Monitoring and predicting fault slip behaviors in subduction zones are essential for understanding earthquake cycles and assessing future earthquake potential. We developed a data assimilation (DA) method for fault slip monitoring and short-term prediction of slow slip events (SSEs), which was applied to the 2010 Bungo Channel SSE in southwest Japan. The observed geodetic data were quantitatively explained using a physics-based model with DA. We investigated short-term predictability by assimilating observation data with limited periods. Without prior constraint on fault slip style, observations solely during slip acceleration predicted the occurrence of a fast slip; however, the inclusion of slip deceleration data successfully predicted a slow transient slip. With prior constraint to exclude unstable slip, the assimilation of data after the SSE occurrence predicted a slow transient slip. This study provided a tool using DA for fault slip monitoring and prediction based on real observation data.

Geodetic fault slip inversions have been generally performed by employing a least squares method with a spatial smoothing constraint. However, this conventional method has various problems: difficulty in strictly estimating non-negative solutions, assumption that unknowns follow the Gaussian distributions, unsuitability for expressing spatially non-uniform slip distributions, and high calculation cost for optimizing many hyper-parameters. Here, we have developed a trans-dimensional geodetic slip inversion method using the reversible-jump Markov chain Monte Carlo (rj-MCMC) technique to overcome the problems. Because sub-fault locations were parameterized by the Voronoi partition and were optimized in our approach, we can estimate a slip distribution without the spatial smoothing constraint. Moreover, we introduced scaling factors for observational errors. We applied the method to the synthetic data and the actual geodetic observational data associated with the 2011 Tohoku-oki earthquake and found that the method successfully reproduced the target slip distributions including a spatially non-uniform slip distribution. The method provided posterior probability distributions with the unknowns, which can express a non-Gaussian distribution such as large slip with low probability. The estimated scaling factors properly adjusted the initial observational errors and provided a reasonable slip distribution. Additionally, we found that checkerboard resolution tests were useful to consider sensitivity of the observational data for performing the rj-MCMC method. It is concluded that the developed method is a powerful technique to solve the problems of the conventional inversion method and to flexibly express fault-slip distributions considering the complicated uncertainties.