Spatiotemporal Functional Modeling of Postseismic Deformation After the 2011 Tohoku-Oki Earthquake

Abstract Postseismic deformation continues for a long duration after major earthquakes. A previous study has shown that temporal changes in postseismic deformation can be approximated through simple functions. Almost 10 years have passed since the 2011 M9 Tohoku-Oki earthquake, and data at continuously operating global navigation satellite system stations have accumulated. We performed statistical processing of the data on postseismic deformations of this earthquake and obtained and verified their spatiotemporal distribution. We were able to approximate the postseismic deformations over a wide area with a standard deviation of 1 cm for approximately 10 years using two logarithmic and one exponential functions. However, the residuals from the functional model showed a sharp deviation from 2015. Although the pattern of postseismic deformation did not change after the earthquake, a change in steady-state velocity occurred from 2015 and continues till date. By improving the functional model to incorporate this steady-state velocity, we can reduce the overall standard deviation of the residuals of more than 200 stations distributed over more than 1000 km to less than 0.4 cm in the horizontal component. Furthermore, the spatial distributions of the coefficients of each time constant are not random and have a natural spread, which makes it possible to grid model them in terms of a spatial function. The spatial distributions of the short- and long-period components of the functional model and the afterslip and viscoelastic relaxation calculated by a physical model are similar to each other, respectively. Each time function has a meaning related to the physical processes in the underground, which provides an understanding of the physical phenomena involved in seismogenesis.