Numerical experiments on estimating the fault frictional properties and the viscosity from the postseismic deformation

Following large earthquakes, postseismic crustal deformations are often observed. They include the afterslip and the viscoelastic deformation of the crust and the upper mantle, activated by the coseismic stress change. In order to predict the future deformations, and the stress change distributions, it is important to divide each deformation. The physical parameters; frictional properties of the fault and the rheological properties are the key to determining the slip behavior, but they are generally unknown.

Data assimilation (DA) studies have attempted to estimate the frictional properties directly from the observational data. DA incorporates the observed data into the physics-based model to construct a more plausible model. When DA works well, we can obtain the physics-based model, including the physical properties, that can quantitatively explain the observed data. The constructed physics-based model can be used to simulate the slip evolution beyond the data period, i.e., prediction of the deformation.

There are two types of DA technique applying to nonlinear system, the sequential method called as Ensemble Kalman filter method (EnKF) and the variational method called as 4DVAR. For the fault system, EnKF is applied to the deformation data to estimate the physical variables (van Dinther et al., 2019, Hirahara and Nishikiori, 2019). 4DVAR is also applied to the afterslip assuming elastic medium to estimate the fault frictional properties (Kano et al., 2015; 2020). If the physics-based model under consideration is linear, the sequential and the variational methods are consistent, but this is not the case for fault systems.

In this presentation, I construct a simple model that include the fault slip that follows the rate- an state- friction law and the viscoelastic deformation. Then I apply both EnKF and 4DVAR, and compare the results to discuss the characteristics of the methods.