At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault... more At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault, where main ruptures occurred, but also along the Hinagu fault. To estimate the slip distribution on these faults, we extend a method of nonlinear inversion analysis (Fukahata and Wright in Geophys J Int 173:353-364, 2008) to a two-fault system. With the method of Fukahata and Wright (2008), we can simultaneously determine the optimal dip angle of a fault and the slip distribution on it, based on Akaike's Bayesian information criterion by regarding the dip angle as an hyperparameter. By inverting the InSAR data with the developed method, we obtain the dip angles of the Futagawa and Hinagu faults as 61° ± 6° and 74° ± 12°, respectively. The slip on the Futagawa fault is mainly strike slip. The largest slip on it is over 5 m around the center of the model fault (130.9° in longitude) with a significant normal slip component. The slip on the Futagawa fault quickly decreases to zero beyond the intersection with the Hinagu fault. On the other hand, the slip has a local peak just inside Aso caldera, which would be a cause of severe damage in this area. A relatively larger reverse fault slip component on a deeper part around the intersection with Aso caldera suggests that something complicated happened there. The slip on the Hinagu fault is almost a pure strike slip with a peak of about 2.4 m. The developed method is useful in clarifying the slip distribution, when a complicated rupture like the Kumamoto earthquake happens in a remote area.
Zisin (Journal of the Seismological Society of Japan. 2nd ser.), 2009
Inversion analyses play a central role in solid earth sciences, since observable quantities are v... more Inversion analyses play a central role in solid earth sciences, since observable quantities are very limited for the earth's interior. Classical least squares method does not work well in these fields, since observed data are commonly inaccurate and/or insufficient. Least squares methods with additional conditions, such as damping or smoothing, have been widely used, but the weight of damping or smoothing have to be manually adjusted, if we do not take in a probabilistic point of view. In 1980, H. Akaike proposed a Bayesian Information Criterion (ABIC), where smoothness constraint is regarded as prior information that is combined with information from observed data by Bayes' rule, and then the optimal weight between the information from observed data and prior constraint is objectively determined by minimizing ABIC. ABIC had been introduced to geophysics by several studies. Among them, Yabuki and Matsu'ura (1992) has been the most influential. The inverse method developed by them has been widely applied to various problems in seismology and geodesy. Recently, it has become clear that the inverse method must be further developed beyond the framework given by Yabuki and Matsu'ura (1992). Generalization has been performed in dealing with prior constraints, hyperparameters, and observed data.
At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault... more At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault, where main ruptures occurred, but also along the Hinagu fault. To estimate the slip distribution on these faults, we extend a method of nonlinear inversion analysis (Fukahata and Wright in Geophys J Int 173:353-364, 2008) to a two-fault system. With the method of Fukahata and Wright (2008), we can simultaneously determine the optimal dip angle of a fault and the slip distribution on it, based on Akaike's Bayesian information criterion by regarding the dip angle as an hyperparameter. By inverting the InSAR data with the developed method, we obtain the dip angles of the Futa-gawa and Hinagu faults as 61° ± 6° and 74° ± 12°, respectively. The slip on the Futagawa fault is mainly strike slip. The largest slip on it is over 5 m around the center of the model fault (130.9° in longitude) with a significant normal slip component. The slip on the Futagawa fault quickly decreases to zero beyond the intersection with the Hinagu fault. On the other hand, the slip has a local peak just inside Aso caldera, which would be a cause of severe damage in this area. A relatively larger reverse fault slip component on a deeper part around the intersection with Aso caldera suggests that something complicated happened there. The slip on the Hinagu fault is almost a pure strike slip with a peak of about 2.4 m. The developed method is useful in clarifying the slip distribution, when a complicated rupture like the Kumamoto earthquake happens in a remote area.
At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault... more At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault, where main ruptures occurred, but also along the Hinagu fault. To estimate the slip distribution on these faults, we extend a method of nonlinear inversion analysis (Fukahata and Wright in Geophys J Int 173:353-364, 2008) to a two-fault system. With the method of Fukahata and Wright (2008), we can simultaneously determine the optimal dip angle of a fault and the slip distribution on it, based on Akaike's Bayesian information criterion by regarding the dip angle as an hyperparameter. By inverting the InSAR data with the developed method, we obtain the dip angles of the Futagawa and Hinagu faults as 61° ± 6° and 74° ± 12°, respectively. The slip on the Futagawa fault is mainly strike slip. The largest slip on it is over 5 m around the center of the model fault (130.9° in longitude) with a significant normal slip component. The slip on the Futagawa fault quickly decreases to zero beyond the intersection with the Hinagu fault. On the other hand, the slip has a local peak just inside Aso caldera, which would be a cause of severe damage in this area. A relatively larger reverse fault slip component on a deeper part around the intersection with Aso caldera suggests that something complicated happened there. The slip on the Hinagu fault is almost a pure strike slip with a peak of about 2.4 m. The developed method is useful in clarifying the slip distribution, when a complicated rupture like the Kumamoto earthquake happens in a remote area.
Zisin (Journal of the Seismological Society of Japan. 2nd ser.), 2009
Inversion analyses play a central role in solid earth sciences, since observable quantities are v... more Inversion analyses play a central role in solid earth sciences, since observable quantities are very limited for the earth's interior. Classical least squares method does not work well in these fields, since observed data are commonly inaccurate and/or insufficient. Least squares methods with additional conditions, such as damping or smoothing, have been widely used, but the weight of damping or smoothing have to be manually adjusted, if we do not take in a probabilistic point of view. In 1980, H. Akaike proposed a Bayesian Information Criterion (ABIC), where smoothness constraint is regarded as prior information that is combined with information from observed data by Bayes' rule, and then the optimal weight between the information from observed data and prior constraint is objectively determined by minimizing ABIC. ABIC had been introduced to geophysics by several studies. Among them, Yabuki and Matsu'ura (1992) has been the most influential. The inverse method developed by them has been widely applied to various problems in seismology and geodesy. Recently, it has become clear that the inverse method must be further developed beyond the framework given by Yabuki and Matsu'ura (1992). Generalization has been performed in dealing with prior constraints, hyperparameters, and observed data.
At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault... more At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault, where main ruptures occurred, but also along the Hinagu fault. To estimate the slip distribution on these faults, we extend a method of nonlinear inversion analysis (Fukahata and Wright in Geophys J Int 173:353-364, 2008) to a two-fault system. With the method of Fukahata and Wright (2008), we can simultaneously determine the optimal dip angle of a fault and the slip distribution on it, based on Akaike's Bayesian information criterion by regarding the dip angle as an hyperparameter. By inverting the InSAR data with the developed method, we obtain the dip angles of the Futa-gawa and Hinagu faults as 61° ± 6° and 74° ± 12°, respectively. The slip on the Futagawa fault is mainly strike slip. The largest slip on it is over 5 m around the center of the model fault (130.9° in longitude) with a significant normal slip component. The slip on the Futagawa fault quickly decreases to zero beyond the intersection with the Hinagu fault. On the other hand, the slip has a local peak just inside Aso caldera, which would be a cause of severe damage in this area. A relatively larger reverse fault slip component on a deeper part around the intersection with Aso caldera suggests that something complicated happened there. The slip on the Hinagu fault is almost a pure strike slip with a peak of about 2.4 m. The developed method is useful in clarifying the slip distribution, when a complicated rupture like the Kumamoto earthquake happens in a remote area.
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