduction Regions  
Understanding stress-deformation cycle (SDC) [32] mechanisms in subduction zones is critically important for the long-term large earthquake prediction and seismic hazard assessment [19]. Over decades, a number of concepts have been proposed to explain the SDC features, with the so-called asperity model being the most promoted one [12]. We believe that it is crucial that those models be validated by comparing the predicted behavior with the observed motion data, which has become possible since the high-precision GNSS-based geodetic observations had been launched. GNSS stations deployed in active regions including subduction zones, had made the long-term displacement and velocity data series available, which totally changed the landscape in tectonics and seismology studies. In a series of previous studies, we analyzed GNSS-measured motions in the Kuril subduction zone following the 2006-2007 Simushir earthquakes [16] (Figure 4), Chile subduction zone following the 2010 Maule earthquake [17] (Figure 5), and Japan subduction zone following the 2011 Tohoku earthquake [18] (Figures 6 and 7), with primary attention paid to horizontal displacements. Main features of the observed Earth's surface motions include a slow background continent-ward motion (Figures 5a and 6a), which lasts up to 75% of the duration of the seismic cycle [32] and then is suddenly interrupted by an abrupt oceanward dislocation in source-neighboring areas at the instance of the seismic event (Figure 6b), followed by the continuous motion of the continent-side lithosphere in source-neighboring areas towards the oceanic plate. These postseismic oceanward displacements are unsteady in time and along the strike of the trench. The Figure 4a,b, Figure 5c,d and Figure 6c-f show annual variations of Earth's surface postseismic motions in the vicinity of source regions of 2006 Simushir, 2010 Maule, and 2011 Tohoku earthquakes, respectively. Despite the fact that each of the regions under consideration has a different tectonic structure and the spatial density of our data varies greatly, we observe similar patterns of postseismic motions: (a) postseismic drift occurs in the direction towards the ocean, and (b) different portions of lithosphere may experience motion in opposite directions at the same time. Such abrupt changes in the direction of motions of adjacent areas of the Earth's surface in the framework of models assuming a continuous medium will cause large deformations between them. This behavior is seen for all three events in consideration and implies the existence of geomechanical process responsible for the above motions. Obviously, the well-known asperity model lacks the ability to explain the post-quake oceanward drift, occurring in particular regions, while the neighboring territories may move in the opposite (normal) direction. At the same time, the proposed keyboard model can provide natural explanation for observed motions during preseismic,oseismic, and postseismic stages of the seismic cycle. The slow background continent-ward motion (Figures 5a and 6a) is associated with stationary elastic compression of frontal and rear blocks during the interseismic stage. These blocks at the instance of the seismic event are abruptly shifted towards the ocean, which triggers the observed continued oceanward motions of the Earth's surface. The almost independent displacements of seismogenic blocks also explain the opposite directions of Earth's surface motions along the oceanic trench during the postseismic stage of the seismic cycle (Figures 4a,b, 5c,d and 6c-f). The observed difference in postseismic motions in the direction perpendicular to the trench (Figure 5c,d) is due to the presence of viscous friction at the bottom of the rear blocks and the presence of a viscous response in the asthenospheric wedge to a coseismic stress drop [19]. Figure 4: GNSS-observed motions in Kuril subduction zone after large Simushir earthquakes modified from [16].