[M-GI26] Data assimilation: A fundamental approach in geosciences

[MGI26-P07] Ensemble Kalman inversion for estimating spatially variable parameters: Application to physics-based model of postseismic deformation

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

Large earthquakes are commonly followed by postseismic deformation that is captured by geodetic observations including Global Navigation Satellite System (GNSS). The postseismic deformation originates primarily from aseismic slip (afterslip) on the fault and viscoelastic relaxation in the upper mantle, both of which are driven by the coseismic stress changes. The spatial and temporal patterns of the postseismic deformation are strongly controlled by the coseismic stress changes and rheological properties of the fault and 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 ensemble Kalman-based method for approximate Bayesian inference of spatially variable parameters of mechanical models of postseismic deformation. The forward model builds on a numerically efficient solver based on the integral method (Barbot, 2018) that incorporates the coupling between stress-driven afterslip 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 and that viscoelastic flow follows the power-law constitutive law appropriate for dislocation creep in the upper mantle. The inversion method estimates a Gaussian approximation of the Bayesian joint posterior probability density function (PDF) of spatially variable parameters, including fault friction law parameters, mantle viscosity 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 smoother, which is referred to as the ensemble Kalman inversion. The method assumes that the prior PDF is Gaussian and introduces a sequence of intermediate PDFs that bridges the gap between the prior and posterior PDFs based on an adaptive tempering approach. At each iteration, the method generates samples from a Gaussian approximation of the corresponding intermediate PDF using the ensemble transform Kalman filter and data with an inflated error covariance matrix. We illustrate and validate the method using synthetic data sets. Results show that our method can reproduce the target spatial variations in the parameters reasonably well. The posterior uncertainties of the parameters are also reasonable in that they are small/large in regions with large/small coseismic stress changes. Additionally, the posterior estimates of the parameters can fit the synthetic data well and accurately recover the contributions of afterslip and viscoelastic relaxation to postseismic surface displacements.