Near-fault deformation and Dc″ during the 2016 Mw7.1 Kumamoto earthquake
© The Author(s) 2016
Received: 29 June 2016
Accepted: 17 November 2016
Published: 29 November 2016
KeywordsNear-fault displacement Slip-weakening distance Strike-slip fault
Ida (1972) proposed a slip-weakening friction law for shear faulting, where friction decreases gradually from the peak friction level to the residual level. In the slip-weakening law, slip-weakening distance (Dc) is defined as the slip needed to reach the residual friction. Dc is considered to be one of the important parameters for characterizing the unstable rupture propagation (e.g., Ohnaka 2013), since slip-weakening behavior represents an important feature of earthquake dynamic rupture propagation.
Ide and Takeo (1997) proposed a method to estimate a slip-weakening distance using the spatiotemporal slip history on the fault; they estimated it as 0.5–1 m for the 1995 Kobe earthquake. In their method, a complete description of the spatiotemporal distribution of the slip on the fault is required, which is usually difficult to estimate reliably. Twardzik et al. (2014) tried to invert observed waveforms of the 2004 Parkfield earthquake to directly obtain the dynamic parameters including the slip-weakening distance. However, as Guatteri and Spudich (2000) suggested, fracture energy could be estimated more stably than Dc when the data do not include sufficient high-frequency waves. Goto and Sawada (2010) discussed the trade-offs among the dynamic parameters when inverting the observed waveforms. Tinti et al. (2005) estimated the fracture energy distribution on the fault using a kinematic slip model. Fracture energy can be stably estimated by integrating the shear stress up to the slip-weakening distance. Therefore, a simple method for the estimation of slip-weakening distance is required.
Mikumo et al. (2003) proposed Dc′ as a proxy of Dc. Usually, to estimate a Dc value, both stress and slip functions are needed at a point on the fault. To estimate the stress function, the whole spatiotemporal history of the slip function on the fault is required, as has been done by Ide and Takeo (1997). However, Dc′ can be estimated using only the slip and slip velocity functions at a point on the fault, and the stress function is not needed. Dc″ proposed by Fukuyama and Mikumo (2007) is an approximated quantity of Dc′ used to roughly estimate the Dc value from the near-fault seismograms; Dc″ is an off-fault version of Dc′.
It should be noted that between these Mw6.1 and Mw7.1 earthquakes, Mw 5.4 (22:07:35 on April 14, 2016, JST) and Mw 6.0 (00:03:46 on April 15, 2016, JST) earthquakes occurred inside the aftershock area of the Mw 6.1 earthquake (NIED 2016c). This suggests that an unusual level of aftershock activity for the Mw 6.1 earthquake, in view of their locations and magnitudes, preceded the Mw 7.1 earthquake (e.g., Kato et al. 2016).
Since the National Research Institute for Earth Science and Disaster Resilience (NIED) has nationwide strong motion seismic networks called K-NET (Kinoshita 1998) and KiK-net (Okada et al. 2004; Aoi et al. 2011), several near-fault seismograms were recorded during this earthquake. Among these waveforms, the waveforms at KMMH16 (Lat. 32.7967°N, Long. 130.8199°E, height 55 m, see Fig. 1) were exceptional, in the sense that they were obtained close to the fault both on the surface and at the bottom of a 252-m-deep borehole. From our limited knowledge, this observation could be the first in which both surface and borehole seismograms were obtained close to the strike-slip faulting, although Fukuyama (2015) reported the near-fault surface and borehole seismograms that were recorded during the reverse faulting of the 2008 Iwate–Miyagi Nairiku earthquake (Mw 6.9).
The near-fault seismograms of vertical strike-slip earthquakes are very important for directly measuring the earthquake source properties. It is well known that because of very little excitation of Rayleigh waves (Okada 1992; Zhang and Chen 2006), the free surface effect becomes negligible and the “Method of Images” can be applied to compute the fault slip history in full space. Then, the observed near-fault seismogram for a vertical strike-slip event can be considered as if it is observed at the middle of the fault at depth.
Once we directly measure the fault-parallel ground motion close to the fault, we will be able to estimate the slip-weakening distance from that observation as Dc″ as proposed by Fukuyama and Mikumo (2007). Dc″ is estimated using the near-fault seismograms that are obtained close to the vertical strike-slip fault. Dc″ is defined as double the fault-parallel ground displacement when the absolute fault-parallel ground velocity is at a maximum (Fukuyama and Mikumo 2007). Cruz-Atienza et al. (2009) investigated the accuracy of the Dc″ estimation using numerical simulations. They concluded that the estimation of Dc″ could be reasonable if the station is located within the distance of Rc (the resolution distance), which is approximately 0.8 times the wavelength at breakdown frequency.
In this manuscript, we investigate the near-fault ground deformation using a set of seismograms observed close to the fault at KMMH16 station. In addition, since this Mw 7.1 earthquake had vertical strike-slip faulting, the ground displacement very close to the fault can be considered a proxy of the fault slip motion. Using this near-fault displacement at KMMH16, we estimate the Dc″ value for the 2016 Mw7.1 Kumamoto earthquake.
To obtain the displacement waveforms, we first subtracted a constant value from each original acceleration waveform to set the onset acceleration to zero. Then, we numerically integrated the original acceleration waveforms twice in the time domain. We rotated the seismograms to fault-parallel (N235°E) and fault-normal (N325°E) directions. We corrected the instrument response by multiplying the waveforms by a constant value to convert the recorded digits to the physical value of acceleration. It should be noted that we did not apply any low-pass or high-pass filtering operations. Therefore, we did not correct the frequency response of the sensor. However, since our focus here is the near-fault displacement and acceleration response at low frequency is flat, the uncorrected high-frequency response does not affect the present analysis.
Results and discussion
In Fig. 3, acceleration, velocity and displacement seismograms are shown. As can be seen, the maximum amplitudes of the accelerations were quite different between the acceleration on the surface and that at the bottom of the borehole. However, the velocity and displacement behaved similarly in these two locations. Since the fault slip motion dominates the right-lateral strike slip, the displacements recorded by these two sensors should be quite similar to those expected theoretically as stated above.
Near the KMMH16 station, Kumamoto prefecture installed an accelerometer at Mashiki town hall (Miyazono, Fig. 2a). Iwata (2016) numerically integrated the accelerogram to obtain the displacement. We confirmed that the fault-parallel and fault-normal displacements at Miyazono were almost identical to those at KMMH16. In addition, the vertical displacement at Miyazono was identical to the vertical displacement at the surface of KMMH16. These similarities warrant the accuracy of ground displacements measured by accelerometers. A small difference between the vertical displacements on the surface and at the bottom of the borehole at KMMH16 might be significant. The amount of strain change can be roughly estimated as 8 × 10−4, which is much larger than the value (~10−6) expected from the slip model of the Mw7.1 earthquake (e.g., Ozawa et al. 2016). In this study, we are not going into further detail regarding this difference.
If more Dc″ data are collected in the future, our understanding of the slip-weakening distance during earthquakes will significantly improve. This is important because during the unstable rupture of earthquakes, the slip-weakening distance plays an important role in the propagation of the rupture.
As stated before, Cruz-Atienza et al. (2009) proposed Rc (the resolution distance) to evaluate the accuracy of Dc″. They proposed that Rc = 0.8 Vs Tc where Vs is the shear wave velocity and Tc is the breakdown time. Vs is 2.7 km/s taken from the logging profile of this station (NIED 2016d). Tc was estimated at about 1.1 s from the time when the displacement started to accelerate until the peak ground velocity occurred (Fig. 4). Thus, in the present case, Rc becomes about 2.4 km. The distance from KMMH16 to the fault is much smaller than this estimate (Fig. 2). Therefore, the present observations were done inside the Rc, and we consider that the estimated value has some meaning on the slip-weakening distance. At the very least, the present estimation suggests the upper bound of the slip-weakening distance.
We investigated the near-fault displacement field using the accelerograms obtained at KMMH16, a KiK-net station, where waveforms were recorded both on the surface and at the bottom of a 252-m-deep borehole. The displacement behavior was similar at both locations, which is consistent with strike-slip fault motion. By using the fault-parallel velocity and displacement, we estimated a Dc″ of 1 m, which could be considered at least as the upper bound value of the slip-weakening distance on the fault. This Dc″ value is consistent with previous estimates, and it falls between 30 and 50% of the measured total slip at the near-fault station.
EF analyzed the data and wrote the manuscript, while WS collected the observed waveforms and the related information. Both authors read and approved the final manuscript.
Waveform data were provided by the KiK-net maintained by the National Research Institute for Earth Science and Disaster Resilience. Comments by two anonymous reviewers were quite valuable.
The authors declare that they have no competing interests.
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