Towards Estimating Postseismic Parameters and Processes Using Ensemble Data Assimilation

Geodetic observations of vertical land motion following a megathrust earthquake are key to a better understanding of processes and parameters controlling the dynamics at subduction margins. The relative contributions of dominant drivers during the postseismic phase, such as viscoelastic relaxation, afterslip and relocking, remain difficult to estimate individually and are often derived at the end of an observation period. Data assimilation can provide the means to estimate model parameters by combining physical models with observations whilst taking their uncertainties into account. We use Bayesian inference in the form of an ensemble smoother to estimate geodynamic parameters during the postseismic phase of the megathrust earthquake cycle. The ensemble smoother uses a Monte Carlo approach to represent the probability density distribution (pdf) of model states with a finite number of realizations. Prior estimates of the imperfect physical model are combined with the likelihood of noisy observations to estimate the posterior pdf of model parameters. We discuss a synthetic data experiment where observations are sampled from a 3D finite element model with noise added to represent errors in the data. With a smoother, observations at all time steps are assimilated in one go, to ensure consistency between estimated parameters and model outputs. We assimilate vertical and horizontal surface displacements into a 2D finite element viscoelastic earthquake cycle model with a power-law rheology. We incorporate heterogeneity into the viscoelastic structure and estimate the viscosity field based on a heterogeneous temperature field and experimental flow laws. Preliminary results show that model parameters, such as the extent of the cold nose, maximum depth of afterslip and flow law parameters can be recovered remarkably well by assimilating synthetic on- and offshore surface observations. We will apply the smoother to postseismic surface displacements of the Tohoku 2011 earthquake to estimate model parameters and driving processes across spatio-temporal domains.