Two-dimensional analysis of post-seismic deformation of the 2011 Tohoku-Oki earthquake with rate-and-state friction and non-linear rock rheology

We conduct a two-dimensional (2D) analysis of the post-seismic deformation of the 2011 Tohoku-Oki earthquake with the nonlinear coupling between frictional afterslip and viscoelastic flow. We consider slip on the plate boundary and distributed viscous flow of the lower crust and mantle. We created 2D transects across the Miyagi-Yamagata area where the largest coseismic slip was observed. We use the stress change by the coseismic slip model of Iinuma et al. (2012) to drive the post-seismic relaxation. The simulation is performed by the integral method (Lambert & Barbot, 2016) expanded to plane strain (Barbot, Moore, & Lambert, 2017). Despite the simple 2D approximation, we look for a realistic model compatible with mineral physics to explain geodetic observations including 5 years of seafloor observations (Tomita et al., 2017). In the ductile regions, the model employs a bi-viscous Burgers rheology with power-law flow (Masuti et al., 2016). The steady-state viscosity is estimated based on a thermal structure obtained by thermal-flow model including the wedge corner flow (Horiuchi & Iwamori, 2016). We model afterslip by the regularized rate-strengthening approximation of the rate-and-state dependent friction law (Barbot et al., 2009). The combination of power-law rheology with stress-driven afterslip explains the observed 2D displacement fields well during the 5-year post-seismic period. We also find that the model requires a low viscosity ( 1018 Pas) body beneath the quaternary volcano (Mt. Naruko) to reproduce the localized subsidence detected in the 9-month post-seismic period (Muto et al., 2016). The introduction of the low-viscosity body also reproduces quick recovery of the subsidence in the 5-year period. Equipped with a reference model that fits available geodetic observations, we discuss the importance of the mechanical coupling between afterslip and viscoelastic flow. We find that ignoring the traction change on the fault by viscoelastic flow introduces variations of the order of 20% on the amplitude of afterslip. This effect is most pronounced late in the post-seismic relaxation. Our model reconciles laboratory constraints on rock rheology and geophysical observations after the earthquake and serves as a first-order reference to better understand the dynamics of subduction at the Japan trench.