InSAR-derived crustal deformation and fault models of normal faulting earthquake (Mj 7.0) in the Fukushima-Hamadori area
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 27 December 2011
Accepted: 31 August 2012
Published: 28 January 2013
Applying interferometric SAR (InSAR) analysis using ALOS/PALSAR data to inland crustal earthquakes in the Fukushima-Hamadori area, we succeeded in mapping a ground displacement associated with the Mj 7.0 earthquake that occurred on 11 April, 2011. The most concentrated crustal deformation is located ~20 km west of the city of Iwaki, showing displacements away from the satellite with ~2.2 m at the maximum. Clear displacement discontinuities are recognized with an offset of ~1.6 m at the maximum, which are just on the Shionohira, Idosawa and Yunotake faults. From field surveys, we found that earthquake surface faults appeared with a vertical offset of ~1.9 m, consistent with the InSAR observation, and their locations correspond to the discontinuities in the interferogram. We inverted the InSAR data to construct slip distribution models, and our models show (1) nearly pure normal fault motions (2) on west-dipping planes (3) with moderate-dip-angles (50–65°). The inferred west-dipping normal fault motion on the Yunotake fault is correlated with the present-day topographic features, consistent with the idea that the historically-repeated normal faultings have developed the topography. On the other hand, for the Shionohira and Idosawa faults antithetical relationships are presented, maybe suggesting that large normal faultings have been infrequent historically.
On 11 April, 2011, a large inland earthquake, with Mj 7.0, struck the Fukushima-Hamadori area. This is the largest event among the inland crustal earthquakes since the Mw 9.0 event, as of the time of writing. The seismic data analyses show that the source mechanism is also a normal fault type, but this event seems to be rather complicated in that the rupture style cannot be accounted for by a slip on a single fault plane. This is because several earthquake surface faults appeared with (sub)meter order, suggesting that seismic ruptures proceeded on multiple fault planes. Despite the several such outstanding features of this event, however, it remains uncertain where and how the faults were involved in the seismic event. Obtaining detailed crustal deformation data and constructing fault models are crucial to understanding the unclear points.
Satellite synthetic aperture radar (SAR) data can provide detailed and spatially-comprehensive ground information, and an interferometric SAR (InSAR) enables us to measure ground deformation with high precision (e.g., Massonnet and Feigl, 1998; Bügmann et al., 2000). One of the advantages of InSAR observation is that local crustal deformation can be detected. Although GNSS sites (GEONET) are densely deployed with an average placement interval of ~20–30 km nationwide, it remains difficult to obtain high quality displacement data for small- to moderate-sized earthquakes, impeding detailed analysis of the source properties, such as fault modeling. Alternatively, the ground resolution of SAR data (ALOS/PALSAR) is ~10 m, and the InSAR observation works well to detect small- to moderate-sized ground deformation anomalies over a large area.
To obtain a further understanding of where and how ruptures proceeded in the Mj 7.0 event, for which a complicated source process is expected from the field survey, the SAR data analyses surely contribute to provide detailed and vital information regarding surface changes quantitatively. The primary aim of this paper is to understand the source properties of the Mj 7.0 event by constructing an elaborated fault model using InSAR-derived crustal deformation data. We first describe the SAR data analysis procedure in Section 2. In Section 3, we describe the characteristics of the crustal deformation associated with the inland crustal earthquakes; in particular, regarding displacement discontinuities corresponding to surface ruptures. On the basis of the InSAR data, we construct fault models using a rectangular fault plane with a uniform slip in Section 4. In Section 5, we construct a slip distribution model for the Mj 7.0 event by an inversion approach. Finally, in Section 6, we discuss the reliability of our derived slip distribution model, the relationship between the inferred fault motions and the present-day topographic features, and the effect of mainshock fault rupture on other fault ruptures.
2. SAR Data Analysis
We collected ALOS/PALSAR images to reveal the crustal deformation due to the earthquake that occurred in Fukushima-Hamadori area. In Japan, many faults, including the seismic source we now study, are located in mountainous areas with a vegetated environment, and thus the PALSAR’s L-band sensor should be a powerful tool for geodetic observation to extract ground information, even in mountains. JAXA (Japan Aerospace Exploration Agency) carried out urgent observations for the great earthquake (Mw 9.0) on 20 March (path 404), 7 April (path 56), and 18 April (path 403) with a fine beam mode, and on 14 March (path 60) and 31 March (path 61) with a ScanSAR mode, respectively, which covers our study area. Among them we used three paths of fine beam mode for the interferometric analysis, because the interferometric coherence of the obtained images using ScanSAR was too low to detect ground displacements, which may have resulted from large perpendicular baselines (~2 km and ~5 km). ALOS had completed its mission on 12 May, 2011, due to a power generation anomaly that occurred on 22 April, 2011. Thus, no image had been acquired since the date. The ALOS/PALSAR data was processed using GSISAR software (Fujiwara and Tobita, 1999; Fujiwara et al., 1999; Tobita et al., 1999; Tobita, 2003).
Obvious long-wavelength phase changes caused by the Mw 9.0 event were included in the original interferograms (Imakiire and Kobayashi, 2011). To pick up the crustal deformation due to the inland earthquakes, we assumed that the far-field displacement was zero and that the residual phases were expressed by a quadratic surface, and we subtracted the evaluated bilinear function from the original interferogram. We use the residual phase changes as the crustal deformation data associated with the inland earthquakes.
3. Crustal Deformation Map
3.1 Characteristics of ground surface displacement
We stress that we succeeded in obtaining the phase change map with high coherence for the whole source region. Some large inland earthquakes had lost the interferometric coherence significantly in the vicinity of the hypocentral area because of serious changes in the scattering conditions on the ground and too high displacement gradients—e.g., the 2008 Iwate-Miyagi Nairiku earthquake (Takada et al., 2009)—which impeded estimates of detailed crustal deformation and source properties. In contrast, owing to the high coherence, the InSAR map of the Mj 7.0 event enables us to investigate the ground surface change over the entire source area in detail.
3.2 Displacement discontinuities corresponding to ground surface ruptures
The photographs C and D show the ground offsets taken at the Yunotake fault (Fig. 2), viewed from south and southeast, respectively. They also evidently show that the hanging wall block in the southwest drops down relative to the footwall one in the northeast, showing normal fault motions.
We also detected some surface cracks along the Idosawa fault in our field survey (Photo E). They suggest that some surface change did occur along the Idosawa fault as identified in the interferogram, but we were not able to infer the fault motion sense and/or amount of offset from the observed cracks.
In addition to the above-mentioned major discontinuities, we can identify several minor displacement boundaries with lengths of a few kilometers, which may not be seismic faults but so-called secondary faults. One of the minor discontinuities can be clearly seen in the cross-section of Fig. 4(a), indicated by a small arrow. A small, but clear, gap is detected. The gap is less than 10 cm. We can find out some cracks at, and around, the offset position (photo F), but they are not so clear that we can estimate the sense of ground movement.
Displacement discontinuities can be recognized associated with not only the Mj 7.0 event but also the Mj 6.1 and the Mj 6.0 events (arrows in Figs. 2 and 3). LOS displacement profiles show the clear gaps of ~10 cm for the Mj 6.0 event (Fig. 4(a)) and ~30 cm for the Mj 6.1 event (Fig. 4(b)). These suggest that significant fault ruptures occurred at a rather shallow depth, although there are no reports of the appearance of earthquake surface faults or surface cracks.
In, and around, the source regions, several GNSS sites are deployed, indicated by white squares (Figs. 2 and 3). Considering the size of the ground deformation, however, GNSS observations can hardly detect the locally-distributed ground anomalies such as the displacement boundaries. The detection of the displacement boundaries and an awareness of their spatial extent demonstrate the advantage of the InSAR analysis in that small- to moderate-sized ground deformation anomalies can be observed over a large area with a high spatial resolution.
4. Rectangular Fault Models with Uniform Slip for the Mj 7.0 and Mj 6.0 Events
On the basis of the obtained interferogram data, we first try to construct a fault model under the assumption of a rectangular fault with a uniform slip in an elastic half-space (Okada, 1985). A rectangular fault model has the advantage that it can represent a macroscopic feature of the source property with its simple notation. In the interferogram of the Mj 7.0 event, the phase changes associated with the Mj 6.1 and the Mj 6.0 events are included. The effect of the Mj 6.0 event, especially, is not negligible for the modelling of the Mj 7.0 event. Thus, we first construct the Mj 6.0 event model. The LOS displacements predicted by the two models are subtracted from the original interferogram, and then the residual is used for the modelling of the Mj 7.0 event. For the Mj 6.1 event, we used a fault model that had already been constructed by Kobayashi et al. (2011).
4.1 Mj 6.0 event on 23 March, 2011
Fault parameters of our preferred model for the Mj 6.0 event (23 March, 2011). We define the location of each fault as the center. The units of length, width, and depth are in kilometers, those of dip, strike, and rake are in degrees, and the unit of slip is in meters. The moment magnitude is calculated with the rigidity of 30 GPa. The parenthesized numbers are the standard deviation (1σ). In the lowest row, the fault parameters from the CMT solution (NIED Earthquake Mechanism Search (http://www.fnet.bosai.go.jp/event/search.php?LANG=en)) are listed for comparison.
4.2 Mj 7.0 event on 11 April, 2011
Fault parameters of our preferred model for the Mj 7.0 event (11 April, 2011). The definition of fault parameters is the same as in Table 1. Faults No. 1 and 2 indicate the fault planes corresponding to the Shionohira and the Yunotake faults, respectively.
5. Slip Distribution Model for the Mj 7.0 Event
To model the ruptures associated with the Mj 7.0 event more precisely, we construct a slip distribution model by a least squares method. The fault geometry is assumed to be a plane fault, and we put each plane by fitting the surface breaks to the interferograms by trial and error. We set three rectangular faults corresponding to the Shionohira, Yunotake, and Idosawa faults. The fault top position is fixed to the depth of 0 km bsl. The individual fault is divided into square patches with a size of 1 × 1 km. We use the dislocation equations derived by Okada (1985) to calculate the surface displacement in the variable LOS directions. In the inversion, only the dip-slip and strike-slip components are estimated for each patch. Because of no constraint on the slip direction, there arose physically implausible slips in places, but they are minor in the overall slip distribution. The increase of model parameters gives rise to instability of the solution. To stabilize the solution, we 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 Baysian information criterion (Akaike, 1980). We assume the Shionohira and the Yunotake planar faults dipping westward, following the results in the previous section, while for the Idosawa fault we tried the possibility of both west- and east-dipping faults. The problem we solve is a nonlinear inversion on a parameter of the dip angle. We here determine the dip angle by a grid search, in which we first conduct the grid search with a coarse interval of 10° and then with a finer interval of 5° surrounding the dip angle determined in the previous step. We set the search range from 40° to 90°, referring to the results in the previous chapter that low-angle fault planes are not favourable.
We cannot neglect the contribution of the cross-terms of the covariance matrix for the InSAR data, because they have a strong spatial correlation in general, which largely results from the variations of atmospheric water vapour (Lohman and Simons, 2005; Fukahata and Wright, 2008). We incorporate the cross-terms of the covariance matrix in the inversion scheme, following the equation presented by Fukahata and Wright (2008), and now take the characteristic correlation distance of errors to be 10 km (Wright et al., 2003; Fukahata and Wright, 2008).
The optimal dip angles for Shionohira, Yunotake, and Idosawa faults are determined to be 50°, 65°, and 50°, respectively. The total seismic moment is 1.55 × 1019 N m (Mw 6.7) assuming a rigidity of 30 GPa, and the released moments for each fault are estimated to be 9.22 × 1018 N m (Mw 6.6), 4.22 × 1018 N m (Mw 6.4), and 2.09 × 1018 N m (Mw 6.1) for the Shionohira, Yunotake, and Idosawa faults, respectively. According to the results of JMA CMT, NIED CMT, and Global CMT solutions, the seismic moments are 1.2 × 1019 N m (Mw 6.7), 9.58 × 1018 N m (Mw 6.6), and 1.2 × 1019 N m (Mw 6.7), respectively. Our result is good agreement with them.
6.1 Reliability of the fault model
6.2 Relationship between fault motions and topography
Also for both the Shionohira and the Idosawa faults, normal fault motions on west-dipping planes are inferred from our modeling. The fault model predicts that the largest ground subsidence occurred in the west of the Shionohira fault (Fig. 12). By analogy with a similar mechanism interpreted for the Yunotake fault, we may speculate that if normal faulting had been experienced on the faults repeatedly actively, a topographic high would have been developed in the east. The topography, however, is antithetical to the coseismic displacements with normal fault motions, although earthquake surface faults are just on the topographic lineaments (Figs. 4 and 12). Little correlation between the fault motions and the present-day topography may suggest that large normal fault slip events have been rare on the Shionohira and the Idosawa faults historically.
6.3 Are the ruptures on the other two faults promoted by that on the Shionohira fault?
Figure 13(b) shows the ΔCFF distribution on the Yunotake fault, but adding the effect of static stress changes caused by the Mw 9.0, the Mj 6.1, and the Mj 6.0 events. We used the fault model proposed by the Geospatial Information Authority of Japan (GSI) for the Mw 9.0 event (GSI, 2011). ΔCFF values with a positive sign are expected over all the fault plane, but negative ACFF values still remain in the major slip area, suggesting that the static stress change does not play a role in promoting the major slip. Although the temporal relationship between the onset of the Shionohira fault and the Idosawa fault is not well-understood, we attempt an estimate of ΔCFF for the Idosawa fault under the assumption that the rupture on the Shionohira fault was followed by that on the Idosawa fault. Also for the Idosawa fault, ΔCFF values with a negative sign are distributed on the major slip area, indicating the suppression of the slip (Figs. 13(c) and (d)).
The analysis result on the static stress change does not support the idea that the static stress change due to the slip on the Shionohira fault is responsible for the initiation of the rupture on both the Yunotake fault and the Idosawa fault. Other mechanisms, such as dynamic triggering, may have played a role in inducing the ruptures on the other two faults. The problem concerning the triggering of ruptures is beyond the scope of this paper. This question is a matter for future studies.
7. Concluding Remarks
The most concentrated crustal deformation is located ~20 km west of the city of Iwaki, showing displacements away from the satellite with ~2.2 m at the maximum.
Clear displacement discontinuities are recognized in the interferograms, with an offset of ~ 1.6 m at the maximum, which are just on the Shionohira, the Yunotake, and the Idosawa faults.
From the field surveys, we found that earthquake surface faults appeared with a vertical offset of ~ 1.9 m at the maximum, equivalent to ΔLOS of ~ 1.5 m. Their locations match the discontinuities identified in the interferogram.
Our slip distribution model shows nearly pure normal fault motions on west-dipping planes with a moderate dip angle for all three faults (Shionohira, Yunotake, and Idosawa).
The west-dipping normal fault motion on the Yunotake fault is correlated with present-day topographic features, while those on both the Shionohira and Idosawa faults are inversely correlated with the topography.
A ΔCFF estimate suggests that the static stress change due to the mainshock fault rupture on the Shionohira fault does not initiate the slips on the other two faults, maybe suggesting that other mechanisms are involved in the triggering of rupture on these two faults.
PALSAR data were provided from the Earthquake Working Group under a cooperative research contract with JAXA (Japan Aerospace Exploration Agency). The ownership of PALSAR data belongs to JAXA and METI (Ministry of Economy, Trade and Industry). We used hypocenter data processed by the Japan Meteorological Agency (JMA). We used GMT (The Generic Mapping Tools) provided by Wessel and Smith (1998) for constructing the figures. We thank two reviewers (Dr. P. S. Agram and an anonymous reviewer) and the editor (Prof. Miura) for their helpful comments to improve our manuscript.
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