Rupture process of the main shock of the 2016 Kumamoto earthquake with special reference to damaging ground motions: waveform inversion with empirical Green’s functions
© The Author(s) 2017
Received: 1 August 2016
Accepted: 24 January 2017
Published: 31 January 2017
A series of damaging earthquakes hit the Kumamoto and Oita prefectures, Kyushu, Japan, including the M w6.1 foreshock (April 14, 21:26 JST) and the M w7.1 main shock (April 16, 1:25 JST). As of July 12, it involved 1879 perceptible earthquakes (Japan Meteorological Agency 2016a). The entire sequence was named “the 2016 Kumamoto earthquake” by the Japan Meteorological Agency (JMA; Japan Meteorological Agency 2016b). Eighty-one people were killed because of the earthquakes according to the Fire and Disaster Management Agency, Japan (as of July 29).
In addition to the damage to buildings, damage to highway bridges was also significant in the near-source region of the Kumamoto earthquake. Although some bridges were clearly affected by landslides, several bridges, including the Ogiribata Bridge (see Fig. 1), could have been simply damaged by strong ground motions (Nikkei Construction 2016). To understand the true damage mechanism of the bridges, it is necessary to estimate the strong ground motions at the bridge sites. For this purpose, again, it is necessary to understand the rupture process of this earthquake especially when the bridge site is located close to the fault, because the rupture process of the earthquake easily affects the strong ground motions near the fault.
Therefore, the rupture process of the main shock of the Kumamoto earthquake was investigated in this study based on the inversion of strong ground motions, in particular the generation of strong ground motions in the frequency range relevant to structural damage. Strong-motion records in the near-source region were mainly used in the study because the authors were interested in the generation mechanism of damaging ground motions in the near-source region.
Empirical Green’s functions (EGFs) were used in the waveform inversion in this study. As discussed in Nozu (2007), the main advantage of the EGFs over numerical Green’s functions is that they allow us to avoid uncertainty in the subsurface structure model used in calculating the numerical Green’s functions, which could affect the estimated rupture process; even complex 2D or 3D effects of the ground motions can be naturally incorporated using EGFs. The 3D nature of the subsurface structure is particularly significant in the near-source region of the Kumamoto earthquake, as represented by the existence of the Aso caldera (Fig. 1). In fact, the effect of the 3D subsurface structure is quite noticeable in the observed waveforms, as discussed later in the article. Therefore, the use of EGFs could be especially advantageous for this particular earthquake.
One of the interesting questions associated with the inversion results obtained using EGFs is to what extent the inversion results are dependent on the selection of the EGFs. To answer this question, four cases of inversions with different combinations of EGFs were used in this study. The results were then compared in terms of final slip distributions and peak slip velocities.
Because the purpose of the study was to reveal the rupture process of the earthquake that caused damaging ground motions in the near-source region, near-source stations were used in the analysis. In particular, five K-NET stations (KMM004, KMM005, KMM006, KMM009, KMM011) and three KiK-net stations (KMMH06, KMMH14, KMMH16) were selected (solid triangles in Fig. 1). The KiK-net station KMMH16 is located in Mashiki. Although it is located outside of the heavily damaged zone (Hata et al. 2016), it is still within 1 km from the temporary stations deployed in the heavily damaged zone. The observed velocity waveforms at KMMH16, both at the surface and in the borehole, were also characterized by a large-amplitude pulse with an approximate period of 1 s, similar to those observed at the temporary stations, although the peak ground velocity at the surface was 20–25% smaller than at the temporary stations. Therefore, information about the effect of the earthquake rupture on the damaging ground motions in Mashiki could be obtained from including KMMH16 in the inversion analysis.
Although the use of near-source stations is advantageous in constraining the detailed spatiotemporal distribution of slip on the fault plane, its downside is that the inversion results could be affected by soil nonlinearity, because the amplitude of the strong ground motions tends to be large in the near-source region. To minimize the effect of soil nonlinearity, borehole records, rather than surface records, were used at the KiK-net stations. However, surface records were used at KMMH06 because the S/N ratio of the borehole records was not sufficient for small events. At the K-NET stations, surface records were used. The potential effects of soil nonlinearity on the results will be discussed in “Discussion” section.
The hypocenters are located close to the respective parts of the main shock fault plane (Fig. 1).
M J ≥ 4.0. This condition was imposed because the records of smaller earthquakes tend to exhibit insufficient S/N ratios at low frequencies.
The records are obtained at all target stations.
Western part of the fault (16 km long)
Eastern part of the fault (24 km long)
Parameters of the main shock and small events
M J a
M 0 b (Nm)
Linear least-squares waveform inversion (Nozu 2007; Nozu and Irikura 2008) was adopted. The inversion follows the multi-time-window approach, which was proposed by Hartzell and Heaton (1983), although empirical Green’s functions were used in the present analysis. The method can be summarized as follows:
The relation between the size of the small event, size of the subfault, and frequency component to be analyzed is as follows: In this formulation, a sufficiently small event that can be regarded as a point source is used (condition 1). Similarly, a sufficiently small subfault, which can be regarded as a point source, is utilized (condition 2). Based on condition 1, sufficiently low-frequency components should be used in the analysis in light of the size of the small event. In general, the corner frequency involved in the source spectrum of an earthquake is related to the finiteness of the fault size and the rise time (e.g., Aki and Richards 2002); the effect of the fault finiteness is recognizable at frequencies higher than the corner frequency. Therefore, condition 1 requires the use of frequency components lower than the corner frequency of the small event. Condition 2 is the same as that for the waveform inversion with numerical Green’s functions. It requires the use of sufficiently small subfaults, depending on the frequency components to be analyzed. Thus, conditions 1 and 2 require that both the area of the small event and that of the subfault are sufficiently small. However, it is not necessary that those areas coincide with each other. In this respect, the present method differs from the empirical Green’s function method of Irikura (1986).
In terms of the second-order derivative with respect to time, Eq. (6) is applied for k = N D but not for k = 1, with the intention of allowing high slip velocity just after passage of the first-time-window triggering front.
For the application to the main shock of the 2016 Kumamoto earthquake, a fault plane that includes the JMA hypocenter with a length of 40 km and width of 20 km was assumed (Fig. 1). The strike and dip angles were initially set to 226° and 84°, respectively, referring to the F-net moment tensor solution (Table 2). The strike angle was then changed to 232° to be more consistent with the surface fault trace.
The fault was divided into 20 × 10 subfaults. It was assumed that the first-time-window triggering front starts at the JMA hypocenter and propagates radially at a constant velocity. The velocity will be referred to as the “first-time-window triggering velocity” in this article. The choice of the velocity will be discussed later. In Eq. (1), an impulse train that spans 3.0 s and consists of 12 impulses at equal time intervals of 0.25 s was used. Thus, the height of each impulse corresponds to the ratio of the moment release during 0.25 s, with respect to the moment of the EGF event. The ratio was determined using the inversion. In terms of the appropriateness of the total time window of 3.0 s, the authors analyzed another case of inversion in which the total time window was extended to 4.0 s. As a result, it was confirmed that the final slip distribution was not significantly affected by this modification.
The shear wave velocity in the source region was assumed to be 3.55 km/s according to Fukuyama et al. (1998).
The synthetic velocities (0.2–2 Hz) were compared with those observed in Case 1 (Fig. 2). The agreement between the observed and synthetic waves is satisfactory at many stations. At KMMH16, the coincidence of the NS components is almost perfect including the pulses, while the amplitude of the EW component is underestimated, which is probably due to the fact that the coincidence of the mechanism between the large and the small evens is not perfect. Similarly, the coincidence of the NS component is almost perfect at KMM011, while the EW component is underestimated. The result for the EW component at KMM006 is good, while the NS component is underestimated.
The effect of rupture process on near-source ground motions
Potential effects of soil nonlinearity on the waveform inversion results
Comparison with other source studies
Potential sources of errors for each of the numerical and empirical Green’s functions
Potential sources of errors
Numerical Green’s functions
Uncertainty in the subsurface structure model
Empirical Green’s functions
Errors associated with the allocation of small events to the subfaults
Effects of the dip angle
One of the main differences between the present source model and those of other studies could be the dip angle. The present model uses the dip angle of 84°, while some of the other source models, including that of Asano and Iwata (2016), employ a lower dip angle. Therefore, the effect of the dip angle was investigated.
The bottom two panels of Fig. 14 show the corresponding final slip distributions. The results are similar to that of Case 1 in spite of the different strike and dip angles; the results imply that the basic features of the slip models (such as the large slip approximately 15 km northeast of the hypocenter) do not significantly depend on the strike and dip angles. The variance reduction was 60.6 and 60.3% for the dip angle of 78° and 72°, respectively. The results are slightly inferior to that of Case 1 with a variance reduction of 62.4%. However, because the difference is small, the authors do not insist that a nearly vertical fault plane is more appropriate.
The rupture process of the main shock of the 2016 Kumamoto earthquake was investigated in this study based on the inversion of strong ground motions, particularly the generation of strong ground motions in the frequency range relevant to structural damage. Strong-motion records in the near-source region were mainly used because the authors were interested in the generation mechanism of the damaging ground motions in the near-source region. Empirical Green’s functions (EGFs) were employed to avoid uncertainty in the subsurface structure model. Four cases of inversions with different combinations of small events were analyzed to investigate the dependence of the inversion results on the selection of the small events. It was found that the dependence of the final slip and peak slip velocity distributions on the selection of the EGF events was small. The results clearly indicate that a region of significantly large slip and slip velocity existed approximately 15 km northeast of the hypocenter. No “asperity” was observed between the hypocenter and Mashiki. Thus, it is not appropriate to conclude that the large-amplitude pulse-like ground motion in Mashiki was generated by the forward-directivity effect associated with the rupture of an asperity. As far as the source effect is concerned, the ground motion in Mashiki cannot be interpreted as the worst case scenario. On the other hand, the rupture of the “asperity” 15 km northeast of the hypocenter should have caused significantly large ground motions in regions close to the asperity. The significant damage of highway bridges in the region, including the Ogiribata Bridge, can potentially be attributed to the rupture of the asperity. The results of this study were compared with an inversion result obtained using numerical Green’s functions for a layered half-space. The two results share the main features in spite of the different Green’s functions and stations used. Therefore, it can be concluded that these two source models capture the main features of the rupture process of the earthquake.
AN conducted the waveform inversion. YN participated in the discussion on the relation between the rupture process and the near-source ground motions. Both authors read and approved the final manuscript.
The authors are grateful to the National Research Institute for Earthquake Science and Disaster Resilience, Japan, for providing strong-motion data of K-NET and KiK-net and the moment tensor solutions by the F-net. The authors appreciate valuable comments from Dr. Haruo Horikawa, Dr. Arben Pitarka, and an anonymous reviewer.
The authors declare that they have no competing interests.
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