MCMCを用いたリアルタイムGNSSデータによる単一矩形断層推定の不確実性定量評価の試み―2011年東北地方太平洋沖地震への適用―

抄録

Rapid understanding of the magnitude of large earthquakes in the offshore region and their associated fault expansions is important for near-field tsunami forecasting. Since September 2012, the Geospatial Information Authority of Japan (GSI) and Tohoku University have been jointly developing the GEONET real-time analysis system (REGARD), which is expected to provide reliable earthquake magnitude estimation. The REGARD system has two different types of coseismic fault model estimation systems. The first system estimates the slip distribution along the plate boundary, while the second comprises single rectangular fault model estimation. One of the challenges of REGARD is the difficulty in the estimation of the quantitative uncertainty in the single rectangular fault estimation. Thus, we focused on quantitatively understanding the single rectangular fault model estimation based on real-time GNSS time series data. We adopted Markov Chain Monte Carlo methods (MCMC) for modeling of the coseismic single fault. We applied the Metropolis–Hastings MCMC method to the 2011 Tohoku-Oki earthquake. The results obtained clearly demonstrated the tradeoff between the fault area and the amount of slip. The posterior probability density function (PDF) of the obtained slip amount showed a complex shape compared with those for the other unknown parameters. Thus, we focused on the stress drop value. Based on multiple Markov chains using Gaussian prior PDF for the stress drop with different mean value (5, 10, 15, 20, and 25 MPa), we successfully obtained the simple posterior PDF shape of the slip amount for each different mean value condition. We also found that the entire fault model explained the data well. These results suggest that the data cannot resolve uncertainties from the tradeoff between the fault area and the slip amount, which are extremely important factors for precise near-field tsunami forecasting. The results obtained using different constraint condition for the stress drop by prior distribution may provide the quantitative uncertainties for the resulting tsunamis.