Function Model Based on Nonlinear Transient Rheology of Rocks: An Analysis of Decadal GNSS Time Series After the 2011 Tohoku‐oki Earthquake

The postseismic Global Navigation Satellite System (GNSS) time series after the 2011 Tohoku‐oki earthquake is often empirically explained by one or more logarithmic and exponential decay functions. However, a function model with these decay functions struggles to illuminate various deformation mechanisms. Here, we propose a new function model incorporating laboratory‐derived constitutive laws (power‐law flow and velocity‐strengthening friction) utilized in mechanical postseismic models of the last decade. We demonstrated that our function model accurately predicts the decade‐long time series of inland GNSS stations, including coastal areas where significant postseismic uplift continues now. Moreover, it decomposes them into displacements due to viscoelastic relaxation and afterslip, similar to results produced by previous stress‐dependent postseismic models of the 2011 Tohoku‐oki earthquake. This physics‐based function model is an effective tool to ease the process of forecasting long‐term GNSS time series by dividing them into two dominant mechanisms at the plate interface and the surrounding viscoelastic mantle. Plain Language Summary Functional modeling is a standard tool to fit and predict the time series of surface displacements by geodetic observations. Previous studies used single or several logarithmic and exponential functions to fit the geodetic time series following the 2011 Tohoku‐oki earthquake. Although these functions work well in fitting the time series, they hardly explain the various elementary processes contributing to the displacement time series. Here, we developed an alternative function model that mimics ground motion after the Tohoku‐oki earthquake. The model includes postseismic slip on the megathrust interface (afterslip) and flow movement of the surrounding mantle (viscoelastic relaxation). The model uses mathematical expressions that are based on the slip and flow behaviors of rocks in laboratory experiments. The newly proposed model predicts the 10‐year time series accurately. Moreover, it breaks them down into viscoelastic relaxation and afterslip contributions. The space‐time patterns of these two components are similar to the results of the previous postseismic deformation models of the 2011 Tohoku‐oki earthquake. Our functional model can help forecast future ground motions and understand the deformation mechanisms related to megathrust earthquakes. Key Points Proposing a function model based on power‐law creep and rate‐stre