This study proposes a new method for the uncertainty estimation of coseismic slip distribution on the plate interface deduced from real-time global navigation satellite system (GNSS) data and explores its application for tsunami inundation prediction. Jointly developed by the Geospatial Information Authority of Japan and Tohoku University, REGARD (REal-time GEONET Analysis system for Rapid Deformation monitoring) estimates coseismic fault models (a single rectangular fault model and slip distribution model) in real time to support tsunami prediction. The estimated results are adopted as part of the Disaster Information System, which is used by the Cabinet Office of the Government of Japan to assess tsunami inundation and damage. However, the REGARD system currently struggles to estimate the quantitative uncertainty of the estimated result, although the obtained result should contain both observation and modeling errors caused by the model settings. Understanding such quantitative uncertainties based on the input data is essential for utilizing this resource for disaster response. We developed an algorithm that estimates the coseismic slip distribution and its uncertainties using Markov chain Monte Carlo methods. We focused on the Nankai Trough of southwest Japan, where megathrust earthquakes have repeatedly occurred, and used simulation data to assume a Hoei-type earthquake. We divided the 2951 rectangular subfaults on the plate interface and designed a multistage sampling flow with stepwise perturbation groups. As a result, we successfully estimated the slip distribution and its uncertainty at the 95% confidence interval of the posterior probability density function. Furthermore, we developed a new visualization procedure that shows the risk of tsunami inundation and the probability on a map. Under the algorithm, we regarded the Markov chain Monte Carlo samples as individual fault models and clustered them using the k-means approach to obtain different tsunami source scenarios. We then calculated the parallel tsunami inundations and integrated the results on the map. This map, which expresses the uncertainties of tsunami inundation caused by uncertainties in the coseismic fault estimation, offers quantitative and real time insights into possible worst-case scenarios.

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