Real-time automatic uncertainty estimation of coseismic single rectangular fault model using GNSS data

Abstract

Rapid estimation of the coseismic fault model for medium-to-large-sized earthquakes is key for disaster response. To estimate the coseismic fault model for large earthquakes, the Geospatial Information Authority of Japan and Tohoku University have jointly developed a real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD can estimate the single rectangular fault model and slip distribution along the assumed plate interface. The single rectangular fault model is useful as a first-order approximation of a medium-to-large earthquake. However, in its estimation, it is difficult to obtain accurate results for model parameters due to the strong effect of initial values. To solve this problem, this study proposes a new method to estimate the coseismic fault model and model uncertainties in real time based on the Bayesian inversion approach using the Markov Chain Monte Carlo (MCMC) method. The MCMC approach is computationally expensive and hyperparameters should be defined in advance via trial and error. The sampling efficiency was improved using a parallel tempering method, and an automatic definition method for hyperparameters was developed for real-time use. The calculation time was within 30 s for 1 × 106 samples using a typical single LINUX server, which can implement real-time analysis, similar to REGARD. The reliability of the developed method was evaluated using data from recent earthquakes (2016 Kumamoto and 2019 Yamagata-Oki earthquakes). Simulations of the earthquakes in the Sea of Japan were also conducted exhaustively. The results showed an advantage over the maximum likelihood approach with a priori information, which has initial value dependence in nonlinear problems. In terms of application to data with a small signal-to-noise ratio, the results suggest the possibility of using several conjugate fault models. There is a tradeoff between the fault area and slip amount, especially for offshore earthquakes, which means that quantification of the uncertainty enables us to evaluate the reliability of the fault model estimation results in real time.

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

“…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.…”

“…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. Another part of M-H conforms to that of Ohno et al (2021).…”

“…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. Another part of M-H conforms to that of Ohno et al (2021).…”

“…In the case of non-interplate earthquakes such as the 2019 Yamagata-Oki earthquake or the 2008 Iwate-Miyagi Nairiku earthquake (MJMA 7.2), fault geometries are complex or unknown, and many earthquakes are difficult to assume the fault geometry in advance (Ohta et al 2008;Ohno et al 2021). The assumption of fault geometry required in the slip distribution model can make inferences ambiguous and affect the inferred result (e.g., Fukahata and Wright 2008;Fukuda and Johnson 2010;Duputel et al 2014;Agata et al 2021;Dutta et al 2021).…”

“…There are some previous studies which are satisfied the two requirements above, rapid estimation and quantitative uncertainty assessment; for example, Minson et al (2014) developed a real-time estimation method using Bayesian linear regression including the fault geometry selection with the assessment of its uncertainty and the slip distribution estimation on that geometry. Ohno et al (2021) also developed Bayesian fault estimation methods that acquire the uncertainty of the fault parameters of a single rectangular fault by directly drawing the PDF using the Markov chain Monte Carlo (MCMC) method.…”