11:15 AM - 11:30 AM
[SSS10-13] Performance Evaluation of Dynamic Source Inversion through Its Synthetic Tests
★Invited Papers
Keywords:Dynamic Source Inversion, Strong Ground Motion, Markov chain Monte Carlo sampling method
Generating mechanisms of strong ground motions is connected to process at an earthquake source. It has been investigated, for example, by estimating rupture processes using kinematic source inversion methods. Dynamic source models resulting in the rupture process which could reproduce the observation near the source fault have also been obtained by dynamic rupture simulations. A Bayesian inversion technique to infer a dynamic source model as a set of probability densities of the dynamic source parameters by using the Markov chain Monte Carlo (MCMC) sampling method has been developed (Gallovič et al., 2019). We have constructed a dynamic source inversion technique following Gallovič et al. (2019) to reveal relationships between strong ground motion generation and the dynamic source parameters (e.g., Miyamoto et al., 2024). In this study, we evaluate synthetic tests using a source model constructed with reference to the previous studies (Asano and Iwata, 2016; Mitsuoka et al., 2020) for the application to the largest foreshock (MJMA 6.5, April 14, 2016) of the 2016 Kumamoto, Japan, earthquake sequence.
Our inversion technique consists mainly of generating synthetic waveforms by convolving the slip time functions, obtained from the dynamic rupture simulation, with the Green’s functions and updating the dynamic source parameters through the MCMC sampling method. An open-source simulation code, fd3d_TSN (Premus et al., 2020), which adopts the finite difference method, is used for the dynamic rupture simulations. The Green’s functions are calculated by the discrete wavenumber method (Bouchon, 1981) and the reflection and transmission matrix (Kennett and Kerry, 1979) for composite one-dimensional velocity models. These velocity models are extracted from three-dimensional velocity models: a local velocity model in and around Kumamoto region (Asano et al., 2019) and the Japan Integrated Velocity Structure Model (JIVSM; Koketsu et al., 2012). Regarding to dynamic source parameters, the prior distributions of the initial shear stress, the peak friction, and the slip-weakening distance are set to uniform distributions. The proposal probability distributions of the initial shear stress and the peak friction are assumed to be the normal distributions, whereas that of the slip-weakening distance is given by the log-normal distribution. The likelihood function is evaluated based on the misfit of waveforms and the moment magnitude. The dynamic source parameters are updated depending on the results of the Metropolis-Hastings criterion. In this synthetic test, 20-s-long velocity waveforms were generated from the target source model, and used as the observed data. These waveforms started from 1 s before P-wave arrival and were filtered in 0.05–0.5 Hz.
As a result of this synthetic test, an ensemble of 80,000 dynamic source models was obtained by the MCMC sampling. Considering the variance reduction (VR) and the seismic moment, we removed initial 20,000 models in the burn-in phase and resampled every 30 models to obtain independent samples. The representative dynamic source model was obtained by averaging values of the dynamic source parameters of the resultant 2,000 models. This estimated model reproduced well the characteristics of the rupture process of the target model, while the rupture duration was about 1 s shorter than the targeted one. The waveforms, which were generated from the estimated model, agreed well with the ones by the target model and resulted in VR of 92%. Estimated values of the initial shear stress and the peak friction were ranged in about 0.5–2 times of the targeted values within the significant slip area of the target model, while the slip-weakening distance was estimated in the range of 0.6–4.5 times. In addition, another synthetic test using waveform data in the frequency range of 0.05–1 Hz is now being conducted. The differences in performance of the parameter estimation will be discussed.
Our inversion technique consists mainly of generating synthetic waveforms by convolving the slip time functions, obtained from the dynamic rupture simulation, with the Green’s functions and updating the dynamic source parameters through the MCMC sampling method. An open-source simulation code, fd3d_TSN (Premus et al., 2020), which adopts the finite difference method, is used for the dynamic rupture simulations. The Green’s functions are calculated by the discrete wavenumber method (Bouchon, 1981) and the reflection and transmission matrix (Kennett and Kerry, 1979) for composite one-dimensional velocity models. These velocity models are extracted from three-dimensional velocity models: a local velocity model in and around Kumamoto region (Asano et al., 2019) and the Japan Integrated Velocity Structure Model (JIVSM; Koketsu et al., 2012). Regarding to dynamic source parameters, the prior distributions of the initial shear stress, the peak friction, and the slip-weakening distance are set to uniform distributions. The proposal probability distributions of the initial shear stress and the peak friction are assumed to be the normal distributions, whereas that of the slip-weakening distance is given by the log-normal distribution. The likelihood function is evaluated based on the misfit of waveforms and the moment magnitude. The dynamic source parameters are updated depending on the results of the Metropolis-Hastings criterion. In this synthetic test, 20-s-long velocity waveforms were generated from the target source model, and used as the observed data. These waveforms started from 1 s before P-wave arrival and were filtered in 0.05–0.5 Hz.
As a result of this synthetic test, an ensemble of 80,000 dynamic source models was obtained by the MCMC sampling. Considering the variance reduction (VR) and the seismic moment, we removed initial 20,000 models in the burn-in phase and resampled every 30 models to obtain independent samples. The representative dynamic source model was obtained by averaging values of the dynamic source parameters of the resultant 2,000 models. This estimated model reproduced well the characteristics of the rupture process of the target model, while the rupture duration was about 1 s shorter than the targeted one. The waveforms, which were generated from the estimated model, agreed well with the ones by the target model and resulted in VR of 92%. Estimated values of the initial shear stress and the peak friction were ranged in about 0.5–2 times of the targeted values within the significant slip area of the target model, while the slip-weakening distance was estimated in the range of 0.6–4.5 times. In addition, another synthetic test using waveform data in the frequency range of 0.05–1 Hz is now being conducted. The differences in performance of the parameter estimation will be discussed.