Bayesian Inference of Rheological Parameters from Observations Before and After the Tohoku Earthquake

Geodetic data covering different phases of the earthquake cycle provide a great opportunity to improve our understanding of the processes and parameters governing the dynamics at subduction margins. However, quantifying the individual contributions of physical processes such as viscoelastic relaxation, afterslip, and (re)locking throughout the earthquake cycle remains challenging. Moreover, it is relevant to account for these processes within a rheological framework that is consistent over the entire earthquake cycle. We address this using Bayesian inference in the form of an ensemble smoother, a Monte Carlo approach that represents the probability density distribution of model states with a finite number of realizations, to estimate geodynamic model parameters. Prior estimates of the imperfect physical model are combined with the likelihood of noisy observations to estimate the posterior probability density distribution of model parameters.

 

We construct a 2D finite element seismic cycle model with a power-law rheology in the mantle. A priori information, such as a realistic temperature field and a coseismic slip distribution, is integrated into the model. Model pre-stresses are initialized during repeated earthquake cycles wherein the accumulated slip deficit is released entirely. We tailor the last earthquake to match the observed co-seismic slip of the 2011 Tohoku earthquake. The heterogeneous rheology structure is derived from the temperature field and experimental flow laws. Additionally, we simulate afterslip using a thin, low-viscosity shear zone with a Newtonian rheology. We focus on constraining power-law flow parameters for the mantle, and the shear zone viscosity.

 

We assimilate 3D GEONET GNSS displacement time series acquired before and after the 2011 Tohoku earthquake. The data require separate viscoelastic domains in the mantle wedge above and below ~50 km depth, and in the sub-slab mantle. Power-law viscosity parameters are successfully retrieved for all three domains. The trade-off between the power-law activation energy and water fugacity hinders their individual estimation. The wedge viscosity is >10¹⁹ Pa·s during the interseismic phase. Postseismic afterslip and bulk viscoelastic relaxation can be individually resolved from the surface deformation data. Afterslip is substantial between 40-50 km depth and extends to 80 km depth. Bulk viscoelastic relaxation in the wedge concentrates above 150 km depth with viscosities <10¹⁸ Pa·s. Landward motion of the near-trench region occurs during the early postseismic period without the need for a separate low-viscosity channel below the slab.