Bayesian Inversion for a Stress‐Driven Model of Afterslip and Viscoelastic Relaxation: Method and Application to Postseismic Deformation Following the 2011 <i>M</i><sub><i>W</i></sub> 9.0 Tohoku‐Oki Earthquake
Jun’ichi Fukuda, K. M. Johnson
Abstract
Abstract Postseismic deformation following great subduction earthquakes is commonly modeled as the sum of the contributions from afterslip on the megathrust and viscoelastic relaxation of the coseismic stress changes in the mantle. However, it is generally difficult to separate the contributions of these mechanisms to geodetically observed postseismic deformation. Here we develop an inversion method for estimating the parameters of a stress‐driven postseismic deformation model that incorporates velocity‐strengthening afterslip and viscoelastic mantle relaxation governed by a biviscous Burgers rheology using coseismic and postseismic geodetic data. We assume that afterslip and viscoelastic relaxation are driven by coseismic stress changes and interact mechanically with each other. The unknown parameters to be estimated include the coseismic slip distribution that drives the postseismic processes, and the fault frictional and mantle viscosity parameters. We present a Bayesian formulation of the inverse problem and an algorithm for estimating the posterior probability density function. This approach allows us to quantify the uncertainties of the model parameters. We apply the method to the coseismic displacements and postseismic displacement time series of the 2011 Tohoku‐Oki earthquake. Our results show that the observations place tight constraints on the model parameters, with the estimated model effectively reproducing the first‐order spatial and temporal patterns of horizontal and vertical postseismic deformation. We find that the relative contributions of afterslip and viscoelastic relaxation to horizontal and vertical postseismic deformation vary in space. We suggest that our method may potentially provide a way to objectively separate the contributions of these two mechanisms to postseismic deformation.