Combined logarithmic and exponential function model for fitting postseismic GNSS time series after 2011 Tohoku-Oki earthquake

The time series of a postseismic deformation is commonly fitted by a logarithmic or exponential decay function. However, the high-quality postseismic Global Navigation Satellite System (GNSS) time series of the 2011 Mw 9 Tohoku-Oki earthquake indicates that a single decay function cannot be used to represent the postseismic behaviour. We therefore combined the logarithmic (log) and exponential (exp) decay functions and developed methods for obtaining global solutions using nonlinear least squares calculations for such complex functions. Our models significantly improved the fitting performance of the postseismic time series and the prediction performance of the evolution of postseismic deformation. The solutions obtained by the proposed models and methods enabled distinction between the contributions of the log and exp functions, and explanation of characteristic phenomena such as the subsidence that occurs immediately after an earthquake is reversed to an uplift. The analysis of the solutions may suggest that there has been a continuous increase in the contribution of viscoelastic relaxation to postseismic deformation in eastern Japan, whereas the contribution of afterslip has rapidly decreased. The short-term prediction performance and the universal applicability of the proposed models to the Tohoku-Oki earthquake have contributed to the detection of a slow-slip event in the Tokai region. Rather than the existence of a unique single relaxation time for each surface site, our results suggest a unique single relaxation time for each postseismic deformation mechanism at a given subsurface location. Although the predictions were highly dependent on the assigned steady velocities and the long-term relaxation time constants, they indicate that the coseismic subsidence of the Yamoto station in Miyagi prefecture will recover around the year 2020. The estimated relaxation time constants of the present models appeared to be uniform throughout eastern Japan.