[S-GD02] Crustal Deformation

[SGD02-P12] Ensemble Kalman inversion for stress-driven models of postseismic deformation with spatially varying parameters

*Junichi Fukuda¹, Sylvain Barbot² (1.Earthquake Research Institute, University of Tokyo, 2.University of Southern California)

The postseismic deformation following great earthquakes originates primarily from afterslip on the fault and viscoelastic relaxation of the lower crust and upper mantle. The spatial and temporal patterns of the postseismic deformation are strongly controlled by the coseismic stress changes and rheological properties of the fault, lower crust, and upper mantle. Thus, geodetic measurements of postseismic deformation, in combination with mechanical models of these deformation processes, have been used to investigate the rheological properties of the fault and lower crust/upper mantle. However, probing the rheological properties from geodetic time series remains particularly challenging because the mechanical response is nonlinear and the parameter space is high dimensional. As a result, the spatial distribution of rheological parameters remains poorly constrained. Here, we develop an approximate Bayesian inference method based on the ensemble Kalman filter for estimating the spatially variable rheological parameters of mechanical models of postseismic deformation. The forward model builds on the integral method (Barbot, 2018) that incorporates the mechanical coupling between coseismic/postseismic fault slip and viscoelastic relaxation. We assume that afterslip is governed by steady-state velocity-strengthening friction derived from a physical model of rate- and state-dependent friction. The viscoelastic relaxation is assumed to follow a nonlinear Burgers rheology that incorporates the steady-state and transient rheology, both of which are modeled as the sum of contributions of diffusion and dislocation creep. Our inversion method estimates a Gaussian approximation of the Bayesian posterior probability density function of spatially variable model parameters, including fault friction law parameters, viscoelastic constitutive parameters, and coseismic stress changes, using postseismic GNSS position time series. To handle the nonlinearity and high dimensionality of the inverse problem, the method employs an iterative version of the ensemble Kalman filter. We illustrate and validate the method using synthetic GNSS data sets. Results show that our method can reproduce the target spatial variations in the model parameters reasonably well. The estimated uncertainties of the model parameters are also reasonable in that they are small/large in regions with large/small coseismic stress changes. Additionally, the estimates of the parameters fit the synthetic data well and accurately recover the contributions of afterslip and viscoelastic relaxation to geodetically observed postseismic displacements.