Rapid and Quantitative Uncertainty Estimation of Coseismic Slip Distribution for Large Interplate Earthquakes Using Real-time GNSS Data and Its Application to Tsunami Inundation Prediction

Abstract

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.

Comparison between the Hamiltonian Monte Carlo method and the Metropolis-Hastings method for coseismic fault model estimation

“…To verify the accuracy and efficiency of our method, we used the random-walk M-H that was adopted by Ohno et al (2021) to compare the estimation by the HMC method to that by the M-H method (Metropolis et al 1953;Hastings 1970), which is often used to solve the geophysical problem (Fukuda and Johnson 2008;Ito et al 2012;Dettmer et al 2014;Minson et al 2014;Ohno et al 2022). Although Ohno et al (2021) introduced an automatic determination method for likelihood variance and parallel tempering, we use the same variance value as HMC and estimate using only a single Markov chain for a single parameter to compare both methods strictly.…”

“…However, the HMC or other MCMC methods have the problem of ensuring minimum global exploration. One of the methods to certainly and efficiently explore more broadly in parameter space is parallel tempering (e.g., Dosso et al 2012;Sambridge 2013;Dettmer et al 2014;Hallo and Gallovič 2020;Ohno et al 2021Ohno et al ,2022. In future work, we will develop a method that introduces this expanding method to the HMC and realize a more efficient and stable fault estimation.…”

“…Amey et al (2018) applied the Bayesian inversion method to the inference of the slip distribution in the 2014 Napa Valley earthquake with self-similarity of the fault slip (Mai and Beroza 2002) as prior information. In addition, many previous studies have used Bayesian inversion (e.g., Sambridge and Mosegaard 2002;Fukuda and Johnson 2008;Dettmer et al 2014;Ohno et al 2022).…”

Tsunami Early Warning From Global Navigation Satellite System Data Using Convolutional Neural Networks

“…In this paper, we show that equally good forecasts can be made using only a few minutes of data from an existing network of Global Navigation Satellite System (GNSS) stations. Tsunami warning centers are already starting to incorporate this data in performing earthquake magnitude estimates, and it has been shown that the use of GNSS data can have great benefits, particularly for near‐field forecasting (Crowell et al., 2018; Melgar, Allen, et al., 2016; Ohno et al., 2022; Ohta et al., 2018; Williamson et al., 2020). We show that this can be taken further by training Convolutional Neural Networks (CNNs) to forecast the tsunami waveforms directly from the GNSS waveforms.…”