Earthquake rupture properties of the 2016 Kumamoto earthquake foreshocks (M j 6.5 and M j 6.4) revealed by conventional and multiple-aperture InSAR
© The Author(s) 2017
Received: 5 July 2016
Accepted: 20 December 2016
Published: 3 January 2017
KeywordsForeshocks Kumamoto earthquake InSAR MAI Crustal deformation Fault model
It is further noted that a seismic intensity of 7, which is the highest rank in the JMA seismic intensity scale, was recorded at Mashiki town (Fig. 1). Some reasons can be considered for why the damage was so major, reportedly leading to 9 fatalities and over 800 injuries in spite of the magnitude of M j 6.5 (M w 6.2). These include bad soil conditions, rupture directivity, building vulnerability. They are all reasonable factors that would increase the damage, but to date, no evidence has definitively shown which factors are dominantly responsible.
An L-band synthetic aperture radar (SAR) satellite, known as the Advanced Land Observing Satellite 2 (ALOS-2), makes observations with an emergency operation for the purpose of detecting crustal deformation using SAR interferometry (InSAR). Although continuous GNSS observation sites (GEONET) are densely deployed in and around the fault zone with an average placement interval of approximately 20 km (Fig. 1), it remains difficult to obtain spatially detailed displacement data for moderate-sized earthquakes, impeding comprehensive analysis of the source properties, such as fault modeling. By contrast, InSAR is capable of detailed mapping of crustal deformation from the foreshocks, which can provide information on the spatial features of the fault rupture.
The primary purpose of this study is to rapidly report the rupture location and style of the foreshocks by retrieving crustal deformation using ALOS-2 data. I first report crustal deformation derived from standard and advanced InSAR analyses and examine the ruptures as a whole, including both the M j 6.5 and M j 6.4 events. Next, I construct a fault model to understand the rupture properties and then analyze the possible factors responsible for why Mashiki town suffered such serious damage.
Data and analysis
SAR data and analysis method
Analyzed ALOS-2 images
November 14, 2014
April 15, 2016
A drawback of InSAR is that no displacement can be measured along the flight direction (azimuth component). The satellite used in this analysis flies parallel to the Hinagu fault zone. According to seismic data analyses, a dextral motion is predominant for both the M j 6.5 and the M j 6.4 events (JMA 2016b). Thus, conventional cross-track, line-of-sight (LOS) InSAR (hereafter called InSAR) is insensitive to ground movement near the fault where along-track displacement is expected to dominate. In this context, to derive further information on crustal deformation, I applied multiple-aperture interferometry, generally known as MAI (Scheiber and Moreira 2000; Bechor and Zebker 2006), where the basic method of Barbot et al. (2008) was followed. Although the azimuth component can be measured also by a pixel offset method (Michel et al. 1999; Kobayashi et al. 2009), the measurement accuracy, in general, is worse than that of MAI. This is why I here applied the MAI method. In this method, the frequency band of the already focused SLC data is divided into two parts. This operation creates two SLC images with positive and negative Doppler frequencies, equivalent to forward- and backward-looking images, respectively. Using these subaperture images, I made forward- and backward-looking interferograms and then converted the displacement to the azimuth component. I took 32 by 32 looks in both range and azimuth directions, resulting in a pixel spacing of about 46 and 59 m, respectively. I applied the adaptive Goldstein filter (Goldstein and Werner 1998) with a coefficient of 1.0 to improve the coherence.
Long spatial wavelength signals, which are presumably due to ionosphere-related noise, are included in both the InSAR and the MAI results. To remove the noise for the InSAR, a GNSS-based noise reduction was applied, which approximates the method utilized by Tobita et al. (2005). For the MAI, I applied a Gaussian filter to model the long-wavelength noise because the spatial pattern of noise is too complicated to correct using the GNSS-based reduction method.
I reduced the atmosphere-related noise using a numerical weather model for the InSAR data (Kobayashi et al. 2014). For the MAI, most of the atmospheric noise was canceled out between the forward- and backward-looking images; thus, no noise reduction was required. The ALOS-2 data were processed using GSISAR software (Fujiwara and Tobita 1999; Fujiwara et al. 1999; Tobita et al. 1999; Tobita 2003), and the software package GAMMA (Wegmüller and Werner 1997) was used for MAI processing.
I utilized GEONET data to obtain the coseismic displacement vectors for the long-wavelength noise correction and a fault modeling. To obtain the coseismic displacement, I took the difference in coordinate data corresponding to the observation dates of the master and slave images. To derive stable coordinate data for the master image, I took an average of amplitudes (positions) in the time series data for F3 data from November 9, 2014, to November 18, 2014 (10 days). F3 data consist of daily coordinates, which are the most accurate data in the analysis strategy of GEONET. For the slave image, I averaged the time series data of Q3 data, which was calculated every 3 h with a 6-h data window (Nakagawa et al. 2009), from 03:00 to 23:59 (JST). Site 940093 had non-negligible noise in the vertical component, and thus, this site was not used for the modeling.
Crustal deformation map
Figure 2b shows the MAI result. The cold and warm colors represent the displacement along and opposite to the satellite flight direction, respectively. Although the original MAI result suffers from serious long-wavelength noise (Additional file 1: Fig. S1a), there is a conspicuous phase change showing northward movement on the western side of the Hinagu fault zone. A sharp, linear contrast in displacement, indicated by arrows in the inset of the figure, can be identified along the Hinagu fault. It is highly probable that this sharp phase contrast reflects the fault motion, and its orientation shows the strike of the source fault.
To clearly map the deformation, I applied a Gaussian filter in order to model the long-wavelength noise (Additional file 1: Fig. S1b) and then subtracted the modeled noise from the original MAI result (Additional file 1: Fig. S1c). I have searched the width of Gaussian filter from 10 to 50 km with an interval of 10 km so as to reproduce well the long-wavelength noise by trial and error, and resultantly a width of 30 km was used for the filtering. Figure 2b shows the noise-reduced MAI image. Northward ground movement clearly appears on the western side of the Hinagu fault zone, with maximum movement of approximately 20 cm. On the other hand, no significant southward movement is shown on the eastern side.
The measurement accuracy of MAI is generally worse than that of InSAR. According to several previous studies, the accuracy of MAI is approximately 10 cm (Bechor and Zebker 2006; Barbot et al. 2008; Jung et al. 2009). To confirm the reliability of the observations, I compared the MAI result to the corresponding GNSS data. The colors of squares in Fig. 2b indicate the displacements converted to the azimuth component at the GEONET sites. The colors of the GNSS site are similar to the background color, suggesting that there is no large difference from GNSS observations. The mean and the standard deviation of residuals between GNSS and MAI results for all stations shown in Fig. 2 are estimated to be 0.4 and 8.7 cm, respectively. The MAI results at GEONET sites 021071 and 950465, which are located in the major deformation area, are −11.1 and −2.7 cm, while the corresponding GNSS-observed displacements are −18.7 and −9.9 cm, respectively. Although a measurement error of ~7 cm remains, it is clear that the large northward movement colored in yellow significantly exceeds the noise level and reflects true crustal deformation.
I further emphasize that local but non-negligible signal can be identified in the junction of the Hinagu and the Futagawa faults where Mashiki town is located. Apart from the two broad deformation signals depicted in Fig. 2a, a significant LOS lengthening signal is locally distributed in and around Mashiki town (Fig. 2a, Additional file 2: Fig. S2). It suggests that this phase change is caused by a different mechanism from the motion on the Hinagu fault responsible for the more widely distributed phase change. This local signal appears to be aligned along the strike of the Futagawa fault. The LOS shortening lobe distributed in the north appears to be oriented somewhat parallel to the strike of the Futagawa fault as indicated by a dotted line in Fig. 2a (Additional file 2: Fig. S2b), suggesting that the responsible fault motion might be related to the Futagawa fault. It is suggested that Mashiki town was subjected to this specific, local deformation.
I first constructed a fault model under the assumption of a rectangular fault with a uniform slip in an elastic half-space (Okada 1985). With the knowledge obtained from the InSAR and the MAI data, I assumed two fault planes, of which one runs along the Hinagu fault while the other is beneath Mashiki town along the strike of the Futagawa fault. I estimated the fault model parameters by a simulated annealing method (e.g., Kobayashi et al. 2012). To estimate the individual confidence of inferred parameters, I employed a bootstrap method (Efron 1979). The parameters for the Hinagu fault were searched as below. The obtained displacement field is consistent with a right-lateral motion along the Hinagu fault, and thus, the rake was assumed to be a right-lateral with no constraint on dip-slip orientation. The major displacement is distributed in the western side of the Hinagu fault for both the components, suggesting that the fault has a west-dipping plane. This is why the strike was fixed to be 205°. Other parameters were assigned search ranges of 130.74°–130.80° in longitude, 32.71°–32.78° in latitude, 0–10 km in depth, 0–20 km in length, 0–20 km in width, 0°–90° in dip, and 0–2 m in slip amount, respectively. The given positions are the fault top center. In the same manner, for the local fault beneath Mashiki town, the search ranges were 130.78°–130.81° in longitude, 32.76°–32.79° in latitude, 0–10 km in depth, 0–10 km in length, 0–10 km in width, and 0–2 m in slip amount, respectively. The strike was fixed to be the strike of the Futagawa fault. I here set both the angles of 240° and 60°, meaning that both the north- and south-dipping faults were searched. Neither the dip nor the rake was constrained.
The InSAR and MAI data have ground surface changes over distances of several tens of kilometers, producing too many values to be easily assimilated in a modeling scheme. In order to reduce the number of data for the modeling analysis, I resampled both the InSAR and the MAI data beforehand, using a quadtree decomposition method. Essentially, I followed an algorithm presented by Jónsson et al. (2002). For a given quadrant, if, after removing the mean, the residue is greater than a prescribed threshold, the quadrant is further divided into four new quadrants. I here set the threshold to be 1 and 2 cm for InSAR and MAI data, respectively. This process is iterated until either each block meets the specified criterion or the quadrant reaches a minimum block size, 4 × 4 and 16 × 16 pixels for InSAR and MAI, respectively. For the MAI, the area used for the modeling is limited in the proximity of the faults to suppress the effect of the noise. The resampled data are shown in Additional file 3: Fig. S3.
For the weight of inversion, I assigned standard deviations of 1.2 and 5.0 cm for InSAR and MAI data, respectively, which are calculated using phase changes outside of the source region. I additionally utilized GNSS data for the modeling and gave the standard deviations of the time series data during the averaged period for the weight of inversion, on average 0.4, 0.3, and 0.9 cm for E–W, N–S, and up–down components, respectively.
Fault parameters for the two-fault model with uniform slips
Same as Table 2 but for the model assuming that the fault of #2 is dipping north
Next, with the knowledge obtained from the uniform slip model, I constructed a model for the foreshocks to map the detailed slip distribution. The slip distribution model is inferred by a least squares method, following the general procedure of Kobayashi et al. (2012). In the inversion, only the dip-slip and strike-slip components are estimated for each patch. The increase of model parameters gives rise to instability of the solution. To stabilize the solution, I here impose a spatial smoothness constraint on the slip distribution using a Laplacian operator. The relative weight of the constraints is determined by Akaike’s Bayesian information criterion (Akaike 1980). For the Hinagu fault, the fault plane was set to a rectangle 20 km long and 20 km wide. The strike angle was set at 205°, so as to be parallel to the Hinagu fault zone. The northern edge of the fault plane is set to be around the junction of the Hinagu fault and the Futagawa fault. For the local fault under Mashiki town, the fault plane was set to a rectangle 10 km long and 10 km wide, and dips to the south with a strike angle of 60°. Both planes are divided into 2 × 2 km squares.
The problem is a nonlinear inversion on a parameter of the dip angle. Here, with the results obtained from the previous modeling, I determined the dip angle by grid searches from 75° to 85° for the Hinagu fault and from 65° to 75° for the local fault with an interval of 5°, for each. The horizontal position is also a linearly unsolved parameter, and thus, I shifted the fault top position westward from [130.820°E, 32.795°N] with an interval of 0.005° for the Hinagu fault. Also for the local fault in the Mashiki town, I shifted the position northward from [130.760°E, 32.760°N] with an interval of 0.005°. The fault top position was fixed to a depth of 0.5 km below the surface by trial and error. The parameter set giving the minimum residuals was adopted as the optimal solution.
The slip on the Hinagu fault significantly extends down to around 10 km depth and reaches around the junction of the Futagawa and the Hinagu faults. A large slip concentrates near the ground surface and extends downward to the north. According to the JMA catalog, the hypocenters for the M j 6.5 and the M j 6.4 events are located in the northern part of the Hinagu fault at 11 (±0.9) km depth and at 6 (±1.6) km depth in the southern part, respectively (Fig. 3a). The InSAR data consist of the displacements produced primarily by these two events (Fig. 1b); thus, the distributed slip model should encompass the source properties of both events. Taking the spatial relationship into consideration, this may suggest that the northern deep slip and the southern shallow slip correspond to the M j 6.5 and the M j 6.4 events, respectively. InSAR analysis cannot further separate the individual crustal deformation due to its poor temporal resolution. The locations where the main slips of each event occurred might be provided by kinematic GNSS data due to its high sampling rate (Kawamoto et al. 2016).
Local normal fault motion: why was the damage so large in Mashiki?
One of the notable points is that the InSAR observation has successfully detected the locally distributed ground motion in and around Mashiki town owing to the high spatial resolution. And it should be noted that the favorable fault model producing the deformation is not right-lateral motion but normal faulting, which is in good agreement with the fact that earthquakes with normal fault motions have occurred in this area in the Kumamoto earthquake sequence (Kyushu University 2016). The spatial proximity with Mashiki town strongly implies that this normal fault motion could be responsible for the damage concentrated within the town. To further inform this discussion, it is vital to know when the fault slip occurred. One of the possibilities is that it occurred simultaneously with the M j 6.5 event. Here, I focus on the focal mechanism. The striking point for the M j 6.5 event is that a significant non-double couple component is included in the JMA focal mechanisms (Fig. 1). The non-double couple component can be identified also in other CMT solutions (GCMT 2016; USGS 2016). It implies that the rupture cannot be accounted for by a simple fault motion on a single fault plane; instead, it is composed of a complicated slip distribution on one fault plane or composite fault motions by multiple fault planes.
In this context, I calculated the total moment tensor components using the estimated parameters for all patches of the distributed slip model of the Hinagu fault alone and made a beach ball plot [Fig. 3c(2)] (Lay and Wallace 1995). For the estimate, I assumed a point source. The beach ball shows simple right-lateral motion, which consists of a double couple component. Hence, it indicates that a different rupture by another fault is necessary. Here, recall the local fault producing the phase change in Mashiki town. Incorporating the contribution of normal fault motion into the estimate of moment tensor, a significant non-double couple component appears [Fig. 3c(3)]. InSAR data include the effects of both the M j 6.5 and M j 6.4 events, and thus, I calculated a seismically estimated focal mechanism combining both the events, using moment tensor components determined by JMA (2016b) [Fig. 3a(1)]. It is striking that the focal mechanism predicted by both the Hinagu fault and the local normal faulting has a considerable resemblance to that determined by the seismic analysis. This pronounced consistency strongly suggests that normal faulting did occur beneath Mashiki town, away from the main right-lateral rupture. The normal fault rupture may be one of the primary causes for locally increased ground shaking and damage to Mashiki town.
Localized normal faulting can effectively explain both the InSAR and seismic data; however, careful interpretation is necessary because there may be other reasons for the local phase change. One of the possibilities is an M j 5.8 event that occurred at 22:07 on April 14, whose hypocenter was located near the local phase change area (Fig. 1). Furthermore, according to the JMA catalog, the strike and dip are concordant with the estimated south-dipping fault model, and the moment magnitude is also similar. However, the focal depth is seismically estimated to be 8 (±1.2) km. If this is true, it cannot produce significant ground displacement with seismic energy of M j 5.8 (M w 5.4). Shallow fault slip is essential to produce the observed ground displacement; hence, the link to the M j 5.8 event seems unlikely but cannot be rejected entirely.
Another possibility is an effect of liquefaction. It is known that liquefaction induces ground subsidence and can be sometimes detected by InSAR (Ishitsuka et al. 2012). Liquefaction occurred in some parts of Mashiki town during the earthquake series, yet the timing of liquefaction does not appear to be known. Therefore, this possibility can also not be excluded.
The existence of a shallow local fault is a reasonable hypothesis for why Mashiki town suffered such locally concentrated damage in spite of the moderate-sized earthquake and why a significant non-double couple component is included in the M j 6.5 event. This investigation, however, is far from exhaustive due to limited observations. At this stage, I claim only that this provisional model is consistent with some facts. I stress that reinvestigation assuming such a local fault rupture beneath Mashiki town is essential to further develop our understanding of the Kumamoto earthquake in other study fields.
The effect on the M j 7.3 event
Finally, I will briefly discuss an effect on the main shock due to a static stress change. The crust in the proximity of the foreshock rupture fault should be subjected to a strong stress change, which presumably culminates in promotion of the main shock. To test this idea quantitatively, I evaluated ΔCFF values (King et al. 1994) at the epicenter of the M j7.3 event. I assumed the focal mechanism of initial motion for the M j 7. 3 event as a receiver mechanism (JMA 2016a). I then evaluated the stress change pattern for an effective coefficient of friction μ ranging from 0.2 to 0.7 and a depth from 1 to 20 km. The estimated ΔCFF is shown in Additional file 6: Fig. S6a. To further evaluate sensitivity to horizontal position errors of the hypocenter, I shifted the epicenter to four directions (northward, southward, westward, and eastward) and calculated ΔCFF for each case in the same manner. The standard deviation of the hypocenter is 260 m in latitude and 310 m in longitude, respectively, and thus, I here shifted to 0.5 km, equivalent to 2σ, in each orientation (Additional file 6: Fig S6b–e). Warm and cold colors represent positive and negative signs, signifying facilitated or suppressed fault slip, respectively. In and around the depth of the hypocenter (12 km), the ΔCFF values tend to be positive with higher μ and negative with lower μ. Although I cannot definitively conclude that the main shock was triggered by the static stress change, it seems possible that the foreshocks promoted the main shock. On the other hand, the ΔCFF values have positive signs deeper than 17 km for any μ, suggesting that fault slips are robustly promoted at depth near the lower edge of the so-called seismogenic zone. Also in other cases, it can be identified that a fault slip tends to be promoted in the deep rather than the shallow (Additional file 6: Fig. S6b–e) although there are slight differences at some points. Of course, care must be taken with these estimates because the source and the receiver faults are near to one another and thus the estimate is sensitive to the position and the given slip mechanism. To clarify this, further study on the rupture for the main shock is vital for developing our understanding of this issue in the future.
A major displacement field in LOS and azimuth components is distributed on the western side of the Hinagu fault with the displacement exceeding 15 cm.
A locally distributed ground displacement which appears along the strike of the Futagawa fault is clearly identified in and around Mashiki town, suggesting that a different local fault slip is also partially responsible for the foreshocks.
The constructed model shows almost pure right-lateral fault motion with M w 6.28 for the Hinagu fault. The slip in the north significantly extends down to around 10 km depth, while in the south a large slip concentrates near the ground surface, perhaps corresponding to the M j 6.5 and the M j 6.4 events, respectively. On the other hand, almost pure normal fault motion with M w 5.79 is inferred for the local fault beneath Mashiki town.
Although the inferred slip distribution for the Hinagu fault alone does not have a significant non-double couple component inferred from seismic analyses, if incorporating the contribution from normal faulting, the focal mechanism bears a great resemblance to the seismically estimated mechanism. This might suggest that the normal faulting occurred simultaneously with the M j 6.5 event, which locally amplified the damage to Mashiki town.
ALOS-2 data were provided from the Earthquake Working Group under a cooperative research contract with JAXA (Japan Aerospace Exploration Agency). The ownership of ALOS-2 data belongs to JAXA. Generic Mapping Tools (GMT) provided by Wessel and Smith (1998) were used to construct the figures. Hypocenter data processed by the Japan Meteorological Agency (JMA) were used. I thank reviewers (Dr. R. Walters and the anonymous reviewers) and the editor for their helpful comments to improve our manuscript.
The author declares that he has no competing interests.
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