Parameter estimation for interseismic surface deformation using data assimilation

Abstract

<p>Geodetic data provide an opportunity to improve our understanding of the processes and parameters controlling the dynamics of deformation during the earthquake cycle at subduction zones. However, the observations contain noise and are temporally and spatially sparse, whereas dynamical models are unequivocally imperfect. Also, the relative contributions from various drivers of surface deformation are poorly constrained by independent observations. Some drivers may be static or vary slowly in time (e.g., plate motion), whilst others vary significantly during the earthquake cycle (e.g., viscoelastic relaxation). Data assimilation combines prior estimates of dynamical models with the likelihood of observations into posterior estimates of the state evolution and time-independent parameters of a physical process. We explore the usefulness of data assimilation by using a particle filter to estimate the (spatially variable) elastic thickness of the overriding plate and the extent of the locked zone. The particle filter uses a Monte Carlo approach to represent the state probability distribution by a finite number of realizations ("particles"). We assimilate vertical interseismic surface displacements into a conceptual 2D elastic flexural model. We perform synthetic and real data assimilation experiments. We apply an Empirical Orthogonal Function analysis to find spatial and temporal variability of the data time series, which we use to make realistic assumptions on the observational errors.</p><p>Synthetic experiments demonstrate that the particle filter effectively estimates 1D elastic thickness from synthetic observations. However, elastic thickness estimates for models with a landward increase in plate thickness show larger uncertainty near the coast as the sensitivity of surface displacements reduces with increasing plate thickness. Interestingly, the effectiveness of the elastic thickness estimation is highly sensitive to network aperture, including GPS/A which greatly increases the quality of the parameter estimation. However, results of the locked zone extent are not as expected, which could be due to missing physics in the relatively conceptual model. Assimilation of interseismic vertical velocities prior to the 2011 Tohoku-Oki earthquake show that model parameters cannot converge with continental data without applying additional parameter constraints. This is due to low wavelength solutions providing a better fit to the noisy observations given the conceptual model. Subsequently, we will set up a 2D elastic finite element model to include horizontal and vertical surface displacements.  The results of the conceptual model demonstrate the potential of the particle filter to better understand the geodynamic process parameters of the earthquake cycle at subduction zones.</p>