## 2 Materials and Methods
### Keyboard Model of Seismic Cycles of Great Subduction-Associated Earthquakes
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Subduction Zone**} & **Block** & **Block Length** & **Cycle Period,** & **Horizontal Coseismic/Aftershock** \\  & **Width/Length, km** & **Segment**, **km** & **yrs** & **Displacement at Rear Segment, cm** \\ \hline \multirow{2}{*}{Kuril-Kamchatka} & 30–100 & 100/100 & 140 \(\pm\) 60 & 50/50 \\  & [15] & [15] & [23] & [19] \\ \hline \multirow{2}{*}{Japan} & 100–150 & 200/300 & 100–1000 & 50–200/10–50 \\  & [24,25] & [24,25] & [21,26] & [18] \\ \hline \multirow{2}{*}{Chile} & 100–200 & 100/300 & 63–176 & 5–50/50–80 \\  & [27, 28, 29, 30] & [27, 28, 29, 31] & [31] & [17] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of the structure and seismic cycle in Kuril-Kamchatka, Japan, and Chile subduction zones, according to our studies and available data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Contact Layer** & **Stationary Viscosity of** & **Postseismic Viscosity of** & **Interblock Fault** & **Interblock** \\
**Thickness, \(h\)** & **the Contact Layer, \(\eta_{f}\)** & **the Contact Layer, \(\eta_{a}\)** & **Thickness, \(h_{g}\)** & **Viscosity, \(\mu\)** \\ \hline \(\sim\)0.5 km & \(\sim\)10\({}^{19}\) Pa-s & \(\sim\)10\({}^{18}\) Pa-s & \(\sim\)1 km & \(\sim\)4 \(\times\) 10\({}^{18}\) Pa-s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Typical values for parameters of viscous elements of the model according to [20]. ical energy) \(\epsilon_{cr}\) (Figure 2l) prespecified according to available estimates within range \((0.5-2)\times 10^{5}\frac{\epsilon\tau_{R}}{cm}\)[20] (\(H_{m}=(H_{0}+H_{l})/2\) is the mean thickness of the block). Obviously, to start the iterative procedure of the solution, one needs the initial displacements to be specified at zeroth step for each point/block. Although not known in practice, since we are lacking historical geodetic data, these might be calculated from random stresses, chosen within the range of 100 to 300 Bar. Over time, the system shows the tendency to stabilize and follow a specific cyclic pattern, no matter what specific initial stresses/displacements had been used at the starting point. The choice of initial values only affects the time instants at which the blocks reach critical energy, while other properties of the cycle (i.e., cycle period and the shape of kinematic parameters variation over time) remain constant. The simulated motion patterns computed for a series of typical parameters mentioned above show a sufficient agreement with observational data in terms of cycle duration (around 150-250 years, Figure 3a) and contain characteristic features, with aftershock oceanward motion of the blocks being the most pronounced one (Figure 3b). Below we discuss its possible geomechanical explanations in the light of the up-to-date GNSS observational data. Figure 3: Displacement variations \(W(x,t)\), simulated with an original single-segment model for an outer edge and midpoint of blocks. Panel (**a**) shows an overall cycle pattern for 2 different blocks (assuming 7-block structure), while panel (**b**) provides a detailed picture showing the postseismic oceanward motion, observed at the outer region of the block.