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Source rupture process of the 2011 Fukushima-ken Hamadori earthquake: how did the two subparallel faults rupture?
© Tanaka et al.; licensee Springer. 2014
Received: 4 April 2014
Accepted: 12 August 2014
Published: 26 August 2014
The 2011 Fukushima-ken Hamadori earthquake (MW 6.6) occurred about a month after the 2011 Great Tohoku earthquake (MW 9.0), and it is thought to have been induced by the 2011 Tohoku earthquake. After the 2011 Hamadori earthquake, two subparallel faults (the Itozawa and Yunodake faults) were identified by field surveys. The hypocenter was located nearby the Itozawa fault, and it is probable that the Itozawa fault ruptured before the Yunodake fault rupture. Here, we estimated the source rupture process of the 2011 Hamadori earthquake using a model with two subparallel faults based on strong motion data. The rupture starting point and rupture delay time of the Yunodake fault were determined based on Akaike’s Bayesian Information Criterion (ABIC). The results show that the Yunodake fault started to rupture from the northern deep point 4.5 s after the Itozawa fault started to rupture. The estimated slip distribution in the shallow part is consistent with the surface slip distribution identified by field surveys. Time-dependent Coulomb failure function changes (ΔCFF) were calculated using the stress change from the Itozawa fault rupture in order to evaluate the effect of the rupture on the Yunodake fault. The ΔCFF is positive at the rupture starting point of the Yunodake fault 4.5 s after the Itozawa fault started to rupture; therefore, it is concluded that during the 2011 Hamadori earthquake, the Yunodake fault rupture was triggered by the Itozawa fault rupture.
In previous studies (Hikima 2012; JMA 2012; Shiba and Noguchi 2012), the source rupture process of this event has been estimated using a two-fault model (the Itozawa and Yunodake faults) based on strong motion data. However, different slip distributions have been identified, particularly in relation to the Yunodake fault. It is considered likely that such differences were caused by variations in the authors’ assumptions used for the fault model, particularly in relation to the rupture starting point and rupture delay time of the Yunodake fault.
In this study, in order to obtain slip distributions on the two faults, we objectively determine not only a hyperparameter describing the strength of smoothing constraint but also a set of additional parameters such as rupture starting point, rupture delay time, and first-time window triggering velocity based on Akaike’s Bayesian information criterion (ABIC) (Akaike 1980), whereas previous source inversions determined only hyperparameters (e.g., Ide and Takeo 1997; Sekiguchi et al. 2000). We then calculate the stress field from the estimated moment release history of the Itozawa fault and get temporal changes in the Coulomb failure function (time-dependent ΔCFF) in order to discuss whether the Yunodake fault rupture was triggered by that of the Itozawa fault.
Estimation of the source rupture process using kinematic waveform inversion
The observed ground motions are represented by the convolution of the source, the propagation path, and site effects. In order to use appropriate Green’s functions in kinematic waveform inversion analysis, it is necessary to check whether observed waveforms can be reproduced using a given velocity structure model. In this study, we selected strong motion stations based on a comparison between the theoretical and observed waveforms of an aftershock (13:39 JST on 18 June 2011, MW 4.4).
Setting of the assumed fault model
22 × 14
18 × 14
where C is a constant term.
The estimated slip model shows that a large slip area is located in the northwestern shallow part of the Itozawa fault (Figure 3b). The estimated large slip areas on the Yunodake fault are located in the shallow part of the fault plane and in the vicinity of the rupture starting point (Figure 3c). The average amount of slip in the northwestern part of the Itozawa fault that lies within a depth of 5 km from the earth’s surface is approximately 1.3 m, and the average amount of slip of the Yunodake fault that lies within a depth of 5 km from the earth’s surface is approximately 1.0 m. The total seismic moment of this event is estimated to be 1.45 × 1019 N · m (MW 6.7), and the seismic moment released from the Itozawa fault is almost the same as that released from the Yunodake fault.
The effects of the Itozawa fault rupture on the Yunodake fault plane
Calculation of the time-dependent ΔCFF
In a previous study, Hikima (2012) calculated the static ΔCFF using his final slip model on the Itozawa fault plane and found an area with a positive ΔCFF that included his rupture starting point when he assumed the apparent friction coefficient to be 0.8. In our results, which were obtained from the kinematic waveform inversion, the Itozawa fault was found to be in the process of rupturing when the Yunodake fault started to rupture. Therefore, we consider it important to calculate the time-dependent ΔCFF using the obtained moment release history of the Itozawa fault in order to evaluate the effect of the Itozawa fault rupture on the Yunodake fault plane.
The stress field was calculated by solving the elastodynamic wave equations with the finite difference method (FDM) using discontinuous grids from Ground Motion Simulator (GMS) (Aoi and Fujiwara 1999). The FDM model space was 60 × 60 km2 in the horizontal direction and 30.1 km in the depth direction. The underground structure model for the stress field calculation was assumed to be a homogeneous half space, with VP, VS, density, and Q of 5.0 km/s, 2.9 km/s, 2.6 × 103 kg/m3, and 680, respectively. The discontinuous grid system consists of two regions with different grid spacings. The grid spacing of the shallower region is small, whereas the grid spacing of the deeper region is three times coarser (Aoi and Fujiwara 1999). We used discontinuous grids that consisted of a grid spacing of 0.05 km in the shallower region up to the depth of 18.55 km (including the Itozawa and Yunodake faults) and of 0.15 km in the deeper region. The moment release history of the Itozawa fault plane is given by the spatially interpolated model of the obtained slip model using the kinematic waveform inversion with intervals of 2.0 to 0.4 km. The time-dependent ΔCFF is calculated according to ΔCFF = Δτ + μ′ Δσ (e.g., Toda et al. 2011), where τ is the shear stress, σ is the normal stress on the fault plane, and μ′ is the apparent friction coefficient. In this study, two cases of μ′ = 0.4 and 0.8 were tried. For shear stress τ, the positive direction is set to the slip direction of the first-time window at the rupture starting point of the Yunodake fault.
In the previous section, it was demonstrated that the rupture of the Yunodake fault was caused by the dynamic effect of the rupture of the Itozawa fault. However, it is possible that the effects of other earthquakes such as the 2011 Tohoku earthquake could have impacted the Yunodake fault; accordingly, this possibility is also investigated.
Toda et al. (2011) calculated the static ΔCFF on known major faults and megathrusts using the source model of the 2011 Tohoku earthquake and the MW 7.9 aftershock, and the results showed that the static ΔCFF on the fault near the Yunodake fault has a positive value of approximately 0.1 MPa when an apparent friction coefficient of 0.4 is adopted. However, the static ΔCFF on the Yunodake fault was not calculated in that study. Therefore, in order to discover whether the Itozawa fault rupture triggered the Yunodake fault rupture, we calculated the effect of the static ΔCFF of the 2011 Tohoku earthquake on the Yunodake fault; the static ΔCFF was calculated based on Okada (1992) using the final slip distribution of the 2011 Tohoku earthquake (Kubo and Kakehi 2013). The value of the static ΔCFF at the rupture starting point of the Yunodake fault was found to have a positive value of approximately 0.15 MPa, which is considerably smaller than the time-dependent ΔCFF of +0.8 MPa from the rupture of the Itozawa fault. Therefore, we consider this to indicate that the rupture of the Yunodake fault was triggered primarily by the rupture of the Itozawa fault.
The source rupture process of the 2011 Hamadori earthquake was estimated using fault model parameters such as the rupture starting point and the rupture delay time of the Yunodake fault. The results show that the Yunodake fault began to rupture from the northern deep point 4.5 s after the Itozawa fault began to rupture. The estimated final slip distributions are consistent with the surface slip distributions found by the field surveys.
The time-dependent ΔCFF was then calculated using the estimated moment release history on the Itozawa fault plane, and it was found to be positive at the rupture starting point of the Yunodake fault, 4.5 s after the Itozawa fault began to rupture. Furthermore, the obtained time-dependent ΔCFF was found to be larger than the static ΔCFF caused by the 2011 Tohoku earthquake, which implies that the effect of the Itozawa fault rupture on the Yunodake fault plane was larger than that of the 2011 Tohoku earthquake. Therefore, we conclude that during the Hamadori earthquake, the rupture of the Yunodake fault was triggered by the rupture of the Itozawa fault. Considering our results, it may be said that the rupturing of these unconjugated faults was due to the dynamic effect.
We thank two anonymous reviewers and Associate Editor Tomomi Okada for their valuable comments that improved our manuscript. Strong motion data of K-NET, KiK-net, F-net, and Ground Motion Simulator (GMS) were provided by the National Research Institute for Earth Science and Disaster Prevention, Japan. The hypocenter catalog and strong motion data were obtained from the Japan Meteorological Agency. The Generic Mapping Tools software (Wessel and Smith 1998) was used to produce the figures. This study was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, under its Earthquake and Volcano Hazards Observation and Research Program.
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